Claude/cuboctahedral tetrahedron array z78a4#2
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…m nucleus Construct, verify, and visualize an array of 64 regular tetrahedra (8 star tetrahedra x 8) on the isotropic vector matrix whose innermost vertices form a central cuboctahedron with radius = edge (Fuller's vector equilibrium), the balanced nuclear space of the array. - tetra64/geometry.mjs: dependency-free construction + verification - tetra64/generate.mjs: emits and checks tetra64.json (10/10 invariants pass) - tetra64/render-svg.mjs: static SVG snapshot - tetra64.html: self-contained interactive 3D viewer (live verification) https://claude.ai/code/session_01H3gemf4BCojCkaK3tNvGB3
A canvas is a replaced element, so position:fixed; inset:0 leaves it at its intrinsic 300x150 anchored top-left. Set explicit width/height:100% so the canvas fills the viewport and W/2,H/2 is the true screen centre. https://claude.ai/code/session_01H3gemf4BCojCkaK3tNvGB3
Compute the canvas size and drawing centre straight from the viewport instead of the canvas client box, eliminating any reliance on replaced-element layout quirks so the artifact always centres on screen. https://claude.ai/code/session_01H3gemf4BCojCkaK3tNvGB3
…tifact Layers (toggle-able in the viewer): - chirality 32+/32- via signed volume sgn(-prod(s)) - radial shells S0..S5 (sizes 1, 12, 6, 24, 12, 8 = 63 unique vertices) - 8 stella centres (+-1,+-1,+-1) with dashed cube edges - 240 bulk edges - 144 dual-graph edges (edge-sharing tetra pairs) - inversion P (31 antipodal pairs + 1 self at origin) - counter-rotating circulation arcs (chirality flow visualisation) Verification module (tetra64/verify-dimensions.mjs, tetra64-dimensions.json): checks every explicit number against the geometry. All match - R^64_tetra=64, R^63_vertex=63, R^240_edge=240, R^144_dual_edge=144, R^81_dual_cycle=81, ker(d1^T)=178 (= |E|-|V|+1, 1-skeleton cycle space), 32+/32- chirality, 6 shells S0..S5. Honest reporting on definition-dependent quantities: dual-edges only matches under edge-sharing; ker(B^T)=178 only matches when B is the standard graph boundary d1 : E -> V (the natural identification). tetra64-extended.svg: snapshot rendering chirality + shells + dual edges + bulk edges + stella centres on top of the original viewer. https://claude.ai/code/session_01H3gemf4BCojCkaK3tNvGB3
Adds analysis-phase2.mjs, oh-character-table.mjs, verify-foundations.mjs,
and the canonical report tetra64-foundations.json.
PASS against the atlas foundations table:
- |F| = 256 triangles (= 4 faces x 64 tetra; 3-cliques in 1-skeleton also = 256)
- Betti numbers beta = (1, 0, 14, 0) of the primal simplicial complex
(ranks: d_1 = 62, d_2 = 178, d_3 = 64; 14 = independent voids/cavities)
- B_op rank = 12 (d_1 restricted to Shell 1 codomain)
- sum a_i * dim_i = 81 for H_1(dual graph) irrep decomposition
- bipartite chirality structure [OBS-BIPARTITE-STRUCTURE]:
0 dual edges intra-chirality, 144 cross + to -
H_1(dual) ~ R^81 decomposition under O_h:
A2g + 2Eg + 7T1g + 5T2g + 2A1u + 2A2u + 6Eu + 4T1u + 4T2u
(T1u + T2u sector = 24 dims, the corpus's "ungerade T1u (+) T2u" channel.)
Honest non-match (definition-dependent):
- Hom_G(V_edge240, V_dual144 (x) chi) = 744 not reproduced under 8
natural rep-signing conventions; closest 768 (no chi), 732 (A2u),
704 (signed dual + det), 676 (unsigned + det). Corpus uses a
specific V_edge / V_dual signing not inferable from the geometry.
- 5 shell ratios within 5% of phi: 0 found under raw shell radii.
Atlas explicitly preserves "NO claim derivacion canonical de phi".
All 10 Phase 1 invariants remain PASS (no regression).
https://claude.ai/code/session_01H3gemf4BCojCkaK3tNvGB3
Numerical additions, no UI change yet, no regression: Phase 1 still 10/10.
- Forman-Ricci graph curvature F(e) = 4 - deg(u) - deg(v):
6 distinct values {-20, -16, -13, -12, -9, -7} with counts
{36, 72, 12, 48, 48, 24} = 240; mean = -13.35.
Degree per shell is uniform (O_h orbit structure):
S0=12, S1=12, S2=8, S3=8, S4=5, S5=3. Sum 2|E| = 480 confirmed.
- closed-walks tr(A^k) for k=1..8 on primal (63x63) and dual (64x64):
tr(A^2) primal = 480 = 2|E| PASS
tr(A^3) primal / 6 = 256 triangles PASS (cross-confirms |F|=256)
dual tr(A^k) = 0 for every odd k PASS (cross-confirms the
bipartite chirality structure from another angle)
- O_h orbits on the 144 dual edges: 6 orbits of sizes
[24, 48, 12, 24, 24, 12].
https://claude.ai/code/session_01H3gemf4BCojCkaK3tNvGB3
Additive UI: two new toggles 'Forman-Ricci' and 'orbits duales (6)' in a
'Fundaciones (atlas v1.0)' section. Existing toggles, default-off state,
geometry, and the 10 baseline PASS are unchanged.
In-browser analyze() now also computes:
- Forman-Ricci F(e) = 4 - deg(u) - deg(v): 6 distinct values across the
240 edges - used to colour the bulk-edges layer when the toggle is on.
- O_h orbits on the 144 dual edges (6 orbits, sizes [24,48,12,24,24,12])
- used to colour the dual-graph layer when the toggle is on.
- tr(A^k) for the primal (63x63) and dual (64x64) adjacency, k=1..6.
Used for live PASS rows in the verification panel:
tr(A^2) primal = 2|E| = 480
tr(A^3) primal / 6 = 256 (= |F| triangles)
tr(A^k) dual = 0 for all odd k (bipartite chirality signature)
New static snapshot tetra64/tetra64-curvature.svg renders the same
curvature + orbit colouring with legends.
https://claude.ai/code/session_01H3gemf4BCojCkaK3tNvGB3
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