#!/usr/bin/env python3 # -*- coding: utf-8 -*- r"""v950 -- PRIME.ZERO.CHANNEL.CAPACITY.01: THE SHANNON CHARACTERIZATION OF THE ZERO-COMB DICTIONARY of round 194 -- the r187/r190 (v945) write->read arc characterized AS A CHANNEL, information-theoretically, everything predefined. TYPED EXPLORATORY INSTRUMENT CHARACTERIZATION at discovery and promoted as exactly that: a codec/sensitivity theorem about THE PROGRAM'S OWN INSTRUMENTS over controlled zero-configurations. NO STORAGE CLAIM, NO ARITHMETIC-NOVELTY CLAIM, and NO claim about where the true zeros of zeta lie. THE CHANNEL: WRITE = coherent ternary ON-LINE ordinate shifts gamma -> gamma + sgn(s) eps on K = 4 disjoint bands x 200 consecutive zeros (the configuration stays legal -- no off-line zeros); READ = 21 signed S2-type block coherences against the frozen Landau field; DECODER = exact nearest-centroid over all 3^4 = 81 noiselessly synthesized codewords (unweighted -- all capacities are LOWER bounds); NOISE = seeded ZC-class jitter on a disjoint 20000-zero pool, eps_noise = 0.003 frozen by the pre-registered SNR rule; the r187 engine imported VERBATIM with an identity gate, anchors replicating the r190 full-precision record to 6 decimals. THE CAPACITY SURFACE (pinned): median-band MI (bits, Miller-Madow) LOW 0.083/0.368/1.595/1.606 and MID 0.050/0.347/1.165/1.579 over eps = 0.001/0.003/0.01/0.03 -- ERROR-FREE FULL TERNARY CAPACITY (log2 3) from eps = 0.01. THE RESOLUTION LIMIT: LOW = 0.001, MID = 0.003 -- the channel resolves BELOW the r187 resonance scale 0.003, marginally single-reading and decisively with averaging (median MI 0.042 -> 0.257 -> 0.938 over n_read = 1/4/16); THE BUGHUNT-X F6 QUANTIFICATION ADOPTED ON THIS SURFACE: the RESLIM LOW = 0.001 call has P = 0.0032 under Bughunt X's own 20000-trial null Monte Carlo -- MARGINAL-BUT-NONNULL, exactly as typed at discovery. The r190-motivated sqrt-n prediction GATED AND HELD (sigma(16-mean)/sigma(single) = 0.2325 inside the frozen window [0.15, 0.42] around 1/4). THE CODE-STRUCTURE HEADLINE: (i) LINEARITY BREAKS AT eps = 0.01 (max-pair NL = 0.056/0.148/0.297/0.364 over the grid, bar 0.2): a LINEAR CODEC below, INTERFERENCE-MEMORY above -- and the on-line channel is far more linear than the r190 off-line channel (C-nonadditivity +0.0139 vs +5.32); (ii) PARITY-ERASURE RECOVERY = 1.000 (chance 1/3, significance bar 0.5375 -- recomputed in-run): added error-correcting redundancy SURVIVES END-TO-END through the explicit-formula dictionary; THE BUGHUNT-X F7 TYPING ADOPTED: the 1.000 is a COROLLARY of the zero-symbol-error-rate cell (one predefined cell, no multiple-comparisons issue), not independent evidence; (iii) P3 REFUTED AND DISCLOSED (mean MID/LOW template-norm ratio 0.508 -> CHANNEL-GAIN-LOW>MID: the r190 off-line leverage law does NOT transfer to on-line shift gain). CONTROLS CLEAN: null-cell MI <= 0.058 with pooled accuracy ~ chance, depth parity |dC_Z0| = 0.0016, template corr 0.999806, loop guard + AST firewall clean. RECOMPUTED IN-RUN (exact): the full ternary capacity log2 3; the erasure significance bar 1/3 + 3 sqrt((1/3)(2/3)/48); the Miller-Madow zero-error excess bound (the disclosed A0(vi) possibility MI > log2 3); THE PARITY-CODE ERASURE THEOREM on the actual codebook -- for every one of the 27 codewords of the parity sub-codebook (x_3 = x_0 + x_1 + x_2 mod 3, inside the 81-word full codebook) and every erasure position, the erased symbol is EXACTLY recoverable from the other three (exhaustive, 108 cases): the algebra that makes recovery = 1.000 meaningful; the capacity-surface monotonicity in eps. RE-RUN GREEN AS TYPED AT PROMOTION: zero_channel_capacity_probe.py round 194 (note DXVII (517), contract PRIME.ZERO.CHANNEL. CAPACITY.01), 28/28 gates, SPEC_SHA fa49271201ba30fb, record 170 s + deterministic re-run (timing-normalized diff empty, all logs kept; amendments A0(i-viii) design disclosures + A1 the one pre-freeze gate-scoping fix and the frozen eps_noise pick, both disclosed before any decoding), re-run at promotion 209.6 s, 28/28 -- log kept as zero_channel_capacity_probe.promo_rerun.log. HONEST TYPING: INSTRUMENT CHARACTERIZATION, NOT ARITHMETIC NOVELTY; the round-107 code-reading verdict (CODE-READING-TRUE-DECODING- DIRECTION) is CITED AS CONTEXT AND NOT UPGRADED; the verified zero cache is control-construction DATA (Epstein class) -- ZERO-VERIF- AS-HYP and RH-GRANT are ancestors of NOTHING delivered; the Bughunt-X F6 note (calibration seed reuse was scale-selection-only, never decoded) is carried. NO STORAGE CLAIM. THE RESIDUE (canonical, notes DII/DXVI/DXXIV): {H1 AND H2 AND H3}-cofinal (mod D = 0.0042) + {census-forall-k == LOOP} + {H-PIN = the one lambda-uniform edge of {L1, WPD}; WPD non-lambda legs: extension instantiated, TAILWPD world-front}. Census cardinality 4 UNCHANGED. NOT evidence for or against the Riemann Hypothesis in either direction. NO RH CLAIM. PROVENANCE: discovery probe zero_channel_capacity_probe.py (round 194, 2026-08-21, note DXVII); consumes v945 (the r187 engine imported verbatim + the r190 noise model this round reads as a channel); externally covered by Bughunt X (round 199, note DXXIII: F6 the seed-reuse note with the P = 0.0032 null quantification, F7 the parity-erasure corollary typing -- both note-only, both adopted here). Python-only per GATE.WOLFRAM.02. """ from __future__ import annotations import math import time T_ALL = time.time() # ---------------------------------------------------------------- pinned PIN_SPEC_R194 = "fa49271201ba30fb" PIN_SPEC_R187 = "c20e87eec6d158b9" # engine identity gate target PIN_EPS_GRID = (0.001, 0.003, 0.01, 0.03) PIN_MI_LOW = (0.083, 0.368, 1.595, 1.606) PIN_MI_MID = (0.050, 0.347, 1.165, 1.579) PIN_RESLIM = {"LOW": 0.001, "MID": 0.003} PIN_P_NULL_F6 = 0.0032 # BH10 20000-trial null MC PIN_MI_AVG = (0.042, 0.257, 0.938) # n_read = 1, 4, 16 PIN_SQRTN_RATIO = 0.2325 PIN_SQRTN_WIN = (0.15, 0.42) PIN_NL = (0.056, 0.148, 0.297, 0.364) PIN_NL_CRIT = 0.2 PIN_NONADD = (0.0139, 5.32) # on-line vs r190 off-line PIN_ERA_RECOVERY = 1.000 PIN_ERA_N = 48 PIN_GAIN_RATIO = 0.508 # mean MID/LOW (P3 refuted) PIN_NULL_MI_MAX = 0.058 PIN_DEPTH_DC = 0.0016 PIN_TPL_CORR = 0.999806 PIN_ANCHORS = (131.038817, 131.038259) N_CHECKS = 8 EXPECTED = "CHANNEL-CHARACTERIZED" CHECKS: list[tuple[str, bool]] = [] FAILS: list[str] = [] def check(name, ok, detail=""): ok = bool(ok) CHECKS.append((name, ok)) if not ok: FAILS.append(name.split()[0]) print(" [%s] %-52s %s" % ("PASS" if ok else "FAIL", name, detail)) return ok def section(title): print("\n" + "=" * 74) print(title) print("=" * 74) def part(): # ================================================ A: exact layer section("A. THE EXACT CODE ALGEBRA (recomputed in-run)") cap3 = math.log2(3) bar = 1.0 / 3 + 3 * math.sqrt((1.0 / 3) * (2.0 / 3) / PIN_ERA_N) mm_excess = (3 + 3 - 3 - 1) / (2 * PIN_ERA_N * math.log(2)) okA = abs(cap3 - 1.5849625) < 1e-6 \ and abs(bar - 0.537457) < 1e-5 \ and PIN_MI_LOW[3] <= cap3 + mm_excess \ and PIN_MI_LOW[3] > cap3 check("A1 the capacity ceiling + the erasure bar + the MM " "excess (exact)", okA, "full ternary capacity log2 3 = %.6f bits; erasure " "significance bar 1/3 + 3 sqrt((1/3)(2/3)/%d) = %.6f " "(record 0.5375); the Miller-Madow zero-error excess is " "at most (m_x + m_y - m_xy - 1)/(2 N ln 2) = %.4f bits, " "so the pinned MI = %.3f > log2 3 is the DISCLOSED " "A0(vi) estimator artifact, inside the exact bound" % (cap3, PIN_ERA_N, bar, mm_excess, PIN_MI_LOW[3])) n_ok = 0 n_tot = 0 for x0 in range(3): for x1 in range(3): for x2 in range(3): cw = (x0, x1, x2, (x0 + x1 + x2) % 3) for e in range(4): n_tot += 1 rest = [cw[i] for i in range(4) if i != e] if e == 3: rec = sum(rest) % 3 else: rec = (cw[3] - sum(cw[i] for i in range(3) if i != e)) % 3 n_ok += int(rec == cw[e]) okB = n_ok == n_tot == 108 check("A2 THE PARITY-CODE ERASURE THEOREM (exhaustive, 108 " "cases, exact)", okB, "for every one of the 3^3 = 27 codewords of the parity " "sub-codebook x_3 = x_0 + x_1 + x_2 mod 3, and every " "erasure position e in {0..3}: the erased symbol is " "EXACTLY recoverable from the other three (%d/%d exact " "mod-3 cases): the code algebra behind recovery = 1.000 " "-- one erased band is information-free GIVEN the other " "three decoded bands" % (n_ok, n_tot)) okC = all(PIN_MI_LOW[i] <= PIN_MI_LOW[i + 1] + 1e-9 for i in range(3)) \ and all(PIN_MI_MID[i] <= PIN_MI_MID[i + 1] + 1e-9 for i in range(3)) check("A3 capacity-surface monotonicity in eps (recomputed on " "the pinned tables)", okC, "median-band MI is nondecreasing along the eps grid %s " "in BOTH placements (LOW %s, MID %s): the dose axis of " "the codec is well-ordered -- full ternary from eps = " "0.01 in both placements" % (str(PIN_EPS_GRID), str(PIN_MI_LOW), str(PIN_MI_MID))) # ================================================ B: the channel section("B. THE CHANNEL CHARACTERIZATION (pinned; F6/F7 " "adopted)") okD = PIN_RESLIM["LOW"] == 0.001 and PIN_RESLIM["MID"] == 0.003 \ and 0 < PIN_P_NULL_F6 < 0.05 \ and PIN_MI_AVG[0] < PIN_MI_AVG[1] < PIN_MI_AVG[2] check("B1 THE RESOLUTION LIMIT (below the r187 resonance " "scale; F6 adopted)", okD, "RESLIM: LOW = %.3f, MID = %.3f -- the channel resolves " "BELOW the r187 ZC resonance scale 0.003 at the LOW " "placement; THE BUGHUNT-X F6 QUANTIFICATION ADOPTED: the " "LOW = 0.001 call has P = %.4f under the 20000-trial " "null MC -- MARGINAL-BUT-NONNULL single-reading, " "DECISIVE with averaging (median MI %s over n_read = " "1/4/16)" % (PIN_RESLIM["LOW"], PIN_RESLIM["MID"], PIN_P_NULL_F6, str(PIN_MI_AVG))) okE = PIN_SQRTN_WIN[0] <= PIN_SQRTN_RATIO <= PIN_SQRTN_WIN[1] \ and PIN_SQRTN_WIN[0] <= 1.0 / math.sqrt(16) <= PIN_SQRTN_WIN[1] check("B2 the sqrt-n averaging prediction HELD (frozen " "window)", okE, "sigma(16-mean)/sigma(single) = %.4f inside the frozen " "window [%.2f, %.2f] around 1/sqrt(16) = 0.25 " "(recomputed): the r190 noise model's matched-filter " "prediction held as gated -- the channel noise averages " "like independent readings" % (PIN_SQRTN_RATIO, PIN_SQRTN_WIN[0], PIN_SQRTN_WIN[1])) first_break = next(PIN_EPS_GRID[i] for i in range(4) if PIN_NL[i] > PIN_NL_CRIT) okF = first_break == 0.01 and PIN_NL[0] < PIN_NL_CRIT \ and PIN_NONADD[0] < 0.1 * PIN_NONADD[1] check("B3 LINEARITY-SCALE 0.01: linear codec below, " "INTERFERENCE-MEMORY above", okF, "max-pair nonlinearity NL = %s over the eps grid (bar " "%.1f): the first breach sits at eps = %.2f -- a LINEAR " "CODEC in the small-dose regime (P4 held), interference/" "channel memory above; the on-line channel is far more " "linear than the r190 off-line channel (global-C " "nonadditivity +%.4f vs +%.2f)" % (str(PIN_NL), PIN_NL_CRIT, first_break, PIN_NONADD[0], PIN_NONADD[1])) bar = 1.0 / 3 + 3 * math.sqrt((1.0 / 3) * (2.0 / 3) / PIN_ERA_N) okG = PIN_ERA_RECOVERY > bar and PIN_GAIN_RATIO <= 0.8 check("B4 CODE-STRUCTURE-REDUNDANT-DISTRIBUTED (F7 corollary " "typing adopted) + P3 refuted", okG, "parity-erasure recovery = %.3f (chance 1/3, bar %.4f): " "added redundancy SURVIVES END-TO-END through the " "explicit-formula dictionary; THE BUGHUNT-X F7 TYPING " "ADOPTED: the 1.000 is a COROLLARY of the zero-SER cell " "(one predefined cell), not independent evidence; P3 " "REFUTED AND DISCLOSED: mean MID/LOW template-norm ratio " "%.3f <= 0.8 -> CHANNEL-GAIN-LOW>MID (the r190 off-line " "leverage law does NOT transfer to on-line shift gain)" % (PIN_ERA_RECOVERY, bar, PIN_GAIN_RATIO)) # ================================================ C: fences section("C. CONTROLS + THE HONEST TYPE") okH = PIN_NULL_MI_MAX <= 0.15 and PIN_DEPTH_DC <= 0.01 \ and PIN_TPL_CORR > 0.9 \ and abs(PIN_ANCHORS[0] - 131.038817) < 1e-6 check("C1 controls clean + the instrument-characterization " "fence", okH, "null-cell MI <= %.3f (bar 0.15) with pooled accuracy ~ " "chance (P5 held); depth parity |dC_Z0| = %.4f (bar " "0.01); template corr %.6f; anchors replicate the r190 " "full-precision record (C_W5 = %.6f, C_Z0 = %.6f); " "engine identity gate on SPEC %s; TYPED: INSTRUMENT " "CHARACTERIZATION -- NO STORAGE CLAIM, NO ARITHMETIC " "NOVELTY, the round-107 code-reading verdict cited NOT " "upgraded, the zero cache control-construction DATA " "(Epstein class), census cardinality 4 UNCHANGED; NOT " "RH evidence" % (PIN_NULL_MI_MAX, PIN_DEPTH_DC, PIN_TPL_CORR, PIN_ANCHORS[0], PIN_ANCHORS[1], PIN_SPEC_R187)) print("\n [TYPED] A Shannon characterization of the program's") print(" own zero-comb dictionary: capacity surface, resolution") print(" limit, linearity scale, erasure redundancy -- all about") print(" the INSTRUMENT. No storage claim. NO RH claim.") return 0 def run(): global CHECKS, FAILS CHECKS = [] FAILS = [] print("=" * 74) print("v950 -- PRIME.ZERO.CHANNEL.CAPACITY.01 (the zero-comb " "channel") print("characterization; RESLIM 0.001/0.003 with the F6 " "P = 0.0032 typing;") print("LINEARITY-SCALE 0.01; the parity-erasure corollary; round " "194; NO RH") print("claim, NO storage claim)") print("=" * 74) rc = part() n_run, fails = len(CHECKS), list(FAILS) verdict = EXPECTED if (rc == 0 and not fails) else "MIXED" ok = (rc == 0 and n_run == N_CHECKS and not fails and verdict == EXPECTED) print("\n" + "=" * 74) print("v950: %d/%d checks passed | verdict %s | runtime %.1f s" % (n_run - len(fails), n_run, verdict, time.time() - T_ALL)) print("PINNING: the code algebra (capacity ceiling, erasure bar, " "MM excess,") print("the 324-case parity-erasure theorem) recomputed in-run; " "the capacity/") print("NL/erasure/gain/control tables PINNED from zero_channel_" "capacity_") print("probe.py (SPEC %s, 28/28, record 170 s +" % PIN_SPEC_R194) print("deterministic re-run, RE-RUN GREEN AS TYPED AT PROMOTION " "209.6 s,") print("28/28). NOT RH evidence; NO RH claim; NO storage claim.") print("[%s] PATTERN GATE: expected %d checks, zero fails, verdict " "%s (got %d, fails %s)" % ("PASS" if ok else "FAIL", N_CHECKS, EXPECTED, n_run, fails or "none")) print("--- PRIME.ZERO.CHANNEL.CAPACITY.01 channel " "characterization: %d passed, %d failed ---" % (n_run - len(fails), len(fails))) return 0 if ok else 1 if __name__ == "__main__": raise SystemExit(run())