"""v423 -- The No-Ambient-Dependency certificate: NO frozen TFPT readout is COMPUTED from the ambient quantum-gravity measure QG.AMB.01, and its back-reaction is gap-decoupled. This sharpens the v369/v384 prose redundancy ("QG.AMB.01 is a [C] redundancy, not dynamics") into a MACHINE-CHECKED dependency-graph + script fact, told HONESTLY: the one place a flavour readout transitively references QG.AMB.01 (theta13) is an ARCHITECTURAL-coherence edge through the 4D-QFT contract spine, never a numerical input. Audit module, Python-only (the gap algebra is already Wolfram-mirrored via v337). [E] 1. GAP-DECOUPLING MARGIN (exact, backs the decoupling). The ambient back-reaction stiffness is 2*dim(E8)*c3^2 = 496/(64 pi^2) = 31/(4 pi^2) (31 = 2^g_car - 1) ~ 0.785; the transport gap is Delta = 6 ln(3/2) ~ 2.433; so the decoupling margin Delta_eff = Delta - 31/(4 pi^2) ~ 1.648 > 0 (v76/v337) and the ambient susceptibility chi = 1/(1-(2/3)^6) = 729/665 is finite. Negative control: as the gap -> 0, chi -> inf (the ambient would re-enter). [E] 2. CERTIFICATION SINK. The claims that LIST QG.AMB.01 as a dependency are ALL gravity-gate / QG-certification rows (GATE.METRIC.01, GRAVITY.COMPLETE.01, QGAMB.*, SEAM.S3.RP.01, ...), NONE a frozen physical prediction -- QG.AMB.01 has no predictive DIRECT dependent. [E] 3. NOT A VALUE SOURCE. QG.AMB.01 has no producing script (ledger script="-"); every frozen prediction of record is COMPUTED by a compiler script (EM.FP.01<-v3, FLAV.TH12.01<-v9, FLAV.TH13.01<-v268, COSMO.*<-v7), NONE of which is an ambient-measure script (v76/v330/v332/v334/v335) -- so no readout VALUE is produced by the ambient measure. [E] 4. THE ONE LINK IS ARCHITECTURAL, NOT NUMERICAL (told honestly). Of the frozen readouts, only theta13 (FLAV.TH13.01) transitively references QG.AMB.01 -- and the path runs through the 4D-QFT CONTRACT spine (PS.DIRAC.02 -> CONTRACT.QFT4D.01 -> QG.G2.01 -> GATE.METRIC.01), i.e. the readout lives INSIDE the unified spectral-action construction, a coherence edge. Its VALUE sin^2 theta13 = phi0 e^{-5/6} (v268) takes no ambient-measure input; alpha, theta12 and all of cosmology have NO route to QG.AMB.01 at all. [C] 5. VERDICT. QG.AMB.01 is a gap-decoupled certification object: no readout VALUE is computed from it, its only predictive link is the architectural 4D-QFT contract, and the gap margin (1.648>0) suppresses its back-reaction -- v369 as a DAG/script fact. HONEST: this does NOT prove SEAM.EQUIV.01 (the readouts depend on the seam being the (E8)_1 net, the one open keystone) -- QG.AMB.01 specifically is dead. Python-only (csv DAG/script audit + gap arithmetic; the exact 31/(4 pi^2) and 729/665 are mirrored via v337). """ import os import csv import re from collections import deque import sympy as sp from tfpt_constants import check, summary, reset, g_car, dim_Splus HERE = os.path.dirname(os.path.abspath(__file__)) LEDGER = os.path.join(HERE, "status_ledger.csv") DIM_E8 = 248 AMB = "QG.AMB.01" AMB_SCRIPTS = ("v76", "v330", "v332", "v334", "v335", "v369", "v337") FROZEN = ["EM.FP.01", "FLAV.TH12.01", "FLAV.TH13.01", "COSMO.LAM.01", "COSMO.INF.01", "COSMO.OMB.01"] SPINE = "CONTRACT.QFT4D.01" # the 4D-QFT contract node on theta13's path _CLAIM = re.compile(r"^[A-Z][A-Z0-9]*(?:\.[A-Z0-9]+)+$") # EM.FP.01, QG.AMB.01 def load(): deps, scr = {}, {} with open(LEDGER, newline="") as fh: r = csv.reader(fh) next(r) for row in r: if len(row) < 6: continue cid = row[0].strip() deps[cid] = [t.strip() for t in row[4].split(";") if _CLAIM.match(t.strip())] scr[cid] = row[5].strip() return deps, scr def reaches(g, start, target): seen, st = set(), [start] while st: n = st.pop() for d in g.get(n, []): if d == target: return True if d not in seen: seen.add(d) st.append(d) return False def path(g, start, target): prev, q = {start: None}, deque([start]) while q: n = q.popleft() for d in g.get(n, []): if d not in prev: prev[d] = n if d == target: p = [d] while prev[p[-1]] is not None: p.append(prev[p[-1]]) return list(reversed(p)) q.append(d) return None def run(): reset() print("v423 No-Ambient-Dependency: no frozen readout is computed from QG.AMB.01") g, scr = load() # ---- 1. gap-decoupling margin (exact) ---- c3 = sp.Rational(1, 1) / (8 * sp.pi) stiff = sp.simplify(2 * DIM_E8 * c3**2) # 31/(4 pi^2) Delta = 6 * sp.log(sp.Rational(3, 2)) margin = sp.N(Delta - stiff) chi = sp.Rational(1, 1) / (1 - sp.Rational(2, 3)**6) check("GAP-DECOUPLING MARGIN [E]: 2 dim(E8) c3^2 = 31/(4 pi^2) (31=2^g_car-1) " "~ 0.785, Delta = 6 ln(3/2) ~ 2.433, so Delta_eff ~ 1.648 > 0 " "(v76/v337); chi = 1/(1-(2/3)^6) = 729/665 finite (neg control: " "gap->0 => chi->inf)", stiff == sp.Rational(31, 4) / sp.pi**2 and 31 == 2**g_car - 1 and margin > 1.6 and chi == sp.Rational(729, 665)) # ---- 2. certification sink (no prediction directly depends on QG.AMB.01) ---- dependents = sorted(c for c, d in g.items() if AMB in d) pred_dependents = [c for c in dependents if c in FROZEN] check("CERTIFICATION SINK [E]: %d claims list QG.AMB.01 as a dependency and " "ALL are gravity-gate/QG-certification rows (%s ...), NONE a frozen " "prediction" % (len(dependents), ", ".join(dependents[:4])), len(dependents) >= 6 and pred_dependents == []) # ---- 3. not a value source (script-level) ---- amb_script = scr.get(AMB, "") pred_clean = {c: scr.get(c, "") for c in FROZEN} no_amb_compute = all(not any(s in v for s in AMB_SCRIPTS) for v in pred_clean.values()) check("NOT A VALUE SOURCE [E]: QG.AMB.01 has no producing script (script=" "'%s'); each frozen prediction is computed by a compiler script " "(%s), none an ambient-measure script %s" % (amb_script, ", ".join("%s<-%s" % (c, v.replace('.py', '')) for c, v in pred_clean.items()), list(AMB_SCRIPTS)), amb_script in ("-", "") and all(pred_clean.values()) and no_amb_compute) # ---- 4. the one transitive link is architectural, not numerical ---- th13_path = path(g, "FLAV.TH13.01", AMB) value_clean = [c for c in FROZEN if c != "FLAV.TH13.01" and not reaches(g, c, AMB)] check("ARCHITECTURAL-ONLY LINK [E]: of the frozen readouts only theta13 " "transitively references QG.AMB.01, via the 4D-QFT CONTRACT spine " "(%s) -- a coherence edge, not a numerical input (value sin^2 th13 = " "phi0 e^{-5/6}, v268); alpha/theta12/cosmology (%s) have NO route at all" % (" -> ".join(th13_path or []), ", ".join(value_clean)), th13_path is not None and SPINE in th13_path and len(value_clean) == len(FROZEN) - 1) # ---- 5. verdict (typed) ---- check("VERDICT [C]: QG.AMB.01 is a gap-decoupled certification object -- no " "readout VALUE is computed from it, its only predictive link is the " "architectural 4D-QFT contract, and the gap (1.648>0) suppresses its " "back-reaction (v369 as a DAG/script fact). HONEST: does NOT prove " "SEAM.EQUIV.01 -- the readouts depend on the seam = (E8)_1 net, the " "one open keystone; QG.AMB.01 specifically is dead", dim_Splus == 16 and pred_dependents == [] and no_amb_compute) return summary("v423 No-Ambient-Dependency (no frozen readout computed from " "QG.AMB.01; gap margin 1.648>0; only link is architectural)") if __name__ == "__main__": raise SystemExit(1 if run() else 0)