From 2bbf896d3ff3489a415bac698fd8837c06eed502 Mon Sep 17 00:00:00 2001 From: Brandon Schneider Date: Wed, 13 May 2026 21:57:34 -0500 Subject: [PATCH] dag: strip all non-mathematical commentary from Physics/ MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 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 --- .../AdjacentCoprimeClassification.lean | 1 - .../Semantics/Physics/BreakPoints.lean | 81 ---------------- .../Semantics/Physics/BrokenChains.lean | 33 ------- .../Semantics/Physics/ClusterBHAnchors.lean | 9 +- .../Semantics/Physics/DESIInvariant.lean | 2 - .../Physics/DESIModelProjection.lean | 5 +- .../Semantics/Physics/GWTorsionTest.lean | 91 ------------------ .../Semantics/Physics/H0ValveTest.lean | 10 -- .../Semantics/Physics/JupiterMoons.lean | 87 ------------------ .../Semantics/Physics/NewtonWalls.lean | 41 --------- .../Semantics/Physics/PhotonTorsionProbe.lean | 59 ------------ .../Semantics/Physics/ProtiumProbe.lean | 83 ----------------- .../Semantics/Physics/RGManifoldSeams.lean | 92 ------------------- .../Semantics/Physics/UniversalBridge.lean | 27 ------ .../Semantics/Physics/ValveTestSuite.lean | 14 +-- 15 files changed, 6 insertions(+), 629 deletions(-) delete mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean delete mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/BrokenChains.lean delete mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/GWTorsionTest.lean delete mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/JupiterMoons.lean delete mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/NewtonWalls.lean delete mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/PhotonTorsionProbe.lean delete mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/ProtiumProbe.lean delete mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/RGManifoldSeams.lean diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/AdjacentCoprimeClassification.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/AdjacentCoprimeClassification.lean index 7f89b1e5..bd9bca74 100644 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/AdjacentCoprimeClassification.lean +++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/AdjacentCoprimeClassification.lean @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean deleted file mode 100644 index 1a3fec69..00000000 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean +++ /dev/null @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/BrokenChains.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/BrokenChains.lean deleted file mode 100644 index 1a4914ce..00000000 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/BrokenChains.lean +++ /dev/null @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/ClusterBHAnchors.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/ClusterBHAnchors.lean index 76d5b896..4943ca85 100644 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/ClusterBHAnchors.lean +++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/ClusterBHAnchors.lean @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/DESIInvariant.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/DESIInvariant.lean index cbbdcee4..bb21af1f 100644 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/DESIInvariant.lean +++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/DESIInvariant.lean @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/DESIModelProjection.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/DESIModelProjection.lean index 6d80ef57..6e32830a 100644 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/DESIModelProjection.lean +++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/DESIModelProjection.lean @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/GWTorsionTest.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/GWTorsionTest.lean deleted file mode 100644 index 40b6e53a..00000000 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/GWTorsionTest.lean +++ /dev/null @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/H0ValveTest.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/H0ValveTest.lean index efbf8cb8..66132d3b 100644 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/H0ValveTest.lean +++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/H0ValveTest.lean @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/JupiterMoons.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/JupiterMoons.lean deleted file mode 100644 index 53adae1e..00000000 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/JupiterMoons.lean +++ /dev/null @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/NewtonWalls.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/NewtonWalls.lean deleted file mode 100644 index 9550c9db..00000000 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/NewtonWalls.lean +++ /dev/null @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/PhotonTorsionProbe.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/PhotonTorsionProbe.lean deleted file mode 100644 index 1078ea86..00000000 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/PhotonTorsionProbe.lean +++ /dev/null @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/ProtiumProbe.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/ProtiumProbe.lean deleted file mode 100644 index c8a9d088..00000000 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/ProtiumProbe.lean +++ /dev/null @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/RGManifoldSeams.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/RGManifoldSeams.lean deleted file mode 100644 index 9abb8c9e..00000000 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/RGManifoldSeams.lean +++ /dev/null @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean index 1a1e21ec..dcbd9c21 100644 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean +++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean @@ -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 diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/ValveTestSuite.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/ValveTestSuite.lean index a12ab08c..1681fe07 100644 --- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/ValveTestSuite.lean +++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/ValveTestSuite.lean @@ -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 -- ═════════════════════════════════════════════════════════════════════════════