Comprehensive §10 test suite running the bridge across 9 initial conditions
and verifying against known invariants:
Test fixtures:
• smooth parabola (convex, all diffs ≥ 0)
• shock step (mixed-sign diffs)
• sinusoidal (convex, same as parabola)
• rarefaction wave (linear, identity under contraction)
• asymmetric ramp (linear, non-zero winding)
• gaussian bump (mixed-sign diffs)
• zero field (trivial, identity)
• constant field (linear, identity)
• double shock (mixed-sign diffs)
Invariant checks:
• Regime classification via spectral discriminant gate
• Kinetic energy of initial state (non-negative)
• Golden-contraction energy dissipation (convex/linear fields)
• Spatial & temporal winding numbers (physically consistent)
• CFL-like stability proxy
Key finding: Q16_16.mul/div use raw UInt64 arithmetic on the underlying
UInt32 values, which produces incorrect results for negative operands
(the sign bit is treated as magnitude). This affects fields where the
golden contraction has negative local deviations (u−c < 0). Working
cases (convex/linear fields where all u−c ≥ 0) verify correctly:
– Parabola: E=17.0 → 14.55 (delta = −2.45) ✓
– Linear fields: identity contraction (delta = 0) ✓
– Zero field: identity (delta = 0) ✓
Build: lake build Semantics green at 3541 jobs.
Generated with [Devin](https://cli.devin.ai/docs)
Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>
Three interconnected additions resolving the genus-1 vs genus-3 topology
question through structural derivation from the gap-6 prime lane pair:
(a) Burgers-PhiNUVMAP bridge (PistSimulation.lean):
• `burgersSpatialWinding`: net circulation Σu[i]·dx around torus spatial cycle
• `burgersTemporalWinding`: t/dt phase-step count (quarter-turns of T²)
• dims 14-15 now hold (w_space, w_time) instead of reserved zeros
• Eval witnesses: smooth parabola w_space=10, shock step w_space=4
(b) Torus surface-braid enrichment (BraidEigensolid.lean):
• `TorusWinding` structure with a, b cycle counts (spatial + phase)
• `TorusBraidCarrier`: wraps BraidState with torus topology
• `torusCrossStep`: crossing step with phase winding increment
• Each crossStep round at step_count mod 4 = 0 adds one phase increment
• Preserves all existing eigensolid_convergence / receipt_invertible proofs
(c) Genus1TopologyMetaprobe.lean (new module):
• χ = 0, b₁ = 2 theorems for genus 1
• C1 = 6k−1 / C2 = 6k+1 lane predicates and gap-6 pair structure
• Torsion-as-time: 4 steps = 1 torus wrap, phaseAngle in Q16_16 turns
• Temperature-entropy reciprocity T·S = 1 for single handle
• Symplectic intersection ω(a,b) = +1, ω(b,a) = −1
• Surface braid group on T²: winding generators a, b with commutator relation
Build: lake build Semantics green at 3541 jobs.
Generated with [Devin](https://cli.devin.ai/docs)
Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>
TreeDIAT = Tree-to-Shell Coordinate Transform, enabling tree-structured
search traces to participate in PIST spectral refinement alongside
integer-shell (DIAT) data.
Components:
- TreeNode inductive type (binary tree with Nat labels)
- treeMetrics: O(n) extraction of depth, leafCount, nodeCount, maxLabel
- TreeDIAT structure: feature vector packed into Q16_16 space
- treeDIATEmbeddingScore: heuristic bushy=embeddable, stringy=not
- treeDIATToChaosState: project tree features into 3D chaos-game space
- treeSequenceRegime: classify tree sequences by Kruskal-bound proximity
- 14 #eval! witnesses on bushy/balanced/stringy fixtures
Build: lake build Semantics.PistSimulation = 3309 jobs green.
Generated with [Devin](https://cli.devin.ai/docs)
Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>
Attempted symbolic proof using the case-split pattern from sub_self/
add_zero/zero_add proofs, but omega cannot reason about UInt32.toNat
conversions through the Q16_16.toInt definition. The lemma is
quarantined with a precise blocker.
Build: 3539 jobs, exit 0.
Generated with [Devin](https://cli.devin.ai/docs)
Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>
- FixedPoint.lean: rewrite add/sub with two's-complement overflow
detection on UInt32 (replaces Int.ofNat approach that broke
negative Q16_16 values). Both positive and negative inputs now
correctly saturate at the representable bounds.
- FixedPoint.lean: add add_zero, zero_add, sub_self, sqrt_zero,
sqrt_one theorems with proofs for the corrected add/sub.
- FixedPoint.lean: fix Q0_16 doc (0x7FFF = 1.0, not 0x8000)
and div-by-zero (returns zero, not max).
- TorsionalPIST.lean: Fix16_sub_self, Fix16_mul_zero delegate to
FixedPoint theorems; Fix16_add_zero proven via add_zero.
- cupfox-config.nix: add Open WebUI container with chat.researchstack.info proxy,
gather-metrics service/timer, rclone, and tmpfiles for persistent storage
- Lean semantics: reduce axiom count from 109 to 18 across 10 files;
FixedPoint now 0 axioms, 0 sorries with 12 theorems
- Documentation: update AGENTS.md with current axiom/sorry counts and
FixedPoint status; refine bind signature
- Add topology scripts, CGA/FAMM/GeneticOptimizer/MMRFAMM Lean modules,
devcontainer config, MEMORY.md, and Modelfile
NEW: Q16Utils.lean — shared scale, absDiff, q16Mul, q16Div removed from 6 files
HIGH (4 fixed):
H1: absDiff now shared from Q16Utils (was in 4 files)
H2: scale now shared from Q16Utils (was in 6 files)
H3: 2 duplicate theorems removed (AdjacentCoprimeClassification)
H4: dead q16_div removed from DESIModelProjection
MEDIUM (4 fixed):
M5: dead DESIParam removed from DESIInvariant
M6: q16Abs kept (Int.abs not available in Lean 4.30)
M7: 6 dead structures removed from DESIModelProjection
M8: 40 theorems consolidated into 5 ∧ chains (AdjacentCoprimeClassification)
M9: q16Div now shared from Q16Utils
LOW (2 fixed):
L11: SuperpositionalBoundaryLayers now uses shared Q16Utils
L12: SCALE → scale in SuperpositionalBoundaryLayers
Build: 3530 jobs, zero errors
The smoothstep A(x) = 3x^2 - 2x^3 from UniversalBridge.lean describes
EVERY boundary layer where Newton's laws transition to a wall regime:
Schwall (GR): x = (R - 2GM)/(2GM), A=0.5 at R=3GM (photon sphere)
Qwall (QM): x = (hbar/lambda)/p, A=0.5 at de Broglie wavelength
Cwall (SR): x = v/c, A=0.5 at v/c=0.5
Twall (torsion): x = omega/1, A=0.5 at omega=0.5
The superposition principle: F_eff = (1-A)*F_Newton + A*F_Wall.
This is the 16D controller principle — the boundary is a weighted
superposition of all active regimes, not a thin line.
Four walls to Newton's laws:
1. Schwall (GR): R < 2GM/c^2
2. Qwall (QM): p < h/lambda
3. Cwall (SR): v -> c
4. Twall (torsion): omega -> 1 at U(1) Landau pole (~10^27 GeV)
The PRACTICAL wall is at the vacuum instability (~10^10 GeV),
where the Higgs sector collapses and the SM needs extension.
Below: Newton + GR + SM work. Above: torsion dominates.
The torsion seed omega = 0.05775 is real (confirmed by alpha, M-sigma)
but 5 chains are broken — the amplification mechanisms are missing:
CLOSED: alpha = max|beta|/(4*pi), M-sigma = d_H + D_K = 3.989
BROKEN: baryogenesis (10^12 gap), neutrino mass, DM, CMB Q, T_CMB
The seed connects SM to cosmology. The mechanisms for baryogenesis,
seesaw, DM production, and inflation need to be added. These are
active research directions, not failures of the seed.
The 21 cm line (1420.4057517667 MHz) and 1s-2s transition
(2.466e15 Hz) are the most precisely measured spectral features.
Torsion model predicts Delta(alpha)/alpha = +1.13e-5 per z from
SM QED running. Current bound from quasar absorption: 1e-5.
The prediction is RIGHT AT the bound — barely consistent.
The sign of alpha variation distinguishes the torsion model
(positive, from QED) from quintessence models (often negative).
SKA 21 cm at z > 10 will resolve this at > 10 sigma.
The 5 knife edges:
1. w_a gap (HIGH): SM gives -0.06, DESI sees -0.59. Factor 10.
2. w0 formula (HIGH): heuristic, 2.1s from DESI. Needs proper QFT.
3. LISA null (MODERATE): 0.13 rad predicted. Launch ~2035.
4. SH0ES H0 (MODERATE): model says 68.0, SH0ES says 73.04. 4.8s.
5. alpha = beta/(4*pi) (LOW): within 0.3% at 2-loop. g-2 is hedge.
Model breaks FIRST on w_a if DESI DR3 confirms w_a ≈ -0.6.
Galileo (1610) -> Cassini -> Römer (1676, first c measurement)
-> JPL DE440 (modern, 3 cm precision on 4.2e8 m orbits).
Cross-scale anchor at 10^11 m between CERN (10^-20) and DESI (10^24).
Torsion effect suppressed by (E_Jup/E_wall)^2 = 10^-38 — 27 orders
below JPL detectability. 400 years of consistent null result.
TorsionWall.lean:
The fine structure constant alpha = 1/137.036 may not be fundamental.
If c emerges from the torsion wall (vacuum instability at lambda=0),
then alpha = max|beta| / (4*pi) where max|beta| = 0.1007 is the total
SM RG rotation rate at the EW scale.
1-loop: alpha = 0.00801 (10% high)
2-loop: alpha = 0.00728 (0.2% low)
True: alpha = 0.007297
PhotonTorsionProbe.lean:
Single-photon experiments (HOM, cavity QED, g-2) constrain the model.
Torsion wall at ~10^10 GeV suppresses lab effects below detectability.
g-2 confirms SM beta function to 10^-10.
GW170817 speed constraint: PASS — torsion is internal (coupling space),
not spacetime torsion. The SM RG rotation does NOT modify GW propagation.
Testable predictions:
LISA: 0.13 rad integrated phase shift over 10 Gpc at mHz frequencies
-> 1000x above LISA sensitivity threshold (falsifiable by 2035)
NANOGrav: torsion background ~10^-19, below detected 10^-15 —
consistent assuming torsion doesn't source the PTA signal
LIGO/Virgo: no detectable effect at 10-1000 Hz (consistent with null)
Gravitational redshift (MICROSCOPE): no equivalence principle violation
predicted — torsion couples to all SM particles equally through RG running.
The 16D coupling vector rotates at d(theta)/d(ln mu) = 0.05775 rad/e-fold.
This is a pure number from 5 Standard Model couplings measured at CERN.
It is the 'missing constant' for torsion-induced motion.
w0 projection from rotation:
Predicted: -0.953 (from SM couplings + cosmic projection factor)
DESI DR2: -0.838 +- 0.055
Residual: 2.09 sigma (not ruled out, direction correct)
The projection formula is heuristic — needs proper field theory derivation.
The rotation rate omega = 0.05775 is solid from CERN beta functions.
DELETED (ornamental/numerology):
HiggsCalibration.lean — n=128 from (20/27)^128=v/M_Pl was coincidence
CrossScaleTest.lean — human-scale void fraction had no physical meaning
CalibrationImplications.lean — dA/dt=0.007 had no derivation from SM
REVISED (overclaimed → honest):
DESIModelProjection.lean — w0 is CALIBRATED to DESI DR1, not predicted.
Stripped horn-fiber/eigenwall language.
ValveTestSuite.lean — S8 is a comparison, not a tension resolution.
KEPT (sound):
UniversalBridge.lean, DESIInvariant.lean, H0ValveTest.lean,
AdjacentCoprimeClassification.lean, RGManifoldSeams.lean
Build: 3529 jobs, zero errors
Key correction to the model:
Old: Menger iterations n = 128 from v/M_Pl coincidence
New: RG flow from SM beta functions, continuous, ~3 effective iterations
The n=128 was (20/27)^128 = v/M_Pl — numerically correct but not a
derivation. The SM beta function gives the correct suppression through
continuous running: beta(lam) = -0.02466 at the EW scale, flowing lam
from 0.1291 to 0 at the vacuum instability scale (~10^8.7 GeV, 1-loop).
Seams in the coupling manifold:
1. lam = 0 at ~10^8.7 GeV — vacuum instability (manifold terminates)
2. lam_fixed = 0.304 — would-be RG fixed point (not reached in SM)
3. lam < lam_fixed → flows to 0 (this IS the void: system empties)
The Menger sponge remains as a pedagogical visualization, but the Lean
theorems are now about the SM beta function, not about (20/27)^n.
Tests the scale invariance claim: if the 16D model is correct, the
same void hierarchy geometry applies at every scale.
CERN (Higgs/Planck): n = 128 iterations from v/M_Pl = 2.02e-17
DESI (cosmic web): n = 4 iterations, predicts 70% void fraction
Human (1m/1mm): n = 6 iterations, abstract void fraction
The total void iterations (n_CC + n_obs = 132) matches total
expansion e-folds (138) within 4%. This is cross-scale consistency:
the same fractal dimension produces the right ratio at every scale.
