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dag: rip/tear — remove 8 broken/empty/tautological theorems, 3 ornamental files
REMOVED theorems (8): BraidCross.lean — 2 trivial zero-strand witnesses FAMM.lean — 2 tautological identities (X = X) MengerSpongeFractalAddressing.lean — 3 empty theorem bodies NBody.lean — verlet_preserves_energy_approximate references nonexistent lemma REMOVED files (3): CMBTorsion.lean — 0 theorems, invented alpha formula CouplingRotation.lean — heuristic w0 projection formula TorsionWall.lean — alpha = max|beta|/(4*pi) invented relation Build: 3529 jobs, zero errors after all removals
This commit is contained in:
Brandon Schneider
parent
e2bcfa62dd
commit
20c3cc252d
7 changed files with 8 additions and 307 deletions
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@ -67,15 +67,9 @@ def braidCross (sᵢ sⱼ : BraidStrand) : BraidStrand × BraidBracket :=
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(mergedStrand, Rᵢⱼ)
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/-- Concrete left-identity witness for the zero strand. -/
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theorem braidCrossZeroLeftWitness :
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(braidCross (BraidStrand.zero 0) (BraidStrand.zero 1)).1.phaseAcc = PhaseVec.zero := by
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native_decide
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-- REMOVED: braidCrossZeroLeftWitness only tested zero strands
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/-- Concrete right-identity witness for the zero strand. -/
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theorem braidCrossZeroRightWitness :
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(braidCross (BraidStrand.zero 1) (BraidStrand.zero 0)).1.phaseAcc = PhaseVec.zero := by
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native_decide
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-- REMOVED: braidCrossZeroRightWitness only tested zero strands
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/-- Parallel crossing: merge multiple strands simultaneously
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@ -137,10 +137,7 @@ def fammAdjustDelay (bank : FAMMBank) (address : Nat) (newDelay : Q16_16) : FAMM
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let bindResult := fammBind bank .adjustDelay address
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{ success := false, value := none, cost := bindResult.cost, invariant := bindResult.invariant }
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/-- Theorem: FAMM bind returns Bool type (reflexivity). -/
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theorem fammBindReflexive (bank : FAMMBank) (mode : FAMMAccessMode) (address : Nat) :
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(fammBind bank mode address).lawful = (fammBind bank mode address).lawful := by
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rfl
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-- REMOVED: fammBindReflexive was tautological (X = X)
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/- MORE FAMM Architecture Integration
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The unified architecture requires capability-based memory isolation
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@ -215,16 +212,7 @@ structure FAMMDelta where
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deriving Repr, Inhabited
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/-- Theorem: FAMM compression achieves space reduction
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Formal guarantee that metadata collapse reduces state size.
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Note: bannedCount tracking is a TODO. Currently proves that
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collapsed state represents the bank's cells count. -/
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theorem famm_compression_property
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(bank : FAMMThermalBank) :
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let collapsed := fammMetadataCollapse bank
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collapsed.cellCount = bank.cells.size := by
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simp [fammMetadataCollapse]
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-- REMOVED: famm_compression_property was tautological (trivial identity)
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/-- Integration with Entropy Phase Engine
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FAMM provides memory substrate for nanokernel isolation,
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@ -193,22 +193,9 @@ theorem mengerHashDeterministic (coord : MengerCoordinate) :
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mengerHash coord = mengerHash coord := by
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rfl
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/-- Fractal occupancy is bounded by lattice size -/
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theorem fractalOccupancyBounded (size : UInt32) (hausdorffDim : Q16_16) (occupancyDensity : Q16_16) :
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let occupancy := fractalOccupancy size hausdorffDim occupancyDensity
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occupancy ≤ size * size * size := by
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/-- Reduction ratio is always less than 1 for d_H < 3 -/
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theorem reductionRatioLessThanOne (size : UInt32) (hausdorffDim : Q16_16) :
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hausdorffDim < to_q16 3.0 →
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let ratio := reductionRatio size hausdorffDim
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ratio < Q16_ONE := by
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/-- Menger sponge addressing preserves PIST manifold convergence -/
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theorem mengerPreservesPistConvergence (lattice : MengerLattice) (action : MengerAction) (threshold : Q16_16) :
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(mengerBind lattice action).lawful →
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blitterConverged action.pistState threshold →
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blitterConverged { action.pistState with manifold := (mengerBind lattice action).manifoldAfter } threshold := by
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-- REMOVED: fractalOccupancyBounded had no proof body
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-- REMOVED: reductionRatioLessThanOne had no proof body
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-- REMOVED: mengerPreservesPistConvergence had no proof body
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 #eval Examples
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@ -1,71 +0,0 @@
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-- CMBTorsion.lean
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--
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-- The CMB is a torsional value — not through a direct formula, but through
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-- the chain: torsion rate omega -> SM couplings -> alpha -> hydrogen binding
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-- -> recombination temperature -> CMB today.
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--
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-- The chain has ZERO free parameters. Every step is determined by the
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-- SM RG flow rate omega = 0.05775 measured at CERN:
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--
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-- omega = 0.05775 (from CERN SM couplings)
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-- -> alpha = max|beta|/(4*pi) = 1/137.036
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-- -> Rydberg = m_e * alpha^2 / 2 = 13.605 eV
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-- -> k_B * T_rec ≈ Rydberg / ln(Saha factor) ≈ 0.26 eV
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-- -> T_rec ≈ 3000 K
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-- -> T_CMB_today = T_rec / (1+z_rec) = 2.725 K
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--
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-- The Saha equation relates the hydrogen binding energy to the recombination
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-- temperature. The exact value (3000 K) comes from requiring 1% ionization,
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-- which gives k_B * T_rec ≈ 0.019 * Rydberg, or T_rec ≈ 3000 K.
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-- This factor (0.019) comes from the baryon-to-photon ratio eta = 6e-10:
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--
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-- k_B * T_rec / Rydberg ≈ 1 / ln(eta^(-1) * (T_rec/Rydberg)^(3/2))
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-- ≈ 0.019 for eta = 6e-10
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--
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-- The baryon-to-photon ratio eta = n_b/n_gamma is determined by
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-- the CMB power spectrum, which is set by the torsion fluctuation
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-- amplitude Q ≈ omega * alpha / pi ≈ 1.3e-4 (vs measured 1e-5).
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-- The factor ~13 discrepancy is within the Saha approximation error.
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namespace Semantics.Physics.CMBTorsion
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def SCALE : Int := 65536
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-- Torsion rate from SM couplings (CERN)
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def omega : Int := 3785 -- 0.05775 * 65536
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-- Fine structure constant from torsion wall
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def alpha : Int := 478 -- 1/137.036 * 65536 ≈ 478
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-- Rydberg constant: m_e * alpha^2 / 2
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-- m_e = 0.511 MeV = 0.000511 GeV
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-- alpha^2 = 1/18779
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-- Rydberg = 0.000511 / 37558 = 1.36e-8 GeV = 13.6 eV
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-- Q16: 1.36e-8 * 65536 ≈ 0 — too small for Q16
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-- Stored as ×10^12: 13605 (13.605 eV)
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def rydberg : Int := 13605
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-- Baryon-to-photon ratio from: eta = n_b / n_gamma
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-- Planck 2018: eta = 6.09e-10
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-- Stored as ×10^12: 609
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def baryonPhotonRatio : Int := 609
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-- Recombination temperature factor:
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-- k_B * T_rec / Rydberg ≈ 1 / ln(eta^(-1) * (T_rec/Rydberg)^(3/2))
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-- For eta = 6e-10, this gives ~0.019
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-- So k_B * T_rec ≈ 0.019 * 13.6 eV ≈ 0.26 eV ≈ 3000 K
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-- The factor 0.019 is determined SOLELY by eta, which is determined
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-- by the CMB power spectrum amplitude Q.
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--
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-- The torsion model predicts Q ≈ omega * alpha / pi ≈ 1.3e-4.
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-- The measured Q ≈ 1e-5. This factor ~13 propagates to T_rec.
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-- Q from torsion: omega * alpha / pi = 0.05775 * 0.007297 / 3.1416 = 1.34e-4
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-- Q measured: ~1e-5
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-- Ratio: ~13. This sets the scale for CMB fluctuations.
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-- The exact Q requires the full inflationary dynamics, not just torsion.
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-- Executable receipts
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#eval rydberg
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end Semantics.Physics.CMBTorsion
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@ -1,100 +0,0 @@
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-- CouplingRotation.lean
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--
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-- The "missing torsion constant" is the SM RG rotation rate.
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-- In 16D coupling space (12 SM + 4 gravitational), the coupling
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-- vector rotates as energy changes. The rotation rate d(theta)/d(ln mu)
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-- is a pure number derived from CERN measurements alone.
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--
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-- The rotation projects to w0 through:
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-- w0 = -1 + 2 * f_lam * omega * P
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-- where:
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-- f_lam = fraction of rotation in Higgs direction (0.263)
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-- omega = angular velocity in coupling space (0.0577 rad/e-fold)
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-- P = sqrt(Omega_DE / Omega_m) = cosmic projection factor (1.565)
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--
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-- Predicted w0 = -0.952. DESI DR2 w0 = -0.838 +- 0.055.
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-- Difference = 2.1 sigma. Prediction is in the right direction (w0 > -1)
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-- but the projection formula is heuristic and needs proper derivation.
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namespace Semantics.Physics.CouplingRotation
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def SCALE : Int := 65536
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-- ═════════════════════════════════════════════════════════════════════════════
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-- §0 SM couplings at EW scale (CERN, 6-sigma)
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-- ═════════════════════════════════════════════════════════════════════════════
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-- g1, g2, g3 are the SM gauge couplings
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-- Stored as Q16_16: round(value * 65536)
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def g1_ew : Int := 23394 -- 0.357
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def g2_ew : Int := 42729 -- 0.652
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def g3_ew : Int := 79954 -- 1.220
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-- Higgs self-coupling
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def lam_ew : Int := 8460 -- 0.1291
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-- Top Yukawa
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def yt_ew : Int := 65030 -- 0.9923
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-- ═════════════════════════════════════════════════════════════════════════════
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-- §1 Beta functions at EW scale (rotation rates, 1-loop)
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-- ═════════════════════════════════════════════════════════════════════════════
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-- beta_lam * (16*pi^2) = 24*lam^2 + 12*lam*yt^2 - 6*yt^4 - 3*lam*(3*g2^2+g1^2) + 3/8*(2*g2^4+(g2^2+g1^2)^2)
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-- At the EW scale, evaluated: -0.026503 * 65536 = -1737
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def beta_lam : Int := -1737
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-- |beta|^2 = sum of squared beta values for g1, g2, g3, yt, lam
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-- Only lam is computed here; full vector requires all five.
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-- Total norm: |beta| = 0.1007 * 65536 = 6601
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-- lam's fraction: |beta_lam| / |beta| = 0.0265 / 0.1007 = 0.263
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-- f_lam^2 = (1737 / 6601)^2
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-- Q16_16: round(0.263 * 65536) = 17236
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def fracLam : Int := 17236
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-- Angular velocity omega = |beta| / |g| = 0.1007 / 1.744 = 0.05775
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-- Q16_16: round(0.05775 * 65536) = 3785
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def omega : Int := 3785
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-- Projection factor P = sqrt(Omega_DE / Omega_m) = sqrt(0.71/0.29) = 1.565
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-- Q16_16: round(1.565 * 65536) = 102564
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def projFactor : Int := 102564
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-- Predicted w0 = -1 + 2 * f_lam * omega * P
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-- = -1 + 2 * 0.263 * 0.05775 * 1.565
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-- = -1 + 0.0475 = -0.9525
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-- Q16_16: round(-0.9525 * 65536) = -62436
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def predW0_rot : Int := -62436
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-- ═════════════════════════════════════════════════════════════════════════════
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-- §2 Comparison against DESI
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-- ═════════════════════════════════════════════════════════════════════════════
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-- DESI DR2 w0 = -0.838 +- 0.055 (Q16: -54919 +- 3604)
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-- Predicted w0 = -0.9525 (Q16: -62436)
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-- Residual: -62436 - (-54919) = -7517
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-- |residual| = 7517, DESI sigma = 3604
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-- sigma distance: 7517 / 3604 = 2.09 sigma
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-- Helper
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def absDiff (a b : Int) : Int := if a ≥ b then a - b else b - a
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-- Predicted w0 is above -1 (dark energy is not a cosmological constant)
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theorem predAboveMach : predW0_rot > -SCALE := by native_decide
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-- Predicted w0 is 2.09 sigma from DESI DR2
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theorem residualTwoSigma : absDiff predW0_rot (-54919) > 2 * 3604 := by native_decide
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-- But it is within 3 sigma (not ruled out)
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theorem residualWithinThreeSigma : absDiff predW0_rot (-54919) < 3 * 3604 := by native_decide
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-- ═════════════════════════════════════════════════════════════════════════════
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-- §3 Executable receipts
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-- ═════════════════════════════════════════════════════════════════════════════
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#eval beta_lam -- Higgs rotation rate
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#eval omega -- Angular velocity in coupling space (the missing constant)
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#eval predW0_rot -- Predicted w0 from coupling rotation alone
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#eval absDiff predW0_rot (-54919) -- Residual vs DESI DR2
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end Semantics.Physics.CouplingRotation
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@ -1390,16 +1390,7 @@ theorem mkvContainerPreserves (steps : List (List OISC_SLUG3_Inst)) (sheet : Sol
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In the Q16.16 manifold, we assume energy drift is bounded by O(dt³) + O(ε)
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where ε is the fixed-point quantization noise.
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-/
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/-- Verlet energy drift bound (external numerical-analytic invariant). -/
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theorem verlet_preserves_energy_approximate (state : NBodyState) (dt : Fix16) (G : Fix16) (tolerance : Fix16) :
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let evolved := velocityVerletStep state dt (gravitationalForce · · G)
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let initialEnergy := computeHamiltonian state G
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let finalEnergy := computeHamiltonian evolved G
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let energyDiff := Fix16.abs (Fix16.sub finalEnergy initialEnergy)
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let toleranceBound := Fix16.add (Fix16.mul dt (Fix16.mul dt dt)) tolerance
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energyDiff.raw ≤ toleranceBound.raw := by
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apply verlet_energy_drift_bound
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-- REMOVED: verlet_preserves_energy_approximate referenced nonexistent lemma
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/-- N-body cost scaling: O(n²) (external algorithmic invariant). -/
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@ -1,88 +0,0 @@
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-- TorsionWall.lean
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--
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-- If the speed of light is not a fundamental limit but the maximum
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-- signal speed through the coupling manifold's torsion field, then
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-- c should be computable from the torsion wall — the seam where
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-- lambda = 0 (vacuum instability scale).
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--
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-- The fine structure constant alpha = e^2/(4*pi) = 1/137.036
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-- emerges from this framework as:
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-- alpha = max|beta| / (4*pi)
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-- where max|beta| = 0.1007 is the total SM RG rotation rate
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-- at the electroweak scale.
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--
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-- 1-loop: alpha_pred = 0.1007 / (4*pi) = 0.00801 (10% high)
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-- 2-loop: alpha_pred = 0.0915 / (4*pi) = 0.00728 (0.2% low)
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-- True: alpha = 0.007297
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--
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-- The speed of light c is then the conversion factor between
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-- the coupling manifold's torsion rate (radians per e-fold) and
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-- physical velocity. In natural units (hbar = c = 1), this sets
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-- the unit system. The DIMENSIONLESS number alpha is what the
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-- model actually predicts.
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namespace Semantics.Physics.TorsionWall
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def SCALE : Int := 65536
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-- ═════════════════════════════════════════════════════════════════════════════
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-- §0 The torsion wall seam
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-- ═════════════════════════════════════════════════════════════════════════════
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-- The wall is at lambda = 0 (vacuum instability scale ~10^8.7 GeV, 1-loop)
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-- At this scale, the Higgs self-coupling vanishes and the torsion reaches
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-- its maximum. This sets both the maximum signal speed (c) and the
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-- dimensionless coupling constants.
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-- SM beta function norm at EW scale: |beta| = 0.1007 (1-loop)
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-- Q16: round(0.1007 * 65536) = 6600
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def maxBeta : Int := 6600
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-- Predicted alpha from torsion:
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-- alpha_pred = maxBeta / (4*pi) = 0.1007 / 12.566 = 0.00801
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-- Q16: round(0.00801 * 65536) = 525
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def alphaPred : Int := 525
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-- True fine structure constant: alpha = 1/137.036 = 0.007297
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-- Q16: round(0.007297 * 65536) = 478
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def alphaTrue : Int := 478
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-- The prediction is within 10% of the true value (1-loop estimate)
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theorem alpha_within_10percent : alphaTrue * 100 < alphaPred * 110 := by native_decide
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-- With 2-loop corrections: maxBeta = 0.0915 gives exact alpha
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-- Q16: round(0.0915 * 65536) = 5997
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def maxBeta_2loop : Int := 5997
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-- alpha_pred_2loop = 0.0915 / (4*pi) = 0.0915 / 12.566 = 0.00728
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-- Q16: round(0.00728 * 65536) = 477
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def alphaPred2l : Int := 477
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-- 2-loop gives alpha within 0.3% of true value
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theorem alpha_2loop_within_1percent : alphaPred2l > alphaTrue * 99 / 100 := by
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native_decide
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-- ═════════════════════════════════════════════════════════════════════════════
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-- §1 What this means
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-- ═════════════════════════════════════════════════════════════════════════════
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-- If alpha = max|beta| / (4*pi), then:
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-- 1. The fine structure constant is NOT a free parameter
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-- 2. It's determined by the SM beta function at the EW scale
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-- 3. The speed of light c is the conversion factor that makes this
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-- equation dimensionally consistent
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-- 4. Changing alpha would mean changing the SM — which we know works
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--
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-- This is a genuine PREDICTION: if new physics modifies the SM beta
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-- function (e.g., supersymmetry, extra dimensions), alpha would shift.
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-- The measured alpha = 1/137.036 constrains any BSM extension.
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-- ═════════════════════════════════════════════════════════════════════════════
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-- §2 Executable receipts
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-- ═════════════════════════════════════════════════════════════════════════════
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#eval maxBeta
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#eval alphaPred
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#eval alphaTrue
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end Semantics.Physics.TorsionWall
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