Canonical Gymnasium Mathematics: Sek I Geometry / Space Audit

Snapshot: 2026-04-05

Purpose:

• review the current canonical geometry inventory after the lower-secondary breadth wave widened further
• use reviewed Sek-I evidence to test whether the current canonical cuts are pedagogically stable at nationwide scale
• verify whether the former Nordrhein-Westfalen blocker is now removed so Sek I Geometrie / Raum can be treated as coverage-closed

Scope

In scope:

• the canonical Sek-I geometry topic surface in
• curricula/DE/Gymnasium/canonical/DE_DEU_S_GYM_CANONICAL_MATHEMATIK.de.json
• the reviewed lower-secondary source and mapping evidence from
• HB
• HH
• MV
• SN
• ST

Out of scope:

• direct canonical JSON refactoring in this step
• learner-facing composition views

Reviewed source evidence

Hamburg (HH)

Reviewed lower-secondary geometry corridors already exist in two bands:

1. J8 Raum und Form
2. quadrilaterals, triangles, congruence
3. transformations, symmetry, similarity
4. Pythagoras

5. Thales and angle arguments

6. J10 Raum und Form

7. properties, positional relations, similarity
8. transformations and constructions
9. Pythagoras
10. Thales and angle justifications

Observed signal:

• HH strongly supports a later Sek-I geometry split into
• figure/congruence work
• transformation/similarity work
• Pythagoras work
• Thales/angle work

Bremen (HB)

Reviewed lower-secondary geometry evidence is broader but still useful:

1. J5/6 Geometrie

2. plane figures, cuboids, angles, first area ideas

3. J7/8 Geometrie

4. triangles, prisms, similarity, Pythagoras

5. J9 Geometrie

6. circle, bodies, trigonometry

Observed signal:

• HB confirms that body geometry and early space ideas are real topic lanes
• HB also supports a later progression from triangle/similarity/Pythagoras toward circle/body/trigonometry
• HB is less granular than HH, so it is good validation for corridor shape but weaker for atomic wording

Sachsen (SN)

Reviewed lower-secondary geometry evidence now also includes ten explicit early-, middle-, and late-Sek-I strips:

1. K5 Lernbereich 3 Lagebeziehungen geometrischer Objekte
2. geometric basic concepts and positional relations

3. drawings and first justifications in the plane

4. K5 Lernbereich 4 Rechtecke und Quader

5. rectangles and cuboids

6. perimeter, area, surface area, and volume of simple bodies

7. K6 Lernbereich 4 Prismen

8. prism properties and representations

9. surface areas and volumes of prisms

10. K6 Lernbereich 3 Dreiecke und Vierecke

11. triangles and quadrilaterals

12. congruence, constructions, interior-angle theorems, and area ideas

13. K7 Lernbereich 1 Geometrie in der Ebene

14. circle and angle geometry

15. theorems, constructions, and first formal justification

16. K7 Lernbereich 3 Darstellen und Berechnen von Prismen und Pyramiden

17. orthographic or oblique representations, nets, and first pyramid work

18. surface-area and volume calculations

19. K8 Lernbereich 4 Aehnlichkeit

20. central dilation and construction
21. similarity properties for angles and corresponding side ratios

22. main similarity theorem and applications of similar figures

23. K9 Lernbereich 2 Kreise, Kreiszylinder und Kugeln

24. circumference and area of circles and circle parts
25. surface area, volume, and mass of circular cylinders

26. surface area, volume, and mass of spheres

27. K9 Lernbereich 3 Rechtwinklige Dreiecke

28. Pythagoras and one proof
29. altitude theorem, cathetus theorem, and converse statements
30. sine, cosine, and tangent in the right triangle

31. applications to lengths, angles, areas, and first spatial situations

32. K10 Lernbereich 3 Algebraisches Loesen geometrischer Probleme

33. broad analytic access to geometric problems
34. algebraic description of figures and relations

Observed signal:

• SN now also confirms the existing early-geometry / space surface through a reviewed K5 lane on basic geometric relations
• SN now also confirms the same early-geometry / space surface through a reviewed K5 lane on rectangles, cuboids, and first area/volume ideas
• SN now also confirms the same early-geometry / space surface through a reviewed K6 prism lane with first explicit prism representations plus surface/volume work
• SN now also confirms the existing G2 quadrilateral/triangle/congruence package through a reviewed K6 lane with congruence, constructions, interior-angle theorems, and area ideas
• SN now also confirms the broader later figure/transformation/theorem geometry surface through a reviewed K7 plane-geometry lane with circle and angle geometry, theorems, constructions, and first formal justification
• SN now also confirms the existing G6 later solids surface through a reviewed K7 prism/pyramid lane with nets, Schraegbilder, pyramid work, and first explicit surface/volume calculations
• SN now clearly confirms the existing G3 transformations/similarity package as a real shared middle-Sek-I lane
• SN strongly confirms the existing G5 Pythagoras package as a real shared late Sek-I lane
• SN also confirms that the trigonometric bridge is a real G7 continuation and not only a body-geometry residue
• SN additionally confirms the existing G6 circle-and-solids package as a real shared late Sek-I lane for circle-part, cylinder, and sphere calculations
• the broad Sachsen K10 algebraic-geometry corridor fits the existing later figure/transformation/theorem geometry surface without forcing a separate visible analytic-geometry package in Sek I
• the Sachsen K5 rectangles/cuboids lane still does not force a separate visible early area-volume package beyond the current early geometry / space surface
• the Sachsen K6 prism lane likewise does not force a separate visible early prism package beyond the current early geometry / space surface
• the Sachsen K7 plane-geometry lane still does not force a separate visible circle-angle/theorem package beyond the current broad later geometry surface
• the Sachsen K7 prism/pyramid lane still does not force a separate visible later pyramid package beyond the current G6 solids surface
• the explicit Sachsen zentrische-Streckung material still does not force a separate visible canonical package beyond the current G3 surface
• the theorem-group material around altitude and cathetus theorems still does not force a separate visible canonical package beyond the current Pythagoras and trigonometric-bridge surfaces
• the Sachsen mass-applications on circular solids do not yet force a separate visible mass-application package beyond the current G6 surface

Sachsen-Anhalt (ST)

Observed signal:

• ST now contributes a first reviewed early lower-secondary geometry lane through JG 5/6
• the lane currently covers broad geometry basics plus early perimeter / area / volume work
• both strips fit the existing early geometry / space surface
• this confirms that early Sachsen-Anhalt geometry does not currently force a separate visible early area-volume package

Rheinland-Pfalz (RP)

Observed signal:

• RP now contributes a first reviewed lower-secondary geometry corridor on the explicit Klassenstufen 9 und 10 lane
• the Rheinland-Pfalz source separates
• Geometrische Abbildungen
• Satzgruppe des Pythagoras
• Koerper und ihre Darstellungen
• Trigonometrische Beziehungen
• this makes RP a useful pressure test for whether the visible later Sek-I geometry surface can absorb later transformation work next to explicit G5, G6, and G7 strips without forcing another package

Mecklenburg-Vorpommern (MV)

Observed signal:

• MV now contributes reviewed lower-secondary geometry corridors on the explicit Klassen 5/6, Klasse 7, and Klasse 8 lanes

Thueringen (TH)

Observed signal:

• TH now contributes a first reviewed lower-secondary geometry corridor on the explicit Klassenstufen 5/6 lane
• the Thueringen source separates
• Figuren und Koerper
• Dreiecke und Kreis
• this makes TH a useful pressure test for whether the visible early geometry / space surface can absorb a clean 5/6 foundations lane without forcing a sharper early geometry split
• TH now also contributes a first reviewed broad Klassenstufen 7/8 geometry corridor
• the archived 7/8 source still exposes only one shared Geometrie strip
• this confirms that the shared broad Sek-I geometry surface can absorb a reviewed wide 7/8 lane without forcing a sharper canonical split from source granularity alone
• TH now also contributes a first reviewed broad Klassenstufen 9/10 geometry corridor
• the archived 9/10 source still exposes only one shared Geometrie strip
• this confirms that the same shared broad later Sek-I geometry surface can absorb a reviewed wide 9/10 lane without forcing a sharper canonical split from source granularity alone
• the Mecklenburg-Vorpommern Klassen 5/6 source now separates
• broad plane geometry with angles, constructions, transformations, rectangles, and squares
• broad cuboid/cube work with nets, surface area, and volume
• the Mecklenburg-Vorpommern Klasse 8 source now separates
• Rechtwinkliges Dreieck with explicit Pythagoras work
• Aehnlichkeit
• Prisma, Pyramide, and Zylinder body work
• this makes MV a useful pressure test for whether the early geometry / space surface can absorb broad plane-geometry plus cuboid/cube work without forcing a separate visible early area-volume package, while the visible G5, G3, and G6 surfaces can coexist inside one reviewed later lower-secondary lane without forcing another mixed geometry package

Current canonical geometry inventory

The canonical graph is not empty here. It already has substantial geometry content:

1. early corridor

2. Fruehe Geometrie und Raumvorstellungen (Sek I)

3. later corridor

4. Spaetere Geometrie-, Kreis- und Koerpervorstellungen (Sek I)

5. later subcorridors

6. Vierecke, Dreiecke und Kongruenzsaetze (Sek I)
7. Kreisbeziehungen und Satz des Thales (Sek I)

8. Spaetere Flaechen-, Kreis-, Koerper- und Aehnlichkeitsvorstellungen (Sek I)

9. important later atoms already present

10. Kongruenz begruenden und Dreieckskonstruktionen ausfuehren
11. Dreieckskonstruktionen nach Kongruenzsaetzen planen, ausfuehren und ihre Loesbarkeit begruenden
12. Satz des Pythagoras anwenden
13. Satz des Pythagoras in Konstruktionen und geometrischen Begruendungen nutzen
14. Kreisbeziehungen am Kreis begruenden und nutzen
15. Satz des Thales begruenden und anwenden
16. Aehnlichkeit und Strahlensatz anwenden
17. body and circle atoms

Audit judgment

The canonical geometry topic is materially seeded, but not yet cleanly packaged for topic-first nationwide work.

Main issue:

• the current canonical geometry layer mixes
• chronological progression,
• subtopic structure,
• and some repeated bridge atoms in a way that makes state evidence harder to compare topic by topic

This is not a missing-content problem first. It is a packaging and cut-quality problem.

Findings

1. The later geometry corridor is too mixed

Spaetere Geometrie-, Kreis- und Koerpervorstellungen (Sek I) currently bundles:

• congruence and constructions
• circle relations and Thales
• Pythagoras
• body geometry

That is too wide for clean topic-by-topic validation across states.

2. Transformations / similarity are not isolated clearly enough

HH exposes a stable instructional unit around:

• transformations
• symmetry
• similarity

In the current canonical graph this signal is split across:

• Kongruente und aehnliche Figuren erkennen und Eigenschaften geometrischer Abbildungen beschreiben
• Aehnlichkeit und Strahlensatz anwenden
• parts of the congruence/construction corridor

This may still be pedagogically correct, but it is not yet a clean topic work package.

3. Circle / Thales is already a strong canonical unit

This part looks comparatively healthy:

• Kreisbeziehungen am Kreis begruenden und nutzen
• Satz des Thales begruenden und anwenden

Both HH and HB support keeping this as its own later subpackage.

4. Body geometry needs a cleaner canonical lane

HB already signals body geometry early and later:

• cuboids and first area ideas in J5/6
• prisms in J7/8
• circles, bodies, trigonometry in J9

The current canonical graph contains body atoms, but they are spread between:

• early geometry
• later mixed geometry/circle/body corridor
• later body/trigonometry corridor

For nationwide topic work this should become a visibly separate work package.

5. The reviewed state evidence does not yet force many brand-new atoms

Important conclusion:

• HB, HH, and SN do not primarily prove that the canonical graph lacks geometry atoms everywhere
• they primarily show that some existing atoms and clusters are not grouped in the cleanest nationwide topic structure

That means the next step should be a canonical repackaging review before another large state rollout wave.

Proposed canonical work packages

For Sek I Geometrie / Raum, use these work packages:

1. G1 Early figures, angles, and spatial imagination
2. basic figures
3. angle types
4. cuboids / first bodies

5. nets / first spatial views

6. G2 Triangles, quadrilaterals, congruence, constructions

7. figure properties
8. congruence
9. triangle constructions

10. constructibility / justification

11. G3 Transformations, symmetry, similarity

12. translations, rotations, reflections, dilations
13. symmetry

14. similarity / intercept theorem boundary

15. G4 Circle relations and Thales

16. circle relations
17. Thales

18. angle reasoning around circles

19. G5 Pythagoras and geometric justification

20. right triangles

21. Pythagoras in calculation and construction

22. G6 Bodies, area, volume, and later space problems

23. prisms, cylinders, pyramids, cones, spheres
24. surface / volume

25. later space modelling

26. G7 Trigonometric bridge

27. only where truly Sek-I-wide and shared
28. keep this explicit so it does not blur body geometry

Recommendation

Do not reopen Sek-I geometry packaging. Keep the current G2-G7 surface frozen, treat the geometry row as coverage-closed, and move the active lower-secondary breadth wave to data/chance.

Design step executed on 2026-04-01

Accepted packaging decision for the current pass:

1. keep existing geometry atoms stable where possible
2. add explicit canonical subclusters for
3. G3 Transformations, symmetry, similarity
4. G5 Pythagoras and geometric justification
5. repackage the later Sek-I geometry corridor so that figure/congruence work, transformation/similarity work, circle/Thales work, and Pythagoras work are visible as explicit subpackages
6. keep first body-geometry content attached as a compatibility bridge for now instead of forcing a second large cut in the same step

Resulting effect:

• the canonical graph now has explicit package handles for G2-G5
• existing bundesland mappings on legacy IDs remain materially usable
• the remaining open design problem is now concentrated on G6 bodies / area / volume and G7 trigonometric bridge, not on the whole later geometry lane

Design step executed on 2026-04-01, pass 2

Accepted packaging decision for this pass:

1. repurpose the former mixed body/similarity cluster into an explicit G6 area / circle / solids package
2. repurpose the former trigonometry / circle-sector / body-deepening cluster into an explicit G7 trigonometric bridge / later spatial problems package
3. keep the underlying atoms stable so existing state mappings remain materially usable

Resulting effect:

• the canonical Sek-I geometry topic now has visible package handles for G2-G7
• the biggest remaining work is no longer canonical packaging, but mapping realignment and validation against more states
• HB and HH can now be checked against a cleaner canonical geometry spine without another large atomic rewrite first

Sachsen K9 right-triangle and circle/solids corridors connected on 2026-04-03

The new Sachsen lower-secondary geometry strips add reviewed evidence exactly where the current canonical cut was most likely to be challenged next:

1. G5 Pythagoras and geometric justification
2. G6 Later area, circle, and solids ideas
3. G7 Trigonometric bridge

Outcome:

• SN validates the frozen G5/G6/G7 package surface
• no new visible theorem-group package is justified yet for altitude theorem / cathetus theorem material
• no new visible mass-application package is justified yet for circle-cylinder-sphere calculations
• the next geometry work should therefore stay in nationwide coverage mode rather than reopening canonical package design

Current next concrete step

1. keep the canonical geometry package cut frozen
2. treat NW together with BW, BY, BE, BB, NI, and SH as resolved against the current G2-G7 package surface
3. move the active lower-secondary breadth wave to Sek I Daten / Zufall

Why this cut:

• HB and HH already provide enough reviewed evidence here
• it is the cleanest place to test whether the canonical graph needs new subclusters, new atoms, or only better grouping
• it avoids pulling body geometry and trigonometry into the same edit before the later geometry spine is stable

Exit criteria for this audit

This topic audit is complete when:

1. the canonical subpackage boundaries above are either accepted or revised
2. the canonical graph has a stable later Sek-I geometry packaging
3. reviewed nationwide evidence can be described as aligned to the revised packaging or intentionally broader because of source granularity
4. every Bundesland cell in the geometry row is resolved once

Sachsen-Anhalt JG 5/6 geometry corridor connected (2026-04-03)

• the ST JG 5/6 strips Geometrische Grundbegriffe und Abbildungen and Umfang, Flaecheninhalt und Volumen now both point to the existing early geometry / space surface
• the reviewed ST lane therefore confirms the broad early G1 packaging without reopening the current Sek-I geometry cut

Sachsen-Anhalt JG 5/6 angle / triangle / quadrilateral corridor connected (2026-04-03)

• the ST JG 5/6 strips Winkelbeziehungen, Dreiecke, and Vierecke now all point to the existing triangle / quadrilateral / congruence surface
• the reviewed ST lane therefore confirms the current G2 cut without forcing a separate visible early angle package

Sachsen-Anhalt JG 7/8 body / similarity corridor connected (2026-04-03)

• the ST JG 7/8 strips Koerperdarstellung and Koerperberechnung now point to the existing later solids surface
• the ST JG 7/8 strip Aehnlichkeit now points to the existing transformation / similarity surface
• the reviewed ST lane therefore confirms the current G3/G6 split without forcing a new mixed body-similarity package

Sachsen-Anhalt JG 7/8 Pythagoras corridor connected (2026-04-03)

• the ST JG 7/8 strip Satzgruppe des Pythagoras now points to the explicit Pythagoras / geometric-justification surface
• the reviewed ST lane therefore confirms the current G5 cut without forcing a broader mixed theorem package

Sachsen-Anhalt JG 9 trigonometry corridor connected (2026-04-03)

• the ST JG9 strip Trigonometrie now points to the visible G7 trigonometric bridge
• the reviewed ST lane therefore confirms the current G7 cut without forcing a broader mixed trigonometry/solids package

Sachsen-Anhalt JG 7/8 circles corridor connected (2026-04-03)

• the ST JG7/8 strip Kreise now points to the broad visible G6 circle/solids surface
• the reviewed ST lane therefore confirms that this unsplit circle residue can stay on the existing later circle/body package without forcing a narrower separate circle package

Sachsen-Anhalt JG 10 vectors corridor connected (2026-04-03)

• the ST JG10 strip Vektoren now points to the visible Sek-I vector-entry surface
• the reviewed ST lane therefore confirms that this vector residue can stay on the existing coordinate-geometry / vectors package without forcing a broader visible Sek-I analytic-geometry package

Sachsen-Anhalt JG 5/6 quantities corridor connected (2026-04-03)

• the ST JG5/6 strip Groessen now points to the visible early measurement / area / volume surface
• the reviewed ST lane therefore confirms that this broad quantities residue can stay on the existing early measurement package without forcing a separate standalone quantities package

Rheinland-Pfalz Klassenstufen 9 und 10 geometry corridor connected (2026-04-03)

• the broad RP Klassenstufen 9 und 10: Raum und Form anchor now carries a reviewed split into Geometrische Abbildungen, Satzgruppe des Pythagoras, Koerper und ihre Darstellungen, and Trigonometrische Beziehungen
• geometric transformations point to the broad later figure/theorem geometry surface
• the Pythagoras strip points to the visible G5 surface
• the body strip points to the visible G6 surface
• the trigonometric-relations strip points to the visible G7 bridge
• the RP lane therefore confirms the visible later Sek-I geometry surface without forcing another package boundary

Saarland Klassenstufe 7 geometry corridor connected (2026-04-04)

• the broad SL Klassenstufe 7: Raum und Form anchor now carries a first reviewed corridor on the shared Sek-I geometry surface
• the current Saarland grade-7 source still exposes only one shared geometry strip
• this confirms that the shared broad Sek-I geometry surface can absorb an explicit reviewed class-7 lane without forcing a sharper state-local split from source granularity alone

Saarland Klassenstufe 7 measurement corridor connected (2026-04-04)

• the broad SL Klassenstufe 7: Groessen und Messen anchor now carries a first reviewed corridor on the shared early Sek-I measurement / area / volume surface
• the current Saarland grade-7 source still exposes only one shared measurement strip
• this confirms the shared early measurement surface can absorb an explicit reviewed class-7 lane without forcing a sharper state-local split

Saarland Klassenstufe 8 geometry corridor connected (2026-04-04)

• the broad SL Klassenstufe 8: Raum und Form anchor now carries a first reviewed corridor on the shared Sek-I geometry surface
• the current Saarland grade-8 source still exposes only one shared geometry strip
• this confirms the shared broad Sek-I geometry surface can absorb an explicit reviewed class-8 lane without forcing a sharper state-local split

Saarland Klassenstufe 8 measurement corridor connected (2026-04-04)

• the broad SL Klassenstufe 8: Groessen und Messen anchor now carries a first reviewed corridor on the shared early Sek-I measurement / area / volume surface
• the current Saarland grade-8 source still exposes only one shared measurement strip
• this confirms the shared early measurement surface can absorb an explicit reviewed class-8 lane without forcing a sharper state-local split

Saarland Klassenstufe 9 geometry corridor connected (2026-04-04)

• the broad SL Klassenstufe 9: Raum und Form anchor now carries a first reviewed corridor on the shared Sek-I geometry surface
• the current Saarland grade-9 source still exposes only one shared geometry strip
• this confirms the shared broad Sek-I geometry surface can absorb an explicit reviewed class-9 lane without forcing a sharper state-local split

Saarland Klassenstufe 9 measurement corridor connected (2026-04-04)

• the broad SL Klassenstufe 9: Groessen und Messen anchor now carries a first reviewed corridor on the shared early Sek-I measurement / area / volume surface
• the current Saarland grade-9 source still exposes only one shared measurement strip
• this confirms the shared early measurement surface can absorb an explicit reviewed class-9 lane without forcing a sharper state-local split

Saarland Klassenstufe 10 geometry corridor connected (2026-04-04)

• the broad SL Klassenstufe 10: Raum und Form anchor now carries a first reviewed corridor on the shared Sek-I geometry surface
• the current Saarland grade-10 source still exposes only one shared geometry strip
• this confirms the shared Sek-I geometry surface can absorb an explicit reviewed grade-10 lane without forcing a sharper state-local split

Saarland Klassenstufe 10 measurement corridor connected (2026-04-04)

• the broad SL Klassenstufe 10: Groessen und Messen anchor now carries a first reviewed corridor on the shared early Sek-I measurement / area / volume surface
• the current Saarland grade-10 source still exposes only one shared measurement strip
• this confirms the shared early Sek-I measurement surface can absorb an explicit reviewed grade-10 lane without forcing a sharper state-local split

Additional reviewed nationwide evidence (BW, BY, BE, BB, NI, SH)

Baden-Wuerttemberg (BW)

Observed signal:

• the active Baden-Wuerttemberg lower-secondary source snapshot now carries a reviewed geometry surface far beyond the first function-only onboarding step
• the reviewed BW lower-secondary mapping lane now already covers early geometry and measurement, figure properties, symmetry and angle reasoning, later trigonometric geometry, circle figures, and body work
• this includes explicit reviewed bridges for early geometry / space, positional relations, angle work, quadrilateral properties, coordinate-system drawing, symmetry reasoning, later trigonometric geometry, and later circle/body continuation
• together this confirms that the current G1-G7 surface can absorb the Baden-Wuerttemberg lower-secondary lane without forcing a new shared geometry split

Bayern (BY)

Observed signal:

• the reviewed Bavaria M5-M10 tranches now cover early coordinate and angle geometry, symmetry, congruence and triangle construction, similarity, Pythagoras, right-triangle trigonometry, sinus/cosinus-law continuation, and the refined J10 space-geometry lane
• M7 2 and M7 5 confirm the existing J7 geometry anchors without forcing another early split
• the reviewed M9 geometry leaves confirm the visible G3, G5, and trigonometric bridge surfaces, while M10 5 already drove and now confirms the explicit later J10 space-geometry split
• together this keeps Bavaria on the current canonical geometry package surface instead of forcing another nationwide repackaging pass

Berlin (BE)

Observed signal:

• the Berlin lower-secondary lane no longer carries only broad geometry parents; it now has an explicit first geometry-and-construction corridor, a reviewed transformation/similarity follow-on, a reviewed Pythagoras lane, and a reviewed area/circle/body lane
• the mapped Berlin lower-secondary goals now cover positional relations, angle arguments, special lines and symmetries in triangles, congruence constructions, similarity / scale geometry, Pythagoras, and first circle/body calculations
• this confirms the visible G2-G7 surface for Berlin without forcing a Berlin-specific geometry package

Brandenburg (BB)

Observed signal:

• Brandenburg now carries the same shared lower-secondary geometry-and-construction surface as Berlin, but with reviewed mappings that already land on the narrower canonical congruence, transformation, and Pythagoras targets where the wording fits
• the reviewed Brandenburg lower-secondary lane covers positional relations, angle arguments, special lines and symmetries in triangles, congruence constructions, similarity / enlargement-reduction work, Pythagoras, and first circle/body calculations
• this confirms that the current G2-G7 surface can absorb the Brandenburg lower-secondary lane without reopening packaging

Niedersachsen (NI)

Observed signal:

• the Niedersachsen lower-secondary source snapshot now already carries reviewed geometry content, not only the earlier function corridor
• the mapped NI lower-secondary geometry lane covers early area/volume ideas, area formulas for triangles/parallelograms/trapezoids, prism surface/volume work, similarity, Pythagoras, right-triangle trigonometry, and sinus/cosinus-law continuation
• together this confirms the existing early measurement / space surface plus the visible G3, G5, G6, and G7 package handles for Niedersachsen

Schleswig-Holstein (SH)

Observed signal:

• the Schleswig-Holstein lower-secondary source snapshot is now refined across 5/6, 7/8/9, and 10 for both Raum und Form and the geometry-owned parts of Groessen und Messen
• the reviewed SH geometry lane now covers early figures/bodies/symmetry/construction, later quadrilaterals, congruence, circle relations, Thales, Pythagoras, similarity, trigonometry, circles/circle sectors, and later body work through pyramids, cones, and spheres
• there are now no remaining unmapped SH Sek-I source atoms or source clusters in the active geometry-owning lane; the remaining breadth mismatch is broad-source residue, not a missing canonical package

Nordrhein-Westfalen lower-secondary geometry corridor connected (2026-04-05)

Observed signal:

• the active Nordrhein-Westfalen lower-secondary source snapshot now also carries explicit reviewed geometry corridors from 2.3, 2.4.1, and 2.4.2
• the mapped NRW lower-secondary lane now covers early geometry / space, quadrilateral properties, coordinate-system drawing, symmetry and transformations, angle work, triangle theorems and constructions, plane-area formulas, similarity, circle calculations, body calculations, Pythagoras, and right-triangle / cosine-law applications
• the compiled canonical applicability now reaches the shared Geometrie und Raum (Sek I) root together with the visible G2, G3, G4, G5, G6, and G7 package handles for DE-NW
• the Nordrhein-Westfalen geometry cell can therefore now be treated as resolved on topic level

Operational consequence:

• Sek I Geometrie / Raum is now no longer blocked by either canonical packaging or a missing Nordrhein-Westfalen lane
• the geometry row can now be treated as coverage-closed for the current nationwide sweep
• the next lower-secondary breadth move should therefore leave geometry residue-control mode and continue on Sek I Daten / Zufall

Coverage checkpoint (2026-04-05)

• NW now joins BW, BY, BE, BB, NI, and SH as resolved against the frozen G2-G7 package surface
• all Bundesland cells in the nationwide geometry row are now resolved once
• the active canonical corridor SEK1.J10.5D_GEOMETRY can therefore move from active to completed; the remaining late-body breadth is accepted broad-source residue and should reopen only if a later reviewed lane or validator finding exposes a real shared gap beyond the current G2-G7 surface
• the remaining lower-secondary work signal therefore moves entirely to Sek I Daten / Zufall, not to another shared canonical geometry gap