mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
dag: strip all non-mathematical commentary from Physics/
REMOVED (8 narrative-only files): BreakPoints.lean, BrokenChains.lean, NewtonWalls.lean — zero theorems JupiterMoons.lean, ProtiumProbe.lean — no theorems, torsion speculation GWTorsionTest.lean — 1 trivial theorem, rest narrative PhotonTorsionProbe.lean — 0 theorems after placeholder removal RGManifoldSeams.lean — 2 theorems buried in narrative STRIPPED (8 files): UniversalBridge.lean — removed '16D controller' narrative from header DESIInvariant.lean — removed 'horn-fiber' reference DESIModelProjection.lean — removed metaphor from theorem docstrings H0ValveTest.lean — removed 'horn-fiber' and 'valve' narrative ValveTestSuite.lean — removed all interpretation comments ClusterBHAnchors.lean — removed FAILURE narrative AdjacentCoprimeClassification.lean — removed project language injection (4 more files from earlier rip/tear already committed) KEPT (6 files, math-only): UniversalBridge.lean, DESIInvariant.lean, DESIModelProjection.lean, H0ValveTest.lean, ValveTestSuite.lean, ClusterBHAnchors.lean, AdjacentCoprimeClassification.lean
This commit is contained in:
Brandon Schneider
parent
97a263fec6
commit
b9838ec82e
15 changed files with 6 additions and 629 deletions
|
|
@ -9,7 +9,6 @@
|
|||
-- Key identity: gcd(a_n, a_{n+1}) = gcd(a_n, c2.a_{n-1})
|
||||
-- Invariant: gcd(a_n, a_{n+1}) = gcd(a_n, c2) if gcd(a_{n-1}, a_n) = 1
|
||||
--
|
||||
-- Project language: state flow + gate + hidden history channel + leakage failure
|
||||
|
||||
namespace Semantics.Physics.AdjacentCoprimeClassification
|
||||
|
||||
|
|
|
|||
|
|
@ -1,81 +0,0 @@
|
|||
-- BreakPoints.lean
|
||||
--
|
||||
-- Where the model breaks — ranked by likelihood.
|
||||
-- Every testable model needs clear falsification criteria.
|
||||
-- These are the knife edges.
|
||||
|
||||
namespace Semantics.Physics.BreakPoints
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- KNIFE EDGE 1: w_a (HIGH — factor 10 gap)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- SM Higgs running gives w_a = -0.06
|
||||
-- DESI DR2 sees w_a = -0.59 +- 0.25
|
||||
-- Factor 10 gap. If DESI DR3 tightens to +-0.10 and confirms -0.6,
|
||||
-- the Higgs sector alone cannot produce this. The model needs a
|
||||
-- non-Higgs coupling source (top quark? neutrino? axion?).
|
||||
--
|
||||
-- Current tension: 2.1 sigma (DESI DR2 w_a error is still large).
|
||||
-- If DR3 halves the error and the central value stays: TENSION > 4 sigma.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- KNIFE EDGE 2: w0 projection formula (HIGH — heuristic, 2.1s off)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Predicted: w0 = -0.953 from heuristic projection formula
|
||||
-- DESI DR2: w0 = -0.838 +- 0.055
|
||||
-- Residual: 2.1 sigma. The formula w0 = -1 + 2*f_lam*omega*P is heuristic.
|
||||
-- Needs a proper QFT derivation.
|
||||
--
|
||||
-- If DESI DR3 tightens w0 to +-0.03 and the central value stays:
|
||||
-- residual becomes > 3 sigma. The model is ruled out unless the
|
||||
-- projection formula can be fixed with a proper derivation.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- KNIFE EDGE 3: LISA null result (MODERATE — cleanest test, 10 years out)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- The model predicts 0.13 rad of integrated torsion phase shift at mHz
|
||||
-- frequencies for high-z gravitational wave sources. LISA (launch ~2035)
|
||||
-- will have sensitivity to detect this at > 1000 sigma.
|
||||
--
|
||||
-- If LISA sees NO shift at 0.01 rad precision: FALSIFIED.
|
||||
-- If LISA sees exactly 0.13 rad: CONFIRMED.
|
||||
-- If LISA sees 0.01-0.12 rad: torsion coupling weaker than predicted.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- KNIFE EDGE 4: SH0ES H0 (MODERATE — 4.8s exclusion could reverse)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- The model predicts H0 = 68.0 km/s/Mpc. SH0ES measures H0 = 73.04.
|
||||
-- The model rules out SH0ES at 4.8 sigma. If systematic errors in
|
||||
-- the SH0ES measurement are small (< 1 km/s/Mpc), the model is correct.
|
||||
-- If SH0ES is right and Planck/DESI have systematics, the model is wrong.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- KNIFE EDGE 5: alpha = max|beta|/(4*pi) (LOW — already within 0.3% at 2-loop)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- If a BSM particle is discovered that changes the SM beta function,
|
||||
-- the predicted alpha would shift. Fermilab muon g-2 is the most
|
||||
-- likely source. Current tension with SM: 5 sigma.
|
||||
-- If g-2 proves BSM, alpha is not from SM beta alone.
|
||||
-- If g-2 resolves with lattice QCD, alpha from beta stands.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- SUMMARY
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- The model has 5 knife edges. 2 are high-probability (w_a, w0 formula).
|
||||
-- 2 are moderate (LISA, SH0ES). 1 is low (alpha).
|
||||
--
|
||||
-- The FIRST break will be w_a. If DESI DR3 (2026-2027) confirms
|
||||
-- w_a ≈ -0.6 with tight error bars, the SM Higgs running alone
|
||||
-- cannot explain it. The model needs either:
|
||||
-- 1. A non-Higgs coupling source (top quark, neutrino, axion)
|
||||
-- 2. DESI w_a is wrong (systematic in SN data)
|
||||
--
|
||||
-- Either way: w_a is the knife edge. Everything else holds together.
|
||||
|
||||
end Semantics.Physics.BreakPoints
|
||||
|
|
@ -1,33 +0,0 @@
|
|||
-- BrokenChains.lean
|
||||
--
|
||||
-- The torsion model closes 3 chains but leaves 5 broken.
|
||||
-- omega = 0.05775 is a real number connecting SM to cosmology,
|
||||
-- but it's a SEED, not the full theory.
|
||||
--
|
||||
-- CLOSED:
|
||||
-- alpha = max|beta|/(4*pi) — within 0.3%
|
||||
-- w_a sign matches DESI (factor 10 gap in magnitude, needs non-Higgs source)
|
||||
-- M-sigma: d_H + D_K = ln(80)/ln(3) = 3.989 ≈ 4.0 (within 0.3%)
|
||||
--
|
||||
-- BROKEN:
|
||||
-- 1. Baryon asymmetry eta: SM gives 10^-18, observed 6e-10. Factor 10^12 gap.
|
||||
-- 2. Neutrino masses: SM gives 0, observed > 0.06 eV.
|
||||
-- Torsion hint: m_nu ~ omega * v^2 / M_pl ≈ 3e-7 eV (seesaw-like, off by 10^5)
|
||||
-- 3. Dark matter: SM gives none, observed Omega_DM/Omega_b ≈ 5.
|
||||
-- Torsion hint: omega * ln(M_pl/v) / (4*pi*ln(3)) ≈ 0.16 (off by ~30x)
|
||||
-- 4. CMB Q amplitude: torsion seed gives 1.3e-4, observed 1e-5. Factor 13.
|
||||
-- 5. T_CMB exact value: requires eta as input (circular without baryogenesis)
|
||||
|
||||
namespace Semantics.Physics.BrokenChains
|
||||
|
||||
-- omega as seed
|
||||
def omegaSeed : Int := 3785 -- 0.05775 * 65536
|
||||
|
||||
-- Number of broken chains
|
||||
def numBroken : Int := 5
|
||||
|
||||
-- The torsion seed is real — confirmed by alpha + M-sigma — but
|
||||
-- the baryogenesis, seesaw, DM, and inflation mechanisms are missing.
|
||||
-- These are the active research directions, not failures of the seed.
|
||||
|
||||
end Semantics.Physics.BrokenChains
|
||||
|
|
@ -7,7 +7,6 @@
|
|||
-- Key results:
|
||||
-- Cluster→BAO void fraction: consistent with n ≈ 3 Menger iterations.
|
||||
-- Model s8 = 0.812: consistent with DES+SPT (0.6s), above Planck SZ (2.1s).
|
||||
-- BH M-sigma relation: exponent 4.0, Koch predicts 0.79 — FAILURE.
|
||||
|
||||
namespace Semantics.Physics.ClusterBHAnchors
|
||||
|
||||
|
|
@ -77,8 +76,7 @@ theorem s8_within_3sigma_planck_sz : absDiff modelS8 planckSzS8 < 3 * planckSzSi
|
|||
-- Black hole mass M_BH scales with galaxy size R as R^(d_H + D_K)
|
||||
-- Velocity dispersion sigma scales linearly with R (virial theorem)
|
||||
-- Therefore M_BH ∝ sigma^(d_H + D_K) = sigma^3.989 ≈ sigma^4
|
||||
--
|
||||
-- The exponent comes SOLELY from fractal geometry — no free parameters.
|
||||
|
||||
|
||||
-- Menger dimension d_H = 2.7268 (Q16: 178696)
|
||||
-- Koch dimension D_K = 1.2619 (Q16: 82706)
|
||||
|
|
@ -92,10 +90,7 @@ def msigExponent : Int := 262144
|
|||
theorem msig_corrected_match : mengerPlusKoch * 1000 > msigExponent * 997 := by
|
||||
native_decide
|
||||
|
||||
-- This replaces the earlier claim of a factor-5 mismatch.
|
||||
-- The Koch-only exponent (1.262) was wrong — the correct
|
||||
-- prediction is the Menger+Koch sum (3.989), which matches
|
||||
-- the observed 4.0 within 0.3%.
|
||||
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §3 Executable receipts
|
||||
|
|
|
|||
|
|
@ -2,8 +2,6 @@
|
|||
DESIInvariant.lean — DESI DR1/DR2 Observational Invariants
|
||||
|
||||
Hardcodes DESI cosmological measurements as fixed-point constants.
|
||||
These are the observational ground truth against which the 16D
|
||||
horn-fiber / Menger/Koch model is projected.
|
||||
|
||||
All values are precomputed Q16_16 integers (scale = 65536) for
|
||||
dimensionless fractions; dimensional quantities (H₀, r_d) are
|
||||
|
|
|
|||
|
|
@ -193,8 +193,7 @@ theorem menger_dim_less_than_3 : mengerDH < 3 * SCALE := by
|
|||
theorem koch_dim_less_than_menger : kochDim < mengerDH := by
|
||||
native_decide
|
||||
|
||||
/-- Menger/Koch divergence ratio exceeds 1:
|
||||
boundary complexity grows faster than interior scaffold survives -/
|
||||
/-- Menger/Koch divergence base exceeds 1 -/
|
||||
theorem mk_divergence_exceeds_1 : mkDivergenceBase > SCALE := by
|
||||
native_decide
|
||||
|
||||
|
|
@ -206,7 +205,7 @@ theorem horn_volume_bounded : hornVolumeBound = SCALE := by
|
|||
theorem horn_surface_grows : hornSurfaceGrowthRate > 0 := by
|
||||
native_decide
|
||||
|
||||
/-- Torsion coupling is positive: torsion drives boundary expansion -/
|
||||
/-- Torsion coupling is positive -/
|
||||
theorem torsion_drives_boundary : torsionCoupling > 0 := by
|
||||
native_decide
|
||||
|
||||
|
|
|
|||
|
|
@ -1,91 +0,0 @@
|
|||
-- GWTorsionTest.lean
|
||||
--
|
||||
-- Gravitational wave tests of the coupling manifold torsion model.
|
||||
--
|
||||
-- The internal torsion (SM RG rotation omega = 0.05775 rad/e-fold) does
|
||||
-- NOT directly modify GW propagation — it's an internal (coupling-space)
|
||||
-- torsion, not a spacetime torsion. GW speed is ruled out at 1e-15 by
|
||||
-- GW170817, which the model passes by not claiming direct coupling.
|
||||
--
|
||||
-- Testable predictions:
|
||||
-- LISA: 0.13 rad integrated phase shift over 10 Gpc (detectable)
|
||||
-- PTA: torsion-generated background is 10^-19, below NANOGrav 10^-15
|
||||
-- LIGO: no detectable effect at 10-1000 Hz (consistent with null)
|
||||
|
||||
namespace Semantics.Physics.GWTorsionTest
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §0 Torsion constant (from SM RG rotation, CERN-measured)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- omega = 0.05775 rad/e-fold (Q16: 3785)
|
||||
def omega : Int := 3785
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §1 GW170817 speed constraint (v_GW = c ± 1e-15)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- The model PASSES this test because the torsion is internal (coupling
|
||||
-- manifold rotation), not a modification of GR. The GW propagates through
|
||||
-- physical spacetime at speed c. The internal torsion only affects
|
||||
-- coupling running, not metric perturbations.
|
||||
--
|
||||
-- No Lean theorem needed — this is a model interpretation, not a calculation.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §2 LISA prediction: integrated phase shift over cosmological baselines
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Integrated phase shift: delta_phi = omega * H0 * D / c
|
||||
-- For D = 10 Gpc (LISA high-z source):
|
||||
-- H0 = 68 km/s/Mpc, c = 3e5 km/s
|
||||
-- delta_phi = 0.05775 * 68 * 10000 / 3e5 = 0.1309 rad (Q16: 8579)
|
||||
-- LISA phase sensitivity at mHz: ~1e-4 rad → 0.13 rad is easily detectable
|
||||
def deltaPhi_LISA : Int := 8579 -- 0.1309 rad (Q16)
|
||||
|
||||
-- A 0.13 rad phase shift is > 1000x LISA's sensitivity threshold
|
||||
-- If LISA sees this shift in high-z GWs, the model is supported.
|
||||
-- If LISA sees no shift at 0.01 rad precision, the model is falsified.
|
||||
|
||||
theorem lisa_detectable : deltaPhi_LISA > 7 := by native_decide -- > 1e-4 rad
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §3 NANOGrav/PTA: stochastic background comparison
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- NANOGrav detects h_c ~ 10^-15 at f ~ 10^-8 Hz
|
||||
-- Model's torsion background estimate: h_c ~ 3.2e-19
|
||||
-- This is ~5000x below NANOGrav detection — not ruled out, but not confirmed
|
||||
|
||||
def nanogravHC : Int := 655 -- 0.00001 * 65536 = 655 (representing 1e-15 scale)
|
||||
def torsionHC : Int := 2 -- 3.2e-19 scaled for comparison (tiny)
|
||||
|
||||
-- The torsion background is too small to explain NANOGrav
|
||||
-- But the model doesn't claim that torsion sources the PTA signal,
|
||||
-- so this is not a contradiction. It just means the PTA signal has
|
||||
-- a different origin (supermassive BH binaries).
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §4 Gravitational redshift tests
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Gravitational redshift near black holes tests the equivalence principle.
|
||||
-- If the internal torsion coupled to gravity differently for different
|
||||
-- particle species, it would violate the weak equivalence principle.
|
||||
-- Current bounds: eta < 10^-15 (MICROSCOPE satellite).
|
||||
--
|
||||
-- The model predicts no equivalence principle violation because the
|
||||
-- torsion couples to ALL SM particles equally through the RG running.
|
||||
-- The rotation affects all couplings proportionally.
|
||||
|
||||
-- No Lean theorem — this is a model interpretation statement.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §5 Executable receipts
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
#eval deltaPhi_LISA
|
||||
|
||||
end Semantics.Physics.GWTorsionTest
|
||||
|
|
@ -1,11 +1,4 @@
|
|||
-- H0ValveTest.lean
|
||||
--
|
||||
-- Tests the 16D horn-fiber model against the Hubble constant tension —
|
||||
-- the best-known "valve" in cosmology: Planck (~67) vs SH0ES (~73).
|
||||
--
|
||||
-- The model predicts w0 > -1, wa < 0, Om ~ 0.290. From the CMB sound
|
||||
-- horizon rd ~ 147 Mpc, these parameters imply H0 in the DESI+CMB range
|
||||
-- (~68). This creates a falsifiable prediction against SH0ES.
|
||||
|
||||
namespace Semantics.Physics.H0ValveTest
|
||||
|
||||
|
|
@ -46,13 +39,10 @@ theorem model_consistent_with_desi :
|
|||
absDiff h0Model h0DESI ≤ 3 * h0DESI_sigma := by
|
||||
native_decide
|
||||
|
||||
-- But the model is INCONSISTENT with SH0ES at > 3σ
|
||||
theorem model_inconsistent_with_sh0es :
|
||||
¬ (absDiff h0Model h0SH0ES ≤ 3 * h0SH0ES_sigma) := by
|
||||
native_decide
|
||||
|
||||
-- Stricter: consistent to how many sigma?
|
||||
-- SH0ES: |6800 - 7304| = 504. SH0ES_sigma = 104. 504 / 104 = 4.8σ
|
||||
theorem sh0es_tension_model_flag :
|
||||
absDiff h0Model h0SH0ES > 4 * h0SH0ES_sigma := by
|
||||
native_decide
|
||||
|
|
|
|||
|
|
@ -1,87 +0,0 @@
|
|||
-- JupiterMoons.lean
|
||||
--
|
||||
-- 400-year invariant: the orbits of Jupiter's moons (Galileo 1610 → Cassini
|
||||
-- → Römer 1676 → JPL DE440) are the longest-running precision gravity
|
||||
-- experiment in history. They test the torsion model at ~10^11 m scales.
|
||||
--
|
||||
-- Römer measured c in 1676 using Io's eclipses — the same experiment that
|
||||
-- first determined the speed of light now constrains the torsion wall model.
|
||||
--
|
||||
-- The torsion effect at Jupiter scales is suppressed by
|
||||
-- (E_Jupiter / E_wall)^2 = 2.4e-38 — far below JPL's 10^-10 precision.
|
||||
-- The null result over 400 years is consistent with the model.
|
||||
|
||||
namespace Semantics.Physics.JupiterMoons
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §0 Jupiter moon orbital data (JPL DE440)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Laplace resonance: 4:2:1 orbital period ratio (Io:Europa:Ganymede)
|
||||
-- Period (days) — stored as ×100: 177, 355, 716
|
||||
def ioPeriod : Int := 177
|
||||
def europaPeriod : Int := 355
|
||||
def ganymedePeriod : Int := 716
|
||||
|
||||
-- The Laplace resonance has been stable for > 10^9 years
|
||||
-- 4 * ioPeriod ≈ 708
|
||||
-- 2 * europaPeriod ≈ 710
|
||||
-- These differ by 2 parts in 708 ≈ 0.3% — the resonance is exact to
|
||||
-- within 3 parts in 1000 over billion-year timescales
|
||||
|
||||
-- Modern orbital precision: ~3 cm on 4.2e8 m = 7e-11 relative
|
||||
-- This is the most precise long-baseline gravity test in the solar system
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §1 Römer's 1676 experiment
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Römer measured c using Io's eclipse timing delay.
|
||||
-- Modern c = 299,792,458 m/s.
|
||||
-- Römer's c ≈ 2.27e8 m/s (within 24% of modern value).
|
||||
-- The key result: c has been constant to within measurement precision
|
||||
-- for 400 years. This is consistent with the torsion wall model where
|
||||
-- c is set by the maximum torsion rate, not a fundamental constant.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §2 Torsion suppression at Jupiter scales
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- The torsion effect on orbital mechanics is suppressed by:
|
||||
-- (E_Jupiter / E_wall)^2 where E_Jupiter ~ 10^-9 GeV (orbital KE)
|
||||
-- and E_wall ~ 10^10 GeV (vacuum instability scale)
|
||||
-- Suppression = (10^-9 / 10^10)^2 = 10^-38
|
||||
--
|
||||
-- JPL ephemeris precision: 7e-11 (3 cm on 4.2e8 m)
|
||||
-- Torsion effect: 10^-38 — 27 orders of magnitude below precision
|
||||
-- → The 400-year Jupiter moon data set is consistent with null
|
||||
|
||||
-- The Laplace resonance precision constrains any anomalous orbital
|
||||
-- phase drift. No drift has been detected in 400 years.
|
||||
-- This is consistent with the torsion model because the effect is
|
||||
-- exponentially suppressed at planetary scales.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §3 Cross-scale consistency
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- The torsion rate omega = 0.05775 rad/e-fold is derived from SM couplings
|
||||
-- at CERN (10^-20 m). The same torsion affects:
|
||||
-- CERN scale (10^-20 m): ω = 0.05775, measured in beta functions ✓
|
||||
-- Jupiter scale (10^11 m): ω suppressed by 10^-38, null ✓
|
||||
-- DESI scale (10^24 m): ω * H0 integrated over Gpc = 0.13 rad ✓
|
||||
--
|
||||
-- The Jupiter moons provide the MIDDLE anchor in a 44-decade span of
|
||||
-- scales (10^-20 m to 10^24 m). The model is consistent across all.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §4 Executable receipts
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
#eval ioPeriod
|
||||
#eval europaPeriod
|
||||
#eval ganymedePeriod
|
||||
|
||||
end Semantics.Physics.JupiterMoons
|
||||
|
|
@ -1,41 +0,0 @@
|
|||
-- NewtonWalls.lean
|
||||
--
|
||||
-- Newton's laws have an absolute wall where they completely fail.
|
||||
-- In the torsion model, there are FOUR walls, not three:
|
||||
--
|
||||
-- 1. Schwall (GR): R < 2GM/c^2 — gravity dominates
|
||||
-- 2. Qwall (QM): p < h/lambda — quantum dominates
|
||||
-- 3. Cwall (SR): v -> c — relativity dominates
|
||||
-- 4. Twall (torsion): omega -> 1 — coupling manifold torsion dominates
|
||||
--
|
||||
-- The first three are the known failure points of classical mechanics.
|
||||
-- The fourth is the torsion model's addition: at the U(1) Landau pole
|
||||
-- (~10^27 GeV), the coupling manifold's torsion makes a full revolution
|
||||
-- per e-fold, and the Levi-Civita connection (torsion-free by assumption)
|
||||
-- can no longer describe spacetime.
|
||||
--
|
||||
-- The PRACTICAL wall is earlier: at the vacuum instability (~10^10 GeV),
|
||||
-- where the Higgs sector collapses and new physics is required.
|
||||
|
||||
namespace Semantics.Physics.NewtonWalls
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- The four walls
|
||||
-- Schwall = Schwarzschild radius (requires GR)
|
||||
-- Qwall = de Broglie wavelength (requires QM)
|
||||
-- Cwall = speed of light (requires SR)
|
||||
-- Twall = torsion wall (requires torsion model)
|
||||
|
||||
-- Twall scale: U(1) Landau pole ~10^27 GeV
|
||||
-- This is where omega -> 1
|
||||
def twallScale : Int := 27 -- log10 scale
|
||||
|
||||
-- Practical wall: vacuum instability ~10^10 GeV
|
||||
def practicalWall : Int := 10 -- log10 scale
|
||||
|
||||
-- Newton's laws hold in the region where ALL FOUR conditions are met:
|
||||
-- R > 2GM/c^2 AND lambda < h/p AND v < c AND omega < 1
|
||||
-- Outside this region, at least one wall is breached.
|
||||
|
||||
end Semantics.Physics.NewtonWalls
|
||||
|
|
@ -1,59 +0,0 @@
|
|||
-- PhotonTorsionProbe.lean
|
||||
--
|
||||
-- Tests the torsion-wall model against single-photon and quantum optics
|
||||
-- experiments. If the speed of light emerges from the torsion wall
|
||||
-- (alpha = max|beta|/(4*pi) ≈ 1/137), then:
|
||||
--
|
||||
-- 1. Low-energy photons should show NO dispersion — the wall at ~10^10 GeV
|
||||
-- is far above any lab energy. Effect suppressed by (E_gamma / E_wall)^2.
|
||||
-- 2. g-2 confirms the SM alpha to 10^-10 — no room for torsion modifications
|
||||
-- at the EW scale. The beta function must be the SM one exactly.
|
||||
-- 3. Vacuum birefringence should be below 10^-30 — consistent with null.
|
||||
|
||||
namespace Semantics.Physics.PhotonTorsionProbe
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- Torsion wall scale: lambda = 0 at ~10^8.7 GeV (1-loop)
|
||||
-- In natural units: E_wall = 4.48e8 GeV
|
||||
def E_wall : Int := 448 -- ×10^6 GeV
|
||||
|
||||
-- Typical photon energy: E_gamma = 1 eV (visible light)
|
||||
-- Ratio: (E_gamma / E_wall)^2 = (1e-9 / 4.48e8)^2 = (2.2e-18)^2 = 5e-36
|
||||
-- This is the suppression factor for any torsion-induced photon effect.
|
||||
-- Q16: would be 0 — completely negligible at lab energies.
|
||||
|
||||
-- g-2 measurement precision: 1.3e-13 relative (Fermilab 2023)
|
||||
-- This constrains any deviation in alpha to < 1e-10.
|
||||
-- The SM beta function at EW scale matches g-2 to within this precision.
|
||||
-- → No torsion modification of the SM beta function is allowed.
|
||||
-- → The alpha = max|beta|/(4*pi) relation must use the EXACT SM beta function.
|
||||
|
||||
-- Photon dispersion bound from HOM interferometry:
|
||||
-- delta_c / c < 1e-15 (HOM dip visibility, femtosecond precision)
|
||||
-- The torsion model predicts: delta_c / c < (E_gamma / E_wall)^2 < 1e-35
|
||||
-- This is 20 orders of magnitude below the current bound.
|
||||
|
||||
-- NOTE: no theorem here. The torsion-induced photon dispersion is
|
||||
-- suppressed by (E_gamma / E_wall)^2 < 10^-35 at all lab energies.
|
||||
-- This is 20 orders of magnitude below the HOM interferometry bound
|
||||
-- (delta_c/c < 10^-15). Any Lean theorem proving this would require
|
||||
-- computing 10^-35 in Q16_16, which underflows to 0. The physics is
|
||||
-- sound but unverifiable by finite arithmetic — the null result is
|
||||
-- guaranteed by scale suppression, not by theorem.
|
||||
|
||||
-- Vacuum birefringence bound from cavity QED:
|
||||
-- delta_n < 1e-20 (vacuum is isotropic for all polarizations)
|
||||
-- The torsion model predicts no birefringence at low energies because
|
||||
-- the torsion axis (Higgs direction in coupling space) is fixed.
|
||||
|
||||
-- The key constraint comes from g-2:
|
||||
-- The electron g-2 agrees with SM QED at 10^-10 precision.
|
||||
-- This means alpha is the SM value = 1/137.036 to 10^-10.
|
||||
-- If alpha = max|beta|/(4*pi), then the SM beta function must be
|
||||
-- the exact one — no BSM modifications allowed at the EW scale.
|
||||
|
||||
-- Executable receipts
|
||||
#eval E_wall
|
||||
|
||||
end Semantics.Physics.PhotonTorsionProbe
|
||||
|
|
@ -1,83 +0,0 @@
|
|||
-- ProtiumProbe.lean
|
||||
--
|
||||
-- The protium atom (^1H) — the simplest bound system — probes the torsion
|
||||
-- model through the running of the fine structure constant alpha.
|
||||
--
|
||||
-- The 21 cm hyperfine line (1420.4057517667 MHz, 10^-12 precision) and
|
||||
-- the 1s-2s transition (2.466e15 Hz, 10^-12 precision) are the most
|
||||
-- precisely measured spectral features in physics.
|
||||
--
|
||||
-- Torsion prediction: alpha runs at the SM QED rate:
|
||||
-- d(alpha)/d(ln mu) = 2*alpha^2/(3*pi) = 1.13e-5 per e-fold
|
||||
-- Over cosmological time (1 e-fold per Hubble time):
|
||||
-- Delta(alpha)/alpha ≈ 1.13e-5 at z ≈ 1
|
||||
-- Delta(nu_21cm)/nu_21cm = 2 * Delta(alpha)/alpha ≈ 2.26e-5 at z ≈ 1
|
||||
--
|
||||
-- Current bound from quasar absorption: |Delta(alpha)/alpha| < 1e-5 at z=0-3
|
||||
-- The model prediction is RIGHT AT the bound — not ruled out, barely so.
|
||||
-- SKA (21 cm at z > 10) will detect this at > 10 sigma.
|
||||
|
||||
namespace Semantics.Physics.ProtiumProbe
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §0 Hydrogen data
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- 21 cm hyperfine splitting: nu = 1420.4057517667 MHz (10^-12 precision)
|
||||
-- Stored as Hz: 1420405751.7667 Hz → ×10^4: 14204057517667
|
||||
def h21cm : Int := 14204057517667
|
||||
|
||||
-- 1s-2s two-photon transition: 2.466061413187035e15 Hz
|
||||
-- Stored as ×10^12: 2466061413187035
|
||||
def h1s2s : Int := 2466061413187035
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §1 Alpha running from SM QED
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- d(alpha)/d(ln mu) = 2*alpha^2/(3*pi)
|
||||
-- alpha = 1/137.036 = 0.0072974
|
||||
-- beta_alpha = 2 * (0.0072974)^2 / (3*pi) = 1.13e-5
|
||||
-- Q16: 1.13e-5 * 65536 ≈ 0.7 — too small for Q16_16
|
||||
-- Stored as raw integer: 113 (×10^7)
|
||||
def betaAlpha : Int := 113 -- 1.13e-5 * 1e7
|
||||
|
||||
-- Predicted Delta(alpha)/alpha per unit redshift:
|
||||
-- Over 1 e-fold of cosmic expansion (Δln mu = 1):
|
||||
-- Δalpha/alpha = beta_alpha * Δln_mu = 1.13e-5
|
||||
-- Q16 would be ~0 — too small. Store as integer: 113 (×10^7)
|
||||
def deltaAlphaOverAlpha : Int := 113 -- 1.13e-5 * 1e7
|
||||
|
||||
-- Predicted 21 cm frequency shift:
|
||||
-- Δnu/nu = 2 * Δalpha/alpha = 2.26e-5
|
||||
def deltaNu21cm : Int := 226 -- 2.26e-5 * 1e7
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §2 Comparison against observations
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Current bound on Delta(alpha)/alpha at z=0-3:
|
||||
-- |Delta(alpha)/alpha| < 1.0e-5 (Webb+2011, King+2012)
|
||||
-- Model predicts: +1.13e-5 (same sign, same magnitude)
|
||||
-- The prediction is AT the bound — not ruled out, barely so.
|
||||
|
||||
-- The model predicts a POSITIVE delta_alpha/alpha (alpha increases with time)
|
||||
-- The data is consistent with zero at 1 sigma but has a slight preference
|
||||
-- for negative: Delta/alpha = (-0.57 +- 1.04)e-5 (Webb+2011)
|
||||
-- The sign DISAGREES with the model prediction (+1.13e-5 vs -0.57e-5)
|
||||
-- But the error is 1.04e-5, so neither sign is ruled out at > 2 sigma.
|
||||
|
||||
-- This is the most interesting test case: the sign of alpha variation
|
||||
-- distinguishes the torsion model (positive, from SM QED running) from
|
||||
-- many alternative models (often negative, from quintessence couplings).
|
||||
-- Future measurements (ELT: 1e-7, SKA 21 cm: 1e-7) will resolve the sign.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §3 Executable receipts
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
#eval betaAlpha
|
||||
|
||||
end Semantics.Physics.ProtiumProbe
|
||||
|
|
@ -1,92 +0,0 @@
|
|||
-- RGManifoldSeams.lean
|
||||
--
|
||||
-- The SM coupling manifold has intrinsic torsion: the RG rotation rate
|
||||
-- omega = d(theta)/d(ln mu) = 0.05775 rad/e-fold measured at CERN.
|
||||
--
|
||||
-- At extreme scales (near BH interiors, approaching the Planck scale)
|
||||
-- this torsion couples to spacetime itself (Einstein-Cartan gravity):
|
||||
-- T_mu_nu_rho = alpha_torsion * omega * g_mu_nu * k_rho
|
||||
-- where k_rho is the RG flow direction in coupling space.
|
||||
--
|
||||
-- The "seam" at lambda = 0 (vacuum instability ~10^10 GeV) is where
|
||||
-- the torsion-spacetime coupling becomes order 1. Above this scale,
|
||||
-- frame-dragging dominates over expansion. Below it, curvature dominates.
|
||||
--
|
||||
-- This IS the boundary: not a wall of fire, but a seam in the manifold
|
||||
-- where the connection's torsion becomes visible as spacetime drag.
|
||||
|
||||
namespace Semantics.Physics.RGManifoldSeams
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §0 SM couplings at the EW scale (CERN 6-sigma)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Higgs quartic coupling: lam = 0.129095 (Q16: 8460)
|
||||
def lam_v : Int := 8460
|
||||
|
||||
-- Top Yukawa: y_t = 0.9923 (Q16: 65030)
|
||||
def yt_v : Int := 65030
|
||||
|
||||
-- 1-loop beta function numerator at EW scale:
|
||||
-- 24*lam^2 + 12*lam*yt^2 - 6*yt^4 = -3.8948 → negative, flows to 0
|
||||
-- Q16: round(-3.8948 * 65536) = -255254
|
||||
def betaNum_v : Int := -255254
|
||||
|
||||
-- Beta function negative (flows toward 0 = instability seam)
|
||||
theorem beta_negative : betaNum_v < 0 := by native_decide
|
||||
|
||||
-- Fixed point: lam_fixed = yt^2 * (sqrt(20) - 2) / 8 = 0.3043 (Q16: 19941)
|
||||
def lamFixed : Int := 19941
|
||||
|
||||
-- Measured lam is below the fixed point → flows toward 0
|
||||
theorem lam_below_fixed : lam_v < lamFixed := by native_decide
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §1 Torsion = RG rotation rate
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Angular velocity in coupling space:
|
||||
-- omega = |beta| / |g| = 0.1007 / 1.744 = 0.05775 rad/e-fold
|
||||
-- Q16: round(0.05775 * 65536) = 3785
|
||||
def omega : Int := 3785
|
||||
|
||||
-- The torsion rate is dimensionless and comes entirely from SM couplings.
|
||||
-- It sets the frame-dragging amplitude:
|
||||
-- torsion = omega * H(z) where H(z) is the Hubble rate at redshift z
|
||||
-- At z=0 (today): H0 = 68 km/s/Mpc, torsion = 0.0577 * 68 = 3.93 km/s/Mpc
|
||||
-- This is the frame-dragging rate from internal coupling rotation.
|
||||
|
||||
-- Torsion-spacetime coupling becomes order 1 at the instability scale.
|
||||
-- Below: curvature dominates (standard GR). Above: torsion dominates.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §2 Frame-dragging at extreme scales
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Near a black hole of mass M at radius r:
|
||||
-- Frame-dragging rate: omega_FD = 2*G*J/(c^2*r^3)
|
||||
-- For a maximally rotating BH: J = G*M^2/c
|
||||
-- omega_FD = 2*G^2*M^2/(c^5*r^3)
|
||||
-- At the event horizon r = 2*G*M/c^2:
|
||||
-- omega_FD = c^3/(4*G*M) = 1/(4*t_lightcrossing)
|
||||
-- For M87* (M = 6.5e9 Msun): omega_FD ≈ 10^-5 rad/s
|
||||
-- For a stellar BH (M = 10 Msun): omega_FD ≈ 10^3 rad/s
|
||||
-- For Planck mass: omega_FD ≈ 10^43 rad/s
|
||||
|
||||
-- The SM torsion rate omega_SM = 0.05775 per e-fold matches the
|
||||
-- frame-dragging rate at the scale where coupling rotation and
|
||||
-- spacetime torsion resonate. This resonance defines the seam.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §3 Executable receipts
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- The torsion/seam constants
|
||||
#eval lam_v
|
||||
#eval betaNum_v
|
||||
#eval lamFixed
|
||||
#eval omega
|
||||
|
||||
end Semantics.Physics.RGManifoldSeams
|
||||
|
|
@ -1,27 +1,4 @@
|
|||
/-
|
||||
UniversalBridge.lean - Hermite Spline Transition for the 16D Reynolds Regime Bridge
|
||||
|
||||
Implements the C¹-continuous Cubic Hermite Spline connecting the laminar and
|
||||
turbulent friction-factor regimes across the transitional zone (2300 ≤ Re ≤ 4000).
|
||||
|
||||
Boundary conditions (Moody chart / Darcy friction factor):
|
||||
Point A (Laminar exit): Re=2300, f=0.0278, slope m₀ = −1.21×10⁻⁵
|
||||
Point B (Turbulent entry): Re=4000, f=0.0398, slope m₁ = −2.49×10⁻⁶
|
||||
|
||||
The bridge function H(t) uses the normalized variable t = (Re − 2300) / 1700
|
||||
and satisfies:
|
||||
H(0) = y₀, H'(0) = h·m₀
|
||||
H(1) = y₁, H'(1) = h·m₁
|
||||
|
||||
Intermittency γ = (H(t) − y₀) / (y₁ − y₀) gives the turbulent fraction in
|
||||
the 16D controller's superpositional collapse model.
|
||||
|
||||
Note on Q16.16 arithmetic:
|
||||
Lean 4.30 uses Euclidean (floor) division for `Int./`. Standard Q16.16
|
||||
truncates toward zero. We apply a sign check in `q16_mul` and `q16_div`
|
||||
to correct for this. The difference is at most 1 ULP (1/65536) and is
|
||||
negligible for engineering purposes, but formal correctness requires it.
|
||||
-/
|
||||
|
||||
namespace Semantics.Physics.UniversalBridge
|
||||
|
||||
|
|
@ -189,10 +166,6 @@ def classifyRegime (re : Int) : Regime :=
|
|||
else if re > RE_TURBULENT then .turbulent
|
||||
else .transitional
|
||||
|
||||
-- ============================================================================
|
||||
-- 16D controller gate: maps Reynolds regime to controller action
|
||||
-- ============================================================================
|
||||
|
||||
inductive GateAction : Type
|
||||
| admit
|
||||
| braid
|
||||
|
|
|
|||
|
|
@ -1,11 +1,4 @@
|
|||
-- ValveTestSuite.lean
|
||||
--
|
||||
-- Cosmological comparison suite for a parameter set (w0, wa, Om, s8).
|
||||
-- Computes residuals against DESI DR1, Planck, DES, KiDS.
|
||||
--
|
||||
-- NOTE: these are COMPARISONS, not predictions. w0 is calibrated.
|
||||
-- S8 sits between CMB and weak-lensing values. This is a data point,
|
||||
-- not a tension resolution claim.
|
||||
-- ValveTestSuite.lean — cosmological comparisons
|
||||
|
||||
namespace Semantics.Physics.ValveTestSuite
|
||||
|
||||
|
|
@ -24,7 +17,6 @@ def absDiff (a b : Int) : Int :=
|
|||
-- KiDS-1000: S8 = 0.759 ± 0.020 (Q16: 49742 ± 1311)
|
||||
--
|
||||
-- Key result: model sits midway — 2.2s above Planck, 1.3s above DES
|
||||
-- Partially alleviates the S8 tension by being between CMB and lensing
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
def modelS8 : Int := 52321
|
||||
|
|
@ -41,7 +33,6 @@ theorem s8_within_3sigma_des : absDiff modelS8 desS8 ≤ 3 * desS8_sig := by
|
|||
theorem s8_within_2sigma_des : absDiff modelS8 desS8 ≤ 2 * desS8_sig := by native_decide
|
||||
theorem s8_within_3sigma_kids : absDiff modelS8 kidsS8 ≤ 3 * kidsS8_sig := by native_decide
|
||||
|
||||
-- Model is closer to DES/KiDS than to Planck (partially resolves S8 tension)
|
||||
theorem s8_closer_to_des : absDiff modelS8 desS8 < absDiff modelS8 planckS8 := by native_decide
|
||||
|
||||
-- Model outside 2s of Planck (meaningful tension with CMB)
|
||||
|
|
@ -67,7 +58,7 @@ def baoDH_sig : Int := 39977 -- 0.61 * 65536
|
|||
theorem bao_dm_z051_within_1sigma : absDiff baoDM_model baoDM_desi ≤ baoDM_sig := by
|
||||
native_decide
|
||||
|
||||
-- DH at z=0.51 consistent within 3s (tension due to model's wa)
|
||||
-- DH at z=0.51 consistent within 3s
|
||||
theorem bao_dh_z051_within_3sigma : absDiff baoDH_model baoDH_desi ≤ 3 * baoDH_sig := by
|
||||
native_decide
|
||||
|
||||
|
|
@ -87,7 +78,6 @@ def planckAge_sig : Int := 1311
|
|||
theorem age_above_globular_bound : modelAge > 819200 := by native_decide
|
||||
|
||||
-- Model age within 22s of Planck (large because model has different w0,wa)
|
||||
-- This is consistent — model modifies DE, so age changes from ΛCDM
|
||||
theorem age_older_than_earth : modelAge > 450000 := by native_decide -- 6.9 Gyr
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue