Passes 3549–3555

Borel orbit models, generalized pentads, and exact graph dynamics

Seven reproducible fronts convert the remaining symmetry and factorization questions into finite model surfaces, complete algebra tables, proof-carrying archives, and exact dynamical formulas.

Borel models

All aggregate 19:9 signatures are emitted as exact edge-orbit and ordered-relation contracts.

1,035

Structure constants

The complete rank-21 Perkel commutant multiplication table is frozen by a semantic digest.

11 + 10

Observable/phase split

Transpose gives eleven symmetric equivariant kernels and ten skew channels.

6,240

K8 census

All labelled one-factorizations are generated and an eight-object pairwise-intersecting family is certified.

82 · 9 · 3

Near-Moore graph

The octad compiler yields 82 vertices, degree nine, and diameter three, with exact short-cycle defects.

64 shards

Proof archive

The 3,720 maximum-clique certificates receive deterministic ranges and a Merkle aggregation contract.

1/4 · 2/7

Quantum-walk bounds

The strongest adjacent-transfer amplitude bounds for W33 and Gewirtz exclude perfect state transfer.

Boundary. The missing Moore graph remains open. No Borel solver verdict or complete proof archive is claimed, and the dynamical formulas are not device measurements.

Reproduction

python analysis/bt3549_3555_borel_pentad_quantum_walk.py
pytest -q tests/test_bt3549_bt3555_borel_pentad_quantum_walk.py
python analysis/bt3549_borel_signature_models.py
python analysis/bt3552_clique_proof_archive.py --self-test