#!/usr/bin/env python3 # -*- coding: utf-8 -*- r""" gap04_cloop_density_sign.py =========================== Gap-04 FRG-2 lane: DERIVE (or precisely gate) the SIGN of c_loop's UNDERLYING heat-kernel density -- the density that sits BEFORE the one-loop -(1/2) prefactor in the e^{-6 sigma} KK-Casimir wall coefficient c_loop = +1.3637e-5. This is the SINGLE deciding fact for the Gap-04 owner-lock: * If c_loop's underlying density is NEGATIVE (c_loop = -(1/2) x negative), then under the SAME global one-loop -(1/2) the a_4 cross-term (whose density is MANIFESTLY POSITIVE) takes the OPPOSITE relative sign -> c_a4>0, a positive wall -> BRANCH-STANDS (the -sigma FRG-4 well stands). * If c_loop's underlying density is POSITIVE (c_loop is a positive Casimir directly, under a DIFFERENT bookkeeping than the global -(1/2)), then a_4 keeps the SAME relative sign as its own positive density under -(1/2), i.e. c_a4<0 -> BRANCH-RUNAWAY (a_4 growth-8 dominates the c_loop growth-6 wall at the -sigma corner -> V -> -inf). CFCA discipline (METHOD_CFCA_June_14.md): - no-target-loading: NO observed value enters on any input side (no A_s, Lambda_obs, r, eta_B, n_s, N_eff, PDG, Omega_DM, H_0, S_8). Every "derived" line is licensed by the committed computation in THIS passage. - NEVER force the favorable branch. The independent countersign (gap04_oneloop_consistency.py / gap04_convention_audit.py) exists to catch exactly that. A prior "well-stands" overwrite was caught and retracted; we do not repeat it. - elegance is the diagnostic: a genuinely irreducible floor feels like a clean floor hit AFTER the elegant routes are exhausted. Here the elegant route (read the sign off a first-principles c_loop computation) is BLOCKED because no such computation exists in the corpus -- so the honest endpoint is a floor, GATED ON the named open object, not a brute-forced sign. ==================================================================== WHAT IS DERIVABLE DATA-BLIND (committed in this passage) ==================================================================== D1. The a_4 cross-DENSITY (pre one-loop) sign is POSITIVE: density = (4 pi)^{-D/2} * (1/36) * R_K6 * R_S2, with the convention-invariant +5/360 master R^2 coefficient (cross 1/36), and the single-signed curvature registry R_K6=+30, R_S2=+2 (geometry-FORCED by the frozen K6 x S2 Einstein constants). All three factors > 0. D2. The global one-loop log-det MAGNITUDE is -(1/2): the universal bosonic V^(1-loop) = -(1/2)(4 pi)^{-D/2} sum_n a_n(D), GLOBAL to every heat-kernel coefficient a_n. (Magnitude, not relative sign.) D3. Therefore the as-run c_a4 under the genuine global -(1/2) on its OWN positive density is NEGATIVE: c_a4 = -(1/2)(4pi)^{-13/2}(1/36)(30)(2) = -5.97e-08. (Matches the on-disk gilkey_a4_cross_terms.json value, byte-checked.) ==================================================================== WHAT IS *NOT* DERIVABLE DATA-BLIND -- and WHY it is the named open object ==================================================================== The relative one-loop sign of c_a4 vs c_loop is fixed ONLY by the sign of c_loop's UNDERLYING heat-kernel density. That sign is NOT banked anywhere: * z_renormalized_c_loop.py reads c_loop as a FROZEN inherited number (C_LOOP_FRG2 = 1.3637877214788921e-05, the "Fable-Latest shell projection") and multiplies it by a wave-function Z-factor ~0.99995. It applies NO -(1/2) log-det and derives NO density sign. (verified on disk) * frozen_inputs.yaml carries c_loop_FRG2 "by reference" from Fable-Latest; NO first-principles producer (a regularized KK-tower Casimir / zero-point sum / shell-projection integral) exists in this corpus. The file c_loop_NLO_match.py referenced by z_renormalized_c_loop.py's spectrum comment is NOT present anywhere in the tree (globbed: 0 hits). * Fable_TOE.md records c_loop as SCAFFOLD-BAND / FRG-2, an explicit Chris-derivation blocker (named object B-UQFC-14-FRG-2: "UQFC SS14 FRG-2 truncation + FRG-6 trajectory closure feeding c_loop | Chris"). Its positivity is ASSUMED (P3: "-inf: V_loop wall (c_loop > 0)") and guarded by falsifier F6 -- not computed. The "underlying-density sign" is one layer BELOW even that assumed wall sign and is nowhere stated. * The nearest first-principles Casimir machinery in the corpus (k6_zeta_casimir_insertion.py) explicitly disclaims: "it does not claim to compute the full finite nonlocal determinant" -- it closes only the LOCAL Seeley-DeWitt/zeta coefficient (and for the Dirac/fermion bundle, a DIFFERENT object than the scalar KK-Casimir wall). So even that does not bank the scalar c_loop underlying-density sign. CONCLUSION (the honest endpoint): The sign of c_loop's underlying heat-kernel density CANNOT be derived without first computing c_loop from first principles -- i.e. running the regularized KK-tower Casimir / shell-projection integral that produces the e^{-6 sigma} coefficient. That computation is itself the NAMED OPEN FRG-2 object (B-UQFC-14-FRG-2, owner = Chris). TOE_FINAL records c_loop OPEN / uncomputed-from-first-principles. Therefore: density_sign_outcome = GENUINELY-INDETERMINATE-gated-on-open-cloop branch = still-owner-locked (BOTH branches live) and the relative-one-loop-sign debit in gap04_reason_hunt.py STAYS BARE-COUNTED (it does NOT become DERIVED), because we did not -- and cannot, data-blind -- derive the sign. Asserting either sign here would be the manufactured favorable-branch step the countersign exists to catch. NON-PROMOTION: no gate flip; no status word emitted for any gate. This is a countersign-ready, gated-on-open analysis the owner signs. exit 0 on an honest gated resolution; exit 2 if an input is unreadable or a forbidden token leaks. """ import hashlib import json import math import os import sys # --------------------------------------------------------------------------- # On-disk real artifacts (no observed value may enter). # --------------------------------------------------------------------------- FA = (r"" r"physics_Journal_and_patents/Final_physics_articles/scripts/gap_04") FROZEN_YAML = os.path.join(FA, "frozen_inputs.yaml") VEFF_YAML = os.path.join(FA, "outputs", "veff_coefficients_frg4.yaml") GILKEY_JSON = os.path.join(FA, "outputs", "gilkey_a4_cross_terms.json") ZRENORM_JSON = os.path.join(FA, "outputs", "z_renormalized_c_loop.json") ZRENORM_SRC = os.path.join(FA, "src", "z_renormalized_c_loop.py") # The frozen-but-missing first-principles producer of c_loop (the named open # object). We probe for it to PROVE its absence (gate evidence), not to read it. CLOOP_FIRSTPRINCIPLES_CANDIDATES = [ os.path.join(FA, "src", "c_loop_NLO_match.py"), os.path.join(FA, "src", "c_loop_NLO_match.json"), os.path.join(FA, "src", "shell_projection_c_loop.py"), os.path.join(FA, "src", "kk_casimir_c_loop.py"), os.path.join(FA, "outputs", "c_loop_NLO_match.json"), ] FORBIDDEN_TOKENS = [ "A_s ", "A_s=", "Lambda_obs", "lambda_obs", "eta_B", "n_s_obs", "N_eff_obs", "PDG", "Planck_n_s", "BICEP", "LiteBIRD_r", "r_obs", "Omega_DM_obs", "H_0_obs", "S_8_obs", ] # --------------------------------------------------------------------------- # FROZEN geometry / master-coefficient constants (NOT observed values). # --------------------------------------------------------------------------- R_K6_0 = 30.0 # 6 * 5 ; Besse Tab 7.107 (Einstein +5) R_S2_0 = 2.0 # 2 * 1 ; round S^2 (Einstein +1) A4_R2_MASTER_COEFF = 5.0 / 360.0 # convention-INVARIANT master R^2 coeff A4_CROSS_PREFACTOR = 2.0 * A4_R2_MASTER_COEFF # = 1/36 (2 from the R^2 cross-term) D_BULK = 13 HK_NORM = 1.0 / (math.pow(4.0 * math.pi, D_BULK / 2.0)) # (4 pi)^{-D/2} > 0 GENUINE_GLOBAL_ONE_LOOP_PREFACTOR = -0.5 # universal bosonic one-loop magnitude 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() def grep_value(path, key): out = [] with open(path, "r", encoding="utf-8") as fh: for line in fh: if key in line: out.append(line.strip()) return out def read_c_loop_Z(path): for ln in grep_value(path, "c_loop_Z"): if ln.startswith("c_loop_Z:"): try: return float(ln.split(":", 1)[1].split("#")[0].strip()) except ValueError: pass return None def zrenorm_applies_minus_half(src_text): """ Does the c_loop producer apply a -(1/2) log-det (from which a density sign could be read)? z_renormalized_c_loop.py only multiplies by a Z-factor; it contains NO one-loop -(1/2) prefactor on c_loop. Detect honestly: look for an explicit log-det prefactor applied to c_loop, not merely the spectral Z power. """ # The producer multiplies c_loop by prod_i Z_i^{g_i/2}: that exponent g_i/2 is # a wave-function power, NOT a one-loop log-det -(1/2) on the c_loop density. # A genuine density-sign derivation would carry "-(1/2)" or "-0.5" acting on a # c_loop heat-kernel density. None present. bad_markers = ["-(1/2) * c_loop", "-0.5 * c_loop", "minus_half_c_loop", "c_loop_density", "c_loop_underlying"] return any(m in src_text for m in bad_markers) def cloop_underlying_density_sign_banked(frozen_text, veff_text, zrenorm_json): """ Is the SIGN of c_loop's underlying heat-kernel density banked anywhere we can read? We require an EXPLICIT underlying-density-sign slot tied to a -(1/2) log-det -- NOT the stored positive WALL value (whose underlying-density sign is precisely the unknown). The corpus banks no such slot -> returns False. """ markers = ["c_loop_underlying_density_sign", "c_loop_density_sign", "c_loop_pre_oneloop_density", "c_loop_heat_kernel_density_sign"] if any(m in frozen_text for m in markers): return True, "explicit underlying-density-sign slot found in frozen_inputs" if any(m in veff_text for m in markers): return True, "explicit underlying-density-sign slot found in veff table" # z_renormalized_c_loop result: confirm it derives no sign (only Z-factor). derived_sign = zrenorm_json.get("c_loop_Z_result", {}).get( "underlying_density_sign") if derived_sign in ("+", "-"): return True, "z_renormalized_c_loop banked an underlying_density_sign" return False, ("no underlying-density-sign slot anywhere; c_loop carried as a " "frozen positive WALL value only; z_renorm applies a Z-factor, " "no -(1/2) log-det") def main(): # ---- locate inputs (refuse if missing) -------------------------------- for p in (FROZEN_YAML, VEFF_YAML, GILKEY_JSON, ZRENORM_JSON, ZRENORM_SRC): if not os.path.exists(p): sys.stderr.write("REFUSE(exit2): missing input %s\n" % p) return 2 with open(FROZEN_YAML, "r", encoding="utf-8") as fh: frozen_text = fh.read() with open(VEFF_YAML, "r", encoding="utf-8") as fh: veff_text = fh.read() with open(ZRENORM_SRC, "r", encoding="utf-8") as fh: zrenorm_src = fh.read() with open(ZRENORM_JSON, "r", encoding="utf-8") as fh: zrenorm_json = json.load(fh) with open(GILKEY_JSON, "r", encoding="utf-8") as fh: gilkey = json.load(fh) # forbidden-input firewall on every source we read. NOTE: the frozen file # and the prereg legitimately NAME forbidden inputs inside attestation / # comment strings ("no_bicep_planck_r_input", "BICEP/Planck r upper bound"). # Naming a forbidden anchor in an attestation is the OPPOSITE of using it. # We therefore flag only a raw leaked numeric VALUE assignment of an anchor, # not the attestation mentions (same discipline as gap04_reason_hunt.py). VALUE_LEAK_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=", ] for name, txt in (("frozen_inputs.yaml", frozen_text), ("veff_coefficients_frg4.yaml", veff_text), ("z_renormalized_c_loop.py", zrenorm_src)): leaked = [t for t in VALUE_LEAK_TOKENS if t in txt] if leaked: sys.stderr.write("REFUSE(exit2): forbidden value assignment in %s: %s\n" % (name, leaked)) return 2 # ===================================================================== # D1. a_4 cross-DENSITY sign (pre one-loop) -- DERIVED POSITIVE # ===================================================================== density_core = A4_CROSS_PREFACTOR * R_K6_0 * R_S2_0 # (1/36)*30*2 = +5/3 a4_density_pre_oneloop = HK_NORM * density_core # strictly > 0 a4_density_sign = "+" if a4_density_pre_oneloop > 0 else ( "-" if a4_density_pre_oneloop < 0 else "0") # ===================================================================== # D3. as-run c_a4 under the genuine global -(1/2) on its OWN positive density # ===================================================================== c_a4_genuine = GENUINE_GLOBAL_ONE_LOOP_PREFACTOR * a4_density_pre_oneloop c_a4_on_disk = float( gilkey["a4_cross_terms"]["K6_x_S2"]["coefficient_value_M13_4_units"]) c_a4_matches_disk = abs(c_a4_genuine - c_a4_on_disk) < 1e-12 * max( 1.0, abs(c_a4_on_disk)) # ===================================================================== # c_loop wall (frozen positive WALL value; F6 load-bearing) -- ASSUMED, not # derived; its UNDERLYING density sign is the open object. # ===================================================================== c_loop_Z = read_c_loop_Z(VEFF_YAML) c_loop_wall_positive = (c_loop_Z is not None and c_loop_Z > 0) # ===================================================================== # GATE EVIDENCE: is there a first-principles c_loop producer on disk? # ===================================================================== firstprinciples_present = { p: os.path.exists(p) for p in CLOOP_FIRSTPRINCIPLES_CANDIDATES } any_firstprinciples = any(firstprinciples_present.values()) # Does the EXISTING producer (z_renormalized_c_loop.py) derive a density sign? zrenorm_derives_sign = zrenorm_applies_minus_half(zrenorm_src) # Is the underlying density sign banked anywhere readable? banked, banked_reason = cloop_underlying_density_sign_banked( frozen_text, veff_text, zrenorm_json) # ===================================================================== # THE GATED RESOLUTION (do NOT force a sign) # ===================================================================== # The relative one-loop sign of c_a4 vs c_loop is fixed iff c_loop's # underlying-density sign is banked. It is not. No first-principles producer # exists; the existing producer derives no sign; the corpus records c_loop # OPEN (B-UQFC-14-FRG-2). Therefore the density sign is GATED ON the named # open object and BOTH branches stay live. if banked and (any_firstprinciples or zrenorm_derives_sign): # Only reachable if the corpus had actually computed c_loop's density # sign from first principles. It has not. (kept honest, not forced) derived_sign = zrenorm_json.get("c_loop_Z_result", {}).get( "underlying_density_sign") if derived_sign == "-": density_sign_outcome = "DERIVED-negative-density" branch_selected = "BRANCH-STANDS" elif derived_sign == "+": density_sign_outcome = "DERIVED-positive-density" branch_selected = "BRANCH-RUNAWAY" else: density_sign_outcome = "GENUINELY-INDETERMINATE-gated-on-open-cloop" branch_selected = "still-owner-locked" debit_reclassification = ( "DERIVED (the c_loop underlying-density sign was actually banked / " "computed from first principles)") else: density_sign_outcome = "GENUINELY-INDETERMINATE-gated-on-open-cloop" branch_selected = "still-owner-locked" debit_reclassification = ( "STAYS BARE-COUNTED (the relative-one-loop-sign debit in " "gap04_reason_hunt.py is NOT promoted to DERIVED: we neither derived " "nor could derive the c_loop underlying-density sign data-blind)") c_loop_underlying_density_sign = "GATED-ON-OPEN-cloop-first-principles (UNBANKED)" result = { "schema": "gap04_cloop_density_sign_result_v1", "purpose": ( "Derive (or precisely gate) the SIGN of c_loop's UNDERLYING " "heat-kernel density -- the density BEFORE the one-loop -(1/2) " "prefactor in the e^{-6 sigma} KK-Casimir wall c_loop = +1.3637e-5."), "density_sign_outcome": density_sign_outcome, "c_loop_underlying_density_sign": c_loop_underlying_density_sign, "branch_selected": branch_selected, "debit_reclassification": debit_reclassification, "what_is_DERIVED_data_blind": { "D1_a4_cross_density_sign_pre_oneloop": a4_density_sign, "D1_a4_cross_density_value": a4_density_pre_oneloop, "D1_reason": ( "geometry-FORCED + convention-INVARIANT: (4pi)^{-D/2} > 0, " "master R^2 coeff +5/360 (cross 1/36) is the same in both Gilkey " "Laplacian conventions (R^2 even in curvature), and the " "single-signed Einstein registry R_K6=+30, R_S2=+2 is fixed by " "the frozen K6 x S2 geometry. All three factors positive."), "D2_global_one_loop_magnitude": GENUINE_GLOBAL_ONE_LOOP_PREFACTOR, "D2_reason": ( "universal bosonic one-loop log-det: V^(1-loop) = " "-(1/2)(4pi)^{-D/2} sum_n a_n. GLOBAL prefactor MAGNITUDE only; " "a global prefactor does NOT force two coefficients same-SIGN."), "D3_c_a4_as_run_under_genuine_minus_half": c_a4_genuine, "D3_c_a4_on_disk": c_a4_on_disk, "D3_matches_on_disk": c_a4_matches_disk, "D3_reason": ( "global -(1/2) acting on a_4's OWN positive density gives c_a4 " "NEGATIVE = -5.97e-08 (byte-matches gilkey_a4_cross_terms.json)."), }, "what_is_NOT_derivable_and_why": { "decisive_unknown": ( "the SIGN of c_loop's UNDERLYING heat-kernel density (is c_loop a " "-(1/2) log-det of a NEGATIVE-density object -> BRANCH-STANDS, or " "a POSITIVE Casimir under a different bookkeeping -> " "BRANCH-RUNAWAY?)."), "underlying_density_sign_banked": banked, "banked_check_reason": banked_reason, "first_principles_producer_present_on_disk": firstprinciples_present, "any_first_principles_producer_present": any_firstprinciples, "existing_producer_derives_a_density_sign": zrenorm_derives_sign, "existing_producer_note": ( "z_renormalized_c_loop.py reads c_loop as a FROZEN inherited " "number (C_LOOP_FRG2 = 1.3637877214788921e-05, 'Fable-Latest " "shell projection') and multiplies by prod_i Z_i^{g_i/2} " "~0.99995. The g_i/2 is a wave-function power, NOT a one-loop " "-(1/2) log-det on the c_loop density; it derives NO density " "sign."), "named_open_object": ( "B-UQFC-14-FRG-2 (owner = Chris): 'UQFC SS14 FRG-2 truncation + " "FRG-6 trajectory closure feeding c_loop'. Fable_TOE.md records " "c_loop SCAFFOLD-BAND / FRG-2, positivity ASSUMED (P3 '-inf: " "V_loop wall (c_loop > 0)') and guarded by falsifier F6 -- the " "underlying-density sign is one layer BELOW even the assumed wall " "sign and is nowhere computed."), "nearest_casimir_machinery_disclaimer": ( "k6_zeta_casimir_insertion.py (the nearest first-principles " "Casimir machinery) explicitly states it 'does not claim to " "compute the full finite nonlocal determinant' -- it closes only " "the LOCAL Seeley-DeWitt/zeta coefficient, and for the " "Dirac/fermion bundle (a DIFFERENT object than the scalar " "KK-Casimir wall). It does NOT bank the scalar c_loop " "underlying-density sign."), }, "two_live_branches": { "BRANCH_STANDS": { "condition": ( "owner/first-principles rules c_loop's UNDERLYING density " "NEGATIVE (c_loop = -(1/2) x negative); under the SAME global " "-(1/2) the positive-density a_4 takes the OPPOSITE relative " "sign -> c_a4 = +5.97e-08, a positive wall"), "c_a4": -c_a4_genuine, "effect": "the -sigma FRG-4 well STANDS", "named_falsifier": "F1_ext (true interior critical point exists)", }, "BRANCH_RUNAWAY": { "condition": ( "c_loop's underlying density POSITIVE (positive Casimir under " "a different bookkeeping); a_4 keeps the SAME relative sign as " "its own positive density under -(1/2) -> c_a4 = -5.97e-08"), "c_a4": c_a4_genuine, "effect": ( "a_4 cross-term (growth 8 at -sigma) DOMINATES the c_loop " "wall (growth 6); a negative dominant term -> V -> -inf, a " "REAL separate 3-modulus -sigma runaway threatening F1"), "named_falsifier": "F1 (any unbounded V_eff -> -inf direction)", }, }, "disjointness_dominance_at_neg_sigma": { "growth_a4_cross_term": 8.0, # exp(-(8 sigma + 4 rho + chi)) "growth_c_loop_wall": 6.0, # exp(-6 sigma) "a4_dominates_neg_sigma_corner": True, }, "well_verdict": ( "OWNER-LOCKED / CONDITIONAL: the -sigma FRG-4 3-modulus well's " "survival is gated on the c_loop underlying-density sign, which is " "the named OPEN first-principles object (B-UQFC-14-FRG-2). It is NOT " "forced to stand (the genuine global -(1/2) on a_4's own positive " "density gives c_a4 NEGATIVE -> runaway) and NOT forced to fail (the " "relative sign vs c_loop is unbanked). Both branches carry named " "falsifiers; the owner must compute c_loop from first principles to " "decide."), "what_requires_chris": ( "Compute c_loop from first principles: run the regularized KK-tower " "Casimir / shell-projection (zero-point / heat-kernel) integral that " "produces the e^{-6 sigma} coefficient, and READ OFF the sign of its " "underlying density BEFORE the one-loop -(1/2) prefactor. This is the " "named open FRG-2 object B-UQFC-14-FRG-2. Until it exists, the " "density sign is GATED-ON-OPEN and the Gap-04 well stays " "owner-locked."), "provenance_hashes": { "frozen_inputs.yaml": sha256_file(FROZEN_YAML), "veff_coefficients_frg4.yaml": sha256_file(VEFF_YAML), "gilkey_a4_cross_terms.json": sha256_file(GILKEY_JSON), "z_renormalized_c_loop.json": sha256_file(ZRENORM_JSON), "z_renormalized_c_loop.py": sha256_file(ZRENORM_SRC), }, "frozen_inputs_used": { "R_K6_0": R_K6_0, "R_S2_0": R_S2_0, "a4_R2_master_coeff_5_over_360": A4_R2_MASTER_COEFF, "a4_cross_prefactor_1_over_36": A4_CROSS_PREFACTOR, "D_bulk": D_BULK, "factor_4pi_to_minus_D_over_2": HK_NORM, "global_one_loop_prefactor": GENUINE_GLOBAL_ONE_LOOP_PREFACTOR, "c_loop_Z_frozen_wall_value": c_loop_Z, "c_loop_FRG2_shell_input": 1.3637877214788921e-05, }, "no_target_loading": True, "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). Every DERIVED line " "(D1/D2/D3) is licensed by the committed computation in this passage " "and byte-checked against on-disk artifacts. The favorable branch was " "NOT forced: the genuine global -(1/2) on a_4's own positive density " "is reported NEGATIVE, and the well is left owner-locked because the " "deciding c_loop underlying-density sign is the named open object."), "non_promotion": ( "no gate flipped; no status word emitted for any gate; " "countersign-ready gated-on-open analysis only."), } out_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)), "outputs") os.makedirs(out_dir, exist_ok=True) out_path = os.path.join(out_dir, "gap04_cloop_density_sign_result.json") with open(out_path, "w", encoding="utf-8") as fh: json.dump(result, fh, indent=2) # ---- decision-grade packet to stdout ---------------------------------- print("=" * 72) print("Gap-04 c_loop UNDERLYING heat-kernel DENSITY SIGN (FRG-2 lane)") print("=" * 72) print("DERIVABLE data-blind:") print(" D1 a_4 cross-density (pre one-loop): %g [sign %s, POSITIVE]" % (a4_density_pre_oneloop, a4_density_sign)) print(" D2 global one-loop magnitude: %g (MAGNITUDE only, not rel. sign)" % GENUINE_GLOBAL_ONE_LOOP_PREFACTOR) print(" D3 c_a4 under genuine -1/2 on own + density: %g [NEGATIVE; " "disk match=%s]" % (c_a4_genuine, c_a4_matches_disk)) print("-" * 72) print("c_loop frozen WALL value (F6 load-bearing): %s [positive=%s, ASSUMED]" % (c_loop_Z, c_loop_wall_positive)) print("c_loop UNDERLYING-density sign banked anywhere: %s" % banked) print(" reason: %s" % banked_reason) print("first-principles c_loop producer present on disk: %s" % any_firstprinciples) print("existing producer (z_renorm) derives a density sign: %s" % zrenorm_derives_sign) print("-" * 72) print("DENSITY SIGN OUTCOME : %s" % density_sign_outcome) print("BRANCH : %s" % branch_selected) print("DEBIT : %s" % debit_reclassification) print("-" * 72) print("REQUIRES CHRIS: compute c_loop from first principles (regularized") print(" KK-tower Casimir / shell-projection integral) -> read the sign of") print(" its underlying density before the -(1/2). Named open: B-UQFC-14-FRG-2.") print(" (we do NOT force a sign; the favorable branch is NOT selected)") print("artifact:", out_path) print("=" * 72) return 0 if __name__ == "__main__": sys.exit(main())