mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
chore: rip ornamental modules, revise overclaimed language
DELETED (ornamental/numerology):
HiggsCalibration.lean — n=128 from (20/27)^128=v/M_Pl was coincidence
CrossScaleTest.lean — human-scale void fraction had no physical meaning
CalibrationImplications.lean — dA/dt=0.007 had no derivation from SM
REVISED (overclaimed → honest):
DESIModelProjection.lean — w0 is CALIBRATED to DESI DR1, not predicted.
Stripped horn-fiber/eigenwall language.
ValveTestSuite.lean — S8 is a comparison, not a tension resolution.
KEPT (sound):
UniversalBridge.lean, DESIInvariant.lean, H0ValveTest.lean,
AdjacentCoprimeClassification.lean, RGManifoldSeams.lean
Build: 3529 jobs, zero errors
This commit is contained in:
Brandon Schneider
parent
8145aff0fe
commit
154e0efb47
5 changed files with 20 additions and 486 deletions
|
|
@ -1,119 +0,0 @@
|
|||
-- CalibrationImplications.lean
|
||||
--
|
||||
-- What the Higgs/DESI calibration implies for the two core applications:
|
||||
-- 1. COMPRESSION: maximum achievable compression ratio from Menger voids
|
||||
-- 2. NAVIER-STOKES: Reynolds regime transition rate from boundary growth
|
||||
--
|
||||
-- Key result: Menger compression ALWAYS outpaces Koch boundary roughening
|
||||
-- per iteration. Net ratio: (27/20) / (4/3) = 1.0125 > 1.
|
||||
|
||||
namespace Semantics.Physics.CalibrationImplications
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §0 Calibrated constants
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Menger void fraction per iteration: 20/27 = 0.7407
|
||||
-- (20 of 27 subcubes survive each iteration)
|
||||
def mengerFrac : Int := 48549
|
||||
|
||||
-- Koch boundary growth per iteration: 4/3 = 1.3333
|
||||
-- (each boundary segment becomes 4 shorter segments)
|
||||
def kochFrac : Int := 87381
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §1 Compression ratios
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Compression ratio per Menger iteration: (27/20) = 1.35x
|
||||
-- Q16_16: 1.35 * 65536 = 88474
|
||||
def compPerIter : Int := 88474
|
||||
|
||||
-- Compression ratio after n iterations: (27/20)^n
|
||||
-- For n=3 (observable cosmic void iterations):
|
||||
-- (27/20)^3 = 1.35^3 = 2.46x
|
||||
-- Q16_16: 2.46 * 65536 = 161218
|
||||
def compN3 : Int := 161218
|
||||
|
||||
-- For n=4 (codebase-memory at N=64):
|
||||
-- (27/20)^4 = 3.32x
|
||||
-- Q16_16: 3.32 * 65536 = 217579
|
||||
def compN4 : Int := 217579
|
||||
|
||||
-- For n=6 (human scale 1m at 1mm):
|
||||
-- (27/20)^6 = 6.05x
|
||||
-- Q16_16: 6.05 * 65536 = 396493
|
||||
def compN6 : Int := 396493
|
||||
|
||||
-- Compression exceeds the benchmark zlib/gzip ratio (~3x) at n=4
|
||||
theorem comp_n4_exceeds_gzip : compN4 > 3 * SCALE := by native_decide
|
||||
|
||||
-- Compression improves with each iteration
|
||||
theorem compression_monotonic : compN3 < compN4 ∧ compN4 < compN6 := by native_decide
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §2 Navier-Stokes regime transition
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Boundary growth coefficient: alpha = ln(4)/ln(3) * (4/3 - 1) = 0.00694
|
||||
-- From Koch dimension D_K = 1.2619. Normalized: ~0.007.
|
||||
-- Q16_16: 0.007 * 65536 = 459
|
||||
def boundaryGrowth : Int := 459
|
||||
|
||||
-- Torsion coupling coefficient: beta = lambda/32 = 0.129/32 = 0.00403
|
||||
-- From Higgs self-coupling calibrated at CERN. Normalized: ~0.003.
|
||||
-- Q16_16: 0.003 * 65536 = 197
|
||||
def torsionCoupl : Int := 197
|
||||
|
||||
-- Boundary growth at turbulent midpoint (Re=4000, A=1):
|
||||
-- dA/dt = boundaryGrowth + torsionCoupl * ||tau||^2
|
||||
-- The growth is always positive at turbulent Re
|
||||
theorem turbulent_growth_positive : boundaryGrowth + torsionCoupl > 0 := by
|
||||
native_decide
|
||||
|
||||
-- Laminar regime (Re < 2300, A=0): no growth
|
||||
def laminarGrowth : Int := 0
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §3 Compression-boundary tradeoff (key result)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Menger compression per iteration: (27/20) = 1.35
|
||||
-- Koch boundary growth per iteration: (4/3) = 1.333
|
||||
-- Net per iteration: (27/20) / (4/3) = 1.0125 > 1
|
||||
-- Q16_16: 1.0125 * 65536 = 66355
|
||||
def netPerIter : Int := 66355
|
||||
|
||||
-- Net > 1 means compression always outpaces boundary roughening
|
||||
theorem net_exceeds_one : netPerIter > SCALE := by
|
||||
native_decide
|
||||
|
||||
-- Boundary complexity grows slower than volume compresses
|
||||
-- This is guaranteed by the fractal dimensions:
|
||||
-- d_H = ln(20)/ln(3) = 2.727 (Menger)
|
||||
-- D_K = ln(4)/ln(3) = 1.262 (Koch)
|
||||
-- d_H - D_K = 1.465 > 0, so compression always wins
|
||||
-- The cumulative advantage grows with each iteration:
|
||||
-- Net after n iterations: (1.0125)^n
|
||||
theorem cumulative_net_advantage_grows : netPerIter * netPerIter > netPerIter := by
|
||||
native_decide -- compound compression outpaces single-iteration growth
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §4 Executable receipts
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Compression ratios
|
||||
#eval compPerIter -- 1.35x per iteration
|
||||
#eval compN4 -- 3.32x at n=4 (codebase-memory N=64)
|
||||
#eval compN6 -- 6.05x at n=6
|
||||
|
||||
-- Navier-Stokes coefficients
|
||||
#eval boundaryGrowth -- 0.007
|
||||
#eval torsionCoupl -- 0.003
|
||||
|
||||
-- Tradeoff
|
||||
#eval netPerIter -- 1.0125x net (compression > boundary)
|
||||
|
||||
end Semantics.Physics.CalibrationImplications
|
||||
|
|
@ -1,156 +0,0 @@
|
|||
-- CrossScaleTest.lean
|
||||
--
|
||||
-- Tests the 16D Menger/Koch model across three vastly different scales:
|
||||
-- CERN (Higgs/Planck): 10^19 GeV — 6-sigma precision
|
||||
-- DESI (cosmic web): 10^2 Mpc — 2-3 sigma precision
|
||||
-- Human (materials): 1 m at 1 mm — everyday scale
|
||||
--
|
||||
-- If the model is correct, the same void hierarchy geometry applies
|
||||
-- at every scale. The number of Menger iterations changes with the
|
||||
-- scale ratio, but the fractal dimension d_H = ln(20)/ln(3) is fixed.
|
||||
|
||||
namespace Semantics.Physics.CrossScaleTest
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §0 Scale-invariant geometry (from Menger/Koch, not fitted)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Menger sponge: d_H = ln(20)/ln(3) = 2.7268
|
||||
-- Q16_16: 2.7268 * 65536 = 178696
|
||||
def mengerDim : Int := 178696
|
||||
|
||||
-- Koch curve: D_K = ln(4)/ln(3) = 1.2619
|
||||
-- Q16_16: 1.2619 * 65536 = 82706
|
||||
def kochDim : Int := 82706
|
||||
|
||||
-- Void fraction per iteration: 20/27 = 0.7407
|
||||
-- Q16_16: 0.7407 * 65536 = 48549
|
||||
def voidFrac : Int := 48549
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §1 Scale 1: CERN (Higgs VEV / Planck mass)
|
||||
-- Ratio = 246.22 GeV / 1.22e19 GeV = 2.02e-17
|
||||
-- Menger iterations: n = ln(2.02e-17) / ln(20/27) = 128.1 -> 128
|
||||
-- (20/27)^128 = 2.08e-17 (2.95% error from v/M_Pl)
|
||||
-- This is the FUNDAMENTAL constraint: Higgs/Planck ratio determines
|
||||
-- the deep void count with sub-percent precision from CERN.
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Higgs VEV v = 246.22 GeV (CERN, 6+ sigma)
|
||||
def higgsVEV : Int := 24622
|
||||
|
||||
-- Planck mass M_Pl = 1.22e19 GeV
|
||||
def planckMass : Int := 12209
|
||||
|
||||
-- Menger iterations from Higgs/Planck: n = 128
|
||||
def n_cern : Int := 128
|
||||
|
||||
-- Predicted (20/27)^128 in Q16_16: would be ~0 (too small)
|
||||
-- The key theorem: the void hierarchy naturally produces the observed
|
||||
-- ratio between the electroweak and Planck scales.
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §2 Scale 2: DESI (cosmic web BAO scale / Menger cell)
|
||||
-- BAO scale r_d = 147 Mpc, Menger cell at N=64: ~2.3 Mpc
|
||||
-- Scale ratio: 147 / 2.3 = 63.9
|
||||
-- Number of 3-merations: log_3(63.9) = 3.8 -> 4
|
||||
-- After 4 iterations: void fraction = 1 - (20/27)^4 = 1 - 0.301 = 0.699
|
||||
-- Observed cosmic void fraction at z=0: 60-80%
|
||||
-- → Model predicts 70% void fraction, consistent with DESI
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- BAO sound horizon: 147 Mpc (raw Int)
|
||||
def baoScale : Int := 147
|
||||
|
||||
-- Menger cell size at N=64: 2.3 Mpc (×10: 23)
|
||||
def cellSize : Int := 23
|
||||
|
||||
-- Menger iterations at DESI scale: n = 4
|
||||
def n_cosmic : Int := 4
|
||||
|
||||
-- Void fraction after 4 iterations: 1 - (20/27)^4 = 1 - 0.301 = 0.699
|
||||
-- Q16_16: 0.699 * 65536 = 45810
|
||||
def voidFrac4 : Int := 45810
|
||||
|
||||
-- Predicted void fraction is between 0.60 and 0.80 (DESI void catalogues)
|
||||
theorem void_fraction_consistent : voidFrac4 > 39322 ∧ voidFrac4 < 52429 := by
|
||||
native_decide -- 0.60*65536=39322, 0.80*65536=52429
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §3 Scale 3: Human (1 m object at 1 mm resolution)
|
||||
-- Scale ratio: 1000
|
||||
-- Menger iterations: log_3(1000) = 6.3 -> 6
|
||||
-- After 6 iterations: void fraction = 1 - (20/27)^6 = 1 - 0.165 = 0.835
|
||||
-- The void fraction at human scale is an abstract metric — it doesn't
|
||||
-- correspond to physical voids in solid objects.
|
||||
-- But the GEOMETRY is the same: the Menger void hierarchy applies
|
||||
-- identically. The interpretation changes with the medium.
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Scale ratio: 1000
|
||||
def humanScaleRatio : Int := 1000
|
||||
|
||||
-- Menger iterations: 6
|
||||
def n_human : Int := 6
|
||||
|
||||
-- Void fraction: 1 - (20/27)^6 = 0.835
|
||||
-- Q16_16: 0.835 * 65536 = 54723
|
||||
def voidFracHuman : Int := 54723
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §4 Scale consistency claim
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- The model uses the SAME mengerDim and voidFrac at ALL scales.
|
||||
-- Only n (the number of iterations) changes with the scale ratio.
|
||||
--
|
||||
-- The Higgs/Planck ratio gives n = 128 iterations for the COSMOLOGICAL
|
||||
-- CONSTANT suppression. The BAO scale gives n = 4 iterations for the
|
||||
-- OBSERVABLE cosmic void fraction. These are consistent:
|
||||
-- n_CC + n_obs = 128 + 4 = 132 ≈ total e-folds from Planck to observable scale
|
||||
--
|
||||
-- Total e-folds from Planck to today: N_total = ln(a_today/a_Planck) ≈ 138
|
||||
-- n_CC + n_obs = 132 matches N_total ≈ 138 within ~4%
|
||||
-- This is additional cross-scale consistency: the sum of void iterations
|
||||
-- across all scales equals the total expansion e-folds.
|
||||
|
||||
-- Total expansion e-folds: 138
|
||||
def totalEfolds : Int := 138
|
||||
|
||||
-- Sum of void iterations: n_CC + n_obs = 132
|
||||
def voidIterationsTotal : Int := 132
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §5 Menger geometry is scale-invariant (the fundamental theorem)
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Menger dimension is strictly between 2 and 3 (fractal, not solid)
|
||||
theorem menger_is_fractal : 2 * SCALE < mengerDim ∧ mengerDim < 3 * SCALE := by
|
||||
native_decide
|
||||
|
||||
-- Koch dimension is strictly between 1 and 2 (boundary is fractal)
|
||||
theorem koch_is_boundary_fractal : SCALE < kochDim ∧ kochDim < 2 * SCALE := by
|
||||
native_decide
|
||||
|
||||
-- Menger dimension exceeds Koch (volume hierarchy dominates boundary roughness)
|
||||
theorem menger_exceeds_koch : kochDim < mengerDim := by
|
||||
native_decide
|
||||
|
||||
-- Void fraction per iteration is less than 1 (suppression is real)
|
||||
theorem void_fraction_suppresses : voidFrac < SCALE := by
|
||||
native_decide
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §6 Executable receipts
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
#eval mengerDim
|
||||
#eval kochDim
|
||||
#eval voidFrac
|
||||
#eval n_cern
|
||||
#eval n_cosmic
|
||||
#eval voidFrac4
|
||||
|
||||
end Semantics.Physics.CrossScaleTest
|
||||
|
|
@ -1,27 +1,14 @@
|
|||
/-
|
||||
DESIModelProjection.lean — 16D Horn-Fiber Projection onto DESI Observables
|
||||
DESIModelProjection.lean — Model Projection onto DESI Observables
|
||||
|
||||
Projects the 16D Menger/Koch/Gabriel-Horn fiber model onto the DESI
|
||||
observational invariant set. Computes residuals and declares which
|
||||
predictions are within tolerance and which are not.
|
||||
Projects a cosmological parameter set (w0, wa, Om, s8) onto the DESI
|
||||
observational invariant set. Computes residuals against DESI DR1/DR2.
|
||||
|
||||
NOTE: w0 is CALIBRATED to DESI DR1, not predicted.
|
||||
wa, Om, s8 are structural projections that happen to be
|
||||
consistent with DESI within 1s.
|
||||
|
||||
Zero Float arithmetic. All values are hardcoded Q16_16 Int literals.
|
||||
|
||||
Model components:
|
||||
1. Menger/Koch divergence ratio: D_MK(n) ~ (9/5)^n → predicts w₀ > -1
|
||||
2. Gabriel horn torsion widening: dA/dt > 0 while dV/dt ≈ 0 → predicts w_a < 0
|
||||
3. Fractal void hierarchy: d_H = ln(20)/ln(3) → predicts Ω_m effective reduction
|
||||
|
||||
Each projection:
|
||||
model_prediction → compare with DESI observation → residual → verdict
|
||||
|
||||
Conventions:
|
||||
PascalCase types, camelCase functions.
|
||||
Q16_16 for dimensionless; raw Int × 100 for dimensional.
|
||||
structure for domain concepts.
|
||||
theorem for residual bounds.
|
||||
#eval! for executable receipts.
|
||||
Namespace: Semantics.Physics.DESIModelProjection
|
||||
-/
|
||||
|
||||
import Semantics.FixedPoint
|
||||
|
|
@ -78,9 +65,8 @@ def torsionCoupling : Int := 197
|
|||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
||||
/--
|
||||
Prediction 1: w₀ > -1 (dark energy not cosmological constant).
|
||||
Menger/Koch divergence D_MK ~ (9/5)^n produces residual boundary pressure.
|
||||
Model calibrated to DESI DR1 w₀ = -0.827.
|
||||
Prediction 1: w₀ > -1 is an observational fact (DESI DR1/DR2).
|
||||
Model w₀ is CALIBRATED to DESI DR1 w₀ = -0.827.
|
||||
Q16_16: -0.827 × 65536 = -54198.
|
||||
-/
|
||||
def predictW0 : Int := -54198
|
||||
|
|
@ -89,14 +75,9 @@ def predictW0 : Int := -54198
|
|||
def predictW0_sigma : Int := 3277
|
||||
|
||||
/--
|
||||
Prediction 2: w_a < 0 (dark energy was stronger in the past).
|
||||
Gabriel horn torsion: dA_boundary/dt = α·A + β·‖τ‖².
|
||||
At higher z, more compact → larger ‖τ‖² → more negative w_a.
|
||||
Model predicts w_a ≈ -0.55.
|
||||
|
||||
Check: -0.55 × 65536 = -36044.8 ≈ -36045.
|
||||
DESI DR1: -0.75. Residual: 0.20 (within 1σ).
|
||||
DESI DR2: -0.59. Residual: 0.04 (within 1σ).
|
||||
Prediction 2: w_a < 0 is an observational fact (DESI DR1/DR2).
|
||||
Model w_a = -0.55 is consistent with DESI DR2 w_a = -0.59 +- 0.25
|
||||
at 0.16 sigma.
|
||||
-/
|
||||
def predictWa : Int := -36045
|
||||
|
||||
|
|
@ -104,12 +85,10 @@ def predictWa : Int := -36045
|
|||
def predictWa_sigma : Int := 9830
|
||||
|
||||
/--
|
||||
Prediction 3: Ω_m effective from Menger void correction.
|
||||
ΛCDM Ω_m ≈ 0.31, Menger (20/27)^3 × 0.31 ≈ 0.13 (too low).
|
||||
Real cosmic void fraction ~10% correction: Ω_m ≈ 0.29.
|
||||
Q16_16: 0.290 × 65536 = 19005.
|
||||
Prediction 3: Ω_m = 0.290 from Menger void correction.
|
||||
ΛCDM Ω_m ≈ 0.31. Menger (20/27)^3 × 0.31 ≈ 0.13 (over-correction).
|
||||
Real cosmic void fraction ~10%: Ω_m ≈ 0.29.
|
||||
DESI DR1: 0.295. Residual: -0.005 (within 1σ).
|
||||
DESI DR2: 0.2975. Residual: -0.0075 (within 1σ).
|
||||
-/
|
||||
def predictOmegaM : Int := 19005
|
||||
|
||||
|
|
|
|||
|
|
@ -1,168 +0,0 @@
|
|||
-- HiggsCalibration.lean
|
||||
--
|
||||
-- Calibrates the 16D Menger/Koch void hierarchy against the Higgs boson
|
||||
-- parameters (PDG 2024: v = 246.22 GeV, m_H = 125.11 GeV).
|
||||
--
|
||||
-- Calibration principle:
|
||||
-- The Higgs VEV sets the electroweak scale. The ratio v/M_Pl determines
|
||||
-- the number of Menger void iterations needed to suppress the Higgs
|
||||
-- vacuum energy to the observed dark-energy level.
|
||||
--
|
||||
-- Menger void fraction per iteration: f = 20/27 (20 of 27 subcubes survive)
|
||||
-- Suppression after n iterations: f^n = (20/27)^n
|
||||
--
|
||||
-- Target: (20/27)^n = v/M_Pl = 246.22 / 1.22e19 = 2.02e-17
|
||||
-- n = ln(v/M_Pl) / ln(20/27) = ln(2.02e-17) / ln(0.7407)
|
||||
-- = (-38.4) / (-0.300) = 128.1
|
||||
--
|
||||
-- Void iterations n = 128 directly from Higgs VEV and Planck scale.
|
||||
-- No free parameters. This is the calibration.
|
||||
|
||||
namespace Semantics.Physics.HiggsCalibration
|
||||
|
||||
def SCALE : Int := 65536
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §0 Higgs scale invariants
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Higgs VEV v = 246.22 GeV (×100: 24622)
|
||||
def hVEV : Int := 24622
|
||||
|
||||
-- Planck mass M_Pl = 1.220910e19 GeV
|
||||
-- Stored as 1.2209 × 10^19 (×10^15 to fit in Int: 12209)
|
||||
def planckMass : Int := 12209
|
||||
|
||||
-- CERN PDG 2024 precision measurements (> 6 sigma):
|
||||
-- Top mass: m_t = 172.76 +- 0.30 GeV
|
||||
-- Higgs mass: m_H = 125.11 +- 0.11 GeV
|
||||
-- W mass: m_W = 80.377 +- 0.012 GeV
|
||||
-- Z mass: m_Z = 91.1876 +- 0.0021 GeV
|
||||
-- Derived from CERN data:
|
||||
-- lambda = m_H^2 / (2*v^2) = 0.129095 (Q16: 8460)
|
||||
-- y_t = sqrt(2)*m_t / v = 0.9923 (Q16: 65030)
|
||||
-- Top-driven running: d(lambda)/d(ln mu) = -6*y_t^4/(16*pi^2) = -0.0369 (Q16: -2418)
|
||||
|
||||
-- Top Yukawa from CERN m_t = 172.76 GeV
|
||||
def topYukawa : Int := 65030
|
||||
|
||||
-- One-loop Higgs running coefficient (dominated by top)
|
||||
def lambdaRunning : Int := -2418
|
||||
|
||||
-- Ratio v/M_Pl = 246.22 / 1.2209e19 = 2.017e-17
|
||||
-- This is the natural suppression factor for the cosmological constant.
|
||||
-- Q16.16: 2.017e-17 × 65536 ≈ 0 (too small for Q16.16)
|
||||
-- The ratio is stored as raw integer: 2017 (×10^20)
|
||||
def vevPlanckRatio : Int := 2017
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §1 Calibration: void iterations from Higgs/Planck ratio
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Menger void fraction per iteration: 20/27 = 0.7407
|
||||
-- Q16.16: 0.7407 × 65536 = 48549
|
||||
def mengerFraction : Int := 48549
|
||||
|
||||
-- ln(20/27) = ln(0.7407) = -0.300
|
||||
-- Q16.16: -0.300 × 65536 = -19661
|
||||
-- Store as absolute value for division: 0.300 × 65536 = 19661
|
||||
def lnFraction : Int := 19661
|
||||
|
||||
-- ln(v/M_Pl) = ln(2.017e-17) = -38.42
|
||||
-- Stored as ×1000: -38420 (too large for Q16)
|
||||
-- Raw Int: -38
|
||||
def lnRatio : Int := -38
|
||||
|
||||
-- Menger void iterations n = ln(v/M_Pl) / ln(20/27) = 38.42 / 0.300 = 128.1
|
||||
-- This is the FUNDAMENTAL calibration: Higgs/Planck ratio → void count.
|
||||
-- n = 128 iterations directly from known particle physics constants.
|
||||
def voidIterations : Int := 128
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §2 Derived cosmological predictions
|
||||
--
|
||||
-- These come from the Menger void iteration count n = 128:
|
||||
--
|
||||
-- Omega_m = 0.31 * (20/27)^(128/3) * correction
|
||||
-- = 0.31 * (5.8e-17)^(1/3)
|
||||
-- = 0.31 * 0.00000387 ← too small, need 0.29
|
||||
--
|
||||
-- The issue: the void iterations that suppress vacuum energy (n = 128)
|
||||
-- are NOT the same as the observable void iterations (n = 2-3 at cosmic scales).
|
||||
-- The Higgs-to-Planck ratio gives the DEEP void count, but only the
|
||||
-- TOP FEW iterations are cosmologically observable.
|
||||
--
|
||||
-- Observable void iterations ≈ 2-3 (from BAO scale / Menger cell size)
|
||||
-- n_obs = ln(BAO_scale / Menger_cell) / ln(3)
|
||||
-- = ln(147 Mpc / 2.3 Mpc) / ln(3)
|
||||
-- = 4.15 / 1.10 = 3.8
|
||||
-- So ~4 iterations are observable at DESI scales.
|
||||
--
|
||||
-- The Higgs-Planck ratio predicts DEEP iterations (n = 128), not
|
||||
-- observable ones (n_obs ≈ 4). This is consistent — the vacuum
|
||||
-- energy suppression happens at all scales, but only the top
|
||||
-- few iterations affect the cosmic web structure.
|
||||
--
|
||||
-- The observable predictions:
|
||||
-- Omega_m ≈ 0.31 - 0.31 * (1 - (20/27)^n_obs) * void_fraction
|
||||
-- ≈ 0.31 - 0.31 * (1 - (20/27)^4) * 0.2
|
||||
-- ≈ 0.31 - 0.31 * 0.699 * 0.2
|
||||
-- ≈ 0.31 - 0.043 = 0.267 (too low)
|
||||
--
|
||||
-- Calibrated using BAO scale → n_obs ≈ 3:
|
||||
-- Omega_m ≈ 0.31 - 0.31 * (1 - (20/27)^3) * 0.2
|
||||
-- ≈ 0.31 - 0.31 * 0.594 * 0.2
|
||||
-- ≈ 0.31 - 0.037 = 0.273 (still too low)
|
||||
--
|
||||
-- The void fraction per iteration needs calibration.
|
||||
-- Observed cosmic void fraction ≈ 12% at z=0 (from DESI void catalogues).
|
||||
-- This gives:
|
||||
-- Omega_m ≈ 0.31 - 0.31 * (1 - (20/27)^3) * 0.12
|
||||
-- ≈ 0.31 - 0.31 * 0.594 * 0.12
|
||||
-- ≈ 0.31 - 0.022 = 0.288
|
||||
-- This matches the model's Omega_m = 0.290.
|
||||
--
|
||||
-- So 3 observable void iterations at 12% void fraction gives Omega_m = 0.290.
|
||||
-- The DEEP void iterations (n = 128 from Higgs) are at energies > GeV,
|
||||
-- where quantum gravity resolves the void structure differently.
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Observable void iterations (from BAO scale / cell size matching)
|
||||
def obsVoidIterations : Int := 3
|
||||
|
||||
-- Void fraction per iteration (from DESI void catalogues: ~12%)
|
||||
def voidFraction : Int := 7864 -- Q16.16: 0.12 × 65536
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §3 Higgs-calibrated theorems
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Higgs VEV is positive (fundamental truth)
|
||||
theorem higgs_vev_positive : hVEV > 0 := by native_decide
|
||||
|
||||
-- Planck mass is much larger than Higgs VEV (> 10^16 times)
|
||||
theorem planck_above_higgs : planckMass > 1000 := by native_decide
|
||||
|
||||
-- Void iterations from Higgs/Planck ratio is positive
|
||||
theorem void_iterations_positive : voidIterations > 0 := by native_decide
|
||||
|
||||
-- Observable void iterations is much less than total
|
||||
theorem obs_less_than_total : obsVoidIterations < voidIterations := by native_decide
|
||||
|
||||
-- The deep void iterations (128) suppress vacuum energy by (20/27)^128
|
||||
-- This factor matches the observed dark energy / Higgs vacuum ratio
|
||||
-- Not directly provable in Lean without big-integer arithmetic for (20/27)^128
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- §4 Executable receipts
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- CERN precision
|
||||
#eval hLambda -- Higgs self-coupling from 1137s measurement
|
||||
#eval topYukawa -- Top Yukawa from 576s measurement
|
||||
#eval lambdaRunning -- One-loop running from CERN masses
|
||||
#eval hVEV
|
||||
#eval voidIterations
|
||||
#eval obsVoidIterations
|
||||
|
||||
end Semantics.Physics.HiggsCalibration
|
||||
|
|
@ -1,13 +1,11 @@
|
|||
-- ValveTestSuite.lean
|
||||
--
|
||||
-- Multi-valve cosmological test suite for the 16D horn-fiber model.
|
||||
-- Cosmological comparison suite for a parameter set (w0, wa, Om, s8).
|
||||
-- Computes residuals against DESI DR1, Planck, DES, KiDS.
|
||||
--
|
||||
-- Valves tested:
|
||||
-- 1. S8 tension (matter fluctuation amplitude)
|
||||
-- 2. BAO distance-redshift consistency (DESI DR1)
|
||||
-- 3. Cosmic age vs known bounds
|
||||
--
|
||||
-- All model predictions from: w0 = -0.827, wa = -0.55, Om = 0.290, s8 = 0.812
|
||||
-- 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.
|
||||
|
||||
namespace Semantics.Physics.ValveTestSuite
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue