Canonical Gymnasium Mathematics DE Expansion Plan

Snapshot: 2026-03-30

This plan focuses on one target:

curricula/DE/Gymnasium/canonical/DE_DEU_S_GYM_CANONICAL_MATHEMATIK.de.json should converge toward reviewed coverage for all 16 German Bundeslaender without cloning canonical goals per state.

The landscape JSON itself should stay pure curriculum data. Rollout planning, steering, and progress tracking should live next to it, not inside it.

Persistent control setup

Use three persisted artifacts:

plan document
docs/dev/canonical-gymnasium-math-de-expansion-plan.md
purpose: stable narrative, rollout phases, rules, and exit criteria
machine-readable tracker
curricula/DE/Gymnasium/provenance/math-bundesland-rollout-tracker.json
purpose: single source of truth for per-state rollout phase, next step, and lane references
quick status view
docs/dev/canonical-gymnasium-math-bundeslaender-status.md
purpose: easy-to-scan overview for humans
generation: python3 scripts/render_canonical_math_bundesland_status.py
topic workboard
docs/dev/canonical-gymnasium-math-topic-workboard.md
purpose: canonical-first decision board by topic and Bundesland
use: one row per high-level topic, one state cell per Bundesland, plus explicit canonical gaps and next action

Working rule:

update the JSON tracker first
regenerate the Markdown quick view second
update the topic workboard whenever the active implementation unit changes
keep plan, tracker, quick view, and workboard aligned

This keeps the plan persisted, diffable, and simple to review in PRs.

Why this setup

This setup keeps concerns separated:

the canonical math landscape remains didactic source data
the rollout tracker remains operational metadata
the quick view remains the simplest place to answer:
which states are already on the canonical spine
what phase each state is in
what the current nationwide implementation score is

It also avoids hiding planning state in a huge curriculum JSON where operational progress would be hard to inspect and easy to forget.

Steering model

The rollout should now be steered in a stricter order than the earlier mainly bundeslandwise queue.

Target stance:

the canonical DE mathematics graph is the pedagogical source of truth
Bundesland mappings are evidence and coverage for that graph, not the primary design driver
Bundesland learner-facing trees should later be projections of that graph, not competing authored content universes

Operational consequence:

the primary implementation unit is now a canonical corridor
the state tracker remains necessary, but it measures projection/readiness on the canonical spine, not the pedagogical quality of the canonical graph itself

Canonical-first execution order:

refine one canonical corridor until its atomic inventory and progression are pedagogically round
map that corridor against all 16 state curricula and classify reviewed bridges as exact, partial, not_applicable, or state_local
only then stabilize state-scoped composition views and learner-facing cluster shapes for the affected scopes

Authoring rule for new canonical atoms:

add a canonical atom only if it improves the shared DE mathematics graph pedagogically
do not add canonical atoms merely to mirror one state's packaging, wording, or table layout
if a source item is only state-specific packaging, keep it in mapping/provenance or later state composition, not in the canonical core

This means the canonical DE view must not become the raw union of all reviewed state atoms. It should instead become a curated, didactically closed competence model whose state-specific projections are then derived as tightly as possible without violating local curriculum constraints.

Progress log

2026-03-30 / Steering model recalibrated

Executed work:

tightened the nationwide math rollout policy from a mainly bundeslandwise queue to a canonical-first corridor-steering model
kept the existing state tracker as operational readiness metadata, but clarified that canonical pedagogical quality is a separate first-order concern
introduced an explicit canonical corridor register in the machine-readable tracker and the generated quick status view
set the new active corridor framing to:
Sek I J10 function families
Sek I J10 bodies, volumes, and plausibility
Sek II analysis
Sek II geometry and linear algebra
Sek II stochastics
moved the early Sek I foundations pass into the canonical next-wave register instead of treating it only as diffuse state-local cleanup

Resulting rollout effect:

the project now has an explicit answer to "what should be designed canonically next?" before asking "which Bundesland should move next?"
the state tracker remains useful, but it is now clearly subordinate to corridor-first canonical design
future state views can converge more cleanly toward curated composition views over the canonical graph instead of broad state-shaped tree drift

2026-03-21 / Step 1 completed

Executed work:

verified the active five-state mathematics base against actual repo evidence
archived the first Brandenburg mathematics source bundle:
shared BE/BB Sek-I mathematics
Brandenburg upper-secondary mathematics
archived the first Berlin mathematics source bundle:
shared BE/BB Sek-I mathematics
Berlin upper-secondary mathematics
created mapping-lane scaffolds for:
DE-BB/lower-secondary
DE-BB/upper-secondary
DE-BE/lower-secondary
DE-BE/upper-secondary
reserved source-landscape identifiers for Brandenburg and Berlin mathematics onboarding notes
moved DE-BB and DE-BE from P0 to P1 in the rollout tracker

Resulting rollout effect:

the first backlog wave is no longer placeholder-only
tracked nationwide score rises from 22.8% to 24.7%
the next derivable task is no longer raw source hunting for BB/BE, but source-snapshot creation and provenance activation

2026-03-21 / Step 2 completed

Executed work:

created the first Brandenburg mathematics source snapshots for:
Sekundarstufe I structural Gymnasium anchors J7-J10
gymnasiale Oberstufe phase anchors E, Q1, Q2, Q3, Q4
created the first Berlin mathematics source snapshots for:
Sekundarstufe I structural Gymnasium anchors J7-J10
gymnasiale Oberstufe phase anchors E, Q1, Q2, Q3, Q4
activated Brandenburg and Berlin in:
source-landscape-registry.json
source-goal-membership-registry.json
source-goal-closure-registry.json
updated the onboarding notes so the active snapshots and covered anchor ranges are explicit
moved DE-BB and DE-BE from P1 to P2 in the rollout tracker

Resulting rollout effect:

Brandenburg and Berlin are no longer only archived-source lanes; they are now real provenance-backed source lanes
tracked nationwide score rises from 24.7% to 26.6%
states with active snapshots rise from 5/16 to 7/16
the next derivable task is now explicit structural-anchor mapping for DE-BB and DE-BE, not more onboarding setup

2026-03-21 / Step 3 completed

Executed work:

mapped Brandenburg Sek-I Gymnasium year anchors J7-J10 onto the canonical lower-secondary year spine
mapped Berlin Sek-I Gymnasium year anchors J7-J10 onto the canonical lower-secondary year spine
mapped Brandenburg upper-secondary phase anchors E, Q1, Q2, Q3, Q4 onto the canonical upper-secondary phase spine as structural partial bridges
mapped Berlin upper-secondary phase anchors E, Q1, Q2, Q3, Q4 onto the canonical upper-secondary phase spine as structural partial bridges
kept the structural-anchor step intentionally narrow:
no new reviewed corridor claims
no broad applicability expansion on the canonical nodes yet
extended the generated quick view with a direct P3+ headline metric for structural-anchor coverage

Resulting rollout effect:

Brandenburg and Berlin now move from P2 to P3
tracked nationwide score rises from 26.6% to 29.1%
states with structural anchors mapped rise from 5/16 to 7/16
the next derivable task is now the first reviewed corridor for each of the shared BE/BB lanes, starting with the lower-secondary functions corridor

2026-03-21 / Step 4 completed

Executed work:

expanded the Brandenburg lower-secondary source snapshot from pure Gymnasium anchors into the first reviewed functions corridor from the shared BE/BB Sek-I source
expanded the Berlin lower-secondary source snapshot in the same corridor shape
activated the new Brandenburg and Berlin corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the shared BE/BB lower-secondary functions corridor onto the canonical lower-secondary math spine:
mappings and representation changes on Niveaustufe E
linear-function descriptions, representation changes, and calculations on Niveaustufe F
moved DE-BB and DE-BE from P3 to P4 in the rollout tracker

Resulting rollout effect:

Brandenburg and Berlin now have a real reviewed lower-secondary corridor, not only structural anchors
tracked nationwide score rises from 29.1% to 30.9%
states with reviewed corridor rise from 5/16 to 7/16
the next derivable task is now the first upper-secondary entry corridor for DE-BB and DE-BE, followed by the next lower-secondary follow-on corridor

2026-03-21 / Step 5 completed

Executed work:

expanded the Brandenburg upper-secondary source snapshot from pure phase anchors into the first reviewed E-phase analysis entry corridor
activated the new Brandenburg upper-secondary corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Brandenburg E-phase derivative starter strip onto the canonical upper-secondary math spine:
E.2 introductory derivative surface
E.3 first derivative applications
reviewed leaf bridges for rates of change, derivative meaning, derivative graph, derivative rules, tangents, monotonicity, curvature, conditions, and simple extremal problems
updated the Brandenburg upper-secondary lane notes so the next follow-on work is now a Q1 follow-on corridor rather than the first E-entry cut

Resulting rollout effect:

Brandenburg now has reviewed corridor coverage on both the lower-secondary shared functions lane and the upper-secondary E-phase analysis entry lane
the nationwide score stays at 30.9% because no state phase transition changed
the Brandenburg total mapping surface rises from 18 to 32 mappings
the next derivable task is now the matching first upper-secondary entry corridor for DE-BE, while Brandenburg can widen from E into the first Q1 follow-on corridor

2026-03-21 / Step 6 completed

Executed work:

expanded the Berlin upper-secondary source snapshot from pure phase anchors into the first reviewed Q1 differential entry corridor
activated the new Berlin upper-secondary corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Berlin Q1 differential starter strip onto the canonical upper-secondary math spine:
E.2 introductory derivative surface
E.3 first derivative applications
reviewed leaf bridges for propedeutic limit use, secant and tangent slopes, rates of change, derivative meaning, derivative graph, rule-based differentiation, monotonicity, inflection points, necessary conditions, and simple extremal problems
updated the Berlin upper-secondary lane notes so the next follow-on work is now a Q2 widening step rather than the first Q1 entry cut

Resulting rollout effect:

Berlin now has reviewed corridor coverage on both the lower-secondary shared functions lane and the upper-secondary Q1 differential entry lane
the nationwide score stays at 30.9% because no state phase transition changed
the Berlin total mapping surface rises from 18 to 32 mappings
the next derivable tasks are now the Brandenburg Q1 follow-on corridor and the Berlin Q2 follow-on corridor, while the lower-secondary shared lane can stay stable until that upper-secondary widening is secured

2026-03-21 / Step 7 completed

Executed work:

expanded the Brandenburg upper-secondary source snapshot from the first reviewed E-phase derivative strip into the first reviewed Q1 model-functions follow-on corridor
activated the new Brandenburg Q1 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Brandenburg Q1 model-functions strip onto the canonical upper-secondary math spine:
E.4 exponential-function surface
E.5 trigonometric-function surface
reviewed leaf bridges for natural exponential growth and decay, parameter interpretation, self-derivative behaviour of e^x, logarithmic equation solving, exponential modelling, periodic functions, parameter effects, trig derivatives, and periodic modelling
updated the Brandenburg upper-secondary lane notes so the next follow-on work is now a Q2 analysis widening step rather than the first Q1 follow-on cut

Resulting rollout effect:

Brandenburg now has reviewed corridor coverage on both the lower-secondary shared functions lane and two reviewed upper-secondary corridors on the active analysis/model-function spine
the nationwide score stays at 30.9% because no state phase transition changed
the Brandenburg total mapping surface rises from 32 to 43 mappings
the next derivable tasks are now the Berlin Q2 follow-on corridor and the Brandenburg Q2 analysis follow-on corridor, while the lower-secondary shared lane can remain stable until those upper-secondary widening steps are secured

2026-03-21 / Step 8 completed

Executed work:

expanded the Berlin upper-secondary source snapshot from the first reviewed Q1 differential strip into the first reviewed Q2 integral-calculus follow-on corridor
activated the new Berlin Q2 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Berlin Q2 integral strip onto the canonical upper-secondary math spine:
Q1.1 introductory integral surface
Q1.2 first integral applications
reviewed leaf bridges for reconstructed stock, stock calculation from rates, geometric Fundamental-Theorem reasoning, antiderivative-based integration, area calculation with definite integrals, and context interpretation of integral terms
updated the Berlin upper-secondary lane notes so the next follow-on work is now a Q2 stochastics widening step rather than the first Q2 analysis cut

Resulting rollout effect:

Berlin now has reviewed corridor coverage on both the lower-secondary shared functions lane and two reviewed upper-secondary corridors on the active analysis spine
the nationwide score stays at 30.9% because no state phase transition changed
the Berlin total mapping surface rises from 32 to 41 mappings
the next derivable tasks are now the Brandenburg Q2 analysis follow-on corridor and the Berlin Q2 stochastics follow-on corridor, while the lower-secondary shared lane can remain stable until those upper-secondary widening steps are secured

2026-03-21 / Step 9 completed

Executed work:

expanded the Brandenburg upper-secondary source snapshot from the first reviewed Q1 model-functions strip into the first reviewed Q2 integral-calculus follow-on corridor
activated the new Brandenburg Q2 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Brandenburg Q2 integral strip onto the canonical upper-secondary math spine:
Q1.1 introductory integral surface
Q1.2 first integral applications
reviewed leaf bridges for upper and lower sums, the definite integral as common limit and reconstructed stock, stock calculation from rates and initial value, geometric Fundamental-Theorem reasoning, antiderivative-based integration, area calculation with definite integrals, and context interpretation of integral terms
updated the Brandenburg upper-secondary lane notes so the next follow-on work is now a Q2 stochastics widening step rather than the first Q2 analysis cut

Resulting rollout effect:

Brandenburg now has reviewed corridor coverage on both the lower-secondary shared functions lane and three reviewed upper-secondary corridors on the active analysis spine
the nationwide score stays at 30.9% because no state phase transition changed
the Brandenburg total mapping surface rises from 43 to 53 mappings
the next derivable tasks are now the Berlin Q2 stochastics follow-on corridor and the Brandenburg Q2 stochastics follow-on corridor, while the lower-secondary shared lane can remain stable until those upper-secondary widening steps are secured

2026-03-21 / Step 10 completed

Executed work:

expanded the Berlin upper-secondary source snapshot from the first reviewed Q2 integral strip into the first reviewed Q2 stochastics follow-on corridor
activated the new Berlin Q2 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Berlin Q2 stochastics strip onto the canonical upper-secondary math spine:
Q3 Stochastik
Q3.1 basic stochastics
reviewed leaf bridges for Baumdiagramme, Vierfeldertafeln, bedingte Wahrscheinlichkeiten, stochastische Unabhaengigkeit, Urnenmodelle mit und ohne Zuruecklegen, and simulations of stochastic situations
updated the Berlin upper-secondary lane notes so the next follow-on work is now a Q2 data-and-survey widening step rather than the first Q2 stochastics cut

Resulting rollout effect:

Berlin now has reviewed corridor coverage on both the lower-secondary shared functions lane and three reviewed upper-secondary corridors on the active analysis/stochastics spine
the nationwide score stays at 30.9% because no state phase transition changed
the Berlin total mapping surface rises from 41 to 50 mappings
the next derivable tasks are now the Brandenburg Q2 stochastics follow-on corridor and the Berlin Q2 data-and-survey follow-on corridor, while the lower-secondary shared lane can remain stable until those upper-secondary widening steps are secured

2026-03-21 / Step 11 completed

Executed work:

expanded the Brandenburg upper-secondary source snapshot from the first reviewed Q2 integral strip into the first reviewed Q2 stochastics follow-on corridor
activated the new Brandenburg Q2 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Brandenburg Q2 stochastics strip onto the canonical upper-secondary math spine:
Q3 Stochastik
Q3.1 basic stochastics
reviewed leaf bridges for Baumdiagramme, Vierfeldertafeln, bedingte Wahrscheinlichkeiten, stochastische Unabhaengigkeit, Urnenmodelle mit und ohne Zuruecklegen, and simulations of stochastic situations
updated the Brandenburg upper-secondary lane notes so the next follow-on work is now a Q2 data-and-distribution widening step rather than the first Q2 stochastics cut

Resulting rollout effect:

Brandenburg now has reviewed corridor coverage on both the lower-secondary shared functions lane and four reviewed upper-secondary corridors on the active analysis/stochastics spine
the nationwide score stays at 30.9% because no state phase transition changed
the Brandenburg total mapping surface rises from 53 to 62 mappings
the next derivable tasks are now the Berlin Q2 data-and-survey follow-on corridor and the Brandenburg Q2 data-and-distribution follow-on corridor, while the lower-secondary shared lane can remain stable until those upper-secondary widening steps are secured

2026-03-21 / Step 12 completed

Executed work:

expanded the Berlin upper-secondary source snapshot from the first reviewed Q2 stochastics strip into the first reviewed Q2 data-and-survey follow-on corridor
activated the new Berlin Q2 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Berlin Q2 data-and-survey strip onto the canonical upper-secondary math spine:
Q3.5 Statistik und weitere Wahrscheinlichkeitsverteilungen
Zufallsexperimente statistisch auswerten
Q3.5 Statistik: Kenngroessen
reviewed leaf bridges for survey planning, data preparation, sample location measures, sample dispersion measures, and survey evaluation with descriptive measures
updated the Berlin upper-secondary lane notes so the next follow-on work is now a Q4 distribution-and-binomial widening step rather than the first Q2 data-and-survey cut

Resulting rollout effect:

Berlin now has reviewed corridor coverage on both the lower-secondary shared functions lane and four reviewed upper-secondary corridors on the active analysis/stochastics/statistics spine
the nationwide score stays at 30.9% because no state phase transition changed
the Berlin total mapping surface rises from 50 to 58 mappings
the next derivable tasks are now the Brandenburg Q2 data-and-distribution follow-on corridor and the Berlin Q4 distribution-and-binomial follow-on corridor, while the lower-secondary shared lane can remain stable until those upper-secondary widening steps are secured

2026-03-21 / Step 13 completed

Executed work:

expanded the Brandenburg upper-secondary source snapshot from the first reviewed Q2 stochastics strip into the first reviewed Q2 data-and-distribution follow-on corridor
activated the new Brandenburg Q2 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Brandenburg Q2 data-and-distribution strip onto the canonical upper-secondary math spine:
Q3.5 Statistik und weitere Wahrscheinlichkeitsverteilungen
Q3.5 Statistik: Kenngroessen
Q3.2 Wahrscheinlichkeitsverteilungen
reviewed leaf bridges for sample location measures, sample dispersion measures, random variables and probability distributions, histograms, binomial descriptive measures, and point/intervall probabilities in binomial situations
updated the Brandenburg upper-secondary lane notes so the next follow-on work is now a Q2 survey-and-critique widening step rather than the first Q2 data-and-distribution cut

Resulting rollout effect:

Brandenburg now has reviewed corridor coverage on both the lower-secondary shared functions lane and five reviewed upper-secondary corridors on the active analysis/stochastics/statistics spine
the nationwide score stays at 30.9% because no state phase transition changed
the Brandenburg total mapping surface rises from 62 to 71 mappings
the next derivable tasks are now the Berlin Q4 distribution-and-binomial follow-on corridor and the Brandenburg Q2 survey-and-critique follow-on corridor, while the lower-secondary shared lane can remain stable until those upper-secondary widening steps are secured

2026-03-21 / Step 14 completed

Executed work:

expanded the Berlin upper-secondary source snapshot from the first reviewed Q2 data-and-survey strip into the first reviewed Q4 distribution-and-binomial follow-on corridor
activated the new Berlin Q4 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Berlin Q4 distribution-and-binomial strip onto the canonical upper-secondary math spine:
Q3.2 Wahrscheinlichkeitsverteilungen
reviewed leaf bridges for binomial models with n and p, Bernoulli chains, binomial probabilities, expected value, standard deviation, and first context use
updated the Berlin upper-secondary lane notes so the next follow-on work is now a Q4 inference, tests, and normal-approximation widening step rather than the first Q4 distribution-and-binomial cut

Resulting rollout effect:

Berlin now has reviewed corridor coverage on both the lower-secondary shared functions lane and five reviewed upper-secondary corridors on the active differential/stochastics/statistics spine
the nationwide score stays at 30.9% because no state phase transition changed
the Berlin total mapping surface rises from 58 to 64 mappings
the next derivable tasks are now the Brandenburg Q2 survey-and-critique follow-on corridor and the Berlin Q4 inference, tests, and normal-approximation follow-on corridor, while the lower-secondary shared lane can remain stable until those upper-secondary widening steps are secured

2026-03-21 / Step 15 completed

Executed work:

expanded the Brandenburg upper-secondary source snapshot from the first reviewed Q2 data-and-distribution strip into the first reviewed Q2 survey-and-critique follow-on corridor
activated the new Brandenburg Q2 corridor goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Brandenburg Q2 survey-and-critique strip onto the canonical upper-secondary math spine:
Q3.5 Statistik und weitere Wahrscheinlichkeitsverteilungen
Zufallsexperimente statistisch auswerten
reviewed leaf bridges for statistical survey planning, data preparation, and the critical evaluation of survey data with descriptive measures
updated the Brandenburg lane notes so the next follow-on work now shifts from this upper-secondary Q2 widening step toward the next lower-secondary corridor on the shared BE/BB functions spine

Resulting rollout effect:

Brandenburg now has reviewed corridor coverage on both the lower-secondary shared functions lane and six reviewed upper-secondary corridors on the active analysis/stochastics/statistics spine
the nationwide score stays at 30.9% because no state phase transition changed
the Brandenburg total mapping surface rises from 71 to 76 mappings
the next derivable tasks are now the Berlin Q4 inference, tests, and normal-approximation follow-on corridor and the first Brandenburg lower-secondary follow-on corridor, while broader lower-secondary widening can stay behind those two clearly bounded moves

2026-03-27 / Step 16 completed

Executed work:

expanded the Berlin upper-secondary source snapshot from the active Q4 distribution-and-binomial strip into the first reviewed Q4 inference/test/normal-approximation follow-on corridor
activated the new Berlin Q4 follow-on goals in:
source-goal-membership-registry.json
source-goal-closure-registry.json
mapped the Berlin Q4 inference/test follow-on strip onto the canonical upper-secondary math spine:
Q3.3 Hypothesentests
Q3.4 Prognose- und Konfidenzintervalle
Normalverteilung als Approximation der Binomialverteilung (LK)
reviewed leaf bridges for sigma rules, sample-to-population interval inference, significance/test interpretation, Type I/II error language, and the first bell-shape normal-approximation idea
updated the Berlin upper-secondary lane notes so the next follow-on work now shifts from this Q4 widening step toward the first tightly shared Brandenburg/Berlin lower-secondary follow-on corridor

Resulting rollout effect:

Berlin now has reviewed corridor coverage on both the lower-secondary shared functions lane and six reviewed upper-secondary corridors on the active differential/stochastics/statistics spine
the nationwide score stays at 30.9% because no state phase transition changed
the Berlin total mapping surface rises from 64 to 69 mappings
the next derivable task is now the first tightly shared Brandenburg/Berlin lower-secondary follow-on corridor, after which the active-lane widening order can be chosen again with the Berlin Q4 follow-on secured

Coverage target

For this rollout, a Bundesland counts as operationally covered only when all of the following are true:

state-owned math source material is archived under curricula/DE/Gymnasium/input/<STATE>/...
the relevant source snapshots and provenance entries are active
the canonical math graph has reviewed overlap for both structural anchors and at least one didactically closed corridor
state-specific visibility is represented through canonical applicability, not cloned goal trees
the remaining delta is narrow enough that the state can be widened corridor by corridor without rethinking the whole spine

Long-term target:

every state reaches at least broad reviewed lower-secondary and upper-secondary coverage on the same canonical math spine
the final per-state runtime behavior is driven by mappings, provenance, and compiled applicability

Program phases

The overall rollout should be managed in clear phases.

Phase 0. Tracking scaffold

Deliverables:

persisted plan
persisted JSON tracker
generated quick view
agreed phase scale for all states

Exit criteria:

every Bundesland has a tracker row
the team can update status without touching the canonical math JSON

Phase 1. Stabilize the active five-state base

Scope:

DE-HE
DE-BY
DE-NW
DE-NI
DE-BW

Deliverables:

keep existing active mapping lanes stable
keep source, provenance, and applicability references clean
remove ambiguity about which of these states are only pilot corridors and which already have broad coverage

Exit criteria:

every active state is at least P4 on the common state scale
DE-HE and DE-BY stay the current broad-coverage reference lanes

Phase 2. Source onboarding for the remaining eleven states

Scope:

DE-BB
DE-BE
DE-HB
DE-HH
DE-MV
DE-RP
DE-SH
DE-SL
DE-SN
DE-ST
DE-TH

Deliverables:

source archive lanes under curricula/DE/Gymnasium/input/<STATE>/
first state-specific math source inventory notes where needed
mapping-lane scaffolds under curricula/DE/Gymnasium/mapping/DE-<STATE>/

Exit criteria:

every remaining state has moved from placeholder-only to archived-source readiness
no state is blocked on "we still need to decide where the source bundle belongs"

Phase 3. Nationwide first-corridor pass

Deliverables per new state:

active source snapshot and provenance registration
canonical structural anchors on the shared spine
one reviewed corridor with explicit mappings

Preferred corridor order:

structural anchors first
then functions
then stochastics
then geometry/algebra

Exit criteria:

all 16 states reach at least P4
the canonical math landscape carries reviewed applicability for every onboarded state

Phase 4. Lower-secondary breadth

Deliverables:

widen each state beyond the first reviewed corridor across the shared J5-J10 grid
close obvious prerequisite strips so lower-secondary learner navigation is not just corridor-deep

Exit criteria:

every state has broad reviewed lower-secondary coverage on the canonical spine

Phase 5. Upper-secondary breadth

Deliverables:

widen upper-secondary state coverage corridor by corridor
keep Hessen as the reference donor, but validate every other state against the shared upper-secondary math structure

Exit criteria:

every state has broad reviewed upper-secondary coverage
the remaining open work is edge cleanup or special-state detail, not missing core curriculum regions

Phase 6. Cutover and maintenance

Deliverables:

stable applicability behavior for all states
stable learner-facing selection into the DE-level canonical math landscape
clear maintenance workflow for future curriculum revisions

Exit criteria:

every state reaches P6
the nationwide tracker no longer reflects rollout debt, only maintenance deltas

State phase scale

Use one simple scale per Bundesland.

State phase	Score	Meaning
`P0`	`0%`	Placeholder only: README/source links, no active math rollout lane
`P1`	`15%`	Source archived in the DE-level input lane
`P2`	`30%`	Source snapshot and provenance active
`P3`	`50%`	Structural anchors mapped on the canonical spine
`P4`	`65%`	First reviewed corridor mapped and usable
`P5`	`85%`	Broad state coverage across the main math spine
`P6`	`100%`	State cutover ready on the canonical math landscape

Interpretation:

P4 is the threshold for "real onboarding happened"
P5 is the threshold for "this state is no longer just a narrow pilot"
P6 should be rare until the final nationwide cleanup phase

Steering rules

Do not store rollout status inside DE_DEU_S_GYM_CANONICAL_MATHEMATIK.de.json.
Do not broaden many subjects in parallel before the math tracker shows nationwide momentum.
Prefer one new didactically closed corridor over a broad, weakly reviewed state import.
Prefer state-independent canonical goals plus state-specific applicability over state-specific goal duplication.
Keep Sek I normalized to the shared J5-J10 grid even if a source curriculum uses G8 / G9 labels differently.
Use the same tracker fields for every state, even if one state currently has only placeholder status.

Current baseline on 2026-03-27

Observed reviewed states already present in canonical math applicability:

DE-BW
DE-BY
DE-HE
DE-NI
DE-NW

Observed active math mapping lanes:

DE-HE/lower-secondary
DE-HE/upper-secondary
DE-BY/gymnasium
DE-NW/lower-secondary
DE-NW/upper-secondary
DE-NI/lower-secondary
DE-NI/upper-secondary
DE-BW/lower-secondary
DE-BW/upper-secondary

Observed remaining backlog states with placeholder input lanes:

DE-HB
DE-HH
DE-MV
DE-RP
DE-SH
DE-SL
DE-SN
DE-ST
DE-TH

Program interpretation:

the repo is beyond pure pilot mode for math
but nationwide state coverage is still in an early stage
the first backlog wave DE-BB / DE-BE has now reached reviewed multi-corridor upper-secondary state on both active lanes
the shared Brandenburg/Berlin lower-secondary lane now also carries its first tightly shared algebra/equation follow-on corridor on top of the earlier functions corridor
the shared Brandenburg/Berlin lower-secondary lane now also carries its first tightly shared geometry/constructions follow-on corridor on top of the earlier functions and algebra/equation corridors
the shared Brandenburg/Berlin lower-secondary lane now also carries its first tightly shared transformations/similarity follow-on corridor on top of the earlier functions, algebra/equation, and geometry/constructions corridors
the shared Brandenburg/Berlin lower-secondary lane now also carries its first tightly shared measurement follow-on corridor on top of the earlier functions, algebra/equation, geometry/constructions, and transformations/similarity corridors
the shared Brandenburg/Berlin lower-secondary lane now also carries its first tightly shared later body/space follow-on corridor on top of the active measurement strip
the shared Brandenburg/Berlin lower-secondary lane now also carries its first tightly shared later triangle-trigonometry follow-on corridor on top of the active measurement and later body/space strips
the shared Brandenburg/Berlin lane has now also returned to upper-secondary widening and carries its first tightly shared Q3 vector/line-plane corridor around spatial vectors, scalar product, parametric lines, plane forms, normal vectors, and first line/plane position relations
the shared Brandenburg/Berlin lane now also carries its first tightly shared upper-secondary Q3 intersections/angles follow-on corridor around systematic line/plane intersections and angle calculations between lines and planes
the shared Brandenburg/Berlin lane now also carries its first tightly shared upper-secondary Q3 distance follow-on corridor around point-point, point-plane, line-plane, and plane-plane distances
the shared Brandenburg/Berlin lane now also carries the remaining tightly shared LK-only Q3 line-distance residue around point-line and line-line distances
the shared Brandenburg/Berlin upper-secondary Q3 geometry strip now also has Brandenburg- and Berlin-side provenance splits that separate the previously broad line/plane source anchors into parametric-line work, coordinate/normal-form plane work, cross-form plane descriptions, and first line/plane relation checks without widening the nationwide canonical phase picture
the Berlin side of the same Q3 strip now also mirrors the later Brandenburg plane-anchor refinement by separating normal-vector work from coordinate-form work before the cross-form plane bridge, still without widening the nationwide canonical phase picture
the Brandenburg side of the same Q3 strip now also has a second and third provenance refinement that separates vector/coordinatization work from scalar-product/length/angle work, feeds the local projection intuition lane from the scalar-product anchor, and now also isolates coordinate-form work from the normal-vector anchor before the cross-form plane bridge
the Berlin side of the same Q3 strip now also mirrors that vector-anchor refinement by separating pure vector/coordinatization work from scalar-product/length/angle work and by feeding the angle follow-on explicitly from the new scalar-product anchor without widening the nationwide canonical phase picture
the Berlin lane now also carries its first state-local matrix / transition side lane from simple matrix representations into first Markov-chain modeling, a separated state-vector propagation step, repeated-transition readings, long-run probability ideas, and a first explicit long-term-development residue
the Berlin matrix / transition side lane now also mirrors that provenance cleanup internally by separating the single-step matrix-vector state update from the later multi-step state calculation before the repeated-transition reading node, still without widening the nationwide canonical phase picture
the Berlin lane now also carries its first state-local sequences / series side lane around convergent / divergent sequences and first limit arguments
the Berlin lane now also carries its first state-local differential-equations side lane around elementary first-order solution methods and second-order oscillation interpretations
the Berlin lane now also carries its first state-local complex-numbers side lane around field-axiom foundations as well as algebraic form, the Gaussian plane, polar representations, and a separate periodic-process residue
the Berlin complex-numbers side lane now also separates algebraic-form work from Gaussian-plane localization before the polar-form step, so the ma-Z8 provenance now mirrors the canonical split more closely without widening the nationwide canonical phase picture
the Berlin complex-numbers side lane now also separates field-axiom classification from the later precise-use residue for arithmetic laws, so the ma-Z8 provenance keeps the canonical LK precision bridge while exposing the source-local conceptual split more honestly
the Berlin lane now also carries its first state-local logic side lane around implication/equivalence work, quantifiers, chains of reasoning, and fallacy detection
the Berlin lane now also carries its first state-local reasoning / proof side lane around direct geometry proofs, quantifier logic, induction, contradiction, and proof-strategy comparison
the Berlin lane now also carries its first state-local analysis-deepening side lane around counterexamples to non-invertibility, theorem assumptions, local/global function properties, and first Rolle/mean-value-theorem proof checking
the Berlin lane now also carries its first state-local numerical-mathematics side lane around computer-supported approximation methods, interpolation and fitting routines, numerical integration, error estimates, and critical reading of numerical results
the Berlin numerical-mathematics side lane now also narrows its general calculator-based base atom to approximation-focused work, with interpolation/fitting and numerical integration kept as separate residues, so the ma-Z4 provenance mirrors the source bundle more honestly without widening the nationwide canonical phase picture
the Brandenburg lane now also carries its first state-local linear-representation / projection side lane around tuple descriptions now split into point/vector notation, tabular tuple reading, and a separate spreadsheet-use residue plus a separated orthogonal-projection anchor for scalar-product interpretation and a narrower first linear-mapping intuition residue
the Brandenburg linear-representation / projection side lane now also separates point-form tuple work from vector-form tuple work, so the narrower BB vector bridge sits on the explicit vector residue instead of the mixed point/vector source atom
the Brandenburg linear-representation / projection side lane now also explicitly bridges the spreadsheet-use residue into the matrix-representation anchor and the point-form tuple residue into the already active coordinate-system anchor, so the current BB side-lane residue is fully mapped without widening the nationwide canonical phase picture
the SH Sek-I lane now also operationalizes the remaining broad Funktionen / Darstellungsformen atoms closer to the active canonical function-concept and representation-switch targets, so the next SH residue is no longer the raw function-label bridge itself
the SH Sek-I lane now also operationalizes the still-generic Proportionale Funktionen / Antiproportionale Funktionen / Lineare Funktionen atoms closer to their active canonical proportional, inverse-proportional, and linear-function targets, so the coarse raw table-label function-family residue is smaller again without changing the nationwide canonical phase picture
the SH Sek-I lane now also operationalizes the still-generic Variablen / Terme / Lineare Gleichungen / Lineare Gleichungssysteme / Quadratische Gleichungen atoms closer to their active canonical algebra and equation targets, so the remaining SH residue shifts away from raw algebra/equation table labels toward the proportionality/rule-of-three and quadratic-parent leftovers
the SH Sek-I lane now also operationalizes the still-generic Dreisatz / Proportionale Funktionen und Dreisatz / Quadratische Funktionen und Gleichungen / Quadratische Funktionen nodes closer to their active canonical rule-of-three and quadratic corridor targets, so the remaining SH residue shifts again from raw table-label parents toward the few still-broad corridor-parent nodes
the SH Sek-I lane now also operationalizes the still-generic Variablen und Terme / Funktionen und ihre Darstellungsformen parent clusters closer to their active canonical variable/term and function-concept/representation corridors, so the remaining SH residue shifts from corridor-parent wording toward the few still-broad stage-parent nodes
the SH Sek-I lane now also operationalizes the still-generic Jahrgangsband 7/8/9: Strukturen und funktionaler Zusammenhang stage-parent closer to the active canonical mixed algebra/function corridor, so the remaining SH residue shifts away from raw area-parent wording toward the few still-broad year-band parents
the SH Sek-I lane now also operationalizes the still-generic Jahrgangsstufe 10 year-parent closer to the active canonical J10 continuation anchor, so the remaining SH residue shifts further from raw year labels toward the still-broad Jg 5/6 and Jg 7/8/9 band parents
the SH Sek-I lane now also operationalizes the still-generic Jahrgangsband 5/6 / Jahrgangsband 7/8/9 year-parents closer to their active canonical early- and later-Sek-I anchors, so the remaining SH residue shifts away from raw band labels toward the top-level SH root or a new explicit follow-on strip
the SH Sek-I lane now also operationalizes the still-generic top-level Mathematik Sekundarstufe I root closer to the refined early-/later-/late-Sek-I progression, so the remaining SH residue shifts away from raw source-table root wording toward opening a new explicit follow-on strip
the SH lane now also opens its first explicit upper-secondary follow-on strip by splitting Einfuehrungsjahr: Geometrie into vectors in R2/R3, lines, and line relations and mapping them onto the canonical space/line corridor, so the next SH residue shifts from Sek-I parent cleanup toward similarly explicit Sek-II phase-table cells such as Q1 geometry or E analysis
the SH lane now also opens a second explicit upper-secondary follow-on strip by splitting 1. Jahr der Qualifikationsphase: Geometrie into scalar product, planes, vector product, line-plane relations, and distances and mapping the canonical-fit subgoals onto the shared space-geometry corridor while retaining Vektorprodukt as an explicit SH-only residue, so the next SH residue shifts from Q1 geometry toward E analysis or another equally explicit Sek-II phase-table cell
the SH lane now also opens an explicit upper-secondary E-analysis strip by splitting Einfuehrungsjahr: Analysis into derivatives, extrema, and inflection-point work and mapping the canonical-fit subgoals onto the shared derivative/extrema/curvature corridor, so the next SH residue shifts from E analysis toward Q1 analysis or another equally explicit Sek-II phase-table cell
the SH lane now also opens an explicit upper-secondary Q1-analysis strip by splitting 1. Jahr der Qualifikationsphase: Analysis into integral-calculus, natural-exponential-function, and differential/integral-calculus deepening atoms and mapping the canonical-fit subgoals onto the shared integral/exponential/deepening corridor, so the next SH residue shifts from Q1 analysis toward an equally explicit stochastics strip or another similarly narrow Sek-II follow-on
the SH lane now also opens its first explicit upper-secondary stochastics strip by splitting Einfuehrungsjahr: Stochastik into random-experiment/Laplace basics and conditional probability and mapping the canonical-fit subgoals onto the shared foundational-stochastics corridor, so the next SH residue shifts from broad first-stochastics wording toward Q1 stochastics or another equally explicit Sek-II follow-on
the SH lane now also opens an explicit upper-secondary Q1-stochastics strip by splitting 1. Jahr der Qualifikationsphase: Stochastik into random-variable/distribution-characteristics work, binomial contexts, hypergeometric-without-replacement modelling, and a retained normal-distribution residue, so the next SH residue shifts from broad Q1-stochastics wording toward Q2 stochastics or another equally explicit Sek-II follow-on instead of forcing a premature LK-specific normal-distribution widening
the SH lane now also opens a first explicit upper-secondary Q2-stochastics strip by splitting 2. Jahr der Qualifikationsphase: Stochastik into significance-test setup and confidence-interval estimation and mapping the canonical-fit subgoals onto the shared hypothesis/interval corridor, so the next SH residue shifts from broad Q2-stochastics wording toward narrower test-decision / interval-interpretation follow-ons or another equally explicit Sek-II strip
the SH lane now also opens a narrower upper-secondary Q2-stochastics follow-on by adding a contextual test-decision atom behind the significance-test setup step and mapping it onto the shared test-result-interpretation node, so the next SH residue shifts from generic Q2 test wording toward interval interpretation or another equally explicit Sek-II strip
the SH lane now also opens a second narrow upper-secondary Q2-stochastics interval follow-on by adding a confidence-level interpretation atom behind the confidence-interval estimation step and mapping it onto the shared confidence-level node, so the next SH residue shifts from generic Q2 interval wording toward a broader interval-context interpretation only if a separate prediction-/interval-context source residue appears
the SH lane now also opens a first explicit upper-secondary Q2-analysis follow-on by splitting the broad Q2 analysis cell into a parameter/function-family atom plus a retained deepening residue and mapping the parameter step onto the shared contextual parameter-determination goal, so the next SH residue shifts away from the raw Q2-analysis parent wording toward another equally explicit Sek-II strip unless the retained deepening residue becomes source-exposed
the SH lane now also opens a narrow upper-secondary Q1-stochastics normal-distribution follow-on by mapping the previously retained Normalverteilung residue onto the shared normal-approximation LK goal, so the next SH residue shifts away from the raw Q1 normal-distribution holdout toward another equally explicit Sek-II strip unless the retained Q2-analysis deepening residue or another separate source cell becomes clearer
the SH lane now also anchors the remaining explicit upper-secondary Q1-geometry Vektorprodukt einsetzen residue on the already active shared normal-vector goal, so the last SH Sek-II holdouts now sit mainly in broader retained cells such as the Q2-analysis deepening residue rather than in another cleanly isolatable geometry atom
the SH lane now also anchors the retained upper-secondary Q2-analysis deepening residue on the same shared differential/integral-calculus deepening cluster already used by the Q1 deepening step, so all currently explicit SH Sek-II source atoms are now mapped and the SH next wave should pause until a genuinely new source-exposed cell appears
the BE lane now also anchors the broad sequences/series, differential-equations, complex-numbers, logic, and reasoning/proof side-lane parents on the corresponding shared canonical clusters, so the next Berlin residue shifts away from those lane roots toward the remaining analysis-deepening / numerical-mathematics holdouts or a return to Brandenburg if a clearer BB-local follow-on appears
the BE lane now also anchors the broad matrix/transition side-lane parent on the shared transition-process matrix cluster, so the next Berlin residue shifts further away from the established optional-course lane roots toward the remaining analysis-deepening / numerical-mathematics holdouts or a return to Brandenburg if a clearer BB-local follow-on appears
the BW lane now also anchors the remaining explicit lower-secondary 3.2.1 algebra/equation parents plus the narrower J9/J10 year parents on the shared Sek-I algebra, power-function, and J10 continuation clusters, so the next BW residue shifts away from still-open fine-grained algebra rows toward the broader 7/8 and 9/10 umbrella parents and the remaining non-core source sections
the eight remaining placeholder states DE-HB, DE-HH, DE-MV, DE-RP, DE-SL, DE-SN, DE-ST, and DE-TH now also have repository-backed lower-secondary and upper-secondary math mapping fixtures plus reserved source-landscape IDs in state-local onboarding notes, so the nationwide backlog is no longer blocked on creating the first mapping-lane scaffold itself and can move directly to source-archive imports for those states
the BW lane now also anchors the still-open lower-secondary 7/8 geometry and data umbrellas plus the broad 9/10 geometry and stochastics umbrellas on the shared Sek-I geometry, Sek-I data/probability, Sek-I geometry, and Sek-II probability/distribution corridors, so the remaining BW residue shifts further toward mixed top-level, function-lane, and vector-lane parents plus the remaining non-core source sections
the BW lane now also anchors the retained lower-secondary top-level pilot root on the shared canonical mathematics root, so the remaining BW residue shifts away from the mixed top-level parent and more narrowly toward function-lane, vector-lane, and early mixed-parent cleanup plus the remaining non-core source sections
the BW lane now also anchors the broad J7/J8 function corridor, its retained J7/J8 representation subcorridor, and the late-Sek-I coordinate/vector follow-on parent on the shared Sek-I function-foundations, functions-and-representations, and coordinate/vector entry clusters, so the remaining BW residue shifts away from those lane parents toward earlier function parents, late mixed parents, and the remaining non-core source sections
the BW lane now also anchors the first broad function corridor plus the split J9 trigonometrie parent and J10 circle/body parent on the shared Sek-I function-foundations, J9 trigonometry, and J10 trigonometry-circle-solids clusters, so the remaining BW residue shifts away from those cleaned parents toward the still-broad J5/J6 mixed-function strip, the broad 9/10 algebra/function mixed parents, and the remaining non-core source sections
the BW lane now also anchors the split J9 four-field/conditional-probability parent and the split J10 random-variable/binomial parent on the shared foundational stochastics-methods cluster and the shared probability-distribution overview cluster, so the remaining BW residue shifts further away from late-Sek-I stochastics split parents toward the still-broad J5/J6 mixed-function strip, the broad 9/10 algebra/function mixed parents, the broad 5/6 and 7/8 mixed umbrellas, and the remaining non-core source sections
the BW lane now also anchors the formerly still-broad J5/J6 mixed-function strip on the shared Sek-I function-foundations cluster, so the remaining BW residue shifts away from that early function parent toward the broad 9/10 algebra/function mixed parents, the broad 5/6 and 7/8 mixed umbrella parents, and the remaining non-core source sections
the BW lane now also anchors the overarching mixed 9/10 connector parent on the shared lower-secondary structures/functional-relationships cluster and the formerly still-broad 9/10 algebra/function follow-on parent on the shared J10 year anchor, so the remaining BW residue shifts away from broad late mixed-function parents toward the broad 5/6 and 7/8 mixed umbrellas and the remaining non-core source sections
the BW lane now also anchors the broad mixed 5/6 umbrella on the shared J6 year anchor, the retained 5/6 Leitidee parents on the shared lower-secondary number/algebra, early measurement, early geometry, and early data clusters, and the broad mixed 7/8 umbrella on the shared J8 year anchor, so the remaining BW residue shifts away from the last open lower-secondary core parent cleanup and narrows to the retained non-core source sections
the NI lane now also opens an explicit later-Sek-I geometry / trigonometry follow-on by importing Entdeckungen an rechtwinkligen Dreiecken und Aehnlichkeit into the active source snapshot and mapping the exact-fit Pythagoras and right-triangle-trigonometry atoms onto the shared J9 geometry corridor, so the next Niedersachsen residue shifts away from a generic geometry/algebra placeholder toward the remaining similarity / root / general-triangle residues or the adjacent quadratics corridor
the NI lane now also anchors the similarity atom and the general-triangle sine/cosine-law atom from that opened right-triangle / similarity corridor on the shared J9 similarity and sine/cosine-law goals, so the next Niedersachsen residue narrows further to the root-based length-calculation atom or the adjacent quadratics corridor
the NI lane now also anchors the remaining root-based length-calculation atom from that opened right-triangle / similarity corridor on the shared J9 square-root-basics goal, so the explicit Niedersachsen residue shifts off that geometry/trigonometry strip and onto the adjacent quadratics corridor
the NI lane now also opens the adjacent explicit later-Sek-I Quadratische Zusammenhaenge corridor and anchors its quadratic-function, quadratic-equation, and quadratic-modelling atoms on the shared lower-secondary quadratic goals, so the next Niedersachsen residue narrows from a generic quadratics front to the still-visible parabola-as-locus atom or the next equally explicit local split inside that corridor
the NI lane now also closes that opened explicit later-Sek-I Quadratische Zusammenhaenge corridor by introducing a dedicated canonical parabola-as-locus atom and exact-bridging the remaining NI source residue onto it, so the current Niedersachsen lower-secondary explicit strips are now exhausted at source-residue level
the BW lane now also reaches the point where the active lower-secondary pilot snapshot has no unmapped source goals left at all, so the former Baden-Wuerttemberg lower-secondary residue collapses from "still-open rows inside the current snapshot" to "import additional retained non-core source sections or another BW lane intentionally"
the NRW lane now also closes the remaining explicit 2.4.1 Funktionen Stage-1 concept/context residue by bridging the mapping-context pair, adding a dedicated canonical function-concept leaf for functions as unique mappings, and anchoring the retained representation-use and Stage-1 proportional/linear parents, so the next NRW lower-secondary move shifts from 2.4.1 cleanup to the still-open 2.4.2 function-class cluster or another equally explicit NRW import
the NRW lane now also anchors the retained lower-secondary 2.4.2 Funktionen Stage-2 umbrella on the shared canonical J10 year anchor, so the current NRW functions snapshot is parent-anchored at both Stage-1 and Stage-2 level and the next NRW move shifts away from umbrella cleanup toward another equally explicit imported corridor
the NRW lane now also anchors the retained upper-secondary Q-phase exponential parent on the shared canonical exponential-functions cluster, so the next NRW upper-secondary move shifts away from that reviewed exponential umbrella and toward the retained E-phase power/polynomial split or another equally explicit imported corridor
the NRW lane now also anchors the retained upper-secondary E-phase power/polynomial split on the shared canonical Funktionen und ihre Darstellung cluster, so the current NRW upper-secondary pilot subset is now parent-anchored on its remaining explicit retained split parents and the next NRW move should come from another equally explicit imported corridor rather than more parent cleanup inside the current pilot subset
the NRW lane now also reaches the explicit lower-secondary Stage-1 algebra prerequisite strip on shared canonical variables/terms, term-evaluation, fraction-term, and broad Sek-I algebra goals, so the remaining unmapped NRW Sek-I goals inside the current snapshot are structural parents rather than still-open explicit atomic residues and the next NRW move should come from another equally explicit imported corridor rather than renewed parent cleanup
the NRW lane now also opens the first explicit upper-secondary 2.3 Analytische Geometrie und Lineare Algebra (G) corridor and anchors its E-phase entry strip on shared canonical space/vector, mixed orientation-in-space, parametric-line, line-relation, and geometric-LGS anchors, so Nordrhein-Westfalen now spans both the initial upper-secondary analysis spine and a first upper-secondary geometry / linear-algebra entry corridor and the next NRW move should be a similarly explicit follow-on such as Q-phase geometry/linear algebra or another clearly exposed corridor
the NRW lane now also opens the first explicit upper-secondary 2.4.1 Analytische Geometrie und Lineare Algebra (G) Grundkurs follow-on and anchors its Q-phase strip on shared scalar-product, plane-form, coordinate-form, line-plane-intersection, and angle anchors, so Nordrhein-Westfalen now spans the initial upper-secondary analysis spine plus both an E-phase and a first Q-phase geometry / linear-algebra corridor and the next NRW move should narrow to the remaining explicit Q-phase geometry residue or another equally exposed corridor
the NRW lane now also opens the first explicit upper-secondary 2.4.1 Stochastik Grundkurs strip and anchors its Baumdiagramm-/Vierfeldertafel-/Unabhaengigkeits-/bedingte-Wahrscheinlichkeit atoms on the shared Q3 stochastics corridor, so Nordrhein-Westfalen now spans upper-secondary analysis plus first explicit geometry / linear-algebra and stochastics coverage and the next NRW move should narrow to the adjacent expectation/distribution strip or another equally exposed corridor
the NRW lane now also opens the adjacent explicit upper-secondary 2.4.1 Stochastik expectation/distribution strip and anchors its Zufallsgroessen-/Kenngroessen-/Binomialverteilungs atoms on the shared Q3 distributions corridor, so Nordrhein-Westfalen now spans upper-secondary analysis plus first explicit geometry / linear-algebra coverage and two explicit stochastics strips; the next NRW move should therefore come from another equally exposed imported corridor rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also opens the first explicit upper-secondary 2.4.2 Stochastik Leistungskurs strip and anchors its Prognoseintervall-, Konfidenzintervall-, and Stichprobenumfang atoms on the shared Q3 interval/statistics corridor, so Nordrhein-Westfalen now spans upper-secondary analysis plus first explicit geometry / linear-algebra coverage and three explicit stochastics strips; the next NRW move should therefore narrow to the adjacent normal-distribution strip or another equally exposed imported corridor
the NRW lane now also opens the adjacent explicit upper-secondary 2.4.2 Stochastik Leistungskurs normal-distribution strip and anchors its diskret/stetig-, Verteilungsfunktions-, normal-approximation-, and density-parameter atoms on the shared Q3 statistics / continuous-distribution corridor, so Nordrhein-Westfalen now spans upper-secondary analysis plus first explicit geometry / linear-algebra coverage and four explicit stochastics strips; the next NRW move should therefore come from another equally exposed imported corridor rather than renewed stochastic parent cleanup inside the reviewed pilot subset
the NRW lane now also opens the first explicit upper-secondary 2.4.2 Analytische Geometrie und Lineare Algebra Leistungskurs strip and anchors its plane-form, line-plane-relation, line-plane-intersection, angle, and distance atoms on the shared Q2 space/plane corridor, so Nordrhein-Westfalen now spans upper-secondary analysis plus explicit E-, GK-, and first LK-geometry/linear-algebra coverage alongside four explicit stochastics strips; the next NRW move should therefore narrow to the remaining explicit 2.4.2 geometry residues or another equally exposed imported corridor rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also opens the adjacent explicit upper-secondary 2.4.2 Analytische Geometrie und Lineare Algebra Leistungskurs linearsystem / solution-set strip and anchors its algorithmic-LGS atom on the shared Q2 space/plane corridor and geometric-LGS anchor, so Nordrhein-Westfalen now spans upper-secondary analysis plus explicit E-, GK-, and two LK-geometry/linear-algebra strips alongside four explicit stochastics strips; the next NRW move should therefore narrow to the remaining explicit 2.4.2 geometry residues around parameter-plane setup, reflections, or another equally exposed imported corridor rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also opens the adjacent explicit upper-secondary 2.4.2 Analytische Geometrie und Lineare Algebra Leistungskurs parameter-form strip and anchors its plane-in-parametric-form atom on the shared Q2 space/plane corridor plus the exact canonical plane-parameter-form goal, so Nordrhein-Westfalen now spans upper-secondary analysis plus explicit E-, GK-, and three LK-geometry/linear-algebra strips alongside four explicit stochastics strips; the next NRW move should therefore narrow to the remaining explicit Parallelogramme und Dreiecke in Parameterform residue, reflections, or another equally exposed imported corridor rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also closes the adjacent explicit upper-secondary 2.4.2 Analytische Geometrie und Lineare Algebra Leistungskurs figures-in-parametric-form residue by adding a small canonical room-geometry atom for Parallelogramme und Dreiecke in Parameterform darstellen and mapping the NRW source goal to it exactly, so Nordrhein-Westfalen now spans upper-secondary analysis plus explicit E-, GK-, and four LK-geometry/linear-algebra strips alongside four explicit stochastics strips; the next NRW move should therefore narrow to reflections or another equally exposed imported corridor rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also opens the adjacent explicit upper-secondary 2.4.2 Analytische Geometrie und Lineare Algebra Leistungskurs reflection strip by splitting Spiegelungen an Ebenen out of the imported source text, adding a small canonical room-geometry atom for Punkte an Ebenen spiegeln, and anchoring the NRW source goal to it exactly, so Nordrhein-Westfalen now spans upper-secondary analysis plus explicit E-, GK-, and five LK-geometry/linear-algebra strips alongside four explicit stochastics strips; the next NRW move should therefore narrow to another equally exposed imported corridor rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also opens the first explicit upper-secondary 2.4.2 Funktionen und Analysis Leistungskurs integral-applications strip and anchors reconstructed stocks / total effects, definite-integral area work, improper-integral area work, and solids of revolution on the shared canonical integral-applications corridor, so Nordrhein-Westfalen now spans upper-secondary analysis plus explicit E-, GK-, and five LK-geometry/linear-algebra strips, four explicit stochastics strips, and a first explicit LK integral-applications strip; the next NRW move should therefore narrow to the adjacent 2.4.2 Funktionen und Analysis Hauptsatz/Stammfunktions strip rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also opens the adjacent explicit upper-secondary 2.4.2 Funktionen und Analysis Leistungskurs integral-theorem / antiderivative strip by splitting out the LK expectations on anschaulichem Hauptsatz, polynomial antiderivatives, ln(x) as antiderivative of 1/x, and interval additivity / linearity of integrals, adding small canonical atoms for the narrower polynomial-antiderivative, ln(x)-antiderivative, and integral-property surfaces, and exact-bridging those NRW source atoms onto them; Nordrhein-Westfalen now spans upper-secondary analysis plus explicit E-, GK-, and five LK-geometry/linear-algebra strips, four explicit stochastics strips, and two explicit LK integral strips, so the next NRW move should therefore come from another equally exposed imported corridor rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also opens the adjacent explicit upper-secondary 2.4.1 Stochastik combinatorics prelude by splitting out Urnenmodelle mit/ohne Zuruecklegen, Ereignisoperationen, verknuepfte Ereignisse, and Binomialkoeffizienten, exact-bridging the event-operations, combined-event, and binomial-coefficient atoms, and reviewed-partial-bridging the with/without-replacement urn-model atoms onto the shared Bernoulli/hypergeometric corridor; Nordrhein-Westfalen now spans upper-secondary analysis plus explicit E-, GK-, and five LK-geometry/linear-algebra strips, five explicit stochastics strips, and two explicit LK integral strips, so the next NRW move should therefore come from another equally exposed imported corridor rather than renewed parent cleanup inside the reviewed pilot subset
the NRW lane now also splits the earlier broad upper-secondary 2.4.1 Stochastik Baumdiagramm-/Vierfeldertafel atom into a small reviewed parent plus two exact child bridges on the shared canonical tree-diagram and fourfold-table atoms, so Nordrhein-Westfalen keeps the same five explicit stochastic pilot strips while reducing one narrower NRW partial debt inside the already opened GK stochastics lane
the NRW lane now also fully resolves the adjacent broad upper-secondary 2.4.1 Stochastik expectation/distribution atom by splitting it into three exact children on random-variable introduction, histogram representation, and simple characteristic-value work, and by adding two small canonical sibling atoms under the existing Q3 distribution overview rather than widening a fresh corridor, so Nordrhein-Westfalen keeps the same five explicit stochastic pilot strips while removing that earlier NRW partial entirely
the NRW lane now also splits the previously broad upper-secondary 2.4.1 Funktionen und Analysis Hauptsatz/Stammfunktions atom into an exact theorem-explanation child on a new canonical Hauptsatz-explanation atom plus an exact polynomial-antiderivative child on the shared canonical antiderivative atom, so Nordrhein-Westfalen keeps the same reviewed GK integral strip while shifting the next NRW follow-on toward the remaining total-stock/effect residue or the retained exponential split
the NRW lane now also fully splits the remaining upper-secondary 2.4.1 Funktionen und Analysis total-stock/effect residue by adding a dedicated GK child and a new shared canonical stock/effect atom, and it simultaneously pulls the matching LK reconstructed-stock atom from a partial bridge onto that same exact canonical surface, so Nordrhein-Westfalen now keeps the reviewed GK integral strip with exact theorem-, antiderivative-, and stock/effect children while the next NRW follow-on should narrow to the retained exponential split or another equally explicit imported corridor
the NRW lane now also exact-resolves the retained upper-secondary exponential three-way split by adding three narrow canonical atoms for a^x properties, the special role of e^x, and growth/decay usage, and by moving the three NRW source children off their broader partial canonical exponential surfaces onto those exact siblings; Nordrhein-Westfalen therefore keeps the retained exponential parent only as a reviewed umbrella while the next NRW follow-on should narrow to the retained E-phase power/polynomial split or another equally explicit imported corridor
the NRW lane now also exact-resolves the explicit upper-secondary 2.3 geometry leaf Geraden und Strecken in Parameterform darstellen by adding a dedicated canonical upper-secondary parameter-form atom with segment and parameter-interpretation scope, and by moving the NRW source goal off the broader shared Geraden im Raum parametrisch darstellen surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the retained E-phase power/polynomial parent as one remaining option, but the next clean NRW follow-on can now also narrow to adjacent explicit geometry leaves such as coordinate-form orientation or line-plane intersections instead of reopening parent cleanup
the NRW lane now also exact-resolves the adjacent explicit upper-secondary 2.4.1 geometry leaf Schnittpunkte von Geraden mit Ebenen berechnen by adding a dedicated canonical upper-secondary line-plane-intersection atom and by moving the NRW source goal off the broader shared Schnittpunkte im Raum berechnen surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed GK/Q2 geometry corridor while the next clean NRW follow-on can now narrow to coordinate-form orientation or scalar-product work, or return to the retained E-phase power/polynomial split
the NRW lane now also exact-resolves the adjacent explicit upper-secondary 2.4.1 geometry leaf Skalarprodukt geometrisch deuten und berechnen by adding a dedicated canonical upper-secondary dot-product atom and by moving the NRW source goal off the broader shared Skalarprodukt und Winkel berechnen surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed GK/Q2 geometry corridor while the next clean NRW follow-on can now narrow to coordinate-form orientation, or return to the retained E-phase power/polynomial split
the NRW lane now also exact-resolves the adjacent explicit upper-secondary 2.4.1 geometry leaf Koordinatenformen von Ebenen zur Orientierung im Raum nutzen by adding a dedicated canonical upper-secondary coordinate-form-orientation atom and by moving the NRW source goal off the broader shared Koordinatenform einer Ebene aufstellen und interpretieren surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed GK/Q2 geometry corridor while the next clean NRW follow-on can now narrow to the remaining intersection-angle leaf, or return to the retained E-phase power/polynomial split
the NRW lane now also exact-resolves the adjacent explicit upper-secondary 2.4.1 geometry leaf Schnittwinkel zwischen geometrischen Objekten berechnen by adding a dedicated canonical upper-secondary intersection-angle atom and by moving the NRW source goal off the broader shared Winkel zwischen Geraden und Ebenen bestimmen surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed GK/Q2 geometry corridor while the next clean NRW follow-on can now narrow to the remaining line-relation leaf, or return to the retained E-phase power/polynomial split
the NRW lane now also exact-resolves the explicit upper-secondary 2.3 line-relation leaf Lagebeziehungen von Geraden im Raum untersuchen by adding a dedicated canonical upper-secondary line-relation atom and by moving the NRW source goal off the broader shared Lagebeziehungen von Geraden und Ebenen untersuchen surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed E-phase geometry entry corridor while the next clean NRW follow-on can now narrow to the remaining LK line-relation leaf, or return to the retained E-phase power/polynomial split
the NRW lane now also exact-resolves the adjacent explicit upper-secondary 2.4.2 LK line-/plane-relation leaf Lagebeziehungen von Ebenen sowie von Geraden und Ebenen untersuchen by adding a dedicated canonical advanced-course relation atom and by moving the NRW source goal off the broader shared Lagebeziehungen von Geraden und Ebenen untersuchen surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed Q2 geometry lane while the next clean NRW follow-on should return to the retained E-phase power/polynomial split or another equally explicit imported corridor
the NRW lane now also exact-resolves the retained upper-secondary E-phase power/polynomial parent by adding a dedicated canonical intro cluster that bundles the already exact power-function and polynomial-description children and by moving the NRW source parent off the broader shared Funktionen und ihre Darstellung surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed intro-analysis lane while the next clean NRW follow-on should move to another equally explicit imported corridor rather than reopening the current parent cleanup residues
the NRW lane now also exact-resolves the explicit upper-secondary GK integral leaf Uebergang von der Produktsumme zum Integral erlaeutern und vollziehen by adding a dedicated canonical transition atom under the shared integral-introduction cluster and by moving the NRW source goal off the broader shared approximate-area surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed GK integral corridor while the next clean NRW follow-on should narrow to another equally explicit imported leaf such as the remaining LK integral residues around Hauptsatz mit anschaulichem Stetigkeitsbegriff or Volumina von Rotationskoerpern
the NRW lane now also exact-resolves the explicit upper-secondary LK integral leaf Volumina von Rotationskoerpern um die Abszisse ermitteln by adding a dedicated canonical rotation-volume atom under the shared integral-applications cluster and by moving the NRW source goal off the broader shared Rotationskoerper mit Integralen untersuchen (LK) surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed LK integral-applications corridor while the next clean NRW follow-on should narrow to another equally explicit imported leaf such as the remaining LK integral residues around Hauptsatz mit anschaulichem Stetigkeitsbegriff or uneigentliche Integrale
the NRW lane now also exact-resolves the explicit upper-secondary LK integral leaf Flaecheninhalte mithilfe uneigentlicher Integrale ermitteln by adding a dedicated canonical improper-integral-area atom under the shared integral-applications cluster and by moving the NRW source goal off the broader shared Uneigentliche Integrale berechnen (LK) surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed LK integral-applications corridor while the next clean NRW follow-on should narrow to the remaining equally explicit LK integral residue around Hauptsatz mit anschaulichem Stetigkeitsbegriff
the NRW lane now also exact-resolves the explicit upper-secondary LK theorem leaf Hauptsatz mit anschaulichem Stetigkeitsbegriff begruenden und anwenden by adding a dedicated canonical LK Hauptsatz atom under the shared integral-introduction cluster and by moving the NRW source goal off the broader shared Hauptsatz der Differential- und Integralrechnung nutzen surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed LK theorem strip while the next clean NRW follow-on should move to another equally explicit imported corridor outside the now exhausted LK integral strip, such as the retained LK normal-distribution residue
the NRW lane now also exact-resolves the explicit upper-secondary LK normal-distribution leaf Einfluss von mu und sigma auf Normalverteilung und Dichtegraph beschreiben by adding a dedicated canonical mu/sigma-normal-distribution atom under the shared LK normal-distribution cluster and by moving the NRW source goal off the broader shared Dichtefunktion der Normalverteilung angeben und deuten (LK) surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed LK normal-distribution strip while the next clean NRW follow-on should narrow to the adjacent retained LK approximation-in-situations residue
the NRW lane now also exact-resolves the explicit upper-secondary LK normal-distribution leaf Annaehernd normalverteilte Zufallsgroessen in Situationen erkennen by adding a dedicated canonical approximation-in-situations atom under the shared LK normal-distribution cluster and by moving the NRW source goal off the broader shared Normalverteilung als Approximation der Binomialverteilung (LK) surface onto that exact sibling; Nordrhein-Westfalen therefore keeps the reviewed LK normal-distribution strip while the next clean NRW follow-on should narrow to the remaining retained LK normal-distribution-computation residue around Diskrete und stetige Zufallsgroessen unterscheiden und Verteilungsfunktion deuten
the NRW lane now also exact-resolves the explicit upper-secondary LK normal-distribution leaf Diskrete und stetige Zufallsgroessen unterscheiden und Verteilungsfunktion deuten by adding a dedicated canonical normal-distribution-concept atom and by moving the NRW source goal off the broader shared Mit der Normalverteilung rechnen (LK) surface onto that exact sibling; Nordrhein-Westfalen therefore treats the currently opened LK normal-distribution strip as exhausted at explicit source-residue level, and the next clean move should be another equally explicit imported NRW corridor or the next active broad comparison lane rather than renewed parent cleanup in the current NRW snapshots
the Bavaria comparison lane now also exact-resolves the explicit J10 logarithm leaf erlaeutern die Definition des Logarithmus und ermitteln Werte von Logarithmen in einfachen Faellen ... by adding a dedicated canonical logarithm-introduction atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Exponentielles Wachstum modellieren und Logarithmen nutzen surface onto that exact sibling; Bayern therefore keeps the broad comparison lane stable while the next clean BY follow-on should remain corridor-specific, preferably on the adjacent J10 exponential characteristics or modelling leaves
the Bavaria comparison lane now also exact-resolves the explicit J10 exponential leaf beschreiben und veranschaulichen die Charakteristika von exponentieller Zunahme und exponentieller Abnahme ... by adding a dedicated canonical characteristics atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Exponentielles Wachstum modellieren und Logarithmen nutzen surface onto that exact sibling; Bayern therefore keeps the broad comparison lane stable while the next clean BY follow-on should remain corridor-specific, preferably on the adjacent J10 modelling leaf for growth and decay contexts
the Bavaria comparison lane now also exact-resolves the adjacent explicit J10 modelling leaf loesen realitaetsnahe Aufgabenstellungen im Zusammenhang mit Wachstums- und Abklingvorgaengen ... by adding a dedicated canonical exponential-modelling-in-context atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Exponentielles Wachstum modellieren und Logarithmen nutzen surface onto that exact sibling; Bayern therefore keeps the broad comparison lane stable while the next clean BY follow-on should move to another equally explicit imported leaf rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the explicit J10 leaf loesen einfache Exponentialgleichungen ... by moving the Bavaria source goal off the broader shared Exponentielles Wachstum modellieren und Logarithmen nutzen surface onto the already existing canonical J10 atom Exponentialgleichungen mit Logarithmen loesen; Bayern therefore keeps the broad comparison lane stable while the next clean BY follow-on should remain on the last explicit J10 exponential graph-shape leaf rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the last explicit J10 exponential graph-shape leaf beschreiben fuer Funktionen mit Termen der Form b · a^x ... den Verlauf des zugehoerigen Graphen by adding a dedicated canonical graph-shape atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Exponentielles Wachstum modellieren und Logarithmen nutzen surface onto that exact sibling; Bayern therefore treats the currently opened J10 exponential corridor as exhausted at explicit source-residue level and should move next to the adjacent J10 sinus/cosinus unit-circle strip rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the first explicit J10 sinus/cosinus leaf verstehen das Bogenmass ... und wechseln sicher zwischen Bogen- und Gradmass by adding a dedicated canonical radian/unit-circle-introduction atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Sinus- und Kosinusfunktionen beschreiben surface onto that exact sibling; Bayern therefore keeps the adjacent trigonometrie strip corridor-specific while the next clean BY follow-on should remain on the neighboring unit-circle-values-and-angle leaf rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the adjacent explicit J10 unit-circle-values leaf veranschaulichen ... Sinus- und Kosinuswerte von Winkelgroessen zwischen 0 und 2π ... und bestimmen ... Winkel by adding a dedicated canonical unit-circle-values-and-angle atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Sinus- und Kosinusfunktionen beschreiben surface onto that exact sibling; Bayern therefore keeps the adjacent trigonometrie strip corridor-specific while the next clean BY follow-on should move to the neighboring unit-circle reduction leaf for angles beyond 2π and negative angles rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the neighboring explicit J10 unit-circle-reduction leaf erlaeutern, wie sich die Werte von Sinus und Kosinus fuer Winkelgroessen groesser als 2π sowie fuer negative Winkelgroessen ... zurueckfuehren lassen by adding a dedicated canonical angle-reduction atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Sinus- und Kosinusfunktionen beschreiben surface onto that exact sibling; Bayern therefore keeps the adjacent trigonometrie strip corridor-specific while the next clean BY follow-on should move to the neighboring sine/cosine graph-derivation leaf for periodicity and the relation between the two functions rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the neighboring explicit J10 sine/cosine graph-derivation leaf leiten mithilfe des Einheitskreises den Verlauf der Graphen der Sinus- und der Kosinusfunktion ab ... by adding a dedicated canonical graph-derivation-and-periodicity atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Sinus- und Kosinusfunktionen beschreiben surface onto that exact sibling; Bayern therefore keeps the adjacent trigonometrie strip corridor-specific while the next clean BY follow-on should move to the neighboring parameter-effect leaf for functions of the form a · sin(b · (x + c)) + d rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the neighboring explicit J10 sine/cosine parameter-effect leaf beschreiben fuer Funktionen mit Termen der Form a · sin(b · (x + c)) + d, wie sich Aenderungen der Parameter ... auswirken by moving the Bavaria source goal off the broader shared Sinus- und Kosinusfunktionen beschreiben surface onto the already existing canonical J10 atom Parameter trigonometrischer Funktionen deuten; Bayern therefore keeps the adjacent trigonometrie strip corridor-specific while the next clean BY follow-on should move to the neighboring graph-drawing leaf for functions of the same form rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the neighboring explicit J10 sine/cosine graph-drawing leaf zeichnen fuer einen gegebenen Funktionsterm der Form a · sin(b · (x + c)) + d ... und ermitteln umgekehrt aus dem Graphen den zugehoerigen Funktionsterm by adding a dedicated canonical graph-drawing-and-term-recovery atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Sinus- und Kosinusfunktionen beschreiben surface onto that exact sibling; Bayern therefore keeps the adjacent trigonometrie strip corridor-specific while the next clean BY follow-on should move to the neighboring periodic real-world modelling leaf rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the neighboring explicit J10 periodic-modelling leaf loesen realitaetsbezogene Problemstellungen zu periodischen Vorgaengen ... by adding a dedicated canonical periodic-real-world-modelling atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Sinus- und Kosinusfunktionen beschreiben surface onto that exact sibling; Bayern therefore treats the currently opened J10 sinus/cosinus strip as exhausted at explicit source-residue level and should move next to the adjacent J10 polynomial/ganzrationale strip rather than broad parent cleanup
the Bavaria comparison lane now also narrows the adjacent broad J10 polynomial/ganzrationale leaf verstehen ganzrationale Funktionen als Summe von Potenzfunktionen ... und begruenden ... das Verhalten an den Raendern des Definitionsbereichs ... onto a dedicated canonical power-sum/end-behaviour atom under the shared J10 anchor; because the Bavaria source leaf still also contains roots, multiplicities, biquadratic substitution, and sketching, the bridge remains reviewed partial, but the active queue is now narrowed to the neighboring explicit graph-to-degree/term leaf instead of staying on the broader generic Ganzrationale Funktionen beschreiben surface
the Bavaria comparison lane now also exact-resolves the neighboring explicit J10 polynomial leaf ziehen aus dem Graphen einer ganzrationalen Funktion ... Rueckschluesse auf den Grad der Funktion oder auch auf den zugehoerigen Funktionsterm by adding a dedicated canonical graph-to-degree-or-term atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Ganzrationale Funktionen beschreiben surface onto that exact sibling; Bayern therefore keeps the opened J10 polynomial strip corridor-specific while the next clean BY follow-on should move to the neighboring symmetry leaf rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the neighboring explicit J10 polynomial leaf ueberpruefen rechnerisch sowie durch Analyse der Struktur des Funktionsterms, ob der Graph einer ganzrationalen Funktion Achsensymmetrie ... bzw. Punktsymmetrie ... aufweist by adding a dedicated canonical symmetry-from-term atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Ganzrationale Funktionen beschreiben surface onto that exact sibling; the opened BY J10 polynomial strip can therefore be treated as exhausted at explicit source-residue level, and the next clean Bavaria follow-on should move to the adjacent M10 geometry plausibility leaf for oblique prisms and pyramids rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the first adjacent explicit M10 geometry plausibility leaf machen ... mithilfe des Prinzips von Cavalieri plausibel, dass auch das Volumen eines schiefen Prismas ... plus Sie machen die Struktur der Formel zur Bestimmung des Volumens einer Pyramide plausibel by adding a dedicated canonical oblique-prism-and-pyramid plausibility atom under the shared J10 anchor and by moving the Bavaria source goal off the broader shared Volumen von Prismen, Pyramiden und Kegeln plausibilisieren und berechnen surface onto that exact sibling; Bayern therefore keeps the opened M10 geometry strip corridor-specific while the next clean BY follow-on should move to the neighboring cone-volume plausibility leaf rather than broad parent cleanup
the Bavaria comparison lane now also exact-resolves the neighboring explicit M10 cone-volume plausibility leaf machen die Formel zur Bestimmung des Volumens eines Kreiskegels plausibel, indem sie diesen Koerper als Grenzfall von Pyramiden betrachten by adding a dedicated canonical cone-volume-limiting atom under the shared J10 anchor, by moving the Bavaria source goal off the broader shared Volumen von Prismen, Pyramiden und Kegeln plausibilisieren und berechnen surface onto that exact sibling, and by reattaching the broader 5D plausibility surface to a still-valid broad Baden-Wuerttemberg provenance source; the opened BY M10 geometry plausibility strip can therefore now be treated as exhausted at explicit source-residue level, and the next clean corridor move should be a reassessment for broader Baden-Wuerttemberg / Schleswig-Holstein projection work rather than more Bavaria-local cleanup
the tightened Sek I J10 5D corridor now also broadens cleanly into Baden-Wuerttemberg by exact-resolving the explicit BW leaf Kugelformeln geometrisch deuten und anwenden on the already existing canonical sphere-formula atom instead of keeping that state on a reviewed partial bridge; this removes the BW-specific APV-202 debt on the shared sphere node and turns the corridor reassessment into a concrete first broader-state projection checkpoint, so the next clean move should inspect whether Schleswig-Holstein's broad Pyramiden und Kegel band can be narrowed without inventing new state-local canonical residue
the follow-on Schleswig-Holstein reassessment keeps that next-wave J10 5D band intentionally broad: the current SH lower-secondary snapshot exposes only the coarse calculation bands Pyramiden und Kegel and Kugeln, but no narrower source atoms that would justify splitting them onto additional shared canonical targets without drifting into state-local packaging. The correct result of that inspection is therefore not another canonical atom, but an explicit queue decision that the SH 5D partials should remain as-is until a cleaner source split exists.
the active Sek II analysis corridor now also exact-resolves the explicit Schleswig-Holstein upper-secondary E-analysis leaf Ableitungen elementarer Funktionen on the already existing shared derivative-technique atom instead of leaving the SH lane on a reviewed partial bridge; this removes the SH-specific APV-202 debt on that canonical analysis goal and sharpens the next clean analysis move to the adjacent explicit SH Extrempunkte / Wendepunkte leaves rather than broad analysis parents
the follow-on Schleswig-Holstein analysis tightening now also exact-resolves the adjacent explicit E-analysis leaves Extrempunkte mit Ableitungen untersuchen and Wendepunkte und Kruemmung untersuchen on the already existing shared extremum-analysis and inflection-analysis atoms; this removes the remaining SH-specific APV-202 debt on the opened E-analysis strip and means the next clean SH analysis move should prefer the adjacent explicit Q1 leaves e-Funktion / Integralrechnung rather than reopening broad analysis parents
the next Schleswig-Holstein analysis step now also exact-resolves the adjacent explicit Q1 leaf e-Funktion und natuerliche Exponentialfunktion on the already existing shared natural-exponential-function atom; this removes the SH-specific APV-202 debt on that canonical exponential-analysis goal and narrows the next clean SH analysis move to the remaining explicit Q1 Integralrechnung leaf rather than broad analysis parent cleanup
the follow-on Schleswig-Holstein Q1 integral step now avoids inventing a new canonical mix-atom by source-splitting the formerly broad Integralrechnung mit Hauptsatz und Integralen cell into two narrower explicit leaves and exact-resolving them on the already existing shared canonical atoms Hauptsatz der Differential- und Integralrechnung nutzen and Einfache Integrale berechnen; the opened SH upper-secondary analysis strip can therefore now be treated as exhausted at explicit source-residue level, and the next clean Sek II analysis move should prefer another equally narrow imported analysis atom instead of reopening broad SH Q1/Q2 analysis parents
the next Sek II analysis tightening now also exact-resolves the explicit Baden-Wuerttemberg Leistungsfach leaf Die eulersche Zahl e naeherungsweise bestimmen by adding a dedicated canonical Euler-number atom under the shared exponential corridor and moving the BW source off the broader natural-exponential-function leaf; this removes the BW-specific APV-202 debt on that shared canonical target and sharpens the next clean analysis move toward another equally narrow imported atom such as Niedersachsen Exponentialgleichungen loesen instead of broad BW/SH parent cleanup
the follow-on Sek II analysis step now also exact-resolves the explicit Niedersachsen gA leaf Exponentialgleichungen loesen on the already existing shared canonical exponential-equation atom instead of leaving the NI lane on a reviewed partial bridge; this removes the NI-specific APV-202 debt on that canonical target and sharpens the next clean analysis move toward another equally narrow Niedersachsen Die e-Funktion atom such as asymptotic limited-growth behavior or derivative use instead of broad SH/BW/NI parent cleanup
the next Sek II analysis tightening now also exact-resolves the explicit Niedersachsen gA leaf Die Basis e durch die Eigenschaft (e^x)' = e^x charakterisieren on the already existing shared canonical leaf Besonderheit der natürlichen Exponentialfunktion erläutern instead of leaving the NI lane on a reviewed partial bridge; this removes the NI-specific APV-202 debt on the broader natural-exponential-function target and sharpens the next clean analysis move toward another equally narrow Niedersachsen Die e-Funktion atom such as derivative use or asymptotic limited-growth behavior instead of broad SH/BW/NI parent cleanup
the follow-on Sek II analysis tightening now also exact-resolves the explicit Niedersachsen eA leaf Die Basis e durch (e^x)' = e^x charakterisieren on that same shared canonical natural-exponential-specialness leaf instead of leaving the imported Wachstumsmodelle - Exponentialfunktion strip on an avoidable broad partial; this removes the last artificial Niedersachsen residue on the wider natural-exponential-function target and keeps the next clean analysis move on another equally narrow NI e-function atom such as derivative use or asymptotic limited-growth behavior instead of broad SH/BW/NI parent cleanup
the next Sek II analysis tightening now also exact-resolves the explicit Niedersachsen gA and eA leaves Ableitungen von e^x und a^x verwenden / Ableitungsfunktionen von e^x und a^x verwenden by adding a dedicated shared canonical derivative-use atom instead of leaving both strips on the broader elementary-derivative-rules surface; this keeps the corridor canonical-first and shifts the next clean analysis move to the remaining equally narrow Niedersachsen asymptotic limited-growth residue instead of broad SH/BW/NI parent cleanup
the follow-on Sek II analysis tightening now also exact-resolves the explicit Niedersachsen gA leaf Asymptotisches Verhalten begrenzten Wachstums beschreiben by adding a dedicated shared canonical bounded-growth-asymptotics atom under the Q1 exponential-deepening cluster instead of leaving that residue on the broader growth/decay-modelling surface; this keeps the corridor pedagogically round and shifts the next clean analysis move to the adjacent Niedersachsen eA asymptotic-in-context or growth-model-comparison atom instead of broad SH/BW/NI parent cleanup
the next Sek II analysis tightening now also exact-resolves the explicit Niedersachsen eA leaf Asymptotisches Verhalten von Wachstumsmodellen im Sachzusammenhang beschreiben by adding a dedicated shared canonical context-asymptotics atom under the same Q1 exponential-deepening cluster instead of leaving that residue on the unrelated logistic-growth surface; this keeps the corridor canonical-first and narrows the next clean analysis move to the adjacent Niedersachsen eA growth-model-comparison atom instead of broad SH/BW/NI parent cleanup
the follow-on Sek II analysis tightening now also exact-resolves the explicit Niedersachsen eA leaf Verschiedene Wachstumsmodelle vergleichen by adding a dedicated shared canonical growth-model-comparison atom under that same Q1 exponential-deepening cluster instead of leaving that residue on the broader growth/decay-modelling surface; this keeps the corridor canonical-first and shifts the next clean analysis move to the adjacent Niedersachsen differential-equation solution-check follow-on or a retained split around the still-broad differential-equation parent instead of broad SH/BW/NI parent cleanup

Update workflow

update curricula/DE/Gymnasium/provenance/math-bundesland-rollout-tracker.json
run python3 scripts/render_canonical_math_bundesland_status.py
review the generated docs/dev/canonical-gymnasium-math-bundeslaender-status.md
update docs/dev/canonical-gymnasium-math-de-expansion-plan.md
commit plan, tracker, and generated status together when the rollout picture changed

Suggested next concrete move

Keep the tracker stable and use it to drive math work in this order:

broaden Nordrhein-Westfalen from its now atom-anchored lower-secondary prerequisite/functions plus upper-secondary analysis, refined GK integral theorem/antiderivative/stock-effect split, exact retained exponential split, and E-phase/Q-phase geometry/linear-algebra pilot coverage toward broader state coverage, but do so via the retained E-phase power/polynomial split or another equally explicit NRW source corridor rather than reopening structural parent cleanup inside the already reviewed NRW snapshots
keep Baden-Wuerttemberg and Niedersachsen stable at their now exhausted explicit lower-secondary pilot-snapshot / strip level unless additional retained source corridors are imported intentionally
keep Brandenburg, Berlin, and Schleswig-Holstein stable at their explicitly source-exposed residue level unless a genuinely clearer local follow-on appears that changes the nationwide rollout picture

That makes nationwide progress visible without overloading the canonical landscape file with project-management metadata.