← Back to the live paper Audit 2026-04-23

Repo Frontier Audit

This page audits the repo itself rather than adding a new theorem layer. It reconciles the live HTML, the current W36_PAPER.tex, the active script/test families, the Qiskit search layer, and the recent literature boundary that the older site language had started to overstate.

The new finite-ladder consolidation is now executable too: scripts/w33_qutrit_ladder_audit.py packages the exact 1q -> 2q -> 3q -> 6q spine and marks where the separate exact E8-side decomposition begins. The new scripts/w33_projective_affine_shell_audit.py now isolates an even cleaner local geometric statement too: the exact 13 + 27 qutrit shell is the tangent-hyperplane / affine-complement split PG(2,3) + AG(3,3) inside PG(3,3), with the familiar 9 x 3 fiber packet appearing as one affine direction class. The new scripts/w33_symplectic_spread_frame_audit.py then closes the exact complete-frame side of that same kernel: the 40 isotropic lines admit exactly 36 spreads, every line lies in 9 spreads, and each spread is exactly one isotropic line at infinity plus 9 affine measurement lines, yielding a full 10-basis two-qutrit stabilizer MUB frame. The companion scripts/w33_e8_correspondence_boundary_audit.py then separates the exact finite W33 <-> E8 content from the older promoted physics inheritance layer. The local cubic side is now separated too: scripts/w33_local_albert_shadow_audit.py packages the exact 45-tritangent signed-cubic support and the cocycle-gauge boundary between naive bare W(E6) transport and the canonical local invariant. The continuum seed is separated as well: scripts/w33_toroidal_continuum_seed_audit.py packages the exact toroidal/decimal coefficient packet 8, 56, 320, 2240, 12480, so the remaining wall is smooth realization rather than finite normalization. Several newer conservative summaries now sit on top of that stack: scripts/w33_q3_master_lock_audit.py packages the cross-layer overdetermination of q=3, scripts/w33_normalization_bridge_audit.py reconciles the per-vertex and lift-normalized q-families exactly, scripts/w33_neutrino_preset_audit.py shows that the 1/mu neutrino branch survives the move from the legacy NuFIT 5.3 baseline to the current official NuFIT 6.0 fits, scripts/w33_electron_seed_packet_audit.py narrows the residual charged-fermion wall to the exact packet 98 x 17 x 208 plus a final physical-identification boundary, scripts/w33_flavor_frontier_audit.py separates the exact q=3 arithmetic from the promoted §83–§91 CKM/PMNS/running-alpha layer, scripts/w33_exact_flavor_spine_bridge.py reconciles the canonical exact flavor spine itself as local generator 3/13, global CKM 9/40 = q^2/v, and exact incidence PMNS data 4/13, 7/13, 2/91, scripts/w33_standard_model_tqc_boundary_audit.py packages the deeper computational read as exact qutrit Clifford/stabilizer backbone plus an exact tetra-qutrit control/transport primitive, scripts/w33_standard_model_magic_packet_audit.py sharpens the non-Clifford side further as exact qutrit processor plus minimal two-slot quartic magic candidate, and scripts/w33_standard_model_minimal_magic_audit.py now refines that one step further: the exact non-Clifford floor is two independent quartic atoms before any octic or degree-16 synthesis.

Bottom line: this repo already has an exact finite qutrit spine, an exact local E6 bridge, and a large promoted global-closure stack. The honest remaining wall is the continuum/dynamical lift together with the last Yukawa spectral packet.

Exact Now

  • W(3,3) as the 40 projective non-identity two-qutrit Pauli observables.
  • The local 12 + 27 Heisenberg/MUB shell with four triangles and nine size-3 fibers.
  • The exact projective/affine shell split: every point-perp is PG(2,3) and every complement is AG(3,3).
  • The exact complete-frame layer: 36 symplectic spreads, each a full 10-line two-qutrit stabilizer MUB frame.
  • The local 27-point Schläfli / cubic-surface line shell and exact local E6 bridge.
  • The local 45-tritangent signed-cubic package, with the exact cocycle-gauge boundary exposed.
  • The toroidal/decimal continuum seed already fixes the exact coefficient packet 8, 56, 320, 2240, 12480.
  • The canonical operator H_can = 12I - A = 16I - BB^T with spectrum 0^1, 10^24, 16^15.

Promoted Now

  • The global E8, moonshine, arithmetic, and phenomenology stack is large and active.
  • Parts of that stack are exact internally, but not all of it sits at the same functorial level as the qutrit kernel.
  • The Qiskit files encode the current bridge wall as local search oracles; they do not replace the missing continuum theorem.

Open Wall

  • Direct integral E8 lift from the chain-complex side remains open.
  • The continuum/dynamical lift remains the real bottleneck.
  • The Yukawa frontier has been reduced to a very small nonlinear spectral packet, not a missing symmetry skeleton.

Repo Map

The repo is large, but the live research surfaces are now fairly clear. docs/build_site.py explicitly treats docs/index.html as the sole site source, docs/REPO_STRUCTURE.md points new readers toward docs/index.html and docs/march_2026_frontier_note.md, and the active source surfaces are concentrated in docs/, exploration/, tests/, tools/, tools/qiskit/, and scripts/.

Surface What it is doing now
docs/index.html The live public surface. It now correctly centers the exact qutrit kernel first and the promoted global closure after that.
W36_PAPER.tex The live manuscript. It already contains the exact qutrit foundation, the local E6 bridge, the spectral determinant layer, the mass-spectrum package, and an explicit open-boundary section.
exploration/ The exact theorem-builder layer. This is where many of the bridge summaries and conservative closure notes live.
scripts/ As of this audit the repo has 513 Python scripts. Some are conservative audits; others are much broader synthesis drivers. Script presence alone is not an evidence tier.
tests/ As of this audit the repo has 1703 pytest files. The exact qutrit/kernel and bridge reductions are heavily covered, but the sheer test count should not be read as a uniform theorem ledger.
tools/qiskit/ There are 30 top-level files here. This is a local oracle/diagnostic stack over the current bridge-support constraints, not a separate physical derivation layer.
archive/, root drop bundles, older snapshots Historical weight is intentionally preserved. These directories are useful context, but they are not the place to infer the current exactness boundary.

Exact Spine

The strongest exact package in the repo is now compact enough to state cleanly.

Layer Backed by Status
Two-qutrit Pauli realization of W(3,3) scripts/w33_two_qutrit_pauli.py, exploration/w33_qutrit_foundation_bridge.py, tests/test_w33_qutrit_foundation_bridge.py Exact
Projective/affine shell split of the local qutrit kernel scripts/w33_projective_affine_shell_audit.py, tests/test_w33_projective_affine_shell_audit.py Exact
Symplectic spread / stabilizer-frame layer of the local qutrit kernel scripts/w33_symplectic_spread_frame_audit.py, tests/test_w33_symplectic_spread_frame_audit.py Exact
Witting deck / spread-control layer scripts/w33_witting_deck_control_audit.py, tests/test_w33_witting_deck_control_audit.py Exact communication/control reading of the same 40-point kernel: 36 decks, rigid 1/4 overlaps, 216 five-deck sweeps, 135 four-deck packets
Balanced packet shell bridge scripts/w33_witting_balanced_packet_shell_audit.py, tests/test_w33_witting_balanced_packet_shell_audit.py Exact bridge from the 36-deck control layer back to the 27-point cubic-surface layer: 27 balanced packets recover the local shell, Schläfli graph, and intersection graph
Packet Heisenberg chart scripts/w33_witting_packet_heisenberg_chart_audit.py, tests/test_w33_witting_packet_heisenberg_chart_audit.py Exact `9 × 3` chart on the balanced packets, with affine `F_3^2` triangle coordinates and a fiber-preserving isomorphism to the canonical local `H27` shell
Packet tritangent-support bridge scripts/w33_witting_packet_tritangent_support_audit.py, tests/test_w33_witting_packet_tritangent_support_audit.py Exact recovery of the local `45 = 36 + 9` support package on the balanced packets, with the same `45` triples reappearing as the rank-intersection-`16` triangles
Packet Hessian split bridge scripts/w33_witting_packet_hessian_split_audit.py, tests/test_w33_witting_packet_hessian_split_audit.py Exact recovery of the full local Hessian decomposition on the balanced packets: `9` fibers plus `12 × 3` affine lifts in `AG(2,3)`, arranged in `4` direction classes
Packet foliation / Pappus bridge scripts/w33_witting_packet_foliation_incidence_audit.py, tests/test_w33_witting_packet_foliation_incidence_audit.py Exact five-foliation incidence architecture on the balanced packets: fiber-vs-affine gives `3K_{3,3}`, affine-vs-affine gives the Pappus graph
Packet quotient-geometry bridge scripts/w33_witting_packet_quotient_geometry_audit.py, tests/test_w33_witting_packet_quotient_geometry_audit.py Exact reconstruction of the full 45-point / 27-line quotient geometry from the Witting packet leaves and packet-induced `K5` cliques
Packet transport-complement bridge scripts/w33_witting_packet_transport_complement_audit.py, tests/test_w33_witting_packet_transport_complement_audit.py Exact reconstruction of the full 45-point transport complement from the same packet leaves, with the 27 packet lines becoming 5-cocliques and each transport edge carrying a unique local S3 packet-line matching
Packet transport local-system bridge scripts/w33_witting_packet_transport_local_system_audit.py, tests/test_w33_witting_packet_transport_local_system_audit.py Exact reconstruction of the same 135-dimensional transport connection bundle, signed holonomy operator, and native A2 standard sector from the packet-side S3 matchings, with raw six-permutation edge counts explicitly separated as label-gauge data
Packet transport path-groupoid bridge scripts/w33_witting_packet_transport_path_groupoid_audit.py, tests/test_w33_witting_packet_transport_path_groupoid_audit.py Exact packet-side path-groupoid lift of the transport A2 local system: no nonzero flat section over characteristic 0, but a unique invariant line [1,2] and exact binary shadow {1,2} over F3
Packet transport ternary-line bridge scripts/w33_witting_packet_transport_ternary_line_audit.py, tests/test_w33_witting_packet_transport_ternary_line_audit.py Exact packet-side lock to the qutrit matter sector: the invariant line selects a canonical 81-dimensional transport-stable sector, and the full reduced A2 fiber gives 162, matching the flat internal dimension
Packet transport ternary-extension bridge scripts/w33_witting_packet_transport_ternary_extension_audit.py, tests/test_w33_witting_packet_transport_ternary_extension_audit.py Exact packet-side non-split extension 0 -> 1 -> rho -> sgn -> 0, tensored with the W33 logical qutrit sector to give the exact 81 -> 162 -> 81 matter-flavour bridge
Packet transport ternary-cocycle bridge scripts/w33_witting_packet_transport_ternary_cocycle_audit.py, tests/test_w33_witting_packet_transport_ternary_cocycle_audit.py Exact packet-side cocycle/operator form of the same extension: a genuine twisted cocycle and a square-zero rank-81 nilpotent operator on the 162-sector
Local Heisenberg/MUB shell and Schläfli geometry scripts/w33_heisenberg_qutrit.py, scripts/w33_exact_lie_bridge_audit.py, tests/test_w33_exact_lie_bridge_audit.py Exact
Local Albert-shadow / signed-cubic boundary audit scripts/w33_local_albert_shadow_audit.py, tests/test_w33_local_albert_shadow_audit.py Exact local determinant-support boundary
Canonical quadratic operator scripts/w33_qutrit_operator_algebra.py, tests/test_w33_qutrit_operator_algebra.py Exact
Finite qutrit ladder audit scripts/w33_qutrit_ladder_audit.py, tests/test_w33_qutrit_ladder_audit.py Exact finite ladder boundary
q=3 master-lock audit scripts/w33_q3_master_lock_audit.py, tests/test_w33_q3_master_lock_audit.py Exact cross-layer overdetermination of the selected point, including the local Parseval target geometry and transport reduction
Normalization bridge audit scripts/w33_normalization_bridge_audit.py, tests/test_w33_normalization_bridge_audit.py Exact reconciliation of the adjacency and lift q-families
Toroidal continuum seed audit scripts/w33_toroidal_continuum_seed_audit.py, tests/test_w33_toroidal_continuum_seed_audit.py Exact continuum coefficient seed
W33-E8 correspondence boundary audit scripts/w33_e8_correspondence_boundary_audit.py, tests/test_w33_e8_correspondence_boundary_audit.py Exact-versus-promoted separation
Electron-seed packet audit scripts/w33_electron_seed_packet_audit.py, tests/test_w33_electron_seed_packet_audit.py Exact residual packet plus honest physical boundary
Flavor frontier audit scripts/w33_flavor_frontier_audit.py, tests/test_w33_flavor_frontier_audit.py Exact-versus-promoted split for the late flavor stack
Exact flavor spine bridge scripts/w33_exact_flavor_spine_bridge.py, tests/test_w33_exact_flavor_spine_bridge.py Canonical exact flavor statement linking local generator, global CKM, and exact PMNS
Standard Model TQC boundary audit scripts/w33_standard_model_tqc_boundary_audit.py, tests/test_w33_standard_model_tqc_boundary_audit.py Exact qutrit Clifford backbone plus exact tetra-qutrit control/transport primitive, with honest universality boundary
Standard Model magic-packet audit scripts/w33_standard_model_magic_packet_audit.py, tests/test_w33_standard_model_magic_packet_audit.py Exact qutrit processor plus minimal two-slot quartic magic candidate
Standard Model minimal-magic audit scripts/w33_standard_model_minimal_magic_audit.py, tests/test_w33_standard_model_minimal_magic_audit.py Exact atomicity theorem: two quartic atoms before any higher-degree synthesis
Temporal / spectral toroidal computer audit scripts/w33_temporal_spectral_toroidal_computer_audit.py, tests/test_w33_temporal_spectral_toroidal_computer_audit.py, docs/temporal_spectral_toroidal_computer.html Exact finite architecture plus conservative single-photon realization dictionary
W(3,q) scaling-family identities scripts/w3q_scaling_family.py, tests/test_w3q_scaling_family.py Exact family scaffold
Finite Yukawa support reduction scripts/w33_yukawa_frontier_audit.py, scripts/w33_yukawa_quartic_lift_audit.py Exact reduction, not final closure
The strongest single computational summary remains: the finite qutrit foundation is closed; the local shell now has its exact PG(2,3) + AG(3,3) projective/affine split exposed; the exact complete-frame layer is now exposed too, with 36 symplectic spreads giving full two-qutrit stabilizer MUB frames; the same spread layer now has its exact Witting communication/control reading exposed too, with 36 full decks on the 40 quantum cards, rigid 1/4 deck overlaps, 216 maximal five-deck sweeps, and 135 maximal four-deck packets; that control layer now folds back onto the local cubic-surface side too, because the 27 balanced four-deck packets reconstruct the honest 8-regular local shell while exact rank-intersection relations on the same packet set recover the Schläfli graph and its SRG(27,10,1,5) intersection complement; the balanced packet layer now carries its own exact 9 × 3 Heisenberg-style chart, with affine F_3^2 triangle coordinates and a fiber-preserving shell isomorphism to the canonical local H27 chart; the packet tritangent-support bridge shows that the same 27 balanced packets already carry the full local 45 = 36 + 9 support package, with each packet on exactly 5 support triples and the same 45 triples reappearing as the rank-intersection-16 triangles; the packet Hessian-split bridge resolves the affine side completely too, because those 36 non-fiber triples are exactly 12 × 3 affine lifts in AG(2,3), grouped into 4 direction classes, with each packet lying on exactly one affine lift in each direction plus its unique fiber; the packet foliation bridge shows that this already closes into a classical control-incidence object, because the five canonical triple foliations have exact leaf-intersection graphs 3K_{3,3} on the fiber-affine side and the Pappus graph on the affine-affine side; and the new packet quotient-geometry bridge now closes the global finite side of that packet program too, because the 45 packet leaves are exactly the exceptional quotient points and the 27 packet-induced K5 cliques are exactly the quotient lines of the dual GQ(4,2) geometry. The local E6 bridge is exact; the continuum coefficient seed is now exact too; q=3 is already overdetermined across the local, spectral, and continuum-seed layers; the charged-fermion frontier has narrowed to one exact residual packet 98 x 17 x 208; the flavor side is now split and reconciled honestly too, with the exact arithmetic selectors separated from the promoted §83–§91 formulas and the canonical exact flavor spine made explicit as tan(theta_C)=3/13, lambda=9/40=q^2/v, and PMNS 4/13, 7/13, 2/91; the deeper TQC read is now separated too, with an exact qutrit Clifford backbone plus an exact tetra-qutrit control/transport primitive; the new temporal/spectral toroidal computer audit converts that exact machine into a conservative single-photon hardware dictionary with temporal and spectral qutrits on a discrete 3 × 3 torus; the remaining non-Clifford side has been localized more sharply as a minimal two-slot quartic magic candidate; and the latest atomicity refinement says those two quartics are already the exact floor, with any canonical mixing jumping straight to octic or degree-16 synthesis. The remaining uncertainty lives at explicit injection/synthesis, the global lift, atmospheric-angle/Yukawa reconciliation, final Yukawa identification, and smooth realization end, not at the level of basic finite geometry or finite normalization.

Promoted Layers

The repo also contains a much larger promoted closure layer. That layer is real work, but it is mixed in strength.

Promoted family Audit reading
scripts/w33_e8_correspondence_theorem.py Ambitious global synthesis. Useful as a program statement, but broader than the newer conservative exactness audits.
Moonshine / modular / transport stack Large and active. Many local identities are exact, but the repo itself now distinguishes this from the exact qutrit kernel.
Curved/K3/continuum bridge files This is where the live bottleneck has been localized. The current frontier note reads the remaining wall as a tightly constrained realization problem, not as freeform guesswork.
Qiskit bridge oracles The Qiskit layer searches exact theorem-backed support shells such as head_line < U1 < transport_avatar. It packages the current bridge wall as a search problem; it does not itself solve the continuum lift.

Concrete Corrections

Issue Audit correction
2410.12488 literature claim The older site language overstated this source. Mizoguchi & Oikawa (2024) explicitly exclude a direct E8 quotient-ring construction in their main ADE code/Narain framework. Their later 2026 follow-up gives a separate direct E8 construction from codes over Mordell-Weil groups of extremal rational elliptic surfaces.
README entrypoint The short README had drifted toward a broader promoted snapshot. It should now be read through the live status note and the audited entrypoints, not as the exactness boundary by itself.
Paper/script GUT-coupling mismatch PHYSICS_INVENTORY.md flags a live disagreement: some scripts derive alpha_GUT^-1 = 26, while the paper also carries a different 240-scale claim. That disagreement is real and should not be smoothed over.
What “finishing” means now The actionable finish route is not “invent more numerology”. It is the narrower path recorded in exploration/ALGEBRA_REVIEW_AND_VOGEL_ROUTE_2026_03_09.md: H27 -> W33 -> s12/Golay Heisenberg lift -> sl(27), then the remaining Yukawa and continuum closure.

Finish Route

The repo already identifies the algebraic ladder worth pushing:

H27 (1 qutrit shell) -> W33 (2 qutrits) -> s12/Golay Heisenberg lift -> sl(27) (3 qutrits)

That is the finite route. The honest remaining work is then twofold: finish the nonlinear Yukawa packet on top of the already-fixed family carrier, and prove the continuum/dynamical lift that explains why the finite package should govern a physical QFT/GR limit.

Literature Anchors