#!/usr/bin/env python3 # -*- coding: utf-8 -*- r""" uv1_frozen_functional.py ======================== UV-1 -- FREEZE THE UV FUNCTIONAL (CFCA Stage 1 + Stage 3 setup). PURPOSE (target-blind, BEFORE any boundedness/stability test): Define and FREEZE -- exactly, and in a way that cannot be reverse-fit from the desired STANDS outcome -- the single UV object whose sigma -> -inf (internal- collapse) behavior the SUBSEQUENT pass will test. This script writes nothing about whether the object is bounded; it ONLY pins down WHAT is tested, WITH WHAT prescription, and WHAT it computes, so the later stability test rides on a frozen definition rather than a tunable one. This is the CFCA "freeze certificate" (METHOD_CFCA_June_14.md Stage 5 / R0): core / auxiliary / normalization / approximation / comparison-scale / data-source are all fixed and hashed BEFORE any measured number or any committed magnitude is read. ================================================================================ WHAT IS FROZEN (the four freezes; each is target-blind by construction) ================================================================================ FREEZE 1 -- THE OPERATOR. D_sigma = the corpus's OWN spin-c Dirac-type operator of the spectral triple over M4 x K6 x S^2 x S^1_Y/Z2, the SAME D whose Borel-Weil-Bott / spin-c index = -3 already generates the three-family matter tower (Fable_GUT(3).md 2557-2558, 2581-2586, 7600-7601; active line bundle R1.4 hash 0fd19c9ae0c1). The fluctuation complex C_sigma is the full gauge-fixed BV/BRST tower sitting inside D_sigma^2: metric (graviton), gauge connection (inner fluctuation of D), scalar/Higgs (inner fluctuation of the finite Dirac), chiral fermion (the spin-c sections themselves), Faddeev- Popov ghosts (the Z2 BRST grading P_BRST), the projected sector, and the Weyl-rigid Cartan slice. NO scalar-only / bosonic-only reduction: Guard (1). FREEZE 2 -- THE FUNCTIONAL. The object tested is the Chamseddine-Connes SPECTRAL ACTION S_sigma[f] = Str f( D_sigma^2 / Lambda^2 ) -- a SINGLE positive functional over the WHOLE graded tower at once. It is explicitly NOT the resummed determinant (1/2)Str log D_sigma^2 (candidate (B)): the two prior runs proved B is exactly where the scheme/finite-part ambiguity lives (zeta pole at s=-1/2, residue survives, Str[1]=n_B-n_F=-55 != 0). The spectral action has NO subtraction, so it cannot re-open the int_loop convention fight. Guards (2),(8). FREEZE 3 -- THE PRESCRIPTION (cutoff-profile CLASS, not a single profile). f is frozen as a CLASS: any admissible cutoff profile -- positive (f >= 0), even, sufficiently decaying, with positive moments f_0, f_2, f_4 > 0. The theorem to be proved downstream MUST hold for ALL admissible f (quantified over the whole class), so NO single f can be tuned to a desired outcome. This is the structural reason the freeze is outcome-blind. Guard (2),(3). FREEZE 4 -- THE BOUNDARY COMPANION (phase-exit / minimum-length). Paired freeze, candidate (C): as Vol(K6) -> 0 the heat/curvature expansion of S_sigma stops converging (gap04_higher_operator_wall.py: curvature reaches the cutoff; a6 >~ a4 >~ c_loop). The companion freeze is the EFT-validity boundary sigma_* at which the asymptotic reading of S_sigma ceases, beyond which the description is declared non-geometric / phase-exiting. (A) owns the bounded interior; (C) owns the boundary. Guard (5). ================================================================================ WHAT IS *NOT* FROZEN HERE (deliberately deferred to the stability pass) ================================================================================ * Whether S_sigma is bounded-below or phase-exits as sigma -> -inf. NOT decided here. Both STANDS and RUNAWAY remain live (Guard (3),(5)). * The sign/branch of int_loop. The spectral action never forms log-det, so no branch sign is taken. The committed c_loop = 1.3637877e-5 is NEVER read and enters NO decision (Guard (2)). * The positivity of the UV spectral measure as a *derived* fact. If the UV completion does not in fact carry a positive spectral measure, "Str f >= 0" is itself a NAMED UV-completion AXIOM (B-UQFC-14-UV-1), declared, not disguised as derived (Guard (7)). This script NAMES it; it does not prove it. ================================================================================ HARD GUARDS (any = FAIL) -- re-stated and enforced as attests in the output ================================================================================ (1) FULL gauge-fixed physical tower (metric/gauge/scalar/fermion/ghost/projected/ Weyl-rigid) -- NOT scalar-only or bosonic-only. (2) NO target-loading: sign/branch not chosen from STANDS; committed c_loop=1.3637877e-5 enters NO sign decision and is never read. (3) NO anthropic "we exist". (4) Finite-order a4/a6/a8 appear ONLY as consistency checks, NEVER as the proof (Lemma 1 banked: along sigma->-inf no finite heat-kernel/FRG truncation is licensed to decide global stability). (5) Boundedness OR phase-exit must be PROVEN before collapse -- here we FREEZE the paired (A)+(C) object that the proof will use; we do NOT yet claim it. (6) Lambda scope preserved -- same hardness class, NOT the same solved problem. (7) If not proven, NAME the result a UV-completion AXIOM, never disguised as derived. (8) NO "leans/leaning runaway" language. NON-PROMOTION: no gate flip; no status word emitted for any gate. This file FREEZES a definition; it asserts no stability verdict. exit 0 on a clean freeze; exit 2 if a corpus authority is unreadable or a forbidden token leaks. """ import hashlib import json import math import os import sys from collections import defaultdict from fractions import Fraction import numpy as np # --------------------------------------------------------------------------- # CORPUS AUTHORITIES (read for provenance + the forbidden-token firewall). The # committed c_loop magnitude file is DELIBERATELY NOT in this list and is NEVER # opened (Guard (2)). # --------------------------------------------------------------------------- FA = (r"" r"physics_Journal_and_patents/Final_physics_articles") QUANTUM_MD = os.path.join(FA, "Fable_Quantum.md") # nine-row field ledger GUT_MD = os.path.join(FA, "Fable_GUT (3).md") # spin-c Dirac, index -3 GILKEY_SRC = os.path.join( FA, "scripts", "gap_04", "src", "gilkey_a4_cross_terms.py") # a4 density + sign SELECTOR_DIR = os.path.join(FA, "scripts", "parent_selector_14d") SELECTOR_GEOM = os.path.join(SELECTOR_DIR, "14D_PARENT_SELECTOR_GEOMETRY.md") SELECTOR_DET = os.path.join(SELECTOR_DIR, "SELECTOR_DETERMINANT_CHANNEL_AUDIT.md") # Prior frozen runs this freeze BUILDS ON (read for provenance only). HERE = os.path.dirname(os.path.abspath(__file__)) PRIOR_SUPERTRACE = os.path.join(HERE, "gap04_full_supertrace_residue.py") PRIOR_ZETA = os.path.join(HERE, "gap04_zeta_continuation_frg2.py") PRIOR_WALL = os.path.join(HERE, "gap04_higher_operator_wall.py") FORBIDDEN_VALUE_TOKENS = [ "A_s=", "A_s =", "eta_B=", "eta_B =", "Lambda_obs=", "Lambda_obs =", "r_obs=", "r_obs =", "n_s_obs=", "N_eff_obs=", "Omega_DM_obs=", "H_0_obs=", "S_8_obs=", ] # The committed FRG-2 c_loop magnitude is named ONLY so we can ATTEST it is never # used in any sign/branch decision in this freeze. It is NOT read from disk. C_LOOP_COMMITTED_NEVER_USED = 1.3637877214788921e-05 # Frozen geometry (Einstein constants of the compactification; data-blind). # K6 = SU(3)/T^2 (dim 6, Lambda=+5): R=30; S^2 (round, Lambda=+1): R=2; S^1_Y flat. GEOM = { "K6": {"name": "SU(3)/T^2", "n": 6, "lam": 5, "R": 30, "Ric2": 150, "Riem2": 60}, "S2": {"name": "round S^2", "n": 2, "lam": 1, "R": 2, "Ric2": 2, "Riem2": 4}, "S1Y": {"name": "S^1_Y/Z2", "n": 1, "lam": 0, "R": 0, "Ric2": 0, "Riem2": 0}, } SPIN_C_INDEX = -3 # banked topological integer (Fable_GUT C2/E) ACTIVE_BUNDLE_HASH = "0fd19c9ae0c1" # R1.4 active line bundle (Fable_GUT 7600-7601) def sha256_file(path): h = hashlib.sha256() with open(path, "rb") as fh: for chunk in iter(lambda: fh.read(65536), b""): h.update(chunk) return h.hexdigest() # =========================================================================== # PART A. FREEZE 1 -- the operator D_sigma and its fluctuation complex C_sigma. # The nine-row physical tower, each row mapped to its PIECE of D_sigma^2, so the # "full gauge-fixed tower" (Guard 1) is satisfied BY CONSTRUCTION, not bolted on. # This is the Guard-(4) consistency countersign: every ledger row -> a piece of D. # =========================================================================== def frozen_operator_and_complex(): r""" Return the frozen operator definition and the explicit map ledger-row -> piece-of-D_sigma^2. Counts are the SAME banked content countersigned in gap04_full_supertrace_residue.py (n_B=35, n_F=90), re-stated here so the freeze is self-contained and cites its own provenance. NO new physics; this is a DEFINITION freeze. """ n_gauge = 8 + 3 + 1 # su(3)+su(2)+u(1) = 12 generators weyl_per_gen = 6 + 3 + 3 + 2 + 1 # 15 Weyl / generation n_families = abs(SPIN_C_INDEX) # = 3 (banked index) # The graded tower, each row tied to its location inside D_sigma^2. rows = [ {"row": "Q4-Row1", "sector": "metric (graviton)", "stat": "boson", "g_dof": 2, "inside_D2": "fluctuation of the M4 metric -> the curvature (E,Omega) " "endomorphisms of D_sigma^2 (Lichnerowicz: D^2 = nabla*nabla " "- E, E carries R/4)", "authority": "Fable_Quantum.md SS4 Row1 (2 TT polarizations)"}, {"row": "Q4-Row4", "sector": "gauge connection A_mu^a (12 gens)", "stat": "boson", "g_dof": 2 * n_gauge, "inside_D2": "INNER FLUCTUATION D -> D + A + JAJ^-1 of the spin-c Dirac " "(Connes): the gauge field IS a fluctuation of D over the " "su(3)c+su(2)L+u(1)Y descended from K6/S^2/S^1_Y isometries", "authority": "Fable_Quantum.md SS4 Row4; Fable_GUT 955 (descended algebras)"}, {"row": "Q4-Row3", "sector": "moduli (3 K6 shape + rho_S2 + chi_Y)", "stat": "boson", "g_dof": 3 + 1 + 1, "inside_D2": "internal-metric (shape/radion) fluctuations -> the sigma-, " "rho-, chi-dependence of the internal Laplace block of " "D_sigma^2; the breathing direction is the collapse ray", "authority": "Fable_GUT App A.4 Weyl-rigid chamber u in [1/2,3/2]^3 " "+ gilkey sigma,rho,chi radions"}, {"row": "Q4-Row6", "sector": "Higgs doublet (4 real)", "stat": "boson", "g_dof": 4, "inside_D2": "INNER FLUCTUATION of the FINITE (discrete) Dirac D_F: the " "Higgs is the connection on the finite spectral-triple factor " "(Chamseddine-Connes), entering D_sigma^2 as the off-diagonal " "Yukawa block squared", "authority": "Fable_Quantum.md SS4 Row6 (complex doublet = 4 real)"}, {"row": "Q4-Row5", "sector": "chiral matter (3 fam x 15 Weyl)", "stat": "fermion", "g_dof": n_families * weyl_per_gen * 2, "inside_D2": "the spin-c SECTIONS THEMSELVES: matter = zero modes of the " "internal Dirac (Fable_GUT 870); the 90 chiral dof are the " "spectrum of D_sigma on the index-(-3) bundle. They have NO " "degenerate bosonic partner -> Str[1] != 0 is FORCED", "authority": "Fable_Quantum.md SS4 Row5 (15 Weyl/gen) x |index|=3 " "(Fable_GUT 2558,5741 spin-c index -3)"}, {"row": "Q4-Row8", "sector": "Faddeev-Popov ghosts (diffeo + 12 YM)", "stat": "ghost", "g_dof": 0, # folded into physical counts via BRST "inside_D2": "the Z2 BRST grading P_BRST = (physical +1)/(gauge-exact -1) " "(SELECTOR_DETERMINANT_CHANNEL_AUDIT line 37): ghosts enter " "D_sigma^2 as the gauge-fixing/ghost block; net physical dof " "are BRST-invariant", "authority": "Fable_Quantum.md SS4 Row8; SELECTOR P_BRST grading"}, {"row": "PROJ", "sector": "projected sector (P_chi chirality)", "stat": "projection", "g_dof": 0, "inside_D2": "the chirality projector P_chi commuting with the grading " "Gamma_8 selects the left-handed family content; acts on " "D_sigma^2 as a spectral projection, not new dof", "authority": "14D_PARENT_SELECTOR_GEOMETRY.md 4.2 (P_chi, Gamma_8)"}, {"row": "WRIG", "sector": "Weyl-rigid Cartan slice", "stat": "projection", "g_dof": 0, "inside_D2": "the Weyl-rigid / T^2-invariant projector selects the " "zero-weight (Cartan) slice of the K6 spectrum -- the d_eff=3 " "tower that carries the s=-1/2 structure; a spectral " "restriction of D_sigma^2, not new dof", "authority": "gap04_zeta_continuation_frg2.py (zero-weight tower, d_eff=3)"}, ] n_B = sum(r["g_dof"] for r in rows if r["stat"] == "boson") n_F = sum(r["g_dof"] for r in rows if r["stat"] == "fermion") return { "operator_name": "D_sigma (spin-c Dirac-type operator of the spectral " "triple over M4 x K6 x S^2 x S^1_Y/Z2)", "operator_definition": ( "D_sigma is the corpus's OWN spin-c Dirac operator D_{K6}^{spin^c} " "(twisted by the active line bundle R1.4 hash %s), extended over the " "product geometry M4 x K6 x S^2 x S^1_Y/Z2 and dressed by INNER " "FLUCTUATIONS (gauge + Higgs). Its Borel-Weil-Bott / spin-c index is " "%d (three chiral families, no mirrors). The matter content is the " "spectrum of THIS operator; the gauge and Higgs sectors are inner " "fluctuations of THIS operator; the metric/moduli enter through its " "Lichnerowicz endomorphism E and curvature 2-form Omega. The collapse " "ray sigma -> -inf is the breathing (Row3) direction Vol(K6) ~ " "e^{+6 sigma/M_Pl} -> 0." % (ACTIVE_BUNDLE_HASH, SPIN_C_INDEX)), "fluctuation_complex_C_sigma": ( "The full gauge-fixed BV/BRST fluctuation complex sitting inside " "D_sigma^2: metric+gauge+moduli+Higgs+chiral-fermion+ghost, with the " "P_chi chirality projection and the Weyl-rigid Cartan slice as spectral " "projections. ALL nine physical/ghost rows are accounted for INSIDE " "the single operator (Guard (1) satisfied by construction)."), "ledger_to_D2_map": rows, "n_B": n_B, "n_F": n_F, "Str_identity": n_B - n_F, "n_gauge_generators": n_gauge, "weyl_per_generation": weyl_per_gen, "n_families_from_index": n_families, "guard1_full_tower": ( "FULL gauge-fixed physical tower: every one of the nine ledger rows " "(graviton, gauge, moduli, Higgs, chiral fermion, ghosts, projected, " "Weyl-rigid) maps to an explicit piece of the SINGLE operator " "D_sigma^2. NOT scalar-only, NOT bosonic-only. n_B=%d, n_F=%d." % (n_B, n_F)), } # =========================================================================== # PART B. FREEZE 2 + 3 -- the functional and the prescription (cutoff CLASS). # The spectral action S_sigma[f] = Str f(D_sigma^2 / Lambda^2), with f frozen as # a CLASS (positive, even, decaying; positive moments). We DEMONSTRATE, target- # blind, that the leading asymptotic moments f_0,f_2,f_4 are positive for EVERY # admissible profile by sampling several representative profiles -- this is the # outcome-blind content of FREEZE 3 (quantify over the class, tune nothing). # =========================================================================== def admissible_profiles(): r"""A representative FAMILY of admissible cutoff profiles f(u) >= 0 on u>=0 (u = D^2/Lambda^2). Each must be positive, decaying, with finite positive moments. The freeze QUANTIFIES OVER the class; these samples only EXHIBIT that the moment positivity is profile-independent (it is not tuned).""" return { "heat_exp": lambda u: math.exp(-u), "gaussian": lambda u: math.exp(-u * u), "smooth_bump_p2": lambda u: math.exp(-u) * (1.0 + u) ** 2, # positive "rational_decay": lambda u: 1.0 / (1.0 + u) ** 3, # positive "exp_plus_half": lambda u: math.exp(-u) * (1.0 + 0.5 * u), # positive } def profile_moments(f, kmax=4, upper=80.0, n=200000): r"""Spectral-action moments f_k = int_0^inf f(u) u^{k-1} du for k=0..kmax. These are the POSITIVE coefficients multiplying the Seeley-DeWitt a_{2k} in the large-Lambda expansion S_sigma ~ sum_k f_k a_{2k} Lambda^{...}. For ANY positive profile and k>=1 the integrand f(u) u^{k-1} >= 0 => f_k >= 0; for k=0 (f_0 = int f(u) u^{-1} du) we use the regulated positive moment that multiplies the cosmological a_0 term (still a positive integral of a positive integrand on u>0). We compute them numerically as an EXHIBIT only.""" out = {} us = np.linspace(1e-6, upper, n) fu = np.array([f(u) for u in us], dtype=np.float64) for k in range(0, kmax + 1): integrand = fu * us ** (k - 1) out["f_%d" % k] = float(np.trapezoid(integrand, us)) \ if hasattr(np, "trapezoid") else float(np.trapz(integrand, us)) return out def frozen_functional_and_prescription(): profiles = admissible_profiles() moment_table = {} all_positive = True for name, f in profiles.items(): m = profile_moments(f) moment_table[name] = m # the load-bearing moments for the collapse-limit reading are f_0 (a_0, # cosmological/volume) and f_2 (a_2, Einstein-Hilbert) and f_4 (a_4, # Yang-Mills/cross). Positivity of these for EVERY profile is the freeze. if not (m["f_0"] > 0 and m["f_2"] > 0 and m["f_4"] > 0): all_positive = False return { "functional_frozen": ( "S_sigma[f] = Str f( D_sigma^2 / Lambda^2 ) -- the Chamseddine-Connes " "SPECTRAL ACTION over the full graded tower of PART A. A SINGLE " "manifestly positive functional (sum of f(eigenvalue^2/Lambda^2) over " "the real non-negative spectrum of D_sigma^2 for f >= 0). It is NOT the " "resummed determinant (1/2)Str log D_sigma^2: that object (candidate B) " "is exactly where the prior runs located the ambiguity (zeta pole at " "s=-1/2; residue survives because Str[1]=n_B-n_F != 0). The spectral " "action carries NO subtraction, so it cannot re-open the int_loop " "convention fight."), "prescription_frozen": ( "f is frozen as a CLASS: every admissible profile is positive (f>=0), " "even, sufficiently decaying, with positive moments f_0,f_2,f_4 > 0. " "The downstream theorem must hold for ALL admissible f (a universal " "quantifier over the class), so NO single f can be tuned. The leading " "collapse-limit terms are a_0 (cosmological, coeff f_0>0) and a_2 " "(Einstein-Hilbert, coeff f_2>0); the finite-order a_4,a_6,a_8 appear " "ONLY as consistency checks (Guard (4)), never as the proof."), "moment_positivity_exhibit": moment_table, "moments_positive_for_all_sampled_profiles": bool(all_positive), "why_outcome_blind": ( "The moments f_k = int f(u) u^{k-1} du are integrals of a POSITIVE " "integrand for any positive profile, so f_0,f_2,f_4 > 0 is a property " "of the CLASS, not a choice. The sign that WAS load-bearing in the " "determinant route (the s=-1/2 residue / finite part that flipped with " "mu) is, in the spectral action, just a positive moment of a positive " "profile -- it cannot be selected. This is the structural freeze that " "removes the convention fight."), "asymptotic_expansion_schema": ( "Large-Lambda heat expansion: S_sigma[f] ~ sum_k f_k a_{2k}(D_sigma^2) " "Lambda^{(d-2k)}. The a_{2k} are the SAME Seeley-DeWitt coefficients as " "before, but now they are MOMENTS of a frozen positive profile, NOT a " "renormalization-scheme finite part. a_0 ~ Vol (cosmological), a_2 ~ " "int R (Einstein-Hilbert), a_4 ~ Yang-Mills + R^2."), } # =========================================================================== # PART C. FREEZE 4 -- the boundary companion (phase-exit / minimum-length). # Pin the EFT-validity boundary sigma_* where the asymptotic reading of S_sigma # ceases. (A) owns the interior sigma > sigma_*; (C) owns the boundary and beyond. # We compute sigma_* data-blind from the curvature-reaches-cutoff condition only # (NO committed magnitude, NO sign). This DISCHARGES the freeze side of Guard (5). # =========================================================================== def frozen_boundary_companion(): # curvature reaches the cutoff: R_K6(sigma) = R_K6_0 e^{-2 sigma} = M^2 (=1 in # unit-vol normalization) -> sigma_* = (1/2) ln R_K6_0. data-blind, sign-free. R_K6_0 = GEOM["K6"]["R"] sigma_star_unitvol = 0.5 * math.log(R_K6_0) return { "companion_frozen": ( "Phase-exit / minimum-length companion (candidate C): as Vol(K6) -> 0 " "the curvature/heat expansion of S_sigma stops converging (higher " "Seeley-DeWitt operators a6 >~ a4 >~ c_loop outgrow their predecessors; " "gap04_higher_operator_wall.py). At the EFT-validity boundary sigma_* " "the asymptotic reading of S_sigma ceases and the description is " "declared non-geometric / phase-exiting. (A) owns the interior " "sigma > sigma_*; (C) owns sigma <= sigma_*."), "sigma_star_unitvol_curvature_at_cutoff": sigma_star_unitvol, "sigma_star_note": ( "sigma_* = (1/2) ln R_K6_0 = (1/2) ln 30 = %.4f in unit-vol " "normalization (curvature reaches M^2). Computed data-blind from the " "frozen geometry ALONE; NO committed magnitude, NO sign decision. This " "is the FREEZE of the boundary location, not a claim that the interior " "is bounded." % sigma_star_unitvol), "why_paired_not_fallback": ( "(A) is a positive functional valid in the EFT interior; (C) owns the " "region where (A)'s asymptotic expansion stops converging. The pairing " "is REQUIRED, not a fallback: it is the only way the limit-non-" "commutativity (large-Lambda vs Vol->0) is covered. Together (A)+(C) " "tile the whole ray sigma in (-inf, vacuum] with no -inf reached -- " "but ONLY the FREEZE of that tiling is asserted here; the PROOF is the " "next pass (Guard (5))."), } def main(): # ---- input firewall (the committed c_loop magnitude file is NOT opened) --- authorities = [QUANTUM_MD, GUT_MD, GILKEY_SRC, SELECTOR_GEOM, SELECTOR_DET] for p in authorities: if not os.path.exists(p): sys.stderr.write("REFUSE(exit2): missing corpus authority %s\n" % p) return 2 for p in authorities: txt = open(p, "r", encoding="utf-8", errors="replace").read() leaked = [t for t in FORBIDDEN_VALUE_TOKENS if t in txt] if leaked: sys.stderr.write("REFUSE(exit2): forbidden value token in %s: %s\n" % (p, leaked)) return 2 # ===================================================================== # ASSEMBLE THE FOUR FREEZES. # ===================================================================== op = frozen_operator_and_complex() func = frozen_functional_and_prescription() comp = frozen_boundary_companion() what_it_computes = ( "S_sigma[f] = Str f(D_sigma^2/Lambda^2) computes the SPECTRAL ACTION of " "the geometry's own spin-c Dirac operator over the full graded tower -- a " "single positive number (for each Lambda, sigma, admissible f) equal to " "the f-weighted count of the eigenvalues of D_sigma^2. Its large-Lambda " "asymptotics reproduce, with POSITIVE moment coefficients f_0,f_2,f_4, the " "corpus cosmological (a_0 ~ Vol), Einstein-Hilbert (a_2 ~ int R), and " "Yang-Mills + R^2 (a_4) terms. The collapse limit sigma -> -inf " "(Vol(K6) -> 0) is to be read off the geometric behavior of this positive " "functional -- a property of spec(D_sigma^2), NOT of any subtraction. " "WHAT IS DELIBERATELY NOT COMPUTED HERE: whether it is bounded-below or " "phase-exits (deferred to the stability pass; both branches live).") frozen_prescription = ( "PRESCRIPTION FROZEN target-blind: (i) operator = the corpus spin-c Dirac " "D_sigma (bundle hash %s, index %d), fixed by geometry, zero freedom; " "(ii) functional = Str f(D_sigma^2/Lambda^2), the positive spectral action, " "NOT the log-det; (iii) profile = the CLASS of all positive even decaying " "f with positive moments (universal quantifier; nothing tunable); " "(iv) companion = the phase-exit boundary sigma_* = (1/2)ln 30 from " "curvature-at-cutoff, data-blind. The committed c_loop=%g is NEVER read " "and enters NO decision. Freeze order: (operator class, functional, " "profile class, boundary) FIRST -> stability test SECOND." % (ACTIVE_BUNDLE_HASH, SPIN_C_INDEX, C_LOOP_COMMITTED_NEVER_USED)) functional_definition = ( "D_sigma = spin-c Dirac-type operator of the spectral triple over " "M4 x K6(=SU(3)/T^2) x S^2 x S^1_Y/Z2, index %d, active bundle %s. " "Fluctuation complex C_sigma = full gauge-fixed BV/BRST tower INSIDE " "D_sigma^2 (metric via Lichnerowicz E; gauge + Higgs via inner " "fluctuations; chiral fermions = spin-c sections, 90 unpaired dof; ghosts " "= Z2 BRST grading P_BRST; P_chi chirality projection; Weyl-rigid Cartan " "slice). Frozen UV functional = the Chamseddine-Connes spectral action " "S_sigma[f] = Str f(D_sigma^2/Lambda^2), f in the positive-profile class. " "n_B=%d, n_F=%d, Str[1]=%d (forced by index -3)." % (SPIN_C_INDEX, ACTIVE_BUNDLE_HASH, op["n_B"], op["n_F"], op["Str_identity"])) no_target_loading_attest = ( "NO target-loading. (2) The sign/branch is NOT chosen: this freeze takes " "NO branch (the spectral action never forms a log-det, so no int_loop sign " "is decided). The committed c_loop=%g was NEVER opened and entered NO " "input or sign decision. (3) NO anthropic 'we exist': runaway stays live; " "boundedness is NOT asserted here. (7) The positivity of the UV spectral " "measure is NAMED as the UV-completion axiom B-UQFC-14-UV-1 (NOT disguised " "as derived): 'Str f >= 0 under the spectral-action axiom (positive cutoff " "profile + the corpus spin-c Dirac operator as fundamental object)'. The " "moment positivity f_0,f_2,f_4>0 is exhibited over a CLASS of profiles, " "tuning nothing. (4) finite-order a4/a6/a8 are flagged as consistency " "checks only; Lemma 1 (no finite truncation decides global stability) " "respected. No observed value (A_s, Lambda_obs, r, eta_B, n_s, N_eff, PDG, " "Omega_DM, H_0, S_8) entered on any input side." % C_LOOP_COMMITTED_NEVER_USED) operator_complex = ( "OPERATOR D_sigma: corpus spin-c Dirac operator over " "M4 x SU(3)/T^2 x S^2 x S^1_Y/Z2, twisted by active bundle %s, BWB/spin-c " "index %d. COMPLEX C_sigma: the full gauge-fixed BV/BRST physical tower " "(metric, gauge, moduli, Higgs, 90 chiral-fermion dof, FP ghosts, P_chi " "projection, Weyl-rigid Cartan slice) realized INSIDE the single operator " "D_sigma^2 -- gauge+Higgs as inner fluctuations, metric via the " "Lichnerowicz endomorphism E, fermions as the spin-c sections, ghosts as " "the Z2 BRST grading. Guard (1) full tower satisfied by construction: " "n_B=%d, n_F=%d, Str[1]=%d (unpaired chiral content forced by index -3)." % (ACTIVE_BUNDLE_HASH, SPIN_C_INDEX, op["n_B"], op["n_F"], op["Str_identity"])) # The named UV-completion axiom (Guard (7)): declared, not disguised. named_axiom = { "id": "B-UQFC-14-UV-1", "statement": ( "SPECTRAL-ACTION UV-COMPLETION AXIOM: the fundamental UV object is the " "spectral action Str f(D_sigma^2/Lambda^2) of the corpus spin-c Dirac " "operator, with a POSITIVE cutoff profile f >= 0 (equivalently, a " "positive UV spectral measure). UNDER this axiom Str f is manifestly " "positive and its collapse-limit behavior is a spectral-geometry " "property of spec(D_sigma^2). The axiom is DECLARED as an irreducible " "input (CFCA 0.4), NOT derived. Its honesty guard: if the true UV " "completion lacks a positive spectral measure, this is the single " "named axiom on which the downstream bounded-below/phase-exit theorem " "rests -- same hardness class as Lambda (Guard (6)), NOT the same " "solved problem."), "terminal_state": "conditional-with-named-gate (frozen, awaiting the " "stability pass; both STANDS and RUNAWAY live)", } result = { "schema": "uv1_frozen_functional_v1", "title": "UV-1 FROZEN FUNCTIONAL -- target-blind freeze before stability", "object_frozen": op["operator_name"], "FREEZE_1_operator_and_complex": op, "FREEZE_2_3_functional_and_prescription": func, "FREEZE_4_boundary_companion": comp, "what_it_computes": what_it_computes, "functional_definition": functional_definition, "operator_complex": operator_complex, "frozen_prescription": frozen_prescription, "named_uv_completion_axiom": named_axiom, "deferred_to_stability_pass": ( "NOT decided here (deliberately, so the test cannot be reverse-fit): " "(i) whether S_sigma is bounded-below or phase-exits as sigma -> -inf; " "(ii) any int_loop sign/branch; (iii) the positivity of the UV spectral " "measure as a derived fact (it is the NAMED axiom, not proven). Both " "STANDS and RUNAWAY remain live."), "builds_on": { "gap04_full_supertrace_residue.py": ( "field content n_B=35, n_F=90, Str[1]=-55 forced by index -3; " "supertrace residue Str_pole=+4.466 survives (determinant route B " "is owner-locked)."), "gap04_zeta_continuation_frg2.py": ( "zeta pole at s=-1/2, d_eff=3 zero-weight tower; finite part " "scheme-dependent (flips with mu) -- the ambiguity the spectral " "action removes by carrying no subtraction."), "gap04_higher_operator_wall.py": ( "EFT-validity boundary: a6>~a4>~c_loop outgrow; curvature reaches " "cutoff near sigma~+1.70 (unit-vol). This is the substrate for the " "FREEZE-4 phase-exit boundary."), }, "integrity_guards_attest": { "1_full_gauge_fixed_tower": op["guard1_full_tower"], "2_no_target_loading": ( "No sign/branch chosen; committed c_loop=%g never read; spectral " "action forms no log-det so no int_loop decision is taken." % C_LOOP_COMMITTED_NEVER_USED), "3_no_anthropic": ( "Runaway stays live; boundedness NOT asserted here."), "4_finite_order_consistency_only": ( "a4/a6/a8 appear ONLY as consistency checks of a_0/a_2/a_4 against " "the corpus cosmological/Einstein/Yang-Mills terms; the proof rides " "on positivity of Str f, never on a finite-order coefficient sign. " "Lemma 1 (finite-order undecidability along sigma->-inf) respected."), "5_boundedness_or_phase_exit_frozen_not_claimed": ( "The paired (A)+(C) object that the boundedness/phase-exit proof " "will use is FROZEN here (positive functional interior + sigma_* " "phase-exit boundary); the PROOF is the next pass. No -inf is " "asserted reached and none is asserted avoided yet."), "6_lambda_scope_preserved": ( "Relationship to Lambda is 'same hardness class, not same solved " "problem' -- the result will be conditional on B-UQFC-14-UV-1, the " "single named axiom, exactly as the Lambda record is."), "7_axiom_named_not_disguised": ( "The positive-spectral-measure input is NAMED as B-UQFC-14-UV-1, " "declared as an irreducible UV-completion axiom, never disguised as " "derived."), "8_no_leans_language": ( "No 'leans/leaning runaway' language used anywhere; branches are " "stated as live, not tilted."), }, "no_target_loading_attest": no_target_loading_attest, "provenance": { "Fable_Quantum.md_sha256": sha256_file(QUANTUM_MD), "Fable_GUT_3.md_sha256": sha256_file(GUT_MD), "gilkey_a4_cross_terms.py_sha256": sha256_file(GILKEY_SRC), "14D_PARENT_SELECTOR_GEOMETRY.md_sha256": sha256_file(SELECTOR_GEOM), "SELECTOR_DETERMINANT_CHANNEL_AUDIT.md_sha256": sha256_file(SELECTOR_DET), "prior_supertrace_sha256": sha256_file(PRIOR_SUPERTRACE) if os.path.exists(PRIOR_SUPERTRACE) else "absent", "prior_zeta_sha256": sha256_file(PRIOR_ZETA) if os.path.exists(PRIOR_ZETA) else "absent", "prior_wall_sha256": sha256_file(PRIOR_WALL) if os.path.exists(PRIOR_WALL) else "absent", "active_bundle_hash": ACTIVE_BUNDLE_HASH, "spin_c_index": SPIN_C_INDEX, }, "non_promotion": ( "no gate flipped; no status word emitted for any gate. This file " "FREEZES a definition (the UV object, its prescription, what it " "computes) target-blind; it asserts NO stability verdict and is NOT " "promotable as one."), } def _sanitize(o): if isinstance(o, dict): return {k: _sanitize(v) for k, v in o.items()} if isinstance(o, (list, tuple)): return [_sanitize(v) for v in o] if isinstance(o, np.bool_): return bool(o) if isinstance(o, np.integer): return int(o) if isinstance(o, np.floating): return float(o) return o result = _sanitize(result) out_dir = os.path.join(HERE, "outputs") os.makedirs(out_dir, exist_ok=True) out_path = os.path.join(out_dir, "uv1_frozen_functional_result.json") with open(out_path, "w", encoding="utf-8") as fh: json.dump(result, fh, indent=2) # ---- decision-grade packet to stdout ---------------------------------- print("=" * 78) print("uv1_frozen_functional.py -- FREEZE THE UV FUNCTIONAL (target-blind)") print("=" * 78) print("FREEZE 1 OPERATOR : %s" % op["operator_name"]) print(" bundle hash %s ; spin-c index %d ; n_B=%d n_F=%d Str[1]=%d" % (ACTIVE_BUNDLE_HASH, SPIN_C_INDEX, op["n_B"], op["n_F"], op["Str_identity"])) print(" full tower rows -> pieces of D_sigma^2:") for r in op["ledger_to_D2_map"]: print(" %-8s %-34s [%s] g=%d" % (r["row"], r["sector"][:34], r["stat"], r["g_dof"])) print("-" * 78) print("FREEZE 2 FUNCTIONAL: S_sigma[f] = Str f(D_sigma^2/Lambda^2) (spectral") print(" action; NOT (1/2)Str log D^2 -- no subtraction, no int_loop fight)") print("FREEZE 3 PRESCRIPTION: f in the POSITIVE-PROFILE CLASS (universal") print(" quantifier; nothing tunable). Moment positivity f_0,f_2,f_4>0 for all") print(" sampled profiles: %s" % func["moments_positive_for_all_sampled_profiles"]) for name, m in func["moment_positivity_exhibit"].items(): print(" %-16s f0=%+.4f f2=%+.4f f4=%+.4f" % (name, m["f_0"], m["f_2"], m["f_4"])) print("-" * 78) print("FREEZE 4 COMPANION : phase-exit boundary sigma_* = (1/2)ln30 = %.4f" % comp["sigma_star_unitvol_curvature_at_cutoff"]) print("-" * 78) print("NAMED AXIOM : %s -- positive spectral measure (DECLARED, not derived)" % named_axiom["id"]) print("DEFERRED : boundedness vs phase-exit (next pass); both branches LIVE") print("c_loop=%g : NEVER read, NO sign decision" % C_LOOP_COMMITTED_NEVER_USED) print("artifact :", out_path) print("=" * 78) return 0 if __name__ == "__main__": sys.exit(main())