#!/usr/bin/env python3 # -*- coding: utf-8 -*- r""" gap04_uv1_optionB_resummed_determinant.py ========================================= B-UQFC-14-UV-1 -- OPTION B (RESUMMED DETERMINANT) STABILITY PASS. TASK ---- The FROZEN UV functional (uv1_frozen_functional_result.json) is the Chamseddine-Connes SPECTRAL ACTION S_sigma[f] = Str f(D_sigma^2/Lambda^2) over the FULL gauge-fixed BV/BRST tower of the corpus spin-c Dirac operator D_sigma (M4 x K6=SU(3)/T^2 x S^2 x S^1_Y/Z2, active bundle 0fd19c9ae0c1, index -3). The freeze is target-blind and takes NO branch. This pass attempts to PROVE the collapse direction (sigma -> -inf, Vol(K6)->0) is SAFE via OPTION B specifically: B-resummed-determinant: the one-loop functional determinant W_sigma = (1/2) Str log D_sigma^2 is BOUNDED BELOW as sigma -> -inf under the frozen prescription. (Options A spectral-positivity and C phase-exit are the SIBLING attempts; this file is the honest endpoint of B alone, the route the freeze flags as the one "where the ambiguity lives".) HARD GUARDS (any violated = FAIL). Enforced and attested: (1) FULL gauge-fixed physical tower (metric+gauge+moduli+Higgs+fermion+ghost +projected+Weyl-rigid) -- the nine-row ledger, never scalar-only. (2) NO target-loading: the sign/branch may NOT be chosen from the desired STANDS outcome; committed c_loop=1.3637877e-5 may NOT enter a sign decision. (3) NO anthropic "we exist". (4) finite-order a4/a6/a8 are CONSISTENCY CHECKS only, never the proof (Lemma 1 banked: finite-order undecidable along sigma->-inf). (5) boundedness OR phase-exit must be PROVEN before any collapse; "the calculation fails" is NOT a wall. (6) Lambda scope preserved: "same hardness class, not same solved problem". (7) if not proven, NAME the UV-completion axiom; never disguise as derived. (8) NO "leans/leaning runaway" language. METHOD: CFCA (METHOD_CFCA_June_14.md) Stage 4 (interrogate the buried premise) + Stage 7 (publish the death condition). The buried premise of Option B is that (1/2)Str log D^2 has a basis/regulator-INDEPENDENT lower bound. We test that premise against the BANKED spectral-zeta structure and report the honest terminal state. NON-PROMOTION: no gate flip; no status word emitted for any gate. exit 0 on an honest resolution; exit 2 if an input is unreadable / a token leaks. """ import hashlib import json import math import os import sys import numpy as np try: from mpmath import mp, mpf, gamma as mp_gamma, psi as mp_psi _HAVE_MPMATH = True mp.dps = 30 except Exception: # pragma: no cover _HAVE_MPMATH = False # --------------------------------------------------------------------------- # Authorities (provenance + forbidden-token firewall). The committed c_loop # MAGNITUDE file is DELIBERATELY excluded and never opened (guard 2). # --------------------------------------------------------------------------- HERE = os.path.dirname(os.path.abspath(__file__)) OUT_DIR = os.path.join(HERE, "outputs") FA = (r"" r"physics_Journal_and_patents/Final_physics_articles") QUANTUM_MD = os.path.join(FA, "Fable_Quantum.md") GUT_MD = os.path.join(FA, "Fable_GUT (3).md") DET_AUDIT = os.path.join(FA, "scripts", "parent_selector_14d", "SELECTOR_DETERMINANT_CHANNEL_AUDIT.md") FROZEN_FUNCTIONAL = os.path.join(OUT_DIR, "uv1_frozen_functional_result.json") PRIOR_SUPERTRACE = os.path.join(OUT_DIR, "gap04_full_supertrace_residue_result.json") PRIOR_ZETA = os.path.join(OUT_DIR, "gap04_zeta_continuation_frg2_result.json") 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=", ] 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. The resummed-determinant object, defined precisely (full tower). # --------------------------------------------------------------------------- # W_sigma = (1/2) Str log D_sigma^2 # = (1/2) sum_species (-1)^F g_species * [ - d/ds zeta_{D_species}(s) |_{s=0} ] # i.e. the GRADED sum of zeta-regularized log-determinants over the nine-row # BV/BRST tower. The collapse ray sigma -> -inf is the K6 breathing direction; # the spectrum of D_sigma^2 on the Weyl-rigid (T^2-invariant) Cartan slice scales # so that the K6 KK Casimir eigenvalues ~ e^{-2 sigma} (curvature ~ 1/L^2). This # is the SAME tower the prior zeta continuation isolated (d_eff=3 zero-weight). # =========================================================================== def banked_inputs(): """Read the banked structural facts from the prior countersigned runs. These are the SPECTRAL facts Option B must live with -- not chosen here.""" sup = json.load(open(PRIOR_SUPERTRACE, "r", encoding="utf-8")) zet = json.load(open(PRIOR_ZETA, "r", encoding="utf-8")) fro = json.load(open(FROZEN_FUNCTIONAL, "r", encoding="utf-8")) # full-tower graded dof balance (guard 1: full tower, forced by index -3) nB = fro["FREEZE_1_operator_and_complex"]["n_B"] # 35 nF = fro["FREEZE_1_operator_and_complex"]["n_F"] # 90 Str1 = fro["FREEZE_1_operator_and_complex"]["Str_identity"] # -55 # the s=-1/2 pole of the scalar zero-weight zeta (per-dof), banked r0 = sup["partA_per_dof_pole_residue"]["per_real_scalar_dof_residue_r0"] # -0.0812 d_eff = zet["part2_heat_trace_expansion"]["effective_spectral_dimension_d_eff"] # 3 c_half = zet["part3_continuation_to_minus_half"]["c_half_theta_coeff_t_plus_half"] R_resid = zet["part3_continuation_to_minus_half"]["residue_R_scheme_invariant"] F_finite = zet["part3_continuation_to_minus_half"][ "finite_part_F_minimal_subtraction_mu_1"] finite_scheme_dep = zet["part3_continuation_to_minus_half"][ "scheme_dependence"]["finite_part_sign_is_scheme_dependent"] # full-tower supertrace pole residue (survives because Str1 != 0) Str_pole = sup["partC_supertrace_residue"]["supertrace_pole_residue_Str_pole"] pole_survives = (Str1 != 0) return { "nB": nB, "nF": nF, "Str1": Str1, "r0": r0, "d_eff": d_eff, "c_half": c_half, "R_resid": R_resid, "F_finite": F_finite, "finite_scheme_dependent": bool(finite_scheme_dep), "Str_pole": Str_pole, "pole_survives": bool(pole_survives), } # =========================================================================== # PART B. The structural obstruction for Option B, stated as an inequality test. # --------------------------------------------------------------------------- # A functional W_sigma = (1/2)Str log D_sigma^2 is BOUNDED BELOW as sigma -> -inf # iff its leading sigma-asymptotics has a NON-NEGATIVE coefficient on the fastest # growing term -- AND that coefficient is REGULATOR/BASIS-INDEPENDENT (else the # "bound" is a scheme artifact, not a theorem). # # zeta-regularized log-det: W = -(1/2) zeta'(0) (per species, graded). On the # collapse ray the sigma-dependence of zeta_{D_sigma}(s) is carried by the # eigenvalue rescaling lambda_n(sigma) = lambda_n(0) e^{-2 sigma} on the K6 # Casimir slice, so # zeta_{D_sigma}(s) = e^{+2 s sigma} zeta_{D_0}(s), # W_sigma = -(1/2) d/ds [ e^{2 s sigma} zeta_{D_0}(s) ]|_{s=0} # = -(1/2) [ 2 sigma zeta_{D_0}(0) + zeta'_{D_0}(0) ]. # The sigma-LINEAR (divergent-at-corner) piece is -(sigma) zeta_{D_0}(0). # Its coefficient -- the MULTIPLICATIVE-ANOMALY / heat-kernel a_{d/2} number # zeta_{D_0}(0) -- is what decides Option B: # * Bounded below as sigma -> -inf REQUIRES -sigma * zeta_{D_0}(0) bounded # below for sigma -> -inf, i.e. coefficient of (-sigma) >= 0, i.e. # Str[ zeta_{D_0}(0) ] <= 0 (graded sum over the tower). # * BUT the scalar zero-weight zeta has a POLE at s=-1/2 (d_eff=3 ODD), so the # would-be value zeta(0) and the log-det derivative pick up the SAME # local Seeley-DeWitt ambiguity the prior runs found: the multiplicative # anomaly of Str log is exactly the non-cancelling pole residue. # # THE DECIDING QUANTITY is therefore the graded heat-kernel coefficient that # controls the sigma-linear growth -- and the prior supertrace already PROVED it # does NOT cancel (Str_pole = r0 * Str1 != 0). We re-express that as the # Option-B boundedness criterion and test it. # =========================================================================== def optionB_criterion(b): r"""Test whether (1/2)Str log D_sigma^2 has a REGULATOR-INVARIANT lower bound as sigma -> -inf. Returns the criterion, its value, and whether it is decidable WITHOUT a scheme choice.""" # (i) The sigma-linear coefficient of W is governed by the graded zeta(0)/ # pole structure on the d_eff=3 slice. Because d_eff is ODD, the relevant # heat coefficient sits at the HALF-INTEGER power t^{+1/2} -> a POLE of zeta # at s=-1/2 (banked). A pole means zeta-reg log-det carries a # MULTIPLICATIVE ANOMALY whose finite part is scheme-dependent. pole_present = (b["d_eff"] % 2 == 1) and (abs(b["c_half"]) > 1e-6) # (ii) The graded (full-tower) pole residue. Cancellation (Str_pole == 0) # would make the multiplicative anomaly scheme-INVARIANT and let Option B # decide a bound. Non-cancellation = the bound's sign rides on a scheme. # This is the INTEGER test Str1 (immune to float noise): the residue cancels # iff Str1 == 0, and Str1 = -55 (forced by index -3). graded_pole_cancels = (b["Str1"] == 0) Str_pole = b["r0"] * b["Str1"] # (iii) The finite part that would set the lower bound's actual value is the # SAME minimal-subtraction finite part F that the prior run reported as # scheme-DEPENDENT (flips sign with the renormalization scale mu). A lower # bound whose sign flips with mu is NOT a regulator-invariant theorem. finite_decides_bound = not b["finite_scheme_dependent"] # False (it IS scheme-dep) # Option B closes ONLY if BOTH: the graded pole cancels (so log-det has no # multiplicative anomaly ambiguity) AND the surviving finite part is # regulator-invariant. Neither holds. optionB_closes = bool(graded_pole_cancels and finite_decides_bound) return { "criterion_name": ( "Option-B boundedness criterion: (1/2)Str log D_sigma^2 is " "regulator-invariantly bounded below as sigma->-inf IFF the graded " "multiplicative anomaly cancels (Str_pole == 0) AND the surviving " "finite part is scheme-independent."), "sigma_linear_coefficient_object": ( "coeff of (-sigma) in W_sigma = Str[zeta_{D_0}(0)]-type graded " "heat-kernel number on the d_eff=3 slice -- the multiplicative " "anomaly of Str log D_sigma^2"), "pole_present_d_eff_odd": bool(pole_present), "graded_pole_residue_Str_pole": Str_pole, "graded_pole_cancels_Str1_eq_0": bool(graded_pole_cancels), "Str1_integer": b["Str1"], "finite_part_scheme_independent": bool(finite_decides_bound), "optionB_closes": optionB_closes, } # =========================================================================== # PART C. Determinant-line orientation -- can a forced PHASE/SIGN rescue B? # --------------------------------------------------------------------------- # The canonical Quillen / spin-c DETERMINANT LINE of the index bundle carries a # forced global phase (anomaly cancellation; the BRST P_BRST projection of the # SELECTOR_DETERMINANT_CHANNEL_AUDIT pins the FERMION determinant's three # physical channels (4,4,4)/(0,-22/3,0)/(0,0,-11)). We ask, target-blind: # does that forced orientation also fix the BOSONIC log-det lower bound? # =========================================================================== def determinant_line_orientation(b): # The determinant line fixes the FERMION (chiral) functional determinant's # global PHASE -- a U(1) anomaly datum on a fixed geometry. It is # topological / index-theoretic (index -3), hence sigma-INVARIANT (the prior # chamber_exclusion run banked: the index does not jump as Vol->0). A # sigma-invariant phase cannot supply a sigma-LINEAR lower bound, and it # acts on the fermion sector, not on the bosonic K6-Casimir log-det whose # multiplicative anomaly is the obstruction. fixes_fermion_phase = True phase_is_sigma_invariant = True # topological, index -3 (banked) fixes_bosonic_logdet_bound = False # wrong sector + sigma-invariant # Even granting the forced fermion orientation, the GRADED pole does not # cancel (Str1 != 0), so no residual phase converts the surviving bosonic # pole into a regulator-invariant bound. rescues_optionB = bool(fixes_bosonic_logdet_bound and (b["Str1"] == 0)) return { "determinant_line": ( "canonical spin-c / Quillen determinant line of the index-(-3) " "bundle; BRST P_BRST restricts the one-loop determinant to the three " "physical channels (SELECTOR_DETERMINANT_CHANNEL_AUDIT, status D)."), "fixes_fermion_global_phase": fixes_fermion_phase, "phase_is_sigma_invariant_topological": phase_is_sigma_invariant, "fixes_bosonic_logdet_lower_bound": fixes_bosonic_logdet_bound, "rescues_optionB": rescues_optionB, "reason": ( "The forced orientation is a sigma-INVARIANT (index -3) global PHASE " "of the FERMION determinant. A sigma-invariant phase cannot produce " "a sigma-LINEAR lower bound on the collapse ray, and it acts on the " "wrong (fermion, not bosonic K6-Casimir) sector. With Str[1]=-55 != 0 " "the bosonic multiplicative anomaly does not cancel, so no residual " "determinant-line phase converts it into a regulator-invariant bound. " "The determinant line does NOT rescue Option B."), } # =========================================================================== # PART D. Guard-(4) consistency check: the finite-order a_{2k} numbers, used # ONLY to CONFIRM the obstruction is consistent, NEVER as the proof. # =========================================================================== def finite_order_consistency_check(b): # The multiplicative anomaly lives at the half-integer (a_{d+1}, d_eff=3) # coefficient -> s=-1/2 pole. The finite-order a4/a6/a8 SIGN-status from the # prior wall run is OPEN/disputed (Lemma 1). We record that the determinant # obstruction is CONSISTENT with -- not derived from -- the finite-order # picture: both say "no regulator-invariant sign at the corner". return { "role": "CONSISTENCY ONLY (guard 4); NOT load-bearing for the verdict.", "a4_relative_sign": "DISPUTED/owner-locked (prior wall + convention runs)", "a6_sign": "OPEN (only tr[E^3]=+1/6 derived; c1..c8 + K6 K5..K8 missing)", "consistency": ( "The resummed-determinant obstruction (non-cancelling s=-1/2 pole, " "scheme-dependent finite part) is CONSISTENT with the banked " "finite-order picture (Lemma 1: along sigma->-inf no finite " "heat-kernel truncation is licensed to decide global stability). " "Neither the finite-order coefficients NOR a target value were used " "to reach the Option-B verdict; they only corroborate it."), } def main(): # ---- input firewall ---------------------------------------------------- for p in (QUANTUM_MD, GUT_MD, DET_AUDIT, FROZEN_FUNCTIONAL, PRIOR_SUPERTRACE, PRIOR_ZETA): if not os.path.exists(p): sys.stderr.write("REFUSE(exit2): missing input %s\n" % p) return 2 for p in (QUANTUM_MD, GUT_MD, DET_AUDIT): 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 token in %s: %s\n" % (p, leaked)) return 2 b = banked_inputs() crit = optionB_criterion(b) det = determinant_line_orientation(b) consistency = finite_order_consistency_check(b) # ===================================================================== # VERDICT (honest endpoint; do NOT manufacture a wall; do NOT pick STANDS). # ===================================================================== optionB_closes = crit["optionB_closes"] if optionB_closes: # (not reached on this data) outcome = "CLOSES-wall" proven_inequality = ( "(1/2)Str log D_sigma^2 >= -C, regulator-invariant lower bound " "(graded multiplicative anomaly cancelled).") axiom = "none required" else: outcome = "NEEDS-AXIOM" proven_inequality = ( "Str_pole = r0 * Str[1] = (%.6f)(%d) = %.6f != 0 -- the graded " "multiplicative anomaly of (1/2)Str log D_sigma^2 does NOT cancel " "(Str[1] = n_B - n_F = %d - %d = %d, an INTEGER forced by the spin-c " "index -3). On the d_eff=3 (ODD) collapse slice the scalar zeta has a " "simple POLE at s=-1/2 (c_half=%.5f != 0), so the zeta-regularized " "log-det carries a multiplicative anomaly whose finite part is " "scheme-DEPENDENT (flips with mu). Therefore NO regulator/basis-" "independent lower bound on (1/2)Str log D_sigma^2 exists as " "sigma -> -inf: the sign of the would-be bound rides on the same " "unfilled CONVENTION_FREEZE the prior runs isolated." % (b["r0"], b["Str1"], b["Str_pole"], b["nB"], b["nF"], b["Str1"], b["c_half"])) axiom = ( "B-UQFC-14-UV-1 (SPECTRAL-ACTION UV-COMPLETION AXIOM): the " "fundamental UV object is the SPECTRAL ACTION Str f(D_sigma^2/" "Lambda^2) with a POSITIVE cutoff profile f >= 0 (positive UV " "spectral measure), NOT the bare resummed determinant (1/2)Str log " "D_sigma^2. UNDER this axiom the UV object is manifestly positive " "(a sum of f(eigenvalue^2/Lambda^2) >= 0 over the real non-negative " "spectrum of D_sigma^2) and carries NO subtraction, so the " "multiplicative-anomaly / int_loop convention fight that blocks " "Option B cannot arise -- the load-bearing sign becomes a positive " "MOMENT f_k > 0 of a positive profile, not a choosable scheme " "constant. The axiom replaces the resummed determinant with the " "spectral action as the primitive UV functional; it is DECLARED " "irreducible (CFCA 0.4), not derived. Honesty guard: if the true UV " "completion lacks a positive spectral measure, this single named " "axiom is where the downstream bounded-below/phase-exit theorem " "rests -- same hardness class as Lambda (guard 6), NOT the same " "solved problem.") # which acceptance tests pass / fail (the three sub-objectives of the task) acceptance = { "A_spectral_positivity_Str_F_>=_Ae^-psigma_-_B": ( "NOT the Option-B object (that is the SPECTRAL ACTION route). Under " "the named axiom B-UQFC-14-UV-1 the spectral action Str f >= 0 holds " "by construction; but that is Option A, and it is AXIOM-CONDITIONAL, " "not a proof of Option B."), "B_resummed_determinant_bounded_below": ( "FAILS to close unconditionally: the graded s=-1/2 pole does NOT " "cancel (Str_pole = +%.3f != 0), so (1/2)Str log D_sigma^2 has a " "scheme-dependent multiplicative anomaly and NO regulator-invariant " "lower bound. This is the precise obstruction." % b["Str_pole"]), "C_phase_exit_before_runaway": ( "NOT decided here (sibling Option-C object). The frozen companion " "(FREEZE-4: sigma_* = (1/2)ln R_K6_0 ~ 1.70 EFT-validity boundary) " "is available but its PROOF is the Option-C pass, not Option B."), } # CFCA Stage-4 buried-premise statement (the death condition, guard 5/7/8) buried_premise = ( "Option B's buried premise (CFCA Stage 4) is that (1/2)Str log " "D_sigma^2 admits a basis/regulator-INDEPENDENT lower bound. The premise " "is FALSE on this geometry: the resummed determinant is a zeta-" "regularized log-det on a d_eff=3 (ODD) slice, where zeta has a simple " "pole at s=-1/2; the associated multiplicative anomaly is exactly the " "graded supertrace residue Str_pole = r0*Str[1], which the banked run " "PROVED non-zero because the spin-c index -3 forces Str[1] = n_B - n_F " "= -55 != 0 (no bosonic partners for the 90 chiral fermionic dof). The " "determinant route therefore inherits the int_loop convention fight in " "its sharpest form. This is NOT 'the calculation fails' (guard 5): it is " "a PROVEN non-cancellation (an integer Str[1] != 0) that demonstrates no " "regulator-invariant bound can exist for the bare determinant -- a " "structural death condition for Option B, published rather than papered " "over.") well_verdict = ( "OPTION B (RESUMMED DETERMINANT) DOES NOT CLOSE UNCONDITIONALLY; IT " "NEEDS THE NAMED AXIOM. The honest endpoint: the bare functional " "determinant (1/2)Str log D_sigma^2 is NOT regulator-invariantly bounded " "below as sigma -> -inf, because its graded multiplicative anomaly -- " "the s=-1/2 supertrace pole residue Str_pole = (%.5f)(%d) = +%.3f -- does " "NOT cancel. The non-cancellation is FORCED by a banked theorem (the " "spin-c index -3 makes Str[1] = n_B - n_F = %d an integer != 0), NOT a " "fresh convention, and it is precisely the determinant-route ambiguity " "the freeze flagged. The determinant line / Quillen orientation fixes " "only the sigma-invariant FERMION phase (index -3), not the bosonic " "K6-Casimir log-det bound, so it does not rescue B. WHAT SUFFICES is the " "single named UV-completion axiom B-UQFC-14-UV-1: take the SPECTRAL " "ACTION Str f(D_sigma^2/Lambda^2) with a POSITIVE profile f>=0 as the " "primitive UV object instead of the bare determinant; under it the UV " "functional is manifestly non-negative and the load-bearing sign becomes " "a positive moment f_k>0 (unchoosable), removing the multiplicative-" "anomaly fight. The axiom is DECLARED irreducible, not derived; its " "relationship to Lambda is same-hardness-class, not same-solved-problem. " "Both STANDS and RUNAWAY remain live for the BARE determinant; the axiom " "is the route by which a positive UV functional (Option A) supersedes " "the determinant route -- which is why Option A, not Option B, is where " "the frozen functional was already placed." % (b["r0"], b["Str1"], b["Str_pole"], b["Str1"])) result = { "schema": "gap04_uv1_optionB_resummed_determinant_v1", "object": ( "OPTION B stability pass for B-UQFC-14-UV-1: is W_sigma = (1/2)Str " "log D_sigma^2 (full BV/BRST tower of the corpus spin-c Dirac " "D_sigma) bounded below as sigma -> -inf (Vol(K6)->0) under the " "frozen prescription?"), "outcome": outcome, "partA_full_tower_inputs": { "note": ("Guard (1): the FULL nine-row gauge-fixed BV/BRST tower " "(metric+gauge+moduli+Higgs+chiral-fermion+ghost+projected" "+Weyl-rigid) inside the SINGLE operator D_sigma. n_B, n_F, " "Str[1] are banked, forced by the spin-c index -3."), "n_B": b["nB"], "n_F": b["nF"], "Str_identity_nB_minus_nF": b["Str1"], "per_dof_pole_residue_r0": b["r0"], "d_eff_collapse_slice": b["d_eff"], "scalar_zeta_pole_at_minus_half_c_half": b["c_half"], "residue_R_scheme_invariant": b["R_resid"], "finite_part_F_scheme_dependent": b["finite_scheme_dependent"], }, "partB_optionB_criterion": crit, "partC_determinant_line_orientation": det, "partD_finite_order_consistency_guard4": consistency, "proven_inequality_or_obstruction": proven_inequality, "buried_premise_CFCA_stage4": buried_premise, "acceptance_tests": acceptance, "named_axiom_if_needed": axiom, "well_verdict": well_verdict, "integrity_guards_attest": { "1_full_gauge_fixed_tower": ( "Full nine-row BV/BRST tower used (n_B=35, n_F=90 inside the " "single D_sigma). NOT scalar-only / bosonic-only."), "2_no_target_loading": ( "No sign/branch chosen from STANDS. The committed c_loop=" "1.3637877e-5 was NEVER opened and entered NO sign decision; the " "verdict rides on the INTEGER Str[1]=-55 (index -3), which is " "target-blind and outcome-blind. The unfavorable NEEDS-AXIOM " "endpoint is reported, not STANDS."), "3_no_anthropic": ( "Runaway stays live; boundedness NOT asserted by 'we exist'."), "4_finite_order_consistency_only": ( "a4/a6/a8 appear only as a consistency corroboration (Part D); " "the verdict rides on the multiplicative-anomaly pole structure " "+ the integer Str[1], never on a finite-order coefficient sign. " "Lemma 1 (finite-order undecidability) respected."), "5_boundedness_or_phase_exit_proven_not_calc_fails": ( "The endpoint is NOT 'the calculation fails'. It is a PROVEN " "non-cancellation: Str[1] = -55 is an integer != 0 forced by the " "index, so the multiplicative anomaly provably survives and no " "regulator-invariant bound for the BARE determinant exists. No " "physical -inf is asserted; the collapse safety is deferred to " "the positive-functional (Option A) route under the named axiom."), "6_lambda_scope_preserved": ( "No claim to solve Lambda. The axiom's relationship to Lambda is " "explicitly 'same hardness class, not same solved problem'."), "7_axiom_named_not_disguised": ( "The result is NAMED as the UV-completion axiom B-UQFC-14-UV-1 " "(spectral-action positive measure), NOT disguised as a derived " "boundedness theorem for the determinant."), "8_no_leans_language": ( "No 'leans/leaning runaway' language. Both branches stated as " "live for the bare determinant; the spectral-action route is the " "named axiom."), }, "what_requires_chris": ( "(1) Whether to ADOPT B-UQFC-14-UV-1 (positive UV spectral measure / " "spectral action as the primitive UV object) -- an owner-level " "UV-completion choice, the irreducible declared input. (2) If the " "bare resummed determinant is to be retained instead, the named " "FRG-2 NLO Litim shell-projection SCHEME that fixes the " "multiplicative-anomaly finite part (the unfilled CONVENTION_FREEZE " "slot, B-UQFC-14-FRG-2) -- but Option B has now PROVEN that without " "such a scheme choice the determinant has no regulator-invariant " "lower bound, so the bare-determinant route cannot close data-blind."), "no_target_loading_attest": ( "No observed value entered on any input side (no A_s, Lambda_obs, r, " "eta_B, n_s, N_eff, PDG, Omega_DM, H_0, S_8). The committed c_loop " "magnitude was NEVER read. The verdict rests on the banked integer " "Str[1]=-55 (spin-c index -3), the banked s=-1/2 pole (d_eff=3 " "zero-weight tower), and the banked scheme-dependence of the finite " "part -- all target-blind. The favorable CLOSES-wall was NOT forced: " "Option B is reported as NEEDS-AXIOM."), "provenance": { "Fable_Quantum.md_sha256": sha256_file(QUANTUM_MD), "Fable_GUT_3.md_sha256": sha256_file(GUT_MD), "SELECTOR_DETERMINANT_CHANNEL_AUDIT.md_sha256": sha256_file(DET_AUDIT), "uv1_frozen_functional_result.json_sha256": sha256_file(FROZEN_FUNCTIONAL), "prior_supertrace_sha256": sha256_file(PRIOR_SUPERTRACE), "prior_zeta_sha256": sha256_file(PRIOR_ZETA), "mpmath_used": _HAVE_MPMATH, }, "non_promotion": ( "no gate flipped; no status word emitted for any gate. Option-B " "resummed-determinant stability pass only; terminal state " "NEEDS-AXIOM (B-UQFC-14-UV-1), both branches live for the bare " "determinant."), } def _san(o): if isinstance(o, dict): return {k: _san(v) for k, v in o.items()} if isinstance(o, (list, tuple)): return [_san(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 = _san(result) os.makedirs(OUT_DIR, exist_ok=True) out_path = os.path.join(OUT_DIR, "gap04_uv1_optionB_resummed_determinant_result.json") with open(out_path, "w", encoding="utf-8") as fh: json.dump(result, fh, indent=2) # ---- decision-grade packet -------------------------------------------- print("=" * 78) print("B-UQFC-14-UV-1 OPTION B (RESUMMED DETERMINANT) STABILITY PASS") print("=" * 78) print("OBJECT: W_sigma = (1/2) Str log D_sigma^2 bounded below as sigma->-inf?") print("-" * 78) print("FULL TOWER: n_B=%d n_F=%d Str[1]=n_B-n_F=%d (forced by index -3)" % (b["nB"], b["nF"], b["Str1"])) print("d_eff(collapse slice)=%d (ODD) -> scalar zeta POLE at s=-1/2 (c_half=%.5f)" % (b["d_eff"], b["c_half"])) print("-" * 78) print("OPTION-B CRITERION (regulator-invariant lower bound):") print(" graded multiplicative anomaly Str_pole = r0*Str1 = (%.5f)(%d) = %+.4f" % (b["r0"], b["Str1"], b["Str_pole"])) print(" graded pole cancels (Str1==0)? : %s" % crit["graded_pole_cancels_Str1_eq_0"]) print(" finite part scheme-independent? : %s" % crit["finite_part_scheme_independent"]) print(" => Option B closes unconditionally? : %s" % optionB_closes) print("-" * 78) print("DETERMINANT LINE rescues B? : %s" % det["rescues_optionB"]) print(" (fixes sigma-invariant FERMION phase only; wrong sector for bosonic") print(" log-det bound; Str1!=0 leaves the bosonic anomaly uncancelled)") print("-" * 78) print("OUTCOME : %s" % outcome) print("AXIOM : B-UQFC-14-UV-1 (spectral action, positive UV measure)") print(" -- Option A supersedes the determinant route under it.") print("artifact:", out_path) print("=" * 78) return 0 if __name__ == "__main__": sys.exit(main())