#!/usr/bin/env python3 # ============================================================================= # eval_s00_masters_v2.py — HARDENED (fail-closed) sibling of the eecLOsector # standalone evaluator eval_s00_masters.py (numeric core UNCHANGED, verbatim). # Hardening (2026-07-06): # 1. Fail-closed printing: output truncated to the per-component CERTIFIED # floor (base-point certs from the independent two-layout run; S-layer # two-precision certs; F-node value certs from dps48-vs-dps60 reruns; F-grid # interpolation floor via LEAVE-ONE-OUT computed AT RUNTIME from the # embedded nodes). --raw prints working precision with an explicit # uncertified-tail label. Nothing here is a hardcoded "31". # 2. Loud gates: blob-sha INTEGRITY_GATE (rc=3), RESID_GATE/TWOPREC_GATE # (rc=2), DEPTH_GATE (rc=5), LOADER_GATE (rc=3), FNODE_CACHE_GATE (rc=4). # 3. --recompute-node: F_true node regeneration AT ANY dps from the EXACT # layer (S00_FLUX_CACHE.json exact rationals -> fluxkernel3 chart totals; # CORNER_SOURCES.json exact corner rationals; K0/K1 wall5713 written # integrals evaluated live) loaded from DECLARED external artifacts with # sha-manifest pinning + fail-loud-if-absent (witness-loader # pattern). Embedded node values demote to a # compare-on-load cache with a raising mismatch gate (--fnodes-json). # 4. NS/NA are SEEDS: Chebyshev-tail refine-until-bound escalation # (WP1 recipe); --no-escalate pins depths and clamps to achieved tail. # 5. Liveness + measured default (2026-09-03; prints only -- the numeric # path is byte-identical at matched settings, verified against pre-change # runs: all 8 certified M-lines, the escalation diagnostics, and max|Im| # compare byte-for-byte at --dps 40 and at the base point). stdout is # line-buffered; a flushed identity line + the up-front certification # floors print right after the INTEGRITY_GATE; stage/heartbeat lines # (at most one per 20 s) cover the S-layer build and both assembly VoP # loops. Default --dps 50 -> 40: measured 2026-09-03, dps 40 is the # smallest default that keeps the certified 29-digit prefixes (the # F-grid LOO floor binds at 29d for every dps >= 30) AND completes -- # at dps 30/35 the S-layer Chebyshev-tail certificate stays under the # escalation target (tails 25.8-27.2d vs targets 35.0/35.9) and the run # ladders NS 80->120->180->... toward the depth cap instead of # finishing (dps 30 measured >2 h without completing; dps 35 stopped 3126 s into its # second pass -- non-completion inferred from the saturation model). # # MEASURED WALLS (UTC stamps from the run logs' date -u lines, # 2026-09-03, CPU-oversubscribed machine, load noted): # default (u=21/50, dps 40) 5162 s wall / 4943 s user CPU # (06:45:37Z..08:11:40Z, ~2.9x CPU-oversubscribed); # two passes, depth history NS 80 (tail # 27.2d) -> NS 120 (tail 36.1d >= target # 35.9d); all 8 masters at 29 certified # digits. BUDGET AN HOUR-CLASS WALL and # watch the heartbeat lines. # --cert-only 2.9 s (04:31:54Z..04:31:56Z) -- floors # only, no transport. # --point 1/2 (base point) 0.8 s (04:35:01Z) -- certified base # vector, no transport; base points 19/50, # 1/2, 13/20 serve up to their 85-89d # base-point floors at any --dps. # --dps 12 --NS 24 --NA 16 --no-escalate # 3684 s (04:35:01Z..05:36:26Z) AND the # achieved tail clamps printing to 6 # digits -- shallow seeds are NOT a # shortcut. # NO TRANSPORTED INVOCATION FITS A MINUTES-CLASS BUDGET: every # any other point pays the full S-layer flux build (>= 243 outer # quadrature nodes, ~4900 s of CPU at working dps 50 in the measured # runs) before the assembly layers. The sub-minute invocations are # --cert-only and the three base points; for everything else budget # an hour-class wall and follow the heartbeat lines. # Ported (with credit) beyond the original's module list: fluxkernel2.py # flux_face_pair, fluxkernel3.py (_quad_fused/flux_group_57/flux_row_total), # scratch/wall5713/wall5713.py (phi_P0/phi_P1/_Ksafe/K0/K1), node_totals.py # parse_groups — all eecLOsector source code, replicated verbatim. # Original header follows. # ============================================================================= # eval_s00_masters.py — STANDALONE evaluator for the 8 REAL bounded-region # masters of sector s00_MI20cal (the EEC LO sector of this work). # # Slice: z12=1/7 z13=1/5 z14=1/3 z23=2/5 z24=3/7 z34=u. # Architecture (identical to the gated production pipeline, 2026-07-04..06): # M(u) = c(u) J(u) + K(u) y(u) # y(u) = PhiD(u)[ PhiD^-1(u0) y0 + int PhiD^-1 (LC*(S1,S2) + L*F) ] (D/PhiD layer) # J(u) = W(u) [ W^-1(u0) J0 + int W^-1 (Gy*y + GS*S + E(F - K L F)) ] (W period VoP) # S1,S2,S3 by flux-sourced first-order VoP (S-layer, FLUX_S90/91/92 families) # F = per-master-row face-flux totals, barycentric interpolant of recorded # F_true nodes (FTRUE_NODES.json; LOO-measured 29-34d per segment). # W(u) periods are computed LIVE by quadrature of the maxcut quartic at the # base point and transported with the exact GM4 ODE (mp.odefun, fwd/bwd). # # Dependencies: mpmath + stdlib ONLY. No files read at runtime — all node/ # base-point/kernel data is embedded at the bottom (_BLOB), provenance inside. # NO oracle values are embedded anywhere; everything downstream of the # embedded base-point values/nodes is COMPUTED analytically at runtime. # # Code replicated (with credit) from the source evalbuild modules: # engine.py — cheb_nodes/cheb_coeffs/cheb_cumint/cheb_eval, W_columns # (CURRENT patched version: analytic endpoint factorization # in both cycle integrals, found 2026-07-06 at dps60), # quartic_roots, ratval/_fr. # phid.py — PhiD fundamental matrix (TRI f=2 + FULL corner). # assembly.py — Pdesc, PhiD_inv/_Qmat, Wprov (fwd/bwd odefun), masters_at. # sprov2.py — SProvider2 (flux-sourced S-layer VoP), FluxFam, SEGMENTS. # fluxkernel.py / fluxkernel2.py — FACEDEF/VIDX, closed-form-inner face flux # with prop denominators (5,13 groups), region guards. # assembly_run.py — leg driver, FP barycentric F provider, DE-residual gate. # # CLI: # python3 eval_s00_masters.py --dps N [--point u] [--check] # --point u : rational (e.g. 21/50, default 21/50); base point/segment chosen # automatically; clear error outside the transport segments. # --check : (a) recompute at working precisions N and N+10, report # per-master agreement digits; (b) evaluate at 47/100 and # verify the DE-residual identity M' = A.M + C.(S1,S2) + F # using the embedded exact A-row rationals at 47/100. # ============================================================================= import sys, json, time, argparse, os, hashlib from fractions import Fraction import mpmath as mp _BLOB = 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04:57:05 EDT","source_sha256_16":{"REDUCTION.json":"d37a7d0cf96dc48d","MAXCUT_symbolic.json":"70f108b2d81d64f1","BLOCKS_SAMPLED.json":"34fa73f95f6e2563","KE_EXACT.json":"6b7dd078ba921fcf","LC_EXACT.json":"e272466e7c540663","GS_EXACT.json":"89543307cb119be0","D_STRATEGY.json":"7cad9fd95dace05b","S_ODES_GATED.json":"ff2e1642c5e7fdc5","S_ANCHORS_U19_50.json":"864174bfb02a521e","S_ANCHORS_U12.json":"524d98e741c59b7e","S_ANCHORS_U13_20.json":"623e5458cfd90cc7","FLUX_S90_GATED.json":"5db5d4aee44ae99f","FLUX_S91_GATED.json":"f5075c5e4606eea0","FLUX_S92_GATED.json":"ed812ba29179238a","anchor_indep/ANCHOR_U19_50.json":"2453f78709f723f8","anchor_indep/ANCHOR_U12.json":"2011872c57f566e4","anchor_indep/ANCHOR_U13_20.json":"ad74a0f2f3ca4117","FTRUE_NODES.json":"6cf121847176d915","CHEB_NODES.json":"045befb1ed951e35","degen/s00_MI20cal/DEFULL_u47_100.json":"14be0dd3c9cbde02"}}}''' EMBED = json.loads(_BLOB) MOMS = EMBED['MOMS'] # --------------------- v2 certification data + integrity --------------------- _BLOB_SHA256 = '518acde51c37d1012dd749cc6b86a9eaf54f44b99accc62f1af8bab282a41e19' # ---- liveness layer (2026-09-03): stage/heartbeat prints ONLY -- no numeric # path is touched; every value-bearing computation is byte-identical to the # original at matched settings. All liveness output is flushed so a reader # piping stdout sees the first line within seconds and progress >= 1/min. _T0_LIVE = time.time() _HB_LIVE = [0.0] def _stage(msg): print(f'[{time.time()-_T0_LIVE:7.1f}s] {msg}', flush=True) def _beat(msg): """Rate-limited heartbeat: at most one line per 20 s (so the gap to the next line stays under a minute even when one node runs long).""" now = time.time() if now - _HB_LIVE[0] >= 20: _HB_LIVE[0] = now _stage(msg) _V2CERT = json.loads(r'''{"basepoint_cert_digits": {"1/2": [86.7, 90.1, 90.0, 89.9, 90.2, 90.3, 90.2, 86.2], "13/20": [85.0, 90.1, 90.0, 89.9, 90.2, 90.3, 90.2, 84.6], "19/50": [85.1, 90.1, 90.0, 89.9, 90.2, 90.3, 90.2, 84.6]}, "built": "2026-07-06 15:52:58 EDT", "cert_sources": {"basepoints": "two-layout (GL + DE-panel) certification of the base-point masters, agreement digits", "fnode_loo": "computed AT RUNTIME from embedded nodes (leave-one-out)", "fnode_values": "dps48 recomputation vs an independent dps60 recomputation, per-row worst agreement", "s_basepoints": "two-precision agreement digits of the S-layer base points"}, "ext_manifest": {"CHEB_NODES.json": "045befb1ed951e35aece6e59cb0ea034ebffbc1abe2086c8bbfe771582d55703", "S00_FLUX_CACHE.json": "2d28406a3cdfe07a05c8505033d6a48a76049970fae6aa868a4fdd0d7d509c97", "scratch/wall5713/CORNER_SOURCES.json": "82cf303ea44c90a95ed4fcc087d93ebf9973c0453e9c885eb7d9b8086f09a1c6"}, "fnode_string_dps": {"seg13_t13": 46, "seg23_t23": 46, "segmid_t2150": 46, "segmid_t2649": 46}, "fnode_value_cert_digits": {"seg13_t13": [36.46156576639693, 34.04020943650392, 35.53997762573335, 35.47195103541617, 35.77181265132892, 35.5950866594945, 35.47953855997093, 35.75902755865404], "seg23_t23": [35.57994949115382, 35.40400766575681, 36.08266841028325, 37.016103614890284, 35.67600236993264, 35.66858043223942, 35.33711924763729, 35.555069035517015], "segmid_t2150": [37.08049527182189, 36.21326827410609, 36.38963778020081, 36.16666142685123, 36.44750148751614, 36.312930018742186, 36.423399171686334, 36.161198911593104], "segmid_t2649": [37.002337400260814, 36.37788214497449, 36.787312236894834, 36.616965769221906, 37.07869915045817, 36.46393314574472, 36.609284008249126, 34.72502705844518]}, "fnode_value_cert_matched": {"seg13_t13": "48/48", "seg23_t23": "59/59", "segmid_t2150": "48/48", "segmid_t2649": "46/46"}, "s_basepoint_cert_digits": {"1/2": 61, "13/20": 61, "19/50": 61}}''') def integrity_gate(): h = hashlib.sha256(_BLOB.encode()).hexdigest() if h != _BLOB_SHA256: print(f'INTEGRITY_GATE FAIL: embedded blob sha256 {h[:16]}... != pinned ' f'{_BLOB_SHA256[:16]}... — embedded data corrupted or rebuilt without ' f'repinning; refusing to print any value.') sys.exit(3) # =========================== engine.py (verbatim) =========================== def _fr(s): if '/' in s: a, b = s.split('/'); return mp.mpf(a)/mp.mpf(b) return mp.mpf(s) def ratval(num, den, x): n = mp.mpf(0) for c in reversed(num): n = n*x + _fr(c) d = mp.mpf(0) for c in reversed(den): d = d*x + _fr(c) return n/d def quartic_roots(Pcs_desc): rs = mp.polyroots(Pcs_desc, maxsteps=600, extraprec=mp.mp.dps*4) tol = mp.mpf(10)**(-mp.mp.dps//2) reals = sorted([r.real for r in rs if abs(r.imag) < tol]) cplx = sorted([r for r in rs if abs(r.imag) >= tol], key=lambda z: z.imag) return reals, cplx def W_columns(Pcs_desc, p4, p3): """4x4 [gamma_a | gamma_b | s_alg | e4] at fixed u. Cycle conventions validated vs exact GM4 (ODE residual at FD floor) and recorded maxcut periods. Endpoint sqrt factors expressed ANALYTICALLY in the substitution variable (deep tanh-sinh nodes round x to the endpoint root exactly at high dps -> ZeroDivision; cure found 2026-07-06).""" reals, cplx = quartic_roots(Pcs_desc) r1, r2 = reals[0], reals[1]; r3 = cplx[0]; r4 = cplx[1] def base(k, t): return (1/(2*t-5)) if k == 'third' else t**int(k) colA = [] for k in (0, 1, 2, 'third'): def f(th): s = mp.sin(th); c = mp.cos(th) if s == 0 or c == 0: return mp.mpf(0) x = r1 + (r2-r1)*s*s dx = (r2-r1)*mp.sin(2*th) rest = mp.re(-p4*(x-r3)*(x-r4)) return base(k, x)/((r2-r1)*s*c*mp.sqrt(rest))*dx colA.append(2*mp.quad(f, [0, mp.pi/2])) colB = [] for k in (0, 1, 2, 'third'): def f(th): s = mp.sin(th); c = mp.cos(th) if s == 0 or c == 0: return mp.mpc(0) x = r2 + (r3-r2)*s*s dx = (r3-r2)*mp.sin(2*th) pref = mp.sqrt(mp.mpc(p4)) if mp.re(mp.mpc(p4)) >= 0 else mp.mpc(0, 1)*mp.sqrt(-p4) den = pref*(mp.sqrt(r3-r2)*s)*(mp.sqrt(r2-r3)*c)*mp.sqrt(x-r1)*mp.sqrt(x-r4) return base(k, x)/den*dx colB.append(2*mp.quad(f, [0, mp.pi/2])) sq = mp.sqrt(mp.mpc(p4)) if p4 >= 0 else mp.mpc(0, 1)*mp.sqrt(-p4) colS = [mp.mpf(0), 1/sq, -p3/(2*sq**3), mp.mpf(0)] colE = [mp.mpf(0)]*3 + [mp.mpf(1)] return mp.matrix([[colA[i], colB[i], colS[i], colE[i]] for i in range(4)]) def cheb_nodes(N, a, b): return [(a+b)/2 + (b-a)/2*mp.cos(mp.pi*j/N) for j in range(N+1)] def cheb_coeffs(vals): N = len(vals)-1 cs = [] for k in range(N+1): s = mp.mpf(0) for j in range(N+1): w = mp.mpf(1) if 0 < j < N else mp.mpf(1)/2 s += w*vals[j]*mp.cos(mp.pi*k*j/N) cs.append(2*s/N) return cs def cheb_cumint(cs): N = len(cs)-1 a = [cs[0]/2] + [cs[k] for k in range(1, N)] + [cs[N]/2] C = [mp.mpf(0)]*(N+2) C[1] = a[0] - (a[2]/2 if N >= 2 else 0) for k in range(2, N+2): am = a[k-1] if k-1 <= N else mp.mpf(0) ap = a[k+1] if k+1 <= N else mp.mpf(0) C[k] = (am-ap)/(2*k) return C def cheb_eval(C, t): b1 = b2 = mp.mpf(0) for k in range(len(C)-1, 0, -1): b1, b2 = 2*t*b1 - b2 + C[k], b1 return t*b1 - b2 + C[0] def cheb_tail_digits(C): """v2: certified-tail estimate for a Chebyshev coefficient array — digits = -log10( max|last 3 coeffs| / max|coeffs| ). Observational only.""" mags = [abs(c) for c in C] top = max(mags) if mags else mp.mpf(0) if top == 0: return float(mp.mp.dps) tail = max(mags[-3:]) if len(mags) >= 3 else mags[-1] if tail == 0: return float(mp.mp.dps) return float(-mp.log10(tail/top)) # ================== fluxkernel.py face map (verbatim) ======================== FACEDEF = { 1: {'vars': ('x2', 'x3'), 'solve': 'x4', 'Ab': lambda u: ((1, -1, -1, mp.mpf(2)/5), (1, -mp.mpf(3)/7, -u))}, 2: {'vars': ('x1', 'x3'), 'solve': 'x4', 'Ab': lambda u: ((1, -1, -1, mp.mpf(1)/5), (1, -mp.mpf(1)/3, -u))}, 3: {'vars': ('x1', 'x2'), 'solve': 'x4', 'Ab': lambda u: ((1, -1, -1, mp.mpf(1)/7), (1, -mp.mpf(1)/3, -mp.mpf(3)/7))}, 4: {'vars': ('x2', 'x3'), 'solve': 'x1', 'Ab': lambda u: ((1, -1, -1, mp.mpf(2)/5), (1, -mp.mpf(1)/7, -mp.mpf(1)/5))}, } VIDX = {'x1': 0, 'x2': 1, 'x3': 2, 'x4': 3} # ============== fluxkernel2.py closed-form face flux (verbatim) ============== class RegionSingularity(RuntimeError): pass def props_from_sector(sector): return tuple(p for p in sector if p in (5, 7)) def _l7(face, t): if face in (1, 4): return (t - 1, 1 - mp.mpf(2)/5*t) return (mp.mpf(-1), mp.mpf(1)) def _pmul(a, b): r = [mp.mpc(0)]*(len(a)+len(b)-1) for i, x in enumerate(a): if x == 0: continue for j, y in enumerate(b): r[i+j] += x*y return r def _ppow(p, n): r = [mp.mpc(1)] for _ in range(n): r = _pmul(r, p) return r def _peval(p, x): v = mp.mpc(0) for c in reversed(p): v = v*x + c return v def _pdivmod(N, D): N = list(N); dd = len(D)-1; lc = D[-1] q = [mp.mpc(0)]*max(1, len(N)-dd) for i in range(len(N)-1, dd-1, -1): f = N[i]/lc; q[i-dd] = f if f != 0: for j in range(dd+1): N[i-dd+j] -= f*D[j] return q, N[:dd] if dd > 0 else [mp.mpc(0)] def _smul(a, b, M): r = [mp.mpc(0)]*M for i in range(M): if a[i] == 0: continue for j in range(M-i): r[i+j] += a[i]*b[j] return r def flux_face(mono_coeffs, face, u, props=(), quad_extra=0, reg=False, _build=False, s_upper=None): props = tuple(sorted(set(props))) m5 = 1 if 5 in props else 0 m7 = 1 if 7 in props else 0 fd = FACEDEF[face] (a0, at, as_, ats), (b0, bt, bs) = fd['Ab'](u) ti, si, ki = VIDX[fd['vars'][0]], VIDX[fd['vars'][1]], VIDX[fd['solve']] fi = [i for i in range(4) if i not in (ti, si, ki)][0] Pk = {} for e, c in mono_coeffs.items(): if e[fi] != 0: continue Pk.setdefault(e[ki], {}).setdefault((e[ti], e[si]), mp.mpf(0)) Pk[e[ki]][(e[ti], e[si])] += c if not Pk: return mp.mpf(0) K = max(Pk.keys()); MB = K + 1 - m5 wdps = 2*mp.mp.dps + 25 + 2*K # guard SCALES with ambient dps (2026-07-05 fix) def AB(t): return (a0 + at*t, as_ + ats*t, b0 + bt*t, bs) def smax(t): al0, al1, be0, be1 = AB(t) cands = [] if al1 < 0: cands.append(-al0/al1) if be1 < 0: cands.append(-be0/be1) return min(cands) if cands else None def inner(t, chan=0): with mp.workdps(wdps): t = mp.mpf(t) sm = smax(t) if sm is None or sm <= 0: return mp.mpc(0) al0, al1, be0, be1 = AB(t) if be0 <= 0: return mp.mpc(0) su = sm if s_upper is not None: sv = s_upper(t) if sv is None or sv <= 0: return mp.mpc(0) if sv < su: su = mp.mpf(sv) N = [mp.mpc(0)]; scs = {} for k, terms in Pk.items(): smax_deg = max(b for (a, b) in terms) sc = [mp.mpc(0)]*(smax_deg+1) for (a, b), c in terms.items(): sc[b] += c*t**a scs[k] = sc term = _pmul(_pmul(sc, _ppow([al0, al1], k)), _ppow([be0, be1], K-k)) if len(N) < len(term): N += [mp.mpc(0)]*(len(term)-len(N)) for i, x in enumerate(term): N[i] += x roots, lead = [], mp.mpc(1) if MB > 0: if be1 == 0: raise RegionSingularity(f"face {face}: B constant in s") roots.append((mp.mpc(-be0/be1), MB)); lead *= be1**MB if m5: g0 = (t-1)*be0 + al0; g1 = (t-1)*be1 + be0 + al1; g2 = be1 G5v = lambda s: (g2*s + g1)*s + g0 v0, v1 = G5v(mp.mpf(0)), G5v(su) bad = (v0 == 0) or (v1 == 0) or (mp.sign(v0) != mp.sign(v1)) if not bad and g2 != 0: vx = -g1/(2*g2) if 0 < vx < su and mp.sign(G5v(vx)) != mp.sign(v0): bad = True if bad: raise RegionSingularity(f"G5 vanishes on [0,smax]: face {face} t={mp.nstr(t,12)} " f"G5(0)={mp.nstr(v0,6)} G5(sm)={mp.nstr(v1,6)}") sq = mp.sqrt(mp.mpc(g1*g1 - 4*g0*g2)) roots += [((-g1+sq)/(2*g2), 1), ((-g1-sq)/(2*g2), 1)]; lead *= g2 l7_ep = None; c_dir = None if m7: if face in (1, 4): l0, l1 = -al0, -al1 else: l0, l1 = _l7(face, t) r7 = -l0/l1 Ar = al0 + al1*r7; Br = be0 + be1*r7 Nv = mp.mpc(0); nsc = mp.mpf(0) for k, sc in scs.items(): pv = _peval(sc, r7) psc = sum(abs(x)*max(mp.mpf(1), abs(r7))**i for i, x in enumerate(sc)) Nv += pv*Ar**k*Br**(K-k) nsc += psc*abs(Ar)**k*abs(Br)**(K-k) if nsc == 0 or abs(Nv) <= nsc*mp.mpf(10)**(-(mp.mp.dps-10)): q = [mp.mpc(0)]*max(1, len(N)-1) for i in range(len(N)-1, 0, -1): q[i-1] = N[i] + (r7*q[i] if i < len(N)-1 else 0) N = [x/l1 for x in q] elif su == sm and ((face in (1, 4) and al1 < 0 and sm == r7) or abs(sm - r7) <= max(mp.mpf(1), sm)*mp.mpf(10)**(-(wdps-12))): r7 = sm if not reg: raise RegionSingularity( f"L7 endpoint pole, N NOT divisible: face {face} t={mp.nstr(t,12)} — " f"log-divergent along stratum x1=x4=0; use reg=True (pair faces 1+4)") dp = lead*l1 for r_o, mu_o in roots: dp *= (r7 - r_o)**mu_o c_dir = Nv/dp roots.append((mp.mpc(r7), 1)); lead *= l1; l7_ep = len(roots) - 1 else: w0, w1 = l0, l0 + l1*su if w0 == 0 or w1 == 0 or mp.sign(w0) != mp.sign(w1): raise RegionSingularity(f"L7 vanishes on [0,smax]: face {face} t={mp.nstr(t,12)} " f"L7(0)={mp.nstr(w0,6)} L7(sm)={mp.nstr(w1,6)}") roots.append((mp.mpc(r7), 1)); lead *= l1 D = [lead] for r, mu in roots: for _ in range(mu): D = _pmul(D, [-r, mp.mpc(1)]) Qp, R = _pdivmod(N, D) Dp = [D[i]*i for i in range(1, len(D))] val = mp.mpc(0); c_ep = mp.mpc(0) for j, cj in enumerate(Qp): if cj != 0: val += cj*su**(j+1)/(j+1) for idx, (r, mu) in enumerate(roots): if mu == 1: if idx == l7_ep: c_ep = c_dir; val += -c_dir*mp.log(sm) else: c = _peval(R, r)/_peval(Dp, r) val += c*(mp.log(su - r) - mp.log(-r)) if MB > 1: rB = roots[0][0] f = [mp.mpc(0)]*MB for i, ci in enumerate(R): if ci == 0: continue for j in range(min(i, MB-1)+1): f[j] += ci*mp.binomial(i, j)*rB**(i-j) for ro, mu in roots[1:]: d = rB - ro f = _smul(f, [(-1)**n/d**(n+1) for n in range(MB)], MB) f = [x/lead for x in f] for j in range(1, MB+1): cj = f[MB-j] if cj == 0: continue if j == 1: val += cj*(mp.log(su - rB) - mp.log(-rB)) else: val += cj*((su - rB)**(1-j) - (-rB)**(1-j))/mp.mpf(1-j) if chan == 1: return c_ep if chan == 2: if c_ep == 0: return mp.mpc(0) return c_ep*mp.log((be0 + be1*sm)/abs(al1)) return val if _build: return inner, AB, smax, m5, m7 return _outer(inner, face, u, AB, smax, m5, m7, reg) def _splits(face, AB, smax, m5, m7): splits = [mp.mpf(0), mp.mpf(1)] def gap(t): al0, al1, be0, be1 = AB(t) sa = -al0/al1 if al1 < 0 else mp.mpf('1e9') sb = -be0/be1 if be1 < 0 else mp.mpf('1e9') return sa - sb try: if mp.sign(gap(mp.mpf('0.001'))) != mp.sign(gap(mp.mpf('0.999'))): r = mp.findroot(gap, mp.mpf('0.5')) if 0 < r < 1: splits.append(mp.mpf(r)) except Exception: pass if m5 or m7: splits += _scan_extra_splits(face, AB, smax, m5, m7) return sorted(set(splits)) def _outer(inner, face, u, AB, smax, m5, m7, reg=False): splits = _splits(face, AB, smax, m5, m7) splits = [splits[0]] + [b for a, b in zip(splits, splits[1:]) if b - a > mp.mpf(10)**(-(mp.mp.dps+15))] if splits[-1] != 1: splits[-1] = mp.mpf(1) tol = mp.mpf(10)**(-(mp.mp.dps - 8)) def qsum(chan): tot = mp.mpc(0) for a, b in zip(splits, splits[1:]): tot += mp.quad(lambda tt: inner(tt, chan), [a, b]) if abs(mp.im(tot)) > tol*max(1, abs(mp.re(tot))): raise RegionSingularity(f"imaginary residue too large: face {face} chan {chan} " f"Im={mp.nstr(mp.im(tot),6)} Re={mp.nstr(mp.re(tot),6)}") return mp.re(tot) if not reg: return qsum(0) return {'J': qsum(0), 'C': qsum(1), 'S': qsum(2)} def _scan_extra_splits(face, AB, smax, m5, m7, n=40): NTRK = (5 if m5 else 0) + (2 if m7 else 0) def tracked(t): sm = smax(t) if sm is None or sm <= 0: return [None]*NTRK al0, al1, be0, be1 = AB(t) out = [] if m5: g0 = (t-1)*be0 + al0; g1 = (t-1)*be1 + be0 + al1; g2 = be1 if g2 == 0: out += [None]*5 else: disc = g1*g1 - 4*g0*g2 out.append(disc) if disc >= 0: sq = mp.sqrt(disc) rlo, rhi = sorted([(-g1+sq)/(2*g2), (-g1-sq)/(2*g2)]) out += [rlo, rlo - sm, rhi, rhi - sm] else: out += [None]*4 if m7: l0, l1 = _l7(face, t) if l1 == 0: out += [None]*2 else: r7 = -l0/l1; out += [r7, r7 - sm] return out grid = [mp.mpf(2*j+1)/(2*n) for j in range(n)] vals = [tracked(t) for t in grid] found = [] for i in range(n-1): for k in range(NTRK): va, vb = vals[i][k], vals[i+1][k] if va is None or vb is None or va == 0 or vb == 0: continue if mp.sign(va) != mp.sign(vb): a, b, fa = grid[i], grid[i+1], va for _ in range(80): m = (a + b)/2; fm = tracked(m)[k] if fm is None or fm == 0: break if mp.sign(fm) == mp.sign(fa): a, fa = m, fm else: b = m found.append((a + b)/2) return [r for r in found if 0 < r < 1] # =================== sprov2.py S-layer (verbatim, embedded data) ============= def _ratf(e): num = [_fr(c) for c in e['num']]; den = [_fr(c) for c in e['den']] def f(x): n = mp.mpf(0) for c in reversed(num): n = n*x + c d = mp.mpf(0) for c in reversed(den): d = d*x + c return n/d return f class FluxFam: def __init__(self, raw): self.groups = [] for key, fam in raw.items(): sect_s, face_s = key.rsplit(',', 1) face = int(face_s.strip(') ')) sect = tuple(int(x) for x in sect_s.strip('( ),').replace('(', '').split(',') if x.strip()) terms = [] for ms, cf in fam.items(): e = tuple(int(x) for x in ms.strip('()').split(',')) terms.append((e, [_fr(c) for c in cf['num']], [_fr(c) for c in cf['den']])) self.groups.append((sect, face, terms)) def __call__(self, t): tot = mp.mpf(0) for sect, face, terms in self.groups: props = tuple(p for p in sect if p in (5, 7)) mono = {} for e, num, den in terms: n = mp.mpf(0) for c in reversed(num): n = n*t + c d = mp.mpf(0) for c in reversed(den): d = d*t + c mono[e] = n/d tot += flux_face(mono, face, t, props=props) return tot class SProvider2: def __init__(self, u0_str='1/2', N=80): A = EMBED['S_ANCH'][u0_str] self.S1a = mp.mpf(A['S1']); self.S2a = mp.mpf(A['S2']); self.S3a = mp.mpf(A['S3']) O = EMBED['S_ODES'] self.a = _ratf(O['a_S2']); self.b = _ratf(O['b_S1']) self.c = _ratf(O['c_S1S3']); self.d = _ratf(O['d_S3']) self.F1 = FluxFam(EMBED['FLUX']['S90']) self.F2 = FluxFam(EMBED['FLUX']['S91']) self.F3 = FluxFam(EMBED['FLUX']['S92']) n, d = u0_str.split('/') self.u0 = mp.mpf(int(n))/int(d) self.N = N; self._c = {} def _prep(self, u): key = (mp.mp.dps, str(u), self.N) if key in self._c: return self._c[key] N = self.N; u0 = self.u0 xs = cheb_nodes(N, u0, u); half = (u-u0)/2 Ca = cheb_cumint(cheb_coeffs([self.a(t) for t in xs])) Cb = cheb_cumint(cheb_coeffs([self.b(t) for t in xs])) Cd = cheb_cumint(cheb_coeffs([self.d(t) for t in xs])) def cum(C, t): tt = (2*t-(u+u0))/(u-u0) return half*(cheb_eval(C, tt)-cheb_eval(C, mp.mpf(-1))) Ea = [mp.e**(cum(Ca, t)) for t in xs] Eb = [mp.e**(cum(Cb, t)) for t in xs] Ed = [mp.e**(cum(Cd, t)) for t in xs] # liveness heartbeats only -- same families, same node order, same values def _fam_vals(F, name): out = [] _tf = time.time() for _j, _t in enumerate(xs): out.append(F(_t)) _beat(f'S-layer flux family {name}: node {_j+1}/{N+1} ' f'({time.time()-_tf:.0f}s in this family)') return out Phi2 = _fam_vals(self.F2, 'S91') Phi3 = _fam_vals(self.F3, 'S92') Phi1 = _fam_vals(self.F1, 'S90') C2 = cheb_cumint(cheb_coeffs([Phi2[j]/Ea[j] for j in range(N+1)])) C3 = cheb_cumint(cheb_coeffs([Phi3[j]/Ed[j] for j in range(N+1)])) S3n = [Ed[j]*(self.S3a+cum(C3, xs[j])) for j in range(N+1)] C1 = cheb_cumint(cheb_coeffs([(self.c(xs[j])*S3n[j]+Phi1[j])/Eb[j] for j in range(N+1)])) data = (xs, cum, Ca, Cb, Cd, C1, C2, C3) self._c[key] = data # v2 diagnostic (observational; values untouched): Chebyshev tail digits self.last_tail_digits = min(cheb_tail_digits(C) for C in (Ca, Cb, Cd, C1, C2, C3)) return data def __call__(self, t, uref=None): u = uref if uref is not None else t xs, cum, Ca, Cb, Cd, C1, C2, C3 = self._prep(u) Ea = mp.e**(cum(Ca, t)); Eb = mp.e**(cum(Cb, t)); Ed = mp.e**(cum(Cd, t)) S2 = Ea*(self.S2a+cum(C2, t)) S3 = Ed*(self.S3a+cum(C3, t)) S1 = Eb*(self.S1a+cum(C1, t)) return (S1, S2, S3) # ====================== phid.py PhiD layer (embedded data) =================== DST = EMBED['DST'] def rv(r, x): n = mp.mpf(0) for c in reversed(r['num']): n = n*x + _fr(c) d = mp.mpf(0) for c in reversed(r['den']): d = d*x + _fr(c) return n/d Tm = lambda x: mp.matrix([[rv(DST['T'][i][j], x) for j in range(4)] for i in range(4)]) Bm = lambda x: mp.matrix([[rv(DST['B'][i][j], x) for j in range(4)] for i in range(4)]) def gval(x): return x*x - mp.mpf(34)/35*x + mp.mpf(1)/1225 def corner_cols(x): CORNER_SCALE = [mp.mpf(1), mp.mpf(10)**39] # exact rescale of free-solution columns cols = [] for ci, col in enumerate(DST['sub']['cols']): v = [rv(col[0], x)*CORNER_SCALE[ci], rv(col[1], x)*CORNER_SCALE[ci]] if DST['sub']['rads'][ci]: s = mp.sqrt(mp.mpc(gval(x))) v = [s*v[0], s*v[1]] cols.append(v) return mp.matrix([[cols[0][0], cols[1][0]], [cols[0][1], cols[1][1]]]) def PhiD(u, u0, N=64): a, b = u0, u xs = cheb_nodes(N, a, b) vals = [[[mp.mpf(0)]*(N+1) for _ in range(2)] for _ in range(2)] for j, t in enumerate(xs): Bt = Bm(t); P22 = corner_cols(t) B12 = mp.matrix([[Bt[0, 2], Bt[0, 3]], [Bt[1, 2], Bt[1, 3]]]) M = B12*P22 for i in range(2): for k in range(2): vals[i][k][j] = M[i, k] Q = mp.matrix(2, 2) half = (b-a)/2 for i in range(2): for k in range(2): C = cheb_cumint(cheb_coeffs(vals[i][k])) Q[i, k] = half*(cheb_eval(C, mp.mpf(1))-cheb_eval(C, mp.mpf(-1))) P22u = corner_cols(u) Z = mp.matrix(4, 4) for i in range(2): Z[i, i] = 1 for k in range(2): Z[i, 2+k] = Q[i, k] Z[2+i, 2+k] = P22u[i, k] Phi = Tm(u)*Z COLSCALE = [mp.mpf(10)**40, mp.mpf(10)**40, mp.mpf(1), mp.mpf(1)] for j in range(4): for i in range(4): Phi[i, j] *= COLSCALE[j] return Phi def Tinv(x): return mp.matrix([[rv(DST['Tinv'][i][j], x) for j in range(4)] for i in range(4)]) def _Qmat(u, u0, N=64): a, b = u0, u xs = cheb_nodes(N, a, b) vals = [[[mp.mpf(0)]*(N+1) for _ in range(2)] for _ in range(2)] for j, t in enumerate(xs): Bt = Bm(t); P22 = corner_cols(t) B12 = mp.matrix([[Bt[0, 2], Bt[0, 3]], [Bt[1, 2], Bt[1, 3]]]) M = B12*P22 for i in range(2): for k in range(2): vals[i][k][j] = M[i, k] Q = mp.matrix(2, 2); half = (b-a)/2 for i in range(2): for k in range(2): C = cheb_cumint(cheb_coeffs(vals[i][k])) Q[i, k] = half*(cheb_eval(C, mp.mpf(1))-cheb_eval(C, mp.mpf(-1))) return Q def PhiD_inv(u, u0, N=64, Qc=None): Zi = mp.matrix(4, 4) P22 = corner_cols(u) det = P22[0, 0]*P22[1, 1]-P22[0, 1]*P22[1, 0] P22i = mp.matrix([[P22[1, 1]/det, -P22[0, 1]/det], [-P22[1, 0]/det, P22[0, 0]/det]]) Q = Qc if Qc is not None else _Qmat(u, u0, N) QP = Q*P22i for i in range(2): Zi[i, i] = 1 for k in range(2): Zi[i, 2+k] = -QP[i, k] Zi[2+i, 2+k] = P22i[i, k] M = Zi*Tinv(u) CS = [mp.mpf(10)**40, mp.mpf(10)**40, mp.mpf(1), mp.mpf(1)] for i in range(4): for j in range(4): M[i, j] /= CS[i] return M # ============ assembly.py kernel tables (embedded exact rationals) =========== def _rat2(nd): """[num_asc, den_asc] Fraction-string lists -> f(x) (mpmath Horner).""" num, den = nd def f(x, num=num, den=den): n = mp.mpf(0) for c in reversed(num): n = n*x + _fr(c) d = mp.mpf(0) for c in reversed(den): d = d*x + _fr(c) return n/d return f def fam(e): if e[0] == '0': return lambda x: mp.mpf(0) num = [str(c) for c in e[0]]; den = [str(c) for c in e[1]] return _rat2([num, den]) GM4F = [[_rat2(EMBED['GM4'][i][j]) for j in range(4)] for i in range(4)] CUf = [[_rat2(EMBED['CU'][m][k]) for k in range(4)] for m in range(8)] Lm = [[_rat2(EMBED['L'][i][j]) for j in range(8)] for i in range(4)] Kf = [[fam(EMBED['K'][i][j]) for j in range(4)] for i in range(8)] Ef = [[fam(EMBED['E'][i][j]) for j in range(8)] for i in range(4)] LCf = [[fam(EMBED['LC'][i][j]) for j in range(2)] for i in range(4)] GSf = [[fam(EMBED['GS'][i][j]) for j in range(2)] for i in range(4)] Gyf = [[fam(EMBED['GY'][i][j]) for j in range(4)] for i in range(4)] def matev(F, x, nr, nc): return mp.matrix([[F[i][j](x) for j in range(nc)] for i in range(nr)]) def Pdesc(uq): """Exact Fraction evaluation of the maxcut quartic's x3-coefficients at rational u (descending in x3), then one rounding to working dps.""" out = [] for cs in EMBED['PDESC']: v = Fraction(0) for c in reversed(cs): v = v*uq + Fraction(c) out.append(mp.mpf(v.numerator)/mp.mpf(v.denominator)) return out # ================= assembly.py W transport + masters (verbatim) ============== class Wprov: """Fix W by direct period quads at the rational base point u0, transport with exact GM4 via mp.odefun (forward interpolant + backward leg via s = u0 - x).""" def __init__(self, u0_frac): self.u0 = mp.mpf(u0_frac.numerator)/u0_frac.denominator pc = Pdesc(u0_frac) p4, p3 = pc[0], pc[1] self.W0 = W_columns(pc, p4, p3) self._ode = None def _rhs(self, x, Wflat): G = mp.matrix([[GM4F[i][j](x) for j in range(4)] for i in range(4)]) W = mp.matrix(4, 4) for i in range(4): for j in range(4): W[i, j] = Wflat[4*i+j] R = G*W return [R[i, j] for i in range(4) for j in range(4)] def _rhs_back(self, s, Wflat): x = self.u0 - s G = mp.matrix([[GM4F[i][j](x) for j in range(4)] for i in range(4)]) W = mp.matrix(4, 4) for i in range(4): for j in range(4): W[i, j] = Wflat[4*i+j] R = -(G*W) return [R[i, j] for i in range(4) for j in range(4)] def start(self): f0 = [self.W0[i, j] for i in range(4) for j in range(4)] tol = mp.mpf(10)**(-(mp.mp.dps-4)) self._ode = mp.odefun(self._rhs, self.u0, f0, tol=tol) self._odeb = mp.odefun(self._rhs_back, mp.mpf(0), f0, tol=tol) def W(self, x): if self._ode is None: self.start() v = self._ode(x) if x >= self.u0 else self._odeb(self.u0-x) return mp.matrix([[v[4*i+j] for j in range(4)] for i in range(4)]) def masters_at(u_target, u0_frac, M0, Sprov, N=64, Fprov=None, diag=None): """M0: 8-vector base-point value at u0. Sprov(t)->(S1,S2,S3). Fprov(t)->8-vector master-row face-flux totals. Returns (M(u_target), J, y). v2: diag dict (optional) receives Chebyshev tail diagnostics; the numeric path is byte-identical to the original.""" u = mp.mpf(u_target) u0 = mp.mpf(u0_frac.numerator)/u0_frac.denominator L0 = matev(Lm, u0, 4, 8); K0 = matev(Kf, u0, 8, 4); E0 = matev(Ef, u0, 4, 8) y0 = L0*M0 J0 = E0*(M0-K0*y0) xs = cheb_nodes(N, u0, u) Phi0i = PhiD_inv(u0, u0, N=8) z0 = Phi0i*y0 yint = [[mp.mpf(0)]*(N+1) for _ in range(4)] Svals = [] for _j, _t in enumerate(xs): # liveness loop -- same order/values as the Svals.append(Sprov(_t)) # original [Sprov(t) for t in xs] _beat(f'assembly: S-layer values at node {_j+1}/{N+1}') Fvals = [Fprov(t) if Fprov else None for t in xs] for j, t in enumerate(xs): _beat(f'assembly: y-layer VoP node {j+1}/{N+1}') Pi = PhiD_inv(t, u0, N=N) LCt = matev(LCf, t, 4, 2) Sv = mp.matrix([Svals[j][0], Svals[j][1]]) rhs = LCt*Sv if Fvals[j] is not None: Lt = matev(Lm, t, 4, 8) rhs = rhs+Lt*Fvals[j] w = Pi*rhs for i in range(4): yint[i][j] = w[i] half = (u-u0)/2 Ccoef = [cheb_cumint(cheb_coeffs(yint[i])) for i in range(4)] def yfun(idx): t = xs[idx] I = mp.matrix([half*(cheb_eval(Ccoef[i], (2*t-(u+u0))/(u-u0))-cheb_eval(Ccoef[i], mp.mpf(-1))) for i in range(4)]) return PhiD(t, u0, N=N)*(z0+I) wp = Wprov(u0_frac); wp.start() Jint = [[mp.mpf(0)]*(N+1) for _ in range(4)] for j, t in enumerate(xs): _beat(f'assembly: W-period transport + J-layer VoP node {j+1}/{N+1}') Wt = wp.W(t) yv = yfun(j) Gyt = matev(Gyf, t, 4, 4); GSt = matev(GSf, t, 4, 2) Sv = mp.matrix([Svals[j][0], Svals[j][1]]) rhs = Gyt*yv+GSt*Sv if Fvals[j] is not None: Lt = matev(Lm, t, 4, 8); Kt = matev(Kf, t, 8, 4); Et = matev(Ef, t, 4, 8) rhs = rhs+Et*(Fvals[j]-Kt*(Lt*Fvals[j])) sol = mp.lu_solve(Wt, rhs) for i in range(4): Jint[i][j] = sol[i] Cj = [cheb_cumint(cheb_coeffs(Jint[i])) for i in range(4)] if diag is not None: diag['tail_y'] = min(cheb_tail_digits(C) for C in Ccoef) diag['tail_J'] = min(cheb_tail_digits(C) for C in Cj) Iend = mp.matrix([half*(cheb_eval(Cj[i], mp.mpf(1))-cheb_eval(Cj[i], mp.mpf(-1))) for i in range(4)]) W0 = wp.W0 Ju = wp.W(u)*(mp.lu_solve(W0, J0)+Iend) Iy = mp.matrix([half*(cheb_eval(Ccoef[i], mp.mpf(1))-cheb_eval(Ccoef[i], mp.mpf(-1))) for i in range(4)]) yu = PhiD(u, u0, N=N)*(z0+Iy) cu = matev(CUf, u, 8, 4); Ku = matev(Kf, u, 8, 4) return cu*Ju+Ku*yu, Ju, yu # ============= assembly_run.py F provider (barycentric, embedded) ============ class FP: def __init__(self, interval): nd = EMBED['FTRUE'][interval] self.xs = [mp.mpf(Fraction(n['u']).numerator)/Fraction(n['u']).denominator for n in nd] self.Y = [[mp.mpf(v) for v in n['F']] for n in nd] n = len(self.xs) self.w = [] for i in range(n): p = mp.mpf(1) for j in range(n): if j != i: p /= (self.xs[i]-self.xs[j]) self.w.append(p) def __call__(self, t): out = mp.matrix(8, 1) num = [mp.mpf(0)]*8; den = mp.mpf(0) for i in range(len(self.xs)): dx = t-self.xs[i] if dx == 0: for r in range(8): out[r] = self.Y[i][r] return out c = self.w[i]/dx den += c for r in range(8): num[r] += c*self.Y[i][r] for r in range(8): out[r] = num[r]/den return out # =========================== segments + top-level ============================ # Pole-free transport segments (spec table of this work): SEGS = [ (Fraction('0.30'), Fraction('0.406319'), Fraction(19, 50), '19/50'), (Fraction('0.406320'), Fraction('0.556967'), Fraction(1, 2), '1/2'), (Fraction('0.626177'), Fraction('0.678361'), Fraction(13, 20), '13/20'), ] def seg_for(uf): for lo, hi, u0, tag in SEGS: if lo <= uf <= hi: return u0, tag lines = ', '.join(f'[{float(lo):.6f}, {float(hi):.6f}] (base point {tag})' for lo, hi, _, tag in SEGS) raise SystemExit(f'ERROR: u = {uf} is outside the pole-free transport segments: {lines}') def interval_for(tag, uf): if tag == '19/50': return 'seg13_t13' if tag == '13/20': return 'seg23_t23' return 'segmid_t2150' if uf < Fraction(1, 2) else 'segmid_t2649' def basepoint_vec(tag): return mp.matrix([mp.mpf(v) for v in EMBED['ANCH'][tag]]) def eval_masters(uf, wdps, NS=80, NA=64, u_shift=None, shared=None, diag=None): """Full gated-architecture evaluation of the 8 masters at rational uf (optionally displaced by mpf u_shift, for FD residual checks) at working dps=wdps. shared: optional dict to reuse the S-provider across calls at the same working precision (uref-pinned; production leg pattern). v2: diag dict (optional) receives Chebyshev tail diagnostics.""" mp.mp.dps = wdps u0f, tag = seg_for(uf) ut = mp.mpf(uf.numerator)/uf.denominator if u_shift is not None: ut = ut + u_shift if uf == u0f and u_shift is None: return basepoint_vec(tag), tag, None interval = interval_for(tag, uf) M0 = basepoint_vec(tag) key = (wdps, tag, NS) if shared is not None and key in shared: S0, UREF = shared[key] else: S0 = SProvider2(u0_str=tag, N=NS) u0m = mp.mpf(u0f.numerator)/u0f.denominator UREF = ut - mp.mpf('1e-9') if ut < u0m else ut + mp.mpf('1e-9') if shared is not None: shared[key] = (S0, UREF) S = lambda t: S0(t, uref=UREF) Fp = FP(interval) Mv, Ju, yu = masters_at(ut, u0f, M0, S, N=NA, Fprov=Fp, diag=diag) if diag is not None: diag['tail_S'] = getattr(S0, 'last_tail_digits', float(wdps)) return Mv, tag, (S, Fp) def de_residual_check(wdps, NS=80, NA=64, h=mp.mpf('1e-12')): # v2.1: h 1e-10 -> 1e-12 lifts the FD floor; row-3 margin 7.98d -> ~12d, # keeping the 8d bar honest (fix the margin, not the bar). """DE-residual identity at u=47/100 (embedded exact A-row rationals): central-FD M' vs A.M + A[:,9] S1 + A[:,10] S2 + F. Oracle-free.""" uf = Fraction(47, 100) mp.mp.dps = wdps shared = {} vals = {} for tagn, sh in (('c', None), ('m', -h), ('p', +h)): vals[tagn] = eval_masters(uf, wdps, NS=NS, NA=NA, u_shift=sh, shared=shared)[0] A = [[Fraction(x) for x in row] for row in EMBED['A47']] _, tag = seg_for(uf) key = (wdps, tag, NS) S0, UREF = shared[key] ut = mp.mpf(47)/100 Sv = S0(ut, uref=UREF) Fv = FP(interval_for(tag, uf))(ut) out = {} for r in range(8): lhs = (vals['p'][r]-vals['m'][r])/(2*h) rhs = sum(mp.mpf(A[r][j].numerator)/A[r][j].denominator*vals['c'][j] for j in range(8)) \ + mp.mpf(A[r][9].numerator)/A[r][9].denominator*Sv[0] \ + mp.mpf(A[r][10].numerator)/A[r][10].denominator*Sv[1] + Fv[r] rel = abs(lhs-rhs)/max(abs(lhs), mp.mpf('1e-30')) out[r] = float(-mp.log10(rel + mp.mpf('1e-60'))) return out def agree_digits(a, b): d = abs(a-b)/max(abs(a), mp.mpf('1e-30')) return float(-mp.log10(d + mp.mpf(10)**(-mp.mp.dps-10))) def provenance_block(): P = EMBED['provenance'] lines = ['--- provenance ---', 'EMBEDDED (data): master base-point values at u=19/50, 1/2, 13/20 (value_dps85;', ' independent quad-ladder certification); S-layer base-point values (dps75) + gated S-ODE rational', ' coefficients; gated flux families FLUX_S90/91/92 (rational-in-u monomial coeffs);', ' F_true node values per segment (FTRUE_NODES; LOO-measured 29-34d) with node u lists;', ' exact rational kernels: GM4, c(u), L, K, E, LC, GS, Gy, PhiD T/Tinv/B/corner data,', ' maxcut quartic P(x3;u); exact A-row rationals at u=47/100 (DE-residual gate only).', 'COMPUTED LIVE: W periods (quadrature of the maxcut quartic at the base point) + GM4 odefun', ' transport; PhiD spectral fundamental matrix + analytic inverse; S1,S2,S3 by flux-', ' sourced VoP (face fluxes via closed-form inner integral + outer tanh-sinh); F(u) by', ' barycentric interpolation of embedded nodes; the y- and J-layer VoP integrals; the', ' final assembly M = c J + K y. NO oracle/gate values embedded; nothing is fitted.', 'seg23 F_true grid consistent with CHEB_NODES at build: %s' % EMBED.get('SEG23_CONSISTENT'), 'sources (sha256/16): ' + '; '.join( f"{k.rsplit('/', 1)[-1]}={v}" # display basenames; the shas identify the files for k, v in P['source_sha256_16'].items()), 'built: ' + P['built']] return '\n'.join(lines) # ============================================================================= # ======================== v2 HARDENING SECTION =============================== # ============================================================================= # ---- fluxkernel2.flux_face_pair (verbatim port, eecLOsector source code) ---- def flux_face_pair(mono_a, face_a, mono_b, face_b, u, props=()): """Fused evaluation of a face pair sharing a log-divergent stratum.""" ia, ABa, sma, m5, m7 = flux_face(mono_a, face_a, u, props, reg=True, _build=True) ib, ABb, smb, _, _ = flux_face(mono_b, face_b, u, props, reg=True, _build=True) for deep, shal, lab in ((mp.mpf('1e-6'), mp.mpf('1e-5'), 't->0'), (1-mp.mpf('1e-6'), 1-mp.mpf('1e-5'), 't->1')): va = abs(ia(deep, 0) + ib(deep, 0)); vb = abs(ia(shal, 0) + ib(shal, 0)) if va > 5*vb and va > mp.mpf(10)**(-(mp.mp.dps//2)): raise RegionSingularity( f"fused pair {face_a}+{face_b} corner-divergent at {lab}") splits = sorted(set(_splits(face_a, ABa, sma, m5, m7) + _splits(face_b, ABb, smb, m5, m7))) splits = [splits[0]] + [b for a, b in zip(splits, splits[1:]) if b - a > mp.mpf(10)**(-(mp.mp.dps+15))] if splits[-1] != 1: splits[-1] = mp.mpf(1) tol = mp.mpf(10)**(-(mp.mp.dps - 8)) def qsum(chan): tot = mp.mpc(0) for a, b in zip(splits, splits[1:]): tot += mp.quad(lambda tt: ia(tt, chan) + ib(tt, chan), [a, b]) if abs(mp.im(tot)) > tol*max(1, abs(mp.re(tot))): raise RegionSingularity(f"pair {face_a}+{face_b}: Im residue chan {chan}") return mp.re(tot) J = qsum(0); C = qsum(1); S = qsum(2) if abs(C) > mp.mpf(10)**(-(mp.mp.dps//2))*max(1, abs(J)): raise RegionSingularity(f"pair {face_a}+{face_b}: divergence coefficients do NOT cancel") return {'J': J, 'C': C, 'S': S} # ---- fluxkernel3 row-total assembly (verbatim port, eecLOsector source) ----- def _fk3_key(sector): return tuple(sorted(props_from_sector(sector))) def _quad_fused(parts, tol_dps, label): splits = set() for inner, mirror, sp in parts: for x in sp: splits.add(1 - x if mirror else x) splits = sorted(splits) splits = [splits[0]] + [b for a, b in zip(splits, splits[1:]) if b - a > mp.mpf(10)**(-(mp.mp.dps+15))] if splits[0] != 0: splits[0] = mp.mpf(0) if splits[-1] != 1: splits[-1] = mp.mpf(1) def Ffn(t): v = mp.mpc(0) for inner, mirror, _ in parts: v += inner(1 - t if mirror else t, 0) return v for deep, shal, lab in ((mp.mpf('1e-6'), mp.mpf('1e-5'), 't->0'), (1 - mp.mpf('1e-6'), 1 - mp.mpf('1e-5'), 't->1')): va, vb = abs(Ffn(deep)), abs(Ffn(shal)) if va > 5*vb and va > mp.mpf(10)**(-(mp.mp.dps//2)): raise RegionSingularity(f"{label}: fused corner-web integrand still ~1/t at {lab}") tot = mp.mpc(0) for a, b in zip(splits, splits[1:]): tot += mp.quad(Ffn, [a, b]) tol = mp.mpf(10)**(-(mp.mp.dps - 8)) if abs(mp.im(tot)) > tol*max(1, abs(mp.re(tot))): raise RegionSingularity(f"{label}: Im residue {mp.nstr(mp.im(tot), 6)}") return mp.re(tot) def flux_group_57(monos, u): parts = [] pair_c = [] for face in (1, 4, 2, 3): inner, AB, sm, m5, m7 = flux_face(monos[face], face, u, (5, 7), reg=True, _build=True) parts.append((inner, face == 3, _splits(face, AB, sm, m5, m7))) if face in (1, 4): pair_c.append(inner) for tprobe in (mp.mpf('0.37'), mp.mpf('0.71')): c1 = pair_c[0](tprobe, 1); c4 = pair_c[1](tprobe, 1) if abs(c1 + c4) > mp.mpf(10)**(-(mp.mp.dps//2))*max(1, abs(c1)): raise RegionSingularity(f"(5,7) pair c-cancellation fails at t={tprobe}") return _quad_fused(parts, mp.mp.dps, "(5,7) 4-face web") def flux_row_total(sources, u, mono_of=None): if mono_of is None: mono_of = lambda s: s['mono'] by = {} for s in sources: by.setdefault(_fk3_key(s['sector']), {})[s['face']] = (s, mono_of(s)) groups = {} tot = mp.mpf(0) for key, faces in sorted(by.items()): if key in ((), (5,)): g = mp.mpf(0) for f, (s, mono) in sorted(faces.items()): g += flux_face(mono, f, u, key) elif key == (7,): g = mp.mpf(0) for f in (2, 3): if f in faces: g += flux_face(faces[f][1], f, u, (7,)) if 1 in faces and 4 in faces: g += flux_face_pair(faces[1][1], 1, faces[4][1], 4, u, (7,))['J'] elif 1 in faces or 4 in faces: raise RegionSingularity("(7,) sector: need BOTH faces 1 and 4") elif key == (5, 7): if set(faces) < {1, 2, 3, 4}: raise RegionSingularity(f"(5,7) sector: need all 4 faces, have {sorted(faces)}") g = flux_group_57({f: faces[f][1] for f in (1, 2, 3, 4)}, u) else: raise RegionSingularity(f"unsupported props {key}") groups[key] = g tot += g return {'total': tot, 'groups': groups} def parse_groups(rowdict): """node_totals.py port: exact-rational cache row -> flux_row_total sources.""" src = [] for key, monod in rowdict.items(): sect_s, face_s = key.rsplit(',', 1) face = int(face_s.strip(') ')) sect = tuple(int(x) for x in sect_s.strip('( ),').replace('(', '').split(',') if x.strip()) mono = {} for ms, cs in monod.items(): e = tuple(int(x) for x in ms.strip('()').split(',')) f = Fraction(cs) mono[e] = mp.mpf(f.numerator) / f.denominator src.append({'sector': list(sect), 'face': face, 'mono': mono}) return src # ---- wall5713 written-integral K0/K1 (verbatim port, eecLOsector source) ---- def _ilin(A0, A1, B0, B1, lo, hi): Wr = A0*B1 - A1*B0 if Wr == 0: k = (B0/A0) if A0 != 0 else (B1/A1) return (1/(A0 + A1*lo) - 1/(A0 + A1*hi))/(A1*k) num = mp.log(abs((B0 + B1*hi)/(B0 + B1*lo))) den = mp.log(abs((A0 + A1*hi)/(A0 + A1*lo))) return (num - den)/Wr def phi_P0(tau, u): one = mp.mpf(1) q4 = -4/(5*(1-u)) q2 = (5*u-1)/(2*(1-u)) kap1 = (one*2/5)*(1-u)*tau kap4 = (one*8/5)*tau h1, h4 = (1-u), one*4/5 R = 5/(2*(1-u)*tau) pairD = R*mp.log((h4*(kap1 + u*h1)*kap4)/((kap4 + h4)*h1*kap1)) w1 = -_ilin(one/5 + 2*tau/5, u, one*4/5, 1-u, 0, 1) w4 = -q4*_ilin(2*tau/5 + u, one/5, 1-u, one*4/5, 0, 1) f2D = mp.mpf(0) if tau < 1: beta = one/5 - u ylo, yhi = 4*tau/5, 4*tau/5 + (1-u) f2D = -q2*_ilin(mp.mpf(0), one, beta*tau, u, ylo, yhi) return pairD - w1 - w4 + f2D def phi_P1(mu, u): one = mp.mpf(1) q4 = -one*3/2 q3 = one*5/4 cg = 5*mu/3 Wc = 2*mu/5 L1 = max(mp.mpf(0), cg - mp.mpf(20)/21) L4 = max(mp.mpf(0), cg - mp.mpf(10)/7) def endpiece(A0, A1, L): return -(mp.log(abs(3*L/5 - mu)) - mp.log(abs(A0 + A1*L))) pairD = (7*one/4)/Wc*endpiece(3*mu/4, -one/20, L1) \ + (7*q4/6)/Wc*endpiece(mu/6, one*3/10, L4) w1 = mp.mpf(0) v1m = min(one, mp.mpf(7)/4*(mu - mp.mpf(6)/7)) if v1m > 0: w1 = (one*5/3)*_ilin(2*mu/3 - mp.mpf(3)/7, one/21, -mp.mpf(6)/7, -mp.mpf(4)/7, 0, v1m) w4 = mp.mpf(0) v4m = min(one, mp.mpf(7)/6*(mu - mp.mpf(4)/7)) if v4m > 0: w4 = (one*5/3)*q4*_ilin(2*mu/3 + one/21, -mp.mpf(3)/7, -mp.mpf(4)/7, -mp.mpf(6)/7, 0, v4m) f3D = mp.mpf(0) if mu < 1: lo, hi = 6*mu/7, 6*mu/7 + one*4/7 f3D = -(7*q3/4)*_ilin(mp.mpf(0), one, -mu/2, one*3/4, lo, hi) return pairD - w1 - w4 + f3D _KCACHE = {} def _geom(a, b, n): r = (b/a)**(mp.mpf(1)/n) return [a*r**k for k in range(n+1)] def _Ksafe(f, bps, M=None, mumax=None): if M is None: M = mp.mpf(50) if mumax is None: mumax = mp.mpf(10)**(mp.mp.dps//3) panels = [mp.mpf(0), mp.mpf(10)**(-mp.mp.dps//3)] panels += _geom(panels[-1], bps[0], 4*mp.mp.dps//2)[1:] for i in range(len(bps)-1): panels += _geom(bps[i], bps[i+1], 16)[1:] panels += _geom(bps[-1], M, 4*mp.mp.dps//2)[1:] tot = mp.mpf(0) for a, b in zip(panels, panels[1:]): tot += mp.quad(f, [a, b], method='gauss-legendre') for a, b in zip(_geom(1/mumax, 1/M, mp.mp.dps), _geom(1/mumax, 1/M, mp.mp.dps)[1:]): tot += mp.quad(lambda w: f(1/w)/w**2, [a, b], method='gauss-legendre') tot += (mumax/2)**2*f(mumax/2)/mumax return tot # ---- K0/K1: CLOSED FORM (v2.1, 2026-07-06) --------------------------------- # Weight-2 Li2 closed forms (recorded in the sunrise paper's mathematics # section: K1 as fifteen dilogarithms, K0(u) as six at cross-ratio arguments; # gated 18/18 at 59-72d vs independently-quadratured K tables). Exact expressions # valid at ANY dps -> the K leg of the recompute floor is removed. The original # written-integral evaluators are kept below as *_integral for cross-checks. # Embedded in an isolated namespace (kclosed uses `mp` = mpmath context; this # file uses `mp` = mpmath module). _KCLOSED_SRC = r'''#!/usr/bin/env python3 r"""kclosed.py -- CLOSED FORMS for the (5,7,13) stratum-exit wall constants. K0(u) = int_0^oo Phi_P0(tau,u) dtau (P0 corner; valid for u in (1/5, 1)) K1 = int_0^oo Phi_P1(mu) dmu (P1 corner; pure constant) of wall5713.py (eecLOsector (5,7,13) fused-corner-web anomaly: Delta_r(u) = Q1_P0(r,u)*K0(u) + Q1_P1(r,u)*K1). Derivation: assemble.py in this directory -- every phi piece is a finite sum of atoms c*ln|P0+P1 t|/(W0+W1 t); each integrates to log products + a real dilogarithm ReLi2(-P1(t-t0)/P(t0)), t0 = -W0/W1; endpoint divergences (ln eps, ln Lam and their squares) cancel exactly across atoms (checked symbolically / by exact log algebra). K0 closes in 6 dilogarithms with algebraic-in-u cross-ratio arguments (5u-1)/(4u), (5u-1)/(u(9-5u))... (see DERIVATION.md); K1 in 15 rational-arg dilogarithms. Generated by gen step from K0_closed.txt / K1_closed.txt. Pure mpmath; no fitted constants anywhere -- all coefficients exact rationals from the corner local models. """ from mpmath import mp, mpf, log, pi, polylog, mpc, fabs as _fabs def _rli2(x): """Real dilogarithm ReLi2(x) = Re Li2(x + i0).""" x = mpf(x) if x <= 1: return polylog(2, x) return polylog(2, mpc(x)).real def Abs(x): return _fabs(x) def _K0_expr(u): return (-5*log(u)**2/(4*u - 4) + 10*log(u)*log(abs(u - 1))/(4*u - 4) - 10*log(u)*log(abs(u/(5*u - 9) - 1/(5*u - 9)))/(4*u - 4) - 10*log(10)*log(u)/(4*u - 4) - 10*log(1/abs(u - 1))*log(abs(u - 1))/(4*u - 4) + 10*log(1/abs(u - 1))*log(abs(5*u - 1))/(4*u - 4) - 10*log(2)*log(1/abs(u - 1))/(4*u - 4) - 10*log(abs(u - 1))*log(abs(5*u - 9))/(4*u - 4) + 10*log(abs(u - 1))*log(abs(5*u/(u - 1) - 9/(u - 1)))/(4*u - 4) - 20*log(2)*log(abs(u - 1))/(4*u - 4) + 10*log(5)*log(abs(u - 1))/(4*u - 4) - 5*log(abs(5*u - 9))**2/(4*u - 4) + 10*log(abs(5*u - 9))*log(abs(5*u - 1))/(4*u - 4) + 20*log(2)*log(abs(5*u - 9))/(4*u - 4) - 10*log(abs(5*u - 1))*log(abs(5*u/(u - 1) - 9/(u - 1)))/(4*u - 4) + 10*log(2)*log(abs(5*u/(u - 1) - 9/(u - 1)))/(4*u - 4) + 5*log(abs(u/(5*u - 9) - 1/(5*u - 9)))**2/(4*u - 4) + 10*log(2)*log(abs(u/(5*u - 9) - 1/(5*u - 9)))/(4*u - 4) - 10*_rli2(-(mpf(1)/mpf(5))/u)/(4*u - 4) - 10*_rli2(mpf(5)/mpf(4) - (mpf(1)/mpf(4))/u)/(4*u - 4) + 10*_rli2(4/(5*u - 5))/(4*u - 4) + 10*_rli2(5*u/(u - 1) - 1/(u - 1))/(4*u - 4) - 10*_rli2(25*u/(5*u - 9) - 5/(5*u - 9))/(4*u - 4) + 10*_rli2(-5*u/(5*u**2 - 9*u) + 1/(5*u**2 - 9*u))/(4*u - 4) - 5*log(40)**2/(4*u - 4) - 30*log(2)*log(5)/(4*u - 4) - 5*log(10)**2/(4*u - 4) - 10*log(2)**2/(4*u - 4) + 10*log(5)*log(20)/(4*u - 4) + 30*log(2)*log(20)/(4*u - 4)) def _K1_expr(): return ((mpf(35)/mpf(8))*_rli2(mpf(-57)/mpf(7)) + (mpf(35)/mpf(8))*_rli2(-8) - mpf(35)/mpf(8)*_rli2(mpf(-19)/mpf(5)) - mpf(35)/mpf(8)*_rli2(mpf(-3)/mpf(2)) - mpf(35)/mpf(4)*_rli2(mpf(-9)/mpf(7)) + (mpf(35)/mpf(8))*_rli2(-1) - mpf(35)/mpf(8)*_rli2(mpf(-19)/mpf(21)) + (mpf(35)/mpf(8))*_rli2(mpf(-5)/mpf(7)) + (mpf(35)/mpf(8))*_rli2(mpf(-1)/mpf(3)) + (mpf(35)/mpf(8))*_rli2(mpf(-1)/mpf(7)) - mpf(35)/mpf(8)*_rli2(mpf(4)/mpf(3)) + (mpf(35)/mpf(8))*_rli2(mpf(9)/mpf(5)) - mpf(35)/mpf(8)*_rli2(mpf(15)/mpf(7)) - mpf(35)/mpf(8)*_rli2(mpf(5)/mpf(2)) + (mpf(35)/mpf(8))*_rli2(mpf(27)/mpf(7)) - mpf(35)/mpf(8)*log(21)*log(1470) - mpf(35)/mpf(4)*log(2)*log(1296540) - mpf(35)/mpf(8)*log(5)*log(47628) - mpf(35)/mpf(8)*log(10)*log(798) - mpf(35)/mpf(8)*log(7)*log(1470) - mpf(35)/mpf(8)*log(38)*log(42) - mpf(35)/mpf(8)*log(3)*log(144060) - mpf(105)/mpf(8)*log(6)*log(7) - mpf(35)/mpf(4)*log(7)*log(14) - mpf(35)/mpf(8)*log(14)*log(15) - mpf(35)/mpf(8)*log(6)*log(12) - mpf(35)/mpf(4)*log(3)**2 - mpf(35)/mpf(16)*log(5)**2 + (mpf(35)/mpf(8))*log(2)*log(50) + (mpf(35)/mpf(8))*log(6)**2 + (mpf(35)/mpf(16))*log(14)**2 + (mpf(35)/mpf(16))*log(15)**2 + (mpf(35)/mpf(16))*pi**2 + (mpf(35)/mpf(2))*log(2)*log(7) + (mpf(105)/mpf(16))*log(7)**2 + (mpf(105)/mpf(8))*log(2)*log(42) + (mpf(35)/mpf(8))*log(14)*log(21) + (mpf(35)/mpf(8))*log(3)*log(2280) + (mpf(35)/mpf(4))*log(2)*log(798) + (mpf(35)/mpf(4))*log(5)*log(21) + (mpf(35)/mpf(4))*log(3)*log(98) + (mpf(35)/mpf(8))*log(5)*log(1064) + (mpf(35)/mpf(8))*log(6)*log(735) + (mpf(35)/mpf(8))*log(7)*log(1330) + (mpf(35)/mpf(8))*log(42)*log(147) + (mpf(35)/mpf(8))*log(10)*log(7938)) def K0_closed(u, dps=50): """K0(u) closed form; u rational/float in (1/5, 1); returns mpf at dps.""" from fractions import Fraction as F old = mp.dps try: mp.dps = dps + 15 uf = F(u) if not isinstance(u, F) else u uu = mpf(uf.numerator)/uf.denominator v = _K0_expr(uu) mp.dps = dps return +v finally: mp.dps = old def K1_closed(dps=50): old = mp.dps try: mp.dps = dps + 15 v = _K1_expr() mp.dps = dps return +v finally: mp.dps = old ''' _KNS = {} exec(compile(_KCLOSED_SRC, 'kclosed_embedded', 'exec'), _KNS) def K0_wall(u): key = ('K0c', str(u), mp.mp.dps) if key in _KCACHE: return _KCACHE[key] v = _KNS['K0_closed'](u, dps=mp.mp.dps) _KCACHE[key] = v return v def K1_wall(): key = ('K1c', mp.mp.dps) if key in _KCACHE: return _KCACHE[key] v = _KNS['K1_closed'](dps=mp.mp.dps) _KCACHE[key] = v return v def K0_wall_integral(u): key = ('K0i', str(u), mp.mp.dps) if key in _KCACHE: return _KCACHE[key] uu = mp.mpf(u.numerator)/u.denominator if isinstance(u, Fraction) else mp.mpf(u) v = _Ksafe(lambda t: phi_P0(t, uu), [mp.mpf(1)]) _KCACHE[key] = v return v def K1_wall_integral(): key = ('K1i', mp.mp.dps) if key in _KCACHE: return _KCACHE[key] v = _Ksafe(lambda m: phi_P1(m, None), [mp.mpf(4)/7, mp.mpf(6)/7, mp.mpf(1), mp.mpf(10)/7]) _KCACHE[key] = v return v # ---- sha-manifest pinned external loader ------------------------------------ _DATA_DIR = None # set by --data-dir; --recompute-node refuses without it def load_ext(relpath): """Load a DECLARED external artifact; refuse loudly if absent or sha-mismatched (sha-manifest pinned witness-loader pattern).""" if _DATA_DIR is None: print('LOADER_GATE FAIL: --data-dir not set (required for external artifacts)'); sys.exit(3) path = os.path.join(_DATA_DIR, relpath) pinned = _V2CERT['ext_manifest'].get(relpath) if pinned is None: print(f'LOADER_GATE FAIL: {relpath} not in the pinned manifest'); sys.exit(3) if not os.path.exists(path): print(f'LOADER_GATE FAIL: declared external artifact ABSENT: {path}\n' f' (check --data-dir; expected sha256 {pinned[:16]}...)') sys.exit(3) h = hashlib.sha256() with open(path, 'rb') as fh: for chunk in iter(lambda: fh.read(1 << 22), b''): h.update(chunk) got = h.hexdigest() if got != pinned: print(f'LOADER_GATE FAIL: sha256 mismatch for {path}\n' f' got {got[:16]}... expected {pinned[:16]}... — artifact changed since pinning') sys.exit(3) print(f'[loader] {relpath}: sha256 {got[:16]}... OK', flush=True) return json.load(open(path)) # ---- runtime LOO on the (embedded or swapped) F grids ----------------------- _LOO_CACHE = {} def runtime_loo_digits(interval): """Leave-one-out barycentric floor per row, computed AT RUNTIME from the node values in EMBED['FTRUE'] (ftrue_loo.py measurement, re-derived live).""" key = (interval, _V2CERT['fnode_string_dps'][interval]) if key in _LOO_CACHE: return _LOO_CACHE[key] nd = EMBED['FTRUE'][interval] with mp.workdps(_V2CERT['fnode_string_dps'][interval] + 12): xs = [mp.mpf(Fraction(n['u']).numerator)/Fraction(n['u']).denominator for n in nd] Y = [[mp.mpf(v) for v in n['F']] for n in nd] n = len(xs) worst = [mp.mpf(0)]*8 for k in range(1, n-1): idx = [i for i in range(n) if i != k] w = [] for i in idx: p = mp.mpf(1) for j in idx: if j != i: p /= (xs[i]-xs[j]) w.append(p) for r in range(8): num = mp.mpf(0); den = mp.mpf(0) for t, i in enumerate(idx): c = w[t]/(xs[k]-xs[i]) num += c*Y[i][r]; den += c pred = num/den rel = abs(pred-Y[k][r])/(abs(Y[k][r]) + mp.mpf('1e-60')) if rel > worst[r]: worst[r] = rel digs = [float(-mp.log10(e + mp.mpf('1e-60'))) for e in worst] _LOO_CACHE[key] = digs return digs # ---- certification floors + fail-closed printing ---------------------------- CLAMP_MARGIN = 1 # safety digit between measured floor and printed claim def cert_components(tag, interval, tails=None): """Per-row list of (floor_digits, dict of named component floors).""" A = _V2CERT['basepoint_cert_digits'][tag] out = [] for r in range(8): comp = {'base point': A[r]} if interval is not None: comp['S-base-point'] = _V2CERT['s_basepoint_cert_digits'][tag] comp['F-node-value'] = _V2CERT['fnode_value_cert_digits'][interval][r] comp['F-node-string'] = _V2CERT['fnode_string_dps'][interval] - 1 comp['F-grid-LOO'] = runtime_loo_digits(interval)[r] if tails: comp['cheb-tail'] = min(tails.values()) out.append((min(comp.values()), comp)) return out def trunc_str(x, n): """Truncate (never round) x to n significant digits; prefix-stable.""" if x == 0: return '0.0' s = mp.nstr(x, n + 8) mant, exp = (s.split('e') + [''])[:2] exp = ('e' + exp) if exp else '' sign = '-' if mant.startswith('-') else '' body = mant.lstrip('-') out, sig, seen_dot, started = [], 0, False, False for ch in body: if ch == '.': seen_dot = True out.append(ch); continue if ch.isdigit(): if sig >= n: if not seen_dot: out.append('0') # preserve magnitude continue out.append(ch) if started or ch != '0': started = True if started: sig += 1 res = ''.join(out).rstrip('.') if seen_dot else ''.join(out) return sign + res + exp def print_cert_block(tag, interval, floors, args, tails=None): print('--- certification floors (fail-closed; computed per-component, not hardcoded) ---') A = _V2CERT['basepoint_cert_digits'][tag] print(f'base point u0={tag} (independent two-layout/two-precision cert): ' f'{min(A):.1f}-{max(A):.1f}d per master') if interval is not None: lo = runtime_loo_digits(interval) nv = _V2CERT['fnode_value_cert_digits'][interval] print(f'S base points (two-precision cert): {_V2CERT["s_basepoint_cert_digits"][tag]:.0f}d') print(f'F-node values [{interval}] (dps48-vs-dps60 run agreement): ' f'{min(nv):.1f}-{max(nv):.1f}d per row; node strings {_V2CERT["fnode_string_dps"][interval]}dps') print(f'F-grid interpolation LOO [{interval}] (computed at runtime from embedded nodes): ' f'{min(lo):.1f}-{max(lo):.1f}d per row <-- binding value-path cap') if tails: print('runtime Chebyshev tails (NS=%d, NA=%d): %s' % ( args.NS, args.NA, ', '.join(f'{k}={v:.1f}d' for k, v in sorted(tails.items())))) print(f'binding certified floor per master (margin {CLAMP_MARGIN}d applied): ' + ' '.join(f'{int(f)-CLAMP_MARGIN}' for f, _ in floors)) print('per-ingredient statement: numeric output gates certify each embedded datum only to') print(' (gate digits) - log10(output leverage). GS[0][0] leverage ~1e-14 => certified to') print(' only ~16 relative digits by a 30d gate (x3-row GS entries less, ~1e-38 leverage);') print(' sub-1e-16-relative corruption there is INVISIBLE to all numeric gates and is') print(' covered ONLY by the blob-sha INTEGRITY_GATE (rc=3).') # ---- compare-on-load F-grid swap (embedded values demote to cache) ---------- def load_fnodes_json(path): if not os.path.exists(path): print(f'LOADER_GATE FAIL: --fnodes-json file absent: {path}'); sys.exit(3) h = hashlib.sha256(open(path, 'rb').read()).hexdigest() J = json.load(open(path)) print(f'[fnodes-json] {path} sha256 {h[:16]}... (RECORD this sha in the adopting ledger)') for interval, seg in J.items(): if interval not in EMBED['FTRUE']: print(f'FNODE_CACHE_GATE FAIL: unknown interval {interval}'); sys.exit(4) newnodes = seg['nodes'] if isinstance(seg, dict) else seg old = EMBED['FTRUE'][interval] if [Fraction(n['u']) for n in newnodes] != [Fraction(n['u']) for n in old]: print(f'FNODE_CACHE_GATE FAIL: node u-grid differs for {interval} ' f'(the grid IS the definition; regenerate on the pinned CHEB grid)') sys.exit(4) old_sd = _V2CERT['fnode_string_dps'][interval] new_sd = int(seg.get('dps', min(len(v) for n in newnodes for v in n['F']))) \ if isinstance(seg, dict) else min(len(v) for n in newnodes for v in n['F']) bar = min(old_sd, new_sd, min(_V2CERT['fnode_value_cert_digits'][interval])) - 3 with mp.workdps(max(old_sd, new_sd) + 12): for i, (a, b) in enumerate(zip(old, newnodes)): for r in range(8): va, vb = mp.mpf(a['F'][r]), mp.mpf(b['F'][r]) ad = float(-mp.log10(abs(va-vb)/(abs(va)+mp.mpf('1e-60')) + mp.mpf('1e-99'))) if ad < bar: print(f'FNODE_CACHE_GATE FAIL: {interval} node {a["u"]} row {r}: ' f'new grid agrees with embedded cache to only {ad:.1f}d ' f'(bar {bar:.0f}d) — refusing the swap') sys.exit(4) EMBED['FTRUE'][interval] = newnodes _V2CERT['fnode_string_dps'][interval] = new_sd vc = (seg.get('value_cert_digits') if isinstance(seg, dict) else None) if vc: _V2CERT['fnode_value_cert_digits'][interval] = vc print(f'[fnodes-json] {interval}: swapped in {len(newnodes)} nodes at {new_sd}dps ' f'with DECLARED value certs {min(vc):.1f}-{max(vc):.1f}d') else: print(f'[fnodes-json] {interval}: swapped in {len(newnodes)} nodes at {new_sd}dps; ' f'NO value_cert_digits declared -> value-cert floor kept at the old ' f'{min(_V2CERT["fnode_value_cert_digits"][interval]):.1f}d (a swap cannot ' f'raise certification without its own two-precision cert)') _LOO_CACHE.clear() # ---- --recompute-node: the DEFINITION of an F_true node at any dps ---------- def recompute_node(ustr, rows, rdps): """Regenerate F_true(u,row) from the EXACT layer at requested dps: chart = fluxkernel3.flux_row_total(S00_FLUX_CACHE exact rationals); Delta = Q1_P0(CORNER_SOURCES exact) * K0(u) + Q1_P1 * K1 (written integrals); F_true = chart - Delta. Compares against the embedded cache value; a mismatch beyond the joint floor is a raising FNODE_CACHE_GATE.""" uf = Fraction(ustr) interval = None; idx = None for k, nd in EMBED['FTRUE'].items(): for i, n in enumerate(nd): if Fraction(n['u']) == uf: interval, idx = k, i if interval is None: raise SystemExit(f'ERROR: u={uf} is not an embedded F_true grid node') print(f'[recompute] node u={uf} ({interval}, node {idx}) at dps {rdps} from the EXACT layer', flush=True) print('[recompute] expect roughly 100-470 s per node for all 8 rows at dps 48; ' 'a single row takes about one eighth of that', flush=True) CS = load_ext('scratch/wall5713/CORNER_SOURCES.json') C = load_ext('S00_FLUX_CACHE.json') ck = [k for k in C if Fraction(k) == uf] sk = [k for k in CS if Fraction(k) == uf] if not ck or not sk: print(f'LOADER_GATE FAIL: node {uf} absent from ' f'{"S00_FLUX_CACHE" if not ck else "CORNER_SOURCES"}'); sys.exit(3) node = C[ck[0]]; rows_cs = CS[sk[0]] # Guards (measured on this work's own artifacts): F_true = chart - Delta is a # ~7-digit cancellation (chart ~1e7 vs F ~1e1), and _Ksafe's tail remainder # scales ~10^-(2*dps/3) (K1@dps34 vs dps90 table: 22d). Recipe: K at # ~2x chart dps (dps90 K for dps48 chart). Mirror both. CANC_GUARD = 12 # floor at 48: the production chart dps of this work (dps 44/46 trip the # (5,7)-web c-cancellation probe's branch-selection window; 34/40/48 pass, # measured 2026-07-06 on node 373/888 — dps48 reproduces the recorded # NODE_TOTALS total to 30/30d) chart_dps = max(48, rdps + 10 + CANC_GUARD) kdps = max(78, 2*rdps + 30) ut = mp.mpf(uf.numerator)/uf.denominator mp.mp.dps = kdps k0 = K0_wall(uf); k1 = K1_wall() print(f'[recompute] K0(u)={mp.nstr(k0, min(rdps, 30))}... K1={mp.nstr(k1, min(rdps, 30))}... ' f'(wall5713 written integrals at dps {kdps})', flush=True) mp.mp.dps = chart_dps sd = _V2CERT['fnode_string_dps'][interval] vc = _V2CERT['fnode_value_cert_digits'][interval] fail = False for r in rows: tr = time.time() chart = None for bump in (0, 4, 8): mp.mp.dps = chart_dps + bump try: chart = flux_row_total(parse_groups(node[r]), mp.mpf(uf.numerator)/uf.denominator)['total'] break except RegionSingularity as e: print(f'row {r}: RegionSingularity at chart_dps {chart_dps+bump} ' f'({str(e)[:60]}) — retrying at +4', flush=True) if chart is None: print(f'FNODE_CACHE_GATE FAIL: chart evaluation failed at all dps bumps for row {r}') sys.exit(4) q10 = Fraction(rows_cs[r]['P0']['1']); q11 = Fraction(rows_cs[r]['P1']['1']) d = (mp.mpf(q10.numerator)/q10.denominator)*k0 + (mp.mpf(q11.numerator)/q11.denominator)*k1 fnew = chart - d femb = mp.mpf(EMBED['FTRUE'][interval][idx]['F'][r]) ad = float(-mp.log10(abs(fnew-femb)/(abs(femb)+mp.mpf('1e-60')) + mp.mpf('1e-99'))) loss = float(mp.log10(abs(chart)/(abs(fnew)+mp.mpf('1e-60')) + 1)) print(f'row {r}: chart-vs-F cancellation loss {loss:.1f}d (chart_dps {chart_dps} ' f'covers rdps {rdps} + guard {CANC_GUARD})') bar = min(rdps, sd, vc[r]) - 3 status = 'PASS' if ad >= bar else 'FAIL' if ad < bar: fail = True print(f'row {r}: F_true(regenerated,dps{rdps}) = {mp.nstr(fnew, min(rdps, 50))}') print(f'row {r}: vs embedded cache agree {ad:.1f}d (bar {bar:.0f}d) ' f'FNODE_CACHE_GATE {status} [{time.time()-tr:.0f}s]', flush=True) if fail: print('FNODE_CACHE_GATE FAIL: embedded cache disagrees with the exact-layer ' 'regeneration — the cache is corrupt or the exact layer changed.') sys.exit(4) print('FNODE_CACHE_GATE PASS: embedded values are a faithful cache of the exact layer ' f'at their {sd}dps/{min(vc):.0f}d cert; at dps>{sd} the REGENERATED value is the definition.') # ---- escalation driver (WP1 refine-until-bound recipe) ---------------------- NS_CAP, NA_CAP = 512, 512 def run_eval_escalating(uf, wdps, NS, NA, escalate, target_d): NSc, NAc = NS, NA history = [] while True: diag = {} _stage(f'evaluation pass: NS={NSc} NA={NAc} (working dps {wdps})') Mv, tag, _ = eval_masters(uf, wdps, NS=NSc, NA=NAc, diag=diag) _stage(f'evaluation pass done: NS={NSc} NA={NAc}') if not diag: return Mv, tag, None, (NSc, NAc), history # base point: no transport ach = min(diag.values()) history.append((NSc, NAc, round(ach, 1))) if not escalate or ach >= target_d: return Mv, tag, diag, (NSc, NAc), history newNS = NSc if diag.get('tail_S', 1e9) >= target_d else NSc*3//2 newNA = NAc if min(diag.get('tail_y', 1e9), diag.get('tail_J', 1e9)) >= target_d else NAc*3//2 if (newNS, newNA) == (NSc, NAc): newNS, newNA = NSc*3//2, NAc*3//2 if newNS > NS_CAP or newNA > NA_CAP: print(f'DEPTH_GATE FAIL: Chebyshev tail bound {ach:.1f}d < target {target_d:.1f}d ' f'and escalation hit the cap (NS={NSc}->{newNS}, NA={NAc}->{newNA}, cap {NS_CAP}); ' f'history={history}. Refusing to print uncertified digits ' f'(rerun with lower --dps or --no-escalate to clamp to achieved).') sys.exit(5) print(f'[escalate] tails {diag} < target {target_d:.1f}d: ' f'NS {NSc}->{newNS}, NA {NAc}->{newNA}', flush=True) NSc, NAc = newNS, newNA def main(): ap = argparse.ArgumentParser(description='HARDENED standalone evaluator: 8 real ' 'bounded-region masters of s00_MI20cal on the slice z34=u ' '(mpmath only; fail-closed certified printing).') ap.add_argument('--dps', type=int, default=40, help='requested digits (default 40 -- measured ' '2026-09-03 as the smallest default that keeps the certified prefixes AND ' 'completes after one escalation (two passes): the F-grid LOO floor caps printing at 29d ' 'at the default point for every dps >= 30, and below dps 40 the S-layer ' 'Chebyshev-tail estimate saturates near (dps+10)-14 digits, under the ' 'escalation target, so dps 30/35 ladder through NS 80->120->180->... ' 'instead of finishing (measured, see the wall table in the header); ' '--dps 50 reproduces the old default); printed digits are clamped to the ' 'certified floor unless --raw') ap.add_argument('--point', type=str, default='21/50', help='rational u (default 21/50)') ap.add_argument('--check', action='store_true', help='two-precision self-check + DE-residual identity at 47/100 (RAISING gates)') ap.add_argument('--NS', type=int, default=80, help='S-layer Chebyshev N SEED (default 80)') ap.add_argument('--NA', type=int, default=64, help='assembly Chebyshev N SEED (default 64)') ap.add_argument('--raw', action='store_true', help='ALSO print full working precision with an explicit uncertified-tail label') ap.add_argument('--no-escalate', action='store_true', help='pin NS/NA (no refinement); certified clamp then also absorbs the ' 'achieved Chebyshev tail (values byte-match the original at matched settings)') ap.add_argument('--cert-only', action='store_true', help='print the certification floors and exit (no transport)') ap.add_argument('--recompute-node', type=str, default=None, metavar='U', help='regenerate F_true at grid node U from the EXACT source layer ' '(sha-pinned loader; needs --data-dir) and gate the embedded cache against it') ap.add_argument('--rows', type=str, default='0,1,2,3,4,5,6,7', help='rows for --recompute-node (default all 8)') ap.add_argument('--rdps', type=int, default=48, help='dps for --recompute-node (default 48)') ap.add_argument('--data-dir', type=str, default=None, metavar='DIR', help='directory holding the external exact-layer artifacts for ' '--recompute-node (sha-pinned manifest; no default)') ap.add_argument('--fnodes-json', type=str, default=None, help='swap in a regenerated FTRUE_NODES-style JSON (compare-on-load gate; ' 'embedded values demote to cache)') args = ap.parse_args() try: # liveness (2026-09-03): line-buffered stdout -- every line lands sys.stdout.reconfigure(line_buffering=True) # as it is printed except Exception: pass t0 = time.time() integrity_gate() _stage('s00-evaluate: 8 real bounded-region masters of s00_MI20cal on the slice ' f'z34=u, u={args.point}, requested dps {args.dps}; INTEGRITY_GATE PASS ' f'(embedded-data sha256 {_BLOB_SHA256[:16]}...)') if args.recompute_node is not None: if args.data_dir is None: print('ERROR: --recompute-node requires --data-dir DIR (the directory holding the external exact-layer artifacts)') sys.exit(2) global _DATA_DIR _DATA_DIR = args.data_dir rows = [int(x) for x in args.rows.split(',')] recompute_node(args.recompute_node, rows, args.rdps) print(f'wall {time.time()-t0:.0f}s') return if args.fnodes_json is not None: load_fnodes_json(args.fnodes_json) uf = Fraction(args.point) if args.cert_only: u0f, tag = seg_for(uf) interval = None if uf == u0f else interval_for(tag, uf) floors = cert_components(tag, interval) print_cert_block(tag, interval, floors, args) print(f'wall {time.time()-t0:.0f}s') return if args.check: print(f'[check] pass 1: working dps = {args.dps}', flush=True) M1 = eval_masters(uf, args.dps, NS=args.NS, NA=args.NA)[0] print(f'[check] pass 1 done [{time.time()-t0:.0f}s]; pass 2: working dps = {args.dps+10}', flush=True) M2 = eval_masters(uf, args.dps+10, NS=args.NS, NA=args.NA)[0] print(f'[check] pass 2 done [{time.time()-t0:.0f}s]', flush=True) mp.mp.dps = args.dps+10 print(f'masters at u = {uf} (u0 = {seg_for(uf)[1]}), {args.dps} digits ' f'(re part; two-precision agreement per master):') ok2 = True for r in range(8): ad = agree_digits(mp.re(M1[r]), mp.re(M2[r])) if ad < 8: ok2 = False print(f'M[{MOMS[r]:>5}] = {mp.nstr(mp.re(M2[r]), args.dps)} [agree {ad:.1f}d]') imax = max(abs(mp.im(M2[r])) for r in range(8)) print(f'max |Im| (numerical noise floor): {mp.nstr(imax, 3)}') print(f'[check] DE-residual identity at u = 47/100 (working dps = {args.dps}, h = 1e-12):', flush=True) res = de_residual_check(args.dps + 8, NS=args.NS, NA=args.NA) # v2.1: +8 guard for h=1e-12 for r in range(8): print(f'row {r}: DE-residual agree {res[r]:.2f}d') ok = all(res[r] >= 8 for r in range(8)) print('TWOPREC_GATE', 'PASS (bar 8d)' if ok2 else 'FAIL (bar 8d)') print('RESID_GATE', 'PASS (bar 8d)' if ok else 'FAIL (bar 8d)') print(provenance_block()) print(f'wall {time.time()-t0:.0f}s') if not (ok and ok2): print('CHECK GATES FAILED — exiting nonzero (fail-closed).') sys.exit(2) return wdps = args.dps + 10 u0f, tag0 = seg_for(uf) interval = None if uf == u0f else interval_for(tag0, uf) pre_floors = cert_components(tag0, interval) _stage('certification floors known up front -- binding certified prefix per master: ' + ' '.join(f'{max(1, min(args.dps, int(f) - CLAMP_MARGIN))}d' for f, _ in pre_floors) + ' (component table printed at the end of the run)') if uf != u0f: _stage(f'transport starting: segment base point u0={tag0}, working dps {wdps}; ' 'the S-layer flux build dominates the wall -- heartbeat lines follow') target_d = min(mp.mpf(args.dps), max(f for f, _ in pre_floors)) + 5 Mv, tag, tails, (NSf, NAf), hist = run_eval_escalating( uf, wdps, args.NS, args.NA, not args.no_escalate, float(target_d)) mp.mp.dps = wdps floors = cert_components(tag, interval, tails=tails if args.no_escalate else None) print(f'masters of s00_MI20cal at u = {uf} (segment base point u0 = {tag}); requested {args.dps} ' f'digits, printing the CERTIFIED prefix per master (fail-closed clamp):') for r in range(8): fd, comp = floors[r] nprint = max(1, min(args.dps, int(fd) - CLAMP_MARGIN)) binding = min(comp, key=comp.get) print(f'M[{MOMS[r]:>5}] = {trunc_str(mp.re(Mv[r]), nprint)} ' f'[certified {nprint}d; floor {fd:.1f}d, binding: {binding}]') if args.raw: print(f'--raw (working dps {wdps}; digits beyond the certified floor are ' f'UNCERTIFIED TAIL, shown for diagnostics only):') for r in range(8): print(f'M[{MOMS[r]:>5}] = {mp.nstr(mp.re(Mv[r]), wdps)} [UNCERTIFIED beyond ' f'{max(1, min(args.dps, int(floors[r][0]) - CLAMP_MARGIN))}d]') try: imax = max(abs(mp.im(Mv[r])) for r in range(8)) print(f'max |Im| (numerical noise floor): {mp.nstr(imax, 3)}') except TypeError: pass if hist and (NSf, NAf) != (args.NS, args.NA): print(f'[escalate] depth history (NS,NA,tail-d): {hist} -> final NS={NSf} NA={NAf}') print_cert_block(tag, interval, floors, args, tails=tails) print(provenance_block()) print(f'wall {time.time()-t0:.0f}s') if __name__ == '__main__': main()