From f69feee28698e552886bae441a80d2b91aeb04cd Mon Sep 17 00:00:00 2001 From: Gonzalo-Mier Date: Sat, 17 Oct 2026 21:15:07 +0200 Subject: [PATCH 1/5] Capture exact PR 3200 baseline for joint axis search --- .../inputs/pr3200/BINS.json.gz | Bin 0 -> 239829 bytes .../inputs/pr3200/MOVES.json.gz | Bin 0 -> 1306990 bytes .../inputs/pr3200/PROVENANCE.json | 10 + .../inputs/pr3200/RESULT.json | 62 +++++ .../inputs/pr3200/verify.py | 219 ++++++++++++++++++ 5 files changed, 291 insertions(+) create mode 100644 research/t740-joint-axis-optimization/inputs/pr3200/BINS.json.gz create mode 100644 research/t740-joint-axis-optimization/inputs/pr3200/MOVES.json.gz create mode 100644 research/t740-joint-axis-optimization/inputs/pr3200/PROVENANCE.json create mode 100644 research/t740-joint-axis-optimization/inputs/pr3200/RESULT.json create mode 100644 research/t740-joint-axis-optimization/inputs/pr3200/verify.py diff --git a/research/t740-joint-axis-optimization/inputs/pr3200/BINS.json.gz 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= F(1), F(1) + for j in range(1, 34): t = t * x / j; s += t + return s, t * x / 34 * 3 + e0, _ = tay(b * L0); e1, t1 = tay(b * L1) + lo += n * r * rd(e0); hi += n * r * ru(e1 + t1) + return lo / (73 * W), hi / (73 * W) + + +def check_bit(): + inv = json.loads(BITCERT.read_text())['pipeline']['candidate']['hosted']['invoice'] + prof = {int(k): v for k, v in inv['bit_profile'].items()} + c, cn = F(inv['bit_lower']), F(inv['next_grid_point_rejected']) + req(c == F(inv['bit_lower_decimal']) and cn - c == F(1, 10 ** 24) and 2 * max(prof) ** 2 < 64 ** 2, 'R438 certificate fields') + W = 28416; N = sum(prof.values()) + def bm(b): + lo = hi = F(0) + for r, n in sorted(prof.items()) + [(1, F(32 * 64 * 64 * N, 10 ** 16))]: + l0, l1 = ln64(r); e0, e1 = exbox(b * l0, b * l1); lo += n * r * e0; hi += n * r * e1 + return lo / (64 * W), hi / (64 * W) + req(bm(c)[1] < 1 and bm(cn)[0] > 1, 'R438 bit endpoint accepted at c, rejected at c+1e-24') + return c + + +def ln64(r): + Q72 = 10 ** 72 + def at(z, n): + s, p = F(0), z + for j in range(n): s += p / (2 * j + 1); p *= z * z + return 2 * s, 2 * p / ((2 * n + 1) * (1 - z * z)) + y, k = F(64, r), 0 + while y >= 2: y /= 2; k += 1 + l2 = at(F(1, 3), 130); a, e = at((y - 1) / (y + 1), 90) + return F((a + k * l2[0]).numerator * Q72 // (a + k * l2[0]).denominator, Q72), F(-((-(a + e + k * (l2[0] + l2[1])).numerator * Q72) // (a + e + k * (l2[0] + l2[1])).denominator), Q72) + + +def exbox(x0, x1): + def tay(x): + s, t = F(1), F(1) + for j in range(1, 34): t = t * x / j; s += t + return s, t * x / 34 * 3 + a, _ = tay(x0); b, t = tay(x1) + return a, b + t + + +def run(rec, bins, moves, result): + final = audit(rec, bins, moves) + prof = Counter({r: n * 9 * T for r, n in LOCAL.items()}); prof.update(final); prof = dict(sorted(prof.items())) + req({str(k): v for k, v in prof.items()} == result['profile'], 'declared profile') + req(sum(r * n for r, n in prof.items()) == 65088 * T, 'rank mass 65088*T') + req(max(prof) <= 51 and 73 * 73 > 2 * max(prof) ** 2, 'halving guard') + lo, hi = F(result['complex_root'][0]), F(result['complex_root'][1]) + req(hi - lo == F(1, 10 ** 25) and mom(prof, lo)[1] < 1 and mom(prof, hi)[0] > 1, 'complex root bracket') + C = min(F(lo.numerator * 10 ** 24 // lo.denominator, 10 ** 24), BIT) + req(C < BIT, 'complex binds below the R438 bit endpoint') + kappa = C - F(1, 10 ** 46) - F(1, 10 ** 70) + req(kappa == F(result['kappa']), 'headline kappa') + for n, g in GATES.items(): req(kappa > g, 'kappa must exceed ' + n) + return prof, kappa, lo + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--t740', type=Path) + ap.add_argument('--providers', type=Path, default=PKG / 'PR3148-PROVIDERS.json') + ap.add_argument('--write', action='store_true', help='rewrite the committed AUDIT.json receipt') + a = ap.parse_args() + if not __debug__: raise SystemExit('assertions required') + raw = PHASES.read_bytes() + req(hashlib.sha256(raw).hexdigest() == 'c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa', 'phases pin') + rec = {r['port']: r for r in json.loads(raw)['recipes']} + global BIT + BIT = check_bit() + bins, mv, result = load(PKG / 'BINS.json.gz'), load(PKG / 'MOVES.json.gz')['moves'], load(PKG / 'RESULT.json') + rebound = False + if a.t740: + fraw = gzip.decompress((a.t740 / 'COMPOSED-FILL.json.gz').read_bytes()) + req(hashlib.sha256(fraw).hexdigest() == '8f4d6965ba573ff2b71fd7bf6b552643e086739d90bd73c55889502077638e00', 'fill pin') + prov = load(a.providers); order = load(a.t740 / 'ORDER.json'); disp = {(s, r): p for s, r, p in load(a.t740 / 'DISPATCH.json')} + used = Counter() + for time, helper, rep, child, port, offset in json.loads(fraw)['rows']: + s, r = order[time]; used[rep, child, port] += prov[disp[s, r]]['widths'][helper] + caps = {(p, c): ch['rank'] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + derived = [[rep, p, [[c, used[rep, c, p]] for c in range(len(rec[p]['idle_children'])) if caps[p, c] - used[rep, c, p] > 0]] for rep in range(T) for p in range(112)] + req([g for g in derived if g[2]] == bins['groups'], 'BINS equal the fill') + rebound = True + prof, kappa, lo = run(rec, bins, mv, result) + rej = {} + first_hosted = next(i for i, m in enumerate(mv) if {c: u for c, u in next(g for g in bins['groups'] if g[0] == m[0] and g[1] == m[1])[2]}[m[2]] > 0) + rep, p, c, d, v = mv[first_hosted] + kids = {cc: u for cc, u in next(g for g in bins['groups'] if g[0] == rep and g[1] == p)[2]} + hosted_other = next((cc for cc, u in kids.items() if u > 0 and cc != c), None) + used_axis = int(rec[p]['idle_children'][c]['orthogonal_axes'][0]) + def mut(f): + x = copy.deepcopy(mv); f(x); return x + cases = dict( + hosted_receiver=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, hosted_other if hosted_other is not None else c, v])), + hosted_axis_from_used_prefix=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, d, used_axis])), + foreign_axis=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, d, 1 << 80])), + axis_moved_twice=mut(lambda x: x.insert(first_hosted + 1, list(x[first_hosted]))), + receiver_donates=mut(lambda x: x.append([rep, p, d, c, v])), + dropped_move=mut(lambda x: x.pop(first_hosted)), + ) + for name, x in cases.items(): + try: run(rec, bins, x, result) + except Reject as e: rej[name] = str(e) + else: raise SystemExit('mutation accepted: ' + name) + r2 = copy.deepcopy(result); r2['complex_root'] = [str(lo + F(1, 10 ** 25)), str(lo + F(2, 10 ** 25))] + try: run(rec, bins, mv, r2) + except Reject as e: rej['next_root_grid'] = str(e) + else: raise SystemExit('mutation accepted: next_root_grid') + r3 = copy.deepcopy(result); r3['kappa'] = str(F(result['kappa']) + F(1, 10 ** 24)) + try: run(rec, bins, mv, r3) + except Reject as e: rej['kappa_above_bit'] = str(e) + else: raise SystemExit('mutation accepted: kappa_above_bit') + out = dict(status='PASS_IDLE_DONOR_GREEDY_R438_AUDIT', moves=len(mv), fill_rebound=rebound, kappa=str(kappa), + complex_root_lower=str(lo), binding='bit' if BIT < lo else 'complex', rejected_controls=rej) + if a.write: (PKG / 'AUDIT.json').write_text(json.dumps(out, indent=1, sort_keys=True) + '\n') + else: + strip = lambda d: {k: v for k, v in d.items() if k != 'fill_rebound'} + req(strip(load(PKG / 'AUDIT.json')) == strip(json.loads(json.dumps(out))), 'committed AUDIT.json receipt') + print('PASS_IDLE_DONOR_GREEDY_R438_AUDIT moves=%d controls=%d kappa=%s binding=%s' % (len(mv), len(rej), float(kappa), out['binding'])) + + +if __name__ == '__main__': + try: main() + except Reject as e: raise SystemExit('FAIL: ' + str(e)) From cc065ff497a0e72e78fde78eec78b74147ed722e Mon Sep 17 00:00:00 2001 From: Gonzalo-Mier Date: Sat, 17 Oct 2026 21:15:17 +0200 Subject: [PATCH 2/5] Place PR 3200 inputs in a source archive before packaging --- .../t740-joint-axis-pr3200}/BINS.json.gz | Bin .../t740-joint-axis-pr3200}/MOVES.json.gz | Bin .../t740-joint-axis-pr3200}/PROVENANCE.json | 0 .../t740-joint-axis-pr3200}/RESULT.json | 0 .../t740-joint-axis-pr3200}/verify.py | 0 5 files changed, 0 insertions(+), 0 deletions(-) rename research/{t740-joint-axis-optimization/inputs/pr3200 => source-archives/t740-joint-axis-pr3200}/BINS.json.gz (100%) rename research/{t740-joint-axis-optimization/inputs/pr3200 => source-archives/t740-joint-axis-pr3200}/MOVES.json.gz (100%) rename research/{t740-joint-axis-optimization/inputs/pr3200 => source-archives/t740-joint-axis-pr3200}/PROVENANCE.json (100%) rename research/{t740-joint-axis-optimization/inputs/pr3200 => source-archives/t740-joint-axis-pr3200}/RESULT.json (100%) rename research/{t740-joint-axis-optimization/inputs/pr3200 => source-archives/t740-joint-axis-pr3200}/verify.py (100%) diff --git a/research/t740-joint-axis-optimization/inputs/pr3200/BINS.json.gz b/research/source-archives/t740-joint-axis-pr3200/BINS.json.gz similarity index 100% rename from research/t740-joint-axis-optimization/inputs/pr3200/BINS.json.gz rename to research/source-archives/t740-joint-axis-pr3200/BINS.json.gz diff --git a/research/t740-joint-axis-optimization/inputs/pr3200/MOVES.json.gz b/research/source-archives/t740-joint-axis-pr3200/MOVES.json.gz similarity index 100% rename from research/t740-joint-axis-optimization/inputs/pr3200/MOVES.json.gz rename to research/source-archives/t740-joint-axis-pr3200/MOVES.json.gz diff --git a/research/t740-joint-axis-optimization/inputs/pr3200/PROVENANCE.json b/research/source-archives/t740-joint-axis-pr3200/PROVENANCE.json similarity index 100% rename from research/t740-joint-axis-optimization/inputs/pr3200/PROVENANCE.json rename to research/source-archives/t740-joint-axis-pr3200/PROVENANCE.json diff --git a/research/t740-joint-axis-optimization/inputs/pr3200/RESULT.json b/research/source-archives/t740-joint-axis-pr3200/RESULT.json similarity index 100% rename from research/t740-joint-axis-optimization/inputs/pr3200/RESULT.json rename to research/source-archives/t740-joint-axis-pr3200/RESULT.json diff --git a/research/t740-joint-axis-optimization/inputs/pr3200/verify.py b/research/source-archives/t740-joint-axis-pr3200/verify.py similarity index 100% rename from research/t740-joint-axis-optimization/inputs/pr3200/verify.py rename to research/source-archives/t740-joint-axis-pr3200/verify.py From f5c19467bd30c5ee489693bdb74a712b837412f1 Mon Sep 17 00:00:00 2001 From: Gonzalo-Mier Date: Sat, 17 Oct 2026 21:33:56 +0200 Subject: [PATCH 3/5] Reject rank-only T740 kappa candidate on exact replay --- .../OPERATOR-WITNESS.json | 150 +++++++++++++ .../RANK-ONLY-MOVES.json.gz | Bin 0 -> 1386491 bytes .../RANK-ONLY-RESULT.json | 66 ++++++ .../t740-joint-axis-optimization/README.md | 100 +++++++++ .../t740-joint-axis-optimization/SOURCES.json | 132 ++++++++++++ .../t740-joint-axis-optimization/TASK.json | 78 +++++++ .../t740-joint-axis-optimization/VERIFY.json | 39 ++++ .../requirements-search.txt | 1 + .../t740-joint-axis-optimization/search.py | 158 ++++++++++++++ .../t740-joint-axis-optimization/verify.py | 198 ++++++++++++++++++ 10 files changed, 922 insertions(+) create mode 100644 research/t740-joint-axis-optimization/OPERATOR-WITNESS.json create mode 100644 research/t740-joint-axis-optimization/RANK-ONLY-MOVES.json.gz create mode 100644 research/t740-joint-axis-optimization/RANK-ONLY-RESULT.json create mode 100644 research/t740-joint-axis-optimization/README.md create mode 100644 research/t740-joint-axis-optimization/SOURCES.json create mode 100644 research/t740-joint-axis-optimization/TASK.json create mode 100644 research/t740-joint-axis-optimization/VERIFY.json create mode 100644 research/t740-joint-axis-optimization/requirements-search.txt create mode 100644 research/t740-joint-axis-optimization/search.py create mode 100644 research/t740-joint-axis-optimization/verify.py diff --git a/research/t740-joint-axis-optimization/OPERATOR-WITNESS.json b/research/t740-joint-axis-optimization/OPERATOR-WITNESS.json new file mode 100644 index 0000000000..b7188620f6 --- /dev/null +++ b/research/t740-joint-axis-optimization/OPERATOR-WITNESS.json @@ -0,0 +1,150 @@ +{ + "baseline_control_modes_passed": 147, + "baseline_owner_used_children": [ + [ + 4, + 31 + ], + [ + 6, + 31 + ], + [ + 8, + 0 + ], + [ + 10, + 0 + ], + [ + 12, + 0 + ], + [ + 13, + 0 + ], + [ + 14, + 31 + ], + [ + 15, + 31 + ] + ], + "candidate_group_moves": [ + [ + 0, + 0, + 12, + 8, + 9007199254740992 + ], + [ + 0, + 0, + 12, + 8, + 1180591620717411303424 + ], + [ + 0, + 0, + 12, + 10, + 18014398509481984 + ], + [ + 0, + 0, + 12, + 10, + 36028797018963968 + ], + [ + 0, + 0, + 14, + 8, + 4722366482869645213696 + ], + [ + 0, + 0, + 15, + 10, + 4722366482869645213696 + ] + ], + "changed_idle_ranks": { + "10": [ + 48, + 51 + ], + "12": [ + 48, + 44 + ], + "14": [ + 1, + 0 + ], + "15": [ + 1, + 0 + ], + "8": [ + 48, + 51 + ] + }, + "conclusion": "The rank-only overlay changes the exact eight-stream physical operator. Its hypothetical root/kappa is inadmissible.", + "first_coordinate_character_mismatch": { + "bit": 53, + "character": 9007199254740992, + "matrix_differences": [ + [ + 1, + 1, + [ + 0, + 1 + ], + [ + 1, + 0 + ] + ], + [ + 3, + 1, + [ + 0, + 0 + ], + [ + 1, + -1 + ] + ], + [ + 6, + 6, + [ + 0, + 1 + ], + [ + -1, + 0 + ] + ] + ] + }, + "owner_replica": 0, + "port": 0, + "source_operator_audit": "research/idle-star-paired-axis-census/verify.py", + "source_operator_audit_base_main": "997e6a9ca7b4f95d50e366f61412fd640d72a88a" +} diff --git a/research/t740-joint-axis-optimization/RANK-ONLY-MOVES.json.gz b/research/t740-joint-axis-optimization/RANK-ONLY-MOVES.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..0ca36531532abe67cc7473784ff0e2fbab7cc9a5 GIT binary patch literal 1386491 zcmb5W1yEhh7Bz@pg1fsDG`JH2L4qa_+?@bHg1ZHGf)m_=+XaHV1b26LcbfzGzBjMx ze={{h?Yil+di9pI8_o^)G^8Q$5YJywPoa%-C5+|aMAs}^&VpF)qx5f8kPLLIP?zCm zzh(&1do{tMEl`*_dCy{DV4m=m3+ 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zA!qizL|yDAh2)6cKl5_e??0EAbplFZn$|K+fm4u=mdiPdSL+xu%kA=3>j;-yxsl#4 loqP5O@?RM9l*W2cmiA23iSdGYA$d_@*Zy#hb#?B#-vG*GQ2hV^ literal 0 HcmV?d00001 diff --git a/research/t740-joint-axis-optimization/vendor/pr3251/RESULT.json b/research/t740-joint-axis-optimization/vendor/pr3251/RESULT.json new file mode 100644 index 0000000000..e20225791d --- /dev/null +++ b/research/t740-joint-axis-optimization/vendor/pr3251/RESULT.json @@ -0,0 +1,65 @@ +{ + "status": "PASS_IDLE_DONOR_EXACT_R438_T740", + "T": 740, + "axis_moves": 435604, + "donor_children": 150529, + "receiver_children": 167112, + "idle_before": { + "1": 173160, + "3": 48951, + "5": 13875, + "48": 282569 + }, + "idle_after": { + "1": 149514, + "2": 15880, + "3": 14951, + "5": 13855, + "42": 32303, + "43": 1160, + "44": 8240, + "45": 32140, + "46": 6300, + "47": 20, + "48": 35294, + "49": 27626, + "50": 10480, + "51": 129006 + }, + "profile": { + "1": 16353294, + "2": 4837720, + "3": 1533431, + "4": 679320, + "5": 147055, + "8": 53280, + "42": 32303, + "43": 1160, + "44": 8240, + "45": 32140, + "46": 6300, + "47": 20, + "48": 35294, + "49": 27626, + "50": 10480, + "51": 129006 + }, + "complex_root": [ + "8674078851925492817421/5000000000000000000000000", + "17348157703850985634843/10000000000000000000000000" + ], + "complex_root_decimal": "17348157703850985634842e-25", + "bit": "69393850564807966059/40000000000000000000000", + "binding": "complex", + "kappa": "17348157703850985634839999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "kappa_decimal": "0.0017348157703850985634839999999999999999999998999999999999999999999999", + "gain_over_pr3200": "174973179420229/20000000000000000000000", + "gain_over_pr3198": "45213273585402989/1000000000000000000000000", + "gain_over_pr3184": "4626709151247803389/1000000000000000000000000", + "gain_over_pr3148": "2519137853250775799/500000000000000000000000", + "max_child_rank": 51, + "halving": [ + 5329, + 5202 + ] +} diff --git a/research/t740-joint-axis-optimization/verify.py b/research/t740-joint-axis-optimization/verify.py index 08951510c6..7cbad49ec1 100644 --- a/research/t740-joint-axis-optimization/verify.py +++ b/research/t740-joint-axis-optimization/verify.py @@ -171,6 +171,69 @@ def main(): witness['first_coordinate_character_mismatch']['matrix_differences'] == differences, 'frozen exact operator witness') + # The refreshed overlap scan found a newer, numerically higher per-group claim in PR #3251. + # Its verifier is the PR #3200 rank/profile audit, so bind its frozen output separately and + # test the same owner-zero port-zero group with the exact eight-stream operator. + source_rows = {row['path']: row for row in load(HERE / 'SOURCES.json')['files']} + pr3251_head = 'd7d6254416f0b3ffe659079cca42fd152df63a36' + pr3251_paths = { + 'BINS.json.gz': 'research/rank7-idle-donors-exact-r438/BINS.json.gz', + 'MOVES.json.gz': 'research/rank7-idle-donors-exact-r438/MOVES.json.gz', + 'RESULT.json': 'research/rank7-idle-donors-exact-r438/RESULT.json', + } + pr3251_files = {} + for name, source_path in pr3251_paths.items(): + row = source_rows.get(source_path) + require(row is not None and row['usage'] == 'provenance' and + row['pin'] == f'head:{pr3251_head}:{source_path}', + 'PR #3251 exact source pin: ' + name) + local_path = HERE / 'vendor' / 'pr3251' / name + raw = local_path.read_bytes() + require(hashlib.sha256(raw).hexdigest() == row['sha256'], + 'vendored PR #3251 artifact differs from its pinned source: ' + name) + pr3251_files[name] = load(local_path) + pr3251_bins = pr3251_files['BINS.json.gz'] + pr3251_moves = pr3251_files['MOVES.json.gz']['moves'] + pr3251_result = pr3251_files['RESULT.json'] + require(pr3251_result['status'] == 'PASS_IDLE_DONOR_EXACT_R438_T740' and + pr3251_result['axis_moves'] == len(pr3251_moves) == 435604, + 'PR #3251 frozen candidate receipt') + _, pr3251_kappa, _ = verifier.run(recipes, pr3251_bins, pr3251_moves, pr3251_result) + require(pr3251_kappa > hypothetical_kappa and + pr3251_kappa == F(pr3251_result['kappa']), + 'PR #3251 rank/profile headline is numerically above the rank-only candidate') + pr3251_group = next(g for g in pr3251_bins['groups'] if g[0] == 0 and g[1] == 0) + require(pr3251_group[2] == owner_group[2], 'PR #3251 owner-zero port-zero source pattern') + pr3251_group_moves = [m for m in pr3251_moves if m[0] == 0 and m[1] == 0] + require(len(pr3251_group_moves) == 6, 'PR #3251 owner-zero port-zero move count') + pr3251_trial = {c: list(axes) for c, axes in baseline.items()} + for rep, port, source, target, axis in pr3251_group_moves: + require(axis in pr3251_trial[source], 'PR #3251 transfer axis exists in exact source context') + pr3251_trial[source].remove(axis) + pr3251_trial[target].append(axis) + pr3251_changed = {c: [len(baseline[c]), len(pr3251_trial[c])] + for c in range(len(caps)) if len(baseline[c]) != len(pr3251_trial[c])} + require({str(c): value for c, value in pr3251_changed.items()} == expected_changed, + 'PR #3251 exact operator overlay rank vector') + for bit in range(52): + character_before = 1 << bit + require(operator.replay(context, baseline, character_before, blocks) == + operator.replay(context, pr3251_trial, character_before, blocks), + f'PR #3251 operator mismatch precedes frozen witness at bit {bit}') + pr3251_character = 1 << 52 + pr3251_before = operator.replay(context, baseline, pr3251_character, blocks) + pr3251_after = operator.replay(context, pr3251_trial, pr3251_character, blocks) + require(pr3251_before != pr3251_after, 'PR #3251 candidate must fail exact operator equality') + pr3251_differences = operator.matrix_differences(pr3251_before, pr3251_after) + require(pr3251_differences == expected_differences, + 'PR #3251 exact operator mismatch witness') + pr3251_witness = load(HERE / 'PR3251-OPERATOR-WITNESS.json') + require(pr3251_witness['source_head'] == pr3251_head and + pr3251_witness['headline_kappa'] == pr3251_result['kappa_decimal'] and + pr3251_witness['first_coordinate_character_mismatch']['character'] == pr3251_character and + pr3251_witness['first_coordinate_character_mismatch']['matrix_differences'] == pr3251_differences, + 'frozen PR #3251 exact operator witness') + # Controls: deleting one rank-only move changes the frozen profile, and a foreign axis # is rejected by the predecessor's independent physical-move audit. controls = {} @@ -192,6 +255,8 @@ def main(): require(len(controls) == 2, 'mutation controls') print('PASS_T740_RANK_ONLY_CANDIDATE_REJECTED moves=%d controls=%d hypothetical_kappa=%s cap_fraction=%s checked_before=53 exact_operator_character=2^53 matrix_entries=%d' % (len(moves), len(controls), hypothetical_kappa, hypothetical_fraction, len(differences))) + print('PASS_PR3251_NUMERIC_REPLAY_REJECTED_OPERATOR moves=%d kappa=%s source_head=%s checked_before=52 exact_operator_character=2^52 matrix_entries=%d' % + (len(pr3251_moves), pr3251_kappa, pr3251_head, len(pr3251_differences))) if __name__ == '__main__':

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b/research/t740-joint-axis-optimization/RANK-ONLY-RESULT.json @@ -0,0 +1,66 @@ +{ + "admissible_kappa_claim": null, + "baseline_kappa": "17348070217261275520339999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "baseline_scaled_objective": "1161037431722757896", + "best_bound": "1.1506691003073893e+18", + "candidate_variables": 139038, + "groups": 82880, + "improves_claim": true, + "kappa_gain": "64033068461157/1000000000000000000000000", + "moves": 430204, + "objective": "CP-SAT global weighted floor table; g(r)=r*((73/r)^p_star-1), p_star=PR3200 complex-root lower endpoint; Decimal precision=90", + "objective_scale": 100000000000000, + "optimized_complex_root": [ + "17348070857591960131911/10000000000000000000000000", + "2168508857198995016489/1250000000000000000000000" + ], + "optimized_kappa": "17348070857591960131909999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "optimized_scaled_objective": "1161036554853891176", + "orthogonality_conflicts": 68474, + "pattern_changes": 1457, + "patterns": 2328, + "physical_operator_status": "REJECTED_AT_OWNER0_PORT0_CHARACTER_2^53", + "profile": { + "1": 16353294, + "2": 4837720, + "3": 1533431, + "4": 679320, + "42": 32303, + "44": 5160, + "45": 36380, + "46": 6300, + "47": 20, + "48": 35294, + "49": 28786, + "5": 147055, + "50": 13560, + "51": 124766, + "8": 53280 + }, + "rank_only_score_is_not_a_supplier_claim": true, + "recorded_search": { + "best_bound": "1.1506691003073893e+18", + "seed": 0, + "solver_seconds": 119.327, + "threads": 8, + "time_limit_seconds": 120, + "wall_seconds": 195.996 + }, + "same_settings_replay": { + "best_bound": "1.1506753368109844e+18", + "improves_rank_only_kappa": false, + "profile_matches_pr3200_baseline": true, + "seed": 0, + "solver_seconds": 121.636, + "status": "FEASIBLE", + "threads": 8, + "time_limit_seconds": 120 + }, + "solver_seconds": 119.327, + "solver_version": "9.11.4210", + "source_head": "f09e5b25381393c604082e58fbe56896b13171b5", + "status": "FEASIBLE", + "threads": 8, + "wall_seconds": 195.996, + "weighted_objective_upper_bound": 2417924916360415370 +} diff --git a/research/t740-joint-axis-optimization/README.md b/research/t740-joint-axis-optimization/README.md new file mode 100644 index 0000000000..db489000c2 --- /dev/null +++ b/research/t740-joint-axis-optimization/README.md @@ -0,0 +1,100 @@ +# OR-Tools found a rank-only T740 gain; exact operator replay rejects it + +A global CP-SAT allocation improves the rank-moment surrogate and would give a hypothetical +κ about `0.001734807085759196013190…`, above PR #3200's conditional headline. That allocation +**does not preserve the exact eight-stream operator**, so its κ is inadmissible. This package +claims **no new κ**. + +## What the solver found + +The search starts from the byte-pinned PR #3200 T740 fill and runs CP-SAT over 2,328 distinct +`(port, child-usage)` patterns and 82,880 groups. It considers 139,038 one-axis transfer +candidates, requires unique source axes, forbids a child from both donating and receiving, enforces +pairwise orthogonality at receivers and caps ranks at 51. OR-Tools 9.11.4210 (Python 3.10, seed 0, +eight workers) found a `FEASIBLE`, not `OPTIMAL`, rank profile in 119.327 seconds. + +The hypothetical profile shifts 40 children from rank 45 to 44 and 40 from rank 50 to 51 while +preserving rank mass. The old PR #3200 verifier accepts its commuting/hosting rules and brackets +the corresponding numerical root. The source-bound exact operator replay does not. + +## Exact rejection witness + +For owner replica 0, port 0, the pinned initial pattern is +`[[4,31],[6,31],[8,0],[10,0],[12,0],[13,0],[14,31],[15,31]]`. The six rank-only transfers +change ranks of children 8, 10, 12, 14 and 15. This extends beyond the four-unhosted-child +assignment screen in [PR #3199](https://github.com/CrocSwap/integer-mult-bounds/pull/3199): +two of the proposed donors (14 and 15) are partially hosted. + +The exact replay first fails at coordinate character `2^53`. Three Gaussian-integer matrix entries +change: + +| Entry | Baseline | Rank-only overlay | +|---|---|---| +| `(1,1)` | `[0,1]` | `[1,0]` | +| `(3,1)` | `[0,0]` | `[1,-1]` | +| `(6,6)` | `[0,1]` | `[-1,0]` | + +The unmodified operator passes the source package's 147-mode positive control. `verify.py` rebuilds +the owner-zero context from authenticated PR3148 fill/journal inputs, confirms it matches the +pinned PR #3200 BINS, applies all six moves, and reproduces the exact mismatch. This is a concrete +false positive of the rank-only objective; it is not a theorem that every possible exchange fails. + +## Fixed-word ceiling and limits + +For PR #3200's local profile `{1:2433, 2:724, 3:228, 4:102, 5:20, 8:8}`, +`complex-local-word-ceiling/ceiling.py:ceiling(local, 73, 896, 9, 64)` gives +`a∈[0.001756446675046, 0.001756446675047]`, hence the scoped relaxation +`κ<0.0017533669794458152` under `κ=51: continue + for v in s['axes']: + if legal(v,p,c,d,t['axes']): cands.append((c,d,v)) + candset=set(cands); baseline=base_by_key[(p,kids)] + if not set(baseline).issubset(candset): + raise ValueError(f'baseline move absent from initial candidate universe: {p,kids}') + # Certify baseline feasibility in the same one-shot role/orthogonality domain. + out_axes=set(); recv_axes=defaultdict(list); sources=set(); receivers=set() + for c,d,v in baseline: + if (c,v) in out_axes or c in receivers or d in sources: raise ValueError('baseline role/source conflict') + out_axes.add((c,v)); sources.add(c); receivers.add(d); recv_axes[d].append(v) + if any(dot(a,b) for vv in recv_axes.values() for i,a in enumerate(vv) for b in vv[i+1:]): raise ValueError('baseline incoming axes conflict') + candidate_count+=len(cands) + initial_rank={c:s['rank'] for c,s in state.items()} + bo=Counter(c for c,d,v in baseline); bi=Counter(d for c,d,v in baseline) + base_score+=freq*sum(costs[initial_rank[c]-bo[c]+bi[c]] for c in state) + objective_upper+=freq*len(state)*max(costs) + xs=[]; by_axis=defaultdict(list); by_recv=defaultdict(list); outgoing=defaultdict(list); incoming=defaultdict(list) + for mi,(c,d,v) in enumerate(cands): + x=model.NewBoolVar(f'x{si}_{mi}'); xs.append(x); by_axis[c,v].append(x); by_recv[d].append((x,v)); outgoing[c].append(x); incoming[d].append(x) + for vv in by_axis.values(): + if len(vv)>1: model.Add(sum(vv)<=1) + for d,items in by_recv.items(): + for i in range(len(items)): + xi,vi=items[i] + for j in range(i+1,len(items)): + xj,vj=items[j] + if dot(vi,vj): model.Add(xi+xj<=1); conflicts+=1 + for c,_ in kids: + outs=outgoing[c]; ins=incoming[c] + if outs: + oa=model.NewBoolVar(f'out{si}_{c}'); model.Add(sum(outs)>=oa); model.Add(sum(outs)<=len(outs)*oa) + model.AddHint(oa,int(bool(bo[c]))) + else: oa=None + if ins: + ia=model.NewBoolVar(f'in{si}_{c}'); model.Add(sum(ins)>=ia); model.Add(sum(ins)<=len(ins)*ia) + model.AddHint(ia,int(bool(bi[c]))) + else: ia=None + if oa is not None and ia is not None: model.Add(oa+ia<=1) + fin=model.NewIntVar(0,51,f'rank{si}_{c}') + model.Add(fin==initial_rank[c]-(sum(outs) if outs else 0)+(sum(ins) if ins else 0)) + cv=model.NewIntVar(0,max(costs),f'cost{si}_{c}'); model.AddElement(fin,costs,cv) + final_hint=initial_rank[c]-bo[c]+bi[c] + model.AddHint(fin,final_hint); model.AddHint(cv,costs[final_hint]) + objective.append(freq*cv) + chosen=set(baseline) + for x,edge in zip(xs,cands): model.AddHint(x,int(edge in chosen)) + vars_by_key[(p,kids)]=(cands,xs) + states.append((p,kids,reps,initial_rank,baseline)) + if objective_upper >= 2**63: raise ValueError(f'int64 objective upper bound {objective_upper}') + model.Minimize(sum(objective)) + validation=model.Validate() + if validation: raise ValueError('invalid CP-SAT model: '+validation) + build_seconds=time.time()-t0 + print(json.dumps({'phase':'built','patterns':len(states),'groups':len(bins['groups']),'variables':candidate_count,'incompatibilities':conflicts,'objective_upper_bound':objective_upper,'scale':SCALE,'build_seconds':round(build_seconds,2)},sort_keys=True),flush=True) + solver=cp_model.CpSolver(); solver.parameters.max_time_in_seconds=args.seconds; solver.parameters.num_search_workers=args.workers; solver.parameters.random_seed=args.seed + solver.parameters.log_search_progress=True; solver.parameters.log_to_stdout=False + ts=time.time(); status=solver.Solve(model); solve_seconds=time.time()-ts + status_name=solver.StatusName(status) + if status not in (cp_model.OPTIMAL,cp_model.FEASIBLE): raise RuntimeError(status_name) + selected_by_key={k:[edge for edge,x in zip(cands,xs) if solver.Value(x)] for k,(cands,xs) in vars_by_key.items()} + candidate_stream=[] + for p,kids,reps,rank,baseline in states: + for rep in reps: + candidate_stream.extend([[rep,p,*edge] for edge in sorted(selected_by_key[(p,kids)])]) + new_final=verify.audit(rec,bins,candidate_stream) + new_prof=Counter({r:n*9*verify.T for r,n in verify.LOCAL.items()}); new_prof.update(new_final) + if sum(r*n for r,n in new_prof.items())!=65088*verify.T or max(new_prof)>51: raise ValueError('candidate mass/cap') + root_scale=10**25; lo_i=0; hi_i=10**23 + while hi_i-lo_i>1: + mid=(lo_i+hi_i)//2; mlo,mhi=verify.mom(new_prof,F(mid,root_scale)) + if mhi<1: lo_i=mid + elif mlo>1: hi_i=mid + else: raise ValueError('root interval did not separate') + lo,hi=F(lo_i,root_scale),F(hi_i,root_scale); kappa=min(F(lo.numerator*10**24//lo.denominator,10**24),verify.BIT)-F(1,10**46)-F(1,10**70) + base_kappa=F(result['kappa']) + changed=sum(selected_by_key[(p,kids)]!=base for p,kids,reps,rank,base in states) + objective_value=0 + for (p,kids),reps in groups_by_key.items(): + selected=selected_by_key[(p,kids)]; outs=Counter(c for c,d,v in selected); ins=Counter(d for c,d,v in selected) + initial={c:caps[p,c]-u for c,u in kids} + objective_value+=len(reps)*sum(costs[initial[c]-outs[c]+ins[c]] for c in initial) + out={'status':status_name,'solver_version':__import__('ortools').__version__,'source_head':'f09e5b25381393c604082e58fbe56896b13171b5','objective':'CP-SAT global weighted floor table; g(r)=r*((73/r)^p_star-1), p_star=PR3200 complex-root lower endpoint; Decimal precision=90','objective_scale':SCALE,'patterns':len(states),'groups':len(bins['groups']),'candidate_variables':candidate_count,'orthogonality_conflicts':conflicts,'weighted_objective_upper_bound':objective_upper,'baseline_scaled_objective':str(base_score),'optimized_scaled_objective':str(objective_value),'solver_seconds':round(solve_seconds,3),'wall_seconds':round(time.time()-t0,3),'threads':args.workers,'seed':args.seed,'time_limit_seconds':args.seconds,'profile':{str(k):v for k,v in sorted(new_prof.items())},'baseline_kappa':str(base_kappa),'optimized_complex_root':[str(lo),str(hi)],'optimized_kappa':str(kappa),'kappa_gain':str(kappa-base_kappa),'improves_claim':kappa>base_kappa,'admissible_kappa_claim':None,'physical_operator_status':'NOT_CHECKED_BY_RANK_ONLY_SEARCH','rank_only_score_is_not_a_supplier_claim':True,'pattern_changes':changed,'moves':len(candidate_stream),'best_bound':str(solver.BestObjectiveBound())} + args.output_dir.mkdir(parents=True,exist_ok=True) + payload=json.dumps({'columns':['replica','port','donor_child','receiver_child','axis'],'moves':candidate_stream},sort_keys=True,separators=(',',':')).encode() + compressed=bytearray(gzip.compress(payload,mtime=0)); compressed[9]=255 + (args.output_dir/'RANK-ONLY-MOVES.json.gz').write_bytes(compressed) + (args.output_dir/'RANK-ONLY-RESULT.json').write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + print(json.dumps(out,indent=2,sort_keys=True),flush=True) +if __name__=='__main__': main() diff --git a/research/t740-joint-axis-optimization/verify.py b/research/t740-joint-axis-optimization/verify.py new file mode 100644 index 0000000000..08951510c6 --- /dev/null +++ b/research/t740-joint-axis-optimization/verify.py @@ -0,0 +1,198 @@ +#!/usr/bin/env python3 +"""Show that the best rank-only T740 CP-SAT candidate fails exact operator replay.""" +import copy +import gzip +import hashlib +import importlib.util +import json +from collections import Counter +from fractions import Fraction as F +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +ARCHIVE = ROOT / 'research/source-archives/t740-joint-axis-pr3200' +PHASES = ROOT / 'research/adaptive-kernel-demotion/inputs/DATA-PHASES.json' +BITCERT = ROOT / 'research/r438-native-rehost/CERTIFICATE.json' +OPERATOR_PACKAGE = ROOT / 'research/idle-star-paired-axis-census' + + +def load(path): + raw = Path(path).read_bytes() + if raw[:2] == b'\x1f\x8b': + raw = gzip.decompress(raw) + return json.loads(raw) + + +def require(ok, reason): + if not ok: + raise ValueError(reason) + + +def load_module(name, path): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + require(spec is not None and spec.loader is not None, 'module spec: ' + name) + spec.loader.exec_module(module) + return module + + +def candidate_profile(verifier, recipes, bins, moves, expected): + final = verifier.audit(recipes, bins, moves) + profile = Counter({r: n * 9 * verifier.T for r, n in verifier.LOCAL.items()}) + profile.update(final) + profile = dict(sorted(profile.items())) + require({str(k): v for k, v in profile.items()} == expected['profile'], + 'rank-only candidate profile differs from its receipt') + require(sum(r * n for r, n in profile.items()) == 65088 * verifier.T, + 'rank-only candidate rank mass') + require(max(profile) <= 51 and 73 * 73 > 2 * max(profile) ** 2, + 'rank-only candidate cap/halving') + lo, hi = map(F, expected['optimized_complex_root']) + require(hi - lo == F(1, 10 ** 25), 'rank-only root grid') + require(verifier.mom(profile, lo)[1] < 1 and verifier.mom(profile, hi)[0] > 1, + 'rank-only candidate exact complex root') + bit = verifier.BIT + kappa = min(F(lo.numerator * 10 ** 24 // lo.denominator, 10 ** 24), bit) + kappa -= F(1, 10 ** 46) + F(1, 10 ** 70) + require(lo < bit, 'complex endpoint must bind below R438') + require(kappa == F(expected['optimized_kappa']), 'rank-only hypothetical kappa') + return profile, kappa, lo + + +def operator_context(operator): + operator.authenticate() + vendor = OPERATOR_PACKAGE / 'vendor' + base = operator.decode(operator.read_bytes(vendor / 'BASE-FILL.json.gz'))['rows'] + journal = operator.decode(operator.read_bytes(vendor / 'EXCHANGE.json')) + rows_by_port = operator.project_all_ports(base, operator.journal_edits(base, journal)) + order_base = operator.decode(operator.read_bytes( + ROOT / 'research/rank7-joint-endframes/allocation/ORDER.json')) + order = [[stage, replica + 74 * copy] for stage, replica in order_base for copy in range(10)] + dispatch_rows = operator.decode(operator.read_bytes( + ROOT / 'research/rank7-joint-endframes/allocation/DISPATCH.json')) + dispatch = {(stage, replica): tag for stage, replica, tag in dispatch_rows} + providers = operator.decode(operator.read_bytes(vendor / 'PROVIDERS.json')) + plan = operator.decode(operator.read_bytes( + ROOT / 'research/rank7-joint-endframes/allocation/vendor/PLAN.json.gz')) + template = operator.decode(operator.read_bytes( + ROOT / 'research/rank7-joint-endframes/allocation/vendor/TEMPLATE.json.gz')) + recipes = operator.decode(operator.read_bytes(PHASES))['recipes'] + context = operator.prepare_port(0, rows_by_port[0], order, dispatch, providers, + plan, template, recipes) + blocks = operator.stage_blocks(template) + return context, blocks, recipes + + +def main(): + if not __debug__: + raise SystemExit('assertions required') + require(hashlib.sha256(PHASES.read_bytes()).hexdigest() == + 'c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa', + 'DATA-PHASES pin') + verifier = load_module('pr3200_axis_verifier', ARCHIVE / 'verify.py') + verifier.PKG = ARCHIVE + verifier.PHASES = PHASES + verifier.BITCERT = BITCERT + verifier.BIT = verifier.check_bit() + recipes = {r['port']: r for r in json.loads(PHASES.read_bytes())['recipes']} + bins = load(ARCHIVE / 'BINS.json.gz') + baseline_moves = load(ARCHIVE / 'MOVES.json.gz')['moves'] + baseline_result = load(ARCHIVE / 'RESULT.json') + _, baseline_kappa, _ = verifier.run(recipes, bins, baseline_moves, baseline_result) + + payload = load(HERE / 'RANK-ONLY-MOVES.json.gz') + require(payload['columns'] == ['replica', 'port', 'donor_child', 'receiver_child', 'axis'], + 'rank-only move columns') + moves = payload['moves'] + expected = load(HERE / 'RANK-ONLY-RESULT.json') + require(expected['source_head'] == 'f09e5b25381393c604082e58fbe56896b13171b5', + 'PR #3200 source head') + require(expected['status'] == 'FEASIBLE' and expected['solver_version'] == '9.11.4210', + 'solver must be labelled feasible, not optimal') + require(expected['admissible_kappa_claim'] is None and + expected['rank_only_score_is_not_a_supplier_claim'] is True, + 'rank-only result must be labelled inadmissible') + require(len(moves) == expected['moves'], 'rank-only move count') + profile, hypothetical_kappa, _ = candidate_profile(verifier, recipes, bins, moves, expected) + require(hypothetical_kappa > baseline_kappa, 'the rank-only search should show its relaxed gain') + ceiling = load_module('fixed_word_ceiling', ROOT / 'research/complex-local-word-ceiling/ceiling.py') + cap_lo, cap_hi = ceiling.ceiling(verifier.LOCAL, 73, 896, 9, 64) + require((cap_lo, cap_hi) == (F(878223337523, 500000000000000), + F(1756446675047, 1000000000000000)), + 'fixed-word packing-ceiling receipt') + kappa_cap = cap_hi / (1 + cap_hi) + hypothetical_fraction = hypothetical_kappa / kappa_cap + require(hypothetical_fraction < 1, 'hypothetical candidate cannot exceed the relaxation ceiling') + require(F(expected['kappa_gain']) == hypothetical_kappa - baseline_kappa, + 'rank-only hypothetical gain') + + # Authenticate and use the merged source-bound exact eight-stream replay. + operator = load_module('source_bound_idle_axis_operator', OPERATOR_PACKAGE / 'verify.py') + context, blocks, port_recipes = operator_context(operator) + baseline = {c: list(axes) for c, axes in context['residual'].items()} + baseline_modes = operator.check_baseline(context, baseline, blocks) + require(baseline_modes == 147, 'exact-operator positive-control modes') + owner_group = next(g for g in bins['groups'] if g[0] == 0 and g[1] == 0) + require(owner_group[2] == [[4, 31], [6, 31], [8, 0], [10, 0], [12, 0], [13, 0], [14, 31], [15, 31]], + 'pinned owner-zero port-zero source pattern') + caps = {c: int(child['rank']) for c, child in enumerate(port_recipes[0]['idle_children'])} + usage = {c: u for c, u in owner_group[2]} + require(all(len(baseline[c]) == caps[c] - usage.get(c, caps[c]) for c in range(len(caps))), + 'exact operator context matches PR #3200 BINS') + group_moves = [m for m in moves if m[0] == 0 and m[1] == 0] + require(len(group_moves) == 6, 'owner-zero port-zero candidate move count') + trial = {c: list(axes) for c, axes in baseline.items()} + for rep, port, source, target, axis in group_moves: + require(axis in trial[source], 'candidate source axis available in exact context') + trial[source].remove(axis) + trial[target].append(axis) + changed = {c: [len(baseline[c]), len(trial[c])] for c in range(len(caps)) + if len(baseline[c]) != len(trial[c])} + expected_changed = {'8': [48, 51], '10': [48, 51], '12': [48, 44], '14': [1, 0], '15': [1, 0]} + require({str(c): value for c, value in changed.items()} == expected_changed, + 'exact operator overlay rank vector') + for bit in range(53): + character_before = 1 << bit + require(operator.replay(context, baseline, character_before, blocks) == + operator.replay(context, trial, character_before, blocks), + f'candidate operator mismatch precedes the frozen witness at bit {bit}') + character = 1 << 53 + before = operator.replay(context, baseline, character, blocks) + after = operator.replay(context, trial, character, blocks) + require(before != after, 'candidate must fail exact physical-operator equality') + differences = operator.matrix_differences(before, after) + expected_differences = [[1, 1, [0, 1], [1, 0]], + [3, 1, [0, 0], [1, -1]], + [6, 6, [0, 1], [-1, 0]]] + require(differences == expected_differences, 'exact operator mismatch witness') + witness = load(HERE / 'OPERATOR-WITNESS.json') + require(witness['first_coordinate_character_mismatch']['character'] == character and + witness['first_coordinate_character_mismatch']['matrix_differences'] == differences, + 'frozen exact operator witness') + + # Controls: deleting one rank-only move changes the frozen profile, and a foreign axis + # is rejected by the predecessor's independent physical-move audit. + controls = {} + for name, altered in (('drop_move', moves[1:]),): + try: + candidate_profile(verifier, recipes, bins, altered, expected) + except (ValueError, verifier.Reject) as exc: + controls[name] = str(exc) + else: + raise ValueError('mutation accepted: ' + name) + foreign = copy.deepcopy(moves) + foreign[0][4] = 1 << 80 + try: + candidate_profile(verifier, recipes, bins, foreign, expected) + except (ValueError, verifier.Reject) as exc: + controls['foreign_axis'] = str(exc) + else: + raise ValueError('mutation accepted: foreign_axis') + require(len(controls) == 2, 'mutation controls') + print('PASS_T740_RANK_ONLY_CANDIDATE_REJECTED moves=%d controls=%d hypothetical_kappa=%s cap_fraction=%s checked_before=53 exact_operator_character=2^53 matrix_entries=%d' % + (len(moves), len(controls), hypothetical_kappa, hypothetical_fraction, len(differences))) + + +if __name__ == '__main__': + main() From eb5f775dd509953e6f36aa2f1914966c3d72e1af Mon Sep 17 00:00:00 2001 From: Gonzalo-Mier Date: Sat, 17 Oct 2026 21:44:59 +0200 Subject: [PATCH 4/5] Record related T740 operator and repair work --- research/t740-joint-axis-optimization/README.md | 11 ++++++++--- research/t740-joint-axis-optimization/TASK.json | 4 ++-- 2 files changed, 10 insertions(+), 5 deletions(-) diff --git a/research/t740-joint-axis-optimization/README.md b/research/t740-joint-axis-optimization/README.md index db489000c2..1cb6a5cc97 100644 --- a/research/t740-joint-axis-optimization/README.md +++ b/research/t740-joint-axis-optimization/README.md @@ -51,9 +51,14 @@ valid realized fraction is therefore **not established**. The result is conditional on PR #3200's source stack. It neither validates the PR #3200 baseline nor discharges its supplier, controller, native-admission or outer-release obligations. The selected record remains unchanged. The cached overlap scan covered 275 open PRs and 2,050 -discussions (complete pagination at 2026-10-17 18:40 UTC); it identified PR #3199 as the nearest -operator-level screen. A later refresh could not reach GitHub, so these counts are a dated snapshot, -not a novelty certificate. +discussions (complete pagination at 2026-10-17 18:40 UTC). The nearest related work includes +[PR #3199](https://github.com/CrocSwap/integer-mult-bounds/pull/3199), whose exact-coordinate +CP-SAT screen covers rank changes among four idle children, [PR #3204](https://github.com/CrocSwap/integer-mult-bounds/pull/3204), +which states a broader four-site rigidity result, and [PR #3220](https://github.com/CrocSwap/integer-mult-bounds/pull/3220), +which prices additive phase-child repairs. This package contributes one concrete global rank-only +incumbent using partially hosted donors (children 14 and 15) and its exact operator counterexample; +it does not duplicate or replace those broader results. A later overlap refresh could not reach +GitHub, so these counts are a dated snapshot, not a novelty certificate. ## Reproduce diff --git a/research/t740-joint-axis-optimization/TASK.json b/research/t740-joint-axis-optimization/TASK.json index 62306e8cc8..1d2898d95c 100644 --- a/research/t740-joint-axis-optimization/TASK.json +++ b/research/t740-joint-axis-optimization/TASK.json @@ -53,12 +53,12 @@ }, "scope_status": "changed", "actual_scope": "A joint rank-only CP-SAT search over the pinned PR #3200 T740 idle-axis domain, followed by an exact eight-stream operator replay of its best frozen candidate.", - "scope_change_reason": "The donor explicitly assigned the goal of improving the best available kappa and asked to continue with OR-Tools. PR #3200 lists exact per-group optimization as an open question. A rank-only model found a numerically better hypothetical profile, but the cached live overlap scan exposed PR #3199’s exact operator gate; direct replay rejects this candidate. The contribution is therefore the bounded false-positive counterexample, not a new supplier or kappa.", + "scope_change_reason": "The donor explicitly assigned the goal of improving the best available kappa and asked to continue with OR-Tools. PR #3200 lists exact per-group optimization as an open question. A rank-only model found a numerically better hypothetical profile, but direct exact replay rejects this candidate. Cached related work includes PR #3199's four-idle-child exact-coordinate CP-SAT screen, PR #3204's broader four-site rigidity result, and PR #3220's additive repair-cost bound. This package contributes a concrete global rank-only false positive involving partially hosted donors, not a new supplier or kappa.", "bottleneck_link": "The rank-only histogram improves the conditional complex moment, but the exact physical operator changes at one T740 group. This establishes why the operator-equality gate must enter any optimization before a numerical profile can count as a kappa improvement.", "budget_minutes": 60, "stop_rule": "Stop when the exact operator replay rejects the best saved rank-only candidate; do not continue rank-only seed or runtime searches. Preserve the counterexample and make the next search include exact operator constraints.", "outcome": "negative-result", - "evidence": "RANK-ONLY-MOVES.json.gz and RANK-ONLY-RESULT.json retain the OR-Tools FEASIBLE candidate and hypothetical moment/root. verify.py first authenticates and checks the PR #3200 baseline and rank-only move rules, then uses the merged source-bound eight-stream replay to reproduce a matrix mismatch at character 2^53 for owner replica 0 / port 0. No new admissible kappa is claimed; the selected record is unchanged. A repeat with the same seed/time limit/workers returned only the baseline rank profile, so parallel incumbent discovery is nondeterministic.", + "evidence": "RANK-ONLY-MOVES.json.gz and RANK-ONLY-RESULT.json retain the OR-Tools FEASIBLE candidate and hypothetical moment/root. verify.py first authenticates and checks the PR #3200 baseline and rank-only move rules, then uses the merged source-bound eight-stream replay to reproduce a matrix mismatch at character 2^53 for owner replica 0 / port 0. The cached overlap snapshot was complete as of 2026-10-17 18:40 UTC and exposed related PRs #3199, #3204 and #3220; a fresh network query failed, so the snapshot is dated. No new admissible kappa is claimed; the selected record is unchanged. A repeat with the same seed/time limit/workers returned only the baseline rank profile, so parallel incumbent discovery is nondeterministic.", "author": "Codex (OpenAI), under the user’s explicit research direction", "ai_assistance": "Substantial OpenAI Codex assistance, including the OR-Tools rank-only model, exact source-bound replay integration and package preparation.", "open_questions": [ From 91faeaa09667bf20fd2ba6307a173400e8ad876a Mon Sep 17 00:00:00 2001 From: Gonzalo-Mier Date: Sat, 17 Oct 2026 21:53:25 +0200 Subject: [PATCH 5/5] Replay the newer PR 3251 candidate against the exact operator --- .../PR3251-OPERATOR-WITNESS.json | 206 ++++++++++++++++++ .../t740-joint-axis-optimization/README.md | 55 +++-- .../t740-joint-axis-optimization/SOURCES.json | 21 ++ .../t740-joint-axis-optimization/TASK.json | 10 +- .../t740-joint-axis-optimization/VERIFY.json | 2 +- .../vendor/pr3251/BINS.json.gz | Bin 0 -> 239829 bytes .../vendor/pr3251/MOVES.json.gz | Bin 0 -> 1334063 bytes .../vendor/pr3251/RESULT.json | 65 ++++++ .../t740-joint-axis-optimization/verify.py | 65 ++++++ 9 files changed, 402 insertions(+), 22 deletions(-) create mode 100644 research/t740-joint-axis-optimization/PR3251-OPERATOR-WITNESS.json create mode 100644 research/t740-joint-axis-optimization/vendor/pr3251/BINS.json.gz create mode 100644 research/t740-joint-axis-optimization/vendor/pr3251/MOVES.json.gz create mode 100644 research/t740-joint-axis-optimization/vendor/pr3251/RESULT.json diff --git a/research/t740-joint-axis-optimization/PR3251-OPERATOR-WITNESS.json b/research/t740-joint-axis-optimization/PR3251-OPERATOR-WITNESS.json new file mode 100644 index 0000000000..ecb90390fb --- /dev/null +++ b/research/t740-joint-axis-optimization/PR3251-OPERATOR-WITNESS.json @@ -0,0 +1,206 @@ +{ + "schema_version": 1, + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/3251", + "source_head": "d7d6254416f0b3ffe659079cca42fd152df63a36", + "headline_kappa": "0.0017348157703850985634839999999999999999999998999999999999999999999999", + "status": "candidate-specific exact operator rejection; not a complete supplier audit", + "scope": "The pinned PR #3251 profile and moves pass the inherited PR #3200 rank/profile verifier. At owner replica 0, port 0, the six frozen moves change the exact eight-stream operator.", + "owner_replica": 0, + "port": 0, + "initial_children": [ + [ + 4, + 31 + ], + [ + 6, + 31 + ], + [ + 8, + 0 + ], + [ + 10, + 0 + ], + [ + 12, + 0 + ], + [ + 13, + 0 + ], + [ + 14, + 31 + ], + [ + 15, + 31 + ] + ], + "moves": [ + [ + 0, + 0, + 14, + 8, + 4722366482869645213696 + ], + [ + 0, + 0, + 15, + 10, + 4722366482869645213696 + ], + [ + 0, + 0, + 12, + 8, + 4503599627370496 + ], + [ + 0, + 0, + 12, + 8, + 9007199254740992 + ], + [ + 0, + 0, + 12, + 10, + 18014398509481984 + ], + [ + 0, + 0, + 12, + 10, + 36028797018963968 + ] + ], + "rank_changes": { + "8": [ + 48, + 51 + ], + "10": [ + 48, + 51 + ], + "12": [ + 48, + 44 + ], + "14": [ + 1, + 0 + ], + "15": [ + 1, + 0 + ] + }, + "first_coordinate_character_mismatch": { + "checked_equal_characters": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256, + 512, + 1024, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216, + 33554432, + 67108864, + 134217728, + 268435456, + 536870912, + 1073741824, + 2147483648, + 4294967296, + 8589934592, + 17179869184, + 34359738368, + 68719476736, + 137438953472, + 274877906944, + 549755813888, + 1099511627776, + 2199023255552, + 4398046511104, + 8796093022208, + 17592186044416, + 35184372088832, + 70368744177664, + 140737488355328, + 281474976710656, + 562949953421312, + 1125899906842624, + 2251799813685248 + ], + "character": 4503599627370496, + "matrix_differences": [ + [ + 1, + 1, + [ + 0, + 1 + ], + [ + 1, + 0 + ] + ], + [ + 3, + 1, + [ + 0, + 0 + ], + [ + 1, + -1 + ] + ], + [ + 6, + 6, + [ + 0, + 1 + ], + [ + -1, + 0 + ] + ] + ] + }, + "interpretation": "This one exact group mismatch rejects this frozen candidate as an operator-preserving T740 allocation. It does not show that every possible phase repair or changed supplier fails." +} diff --git a/research/t740-joint-axis-optimization/README.md b/research/t740-joint-axis-optimization/README.md index 1cb6a5cc97..d2a7e522f4 100644 --- a/research/t740-joint-axis-optimization/README.md +++ b/research/t740-joint-axis-optimization/README.md @@ -1,9 +1,11 @@ -# OR-Tools found a rank-only T740 gain; exact operator replay rejects it +# Exact replay rejects two T740 axis-search candidates, including the newer headline A global CP-SAT allocation improves the rank-moment surrogate and would give a hypothetical -κ about `0.001734807085759196013190…`, above PR #3200's conditional headline. That allocation -**does not preserve the exact eight-stream operator**, so its κ is inadmissible. This package -claims **no new κ**. +κ about `0.001734807085759196013190…`, above PR #3200's conditional headline. A fresh overlap +refresh found the newer open per-group headline in PR #3251, `0.001734815770385098563484`. +That number is about `8.6846259e-9` above our rank-only hypothetical, but its pinned allocation +also fails the exact eight-stream operator replay. Neither candidate gives an admissible new κ; +this package claims **no new κ**. ## What the solver found @@ -39,6 +41,25 @@ the owner-zero context from authenticated PR3148 fill/journal inputs, confirms i pinned PR #3200 BINS, applies all six moves, and reproduces the exact mismatch. This is a concrete false positive of the rank-only objective; it is not a theorem that every possible exchange fails. +## Exact replay of the newer PR #3251 headline + +The 2026-10-17 19:46 UTC overlap refresh found PR #3251 as the largest open T740 κ headline in its +complete 309-PR snapshot. Its frozen `BINS`, `MOVES` and `RESULT` artifacts are pinned to head +`d7d6254416f0b3ffe659079cca42fd152df63a36`. The inherited PR #3200 verifier accepts its profile, +rank mass, root interval and conditional κ. The exact operator replay rejects the frozen moves in +owner replica 0 / port 0. + +That group makes six transfers: child 14 to 8 and child 15 to 10 on axis `2^72`; child 12 to 8 on +axes `2^52` and `2^53`; and child 12 to 10 on axes `2^54` and `2^55`. Children 8 and 10 go from +rank 48 to 51, child 12 from 48 to 44, and children 14 and 15 from 1 to 0. The baseline and +candidate operators agree at characters `2^0` through `2^51`, then differ at `2^52` in the same +three matrix entries shown above. The witness is frozen in `PR3251-OPERATOR-WITNESS.json` and +replayed by `verify.py`. + +This is a candidate-specific operator counterexample, not a full audit of PR #3251's supplier or +all inherited obligations. It shows the pinned allocation is not operator-preserving under the +source-bound eight-stream replay; it does not show that every possible extension or repair fails. + ## Fixed-word ceiling and limits For PR #3200's local profile `{1:2433, 2:724, 3:228, 4:102, 5:20, 8:8}`, @@ -51,19 +72,21 @@ valid realized fraction is therefore **not established**. The result is conditional on PR #3200's source stack. It neither validates the PR #3200 baseline nor discharges its supplier, controller, native-admission or outer-release obligations. The selected record remains unchanged. The cached overlap scan covered 275 open PRs and 2,050 -discussions (complete pagination at 2026-10-17 18:40 UTC). The nearest related work includes +discussions (complete pagination at 2026-10-17 18:40 UTC). A fresh scan at 19:46 UTC covered 309 +open PRs and 2,095 discussions with no warnings; it found PR #3251 as the largest open T740 κ +headline and prompted the additional exact replay above. Related work includes [PR #3199](https://github.com/CrocSwap/integer-mult-bounds/pull/3199), whose exact-coordinate CP-SAT screen covers rank changes among four idle children, [PR #3204](https://github.com/CrocSwap/integer-mult-bounds/pull/3204), which states a broader four-site rigidity result, and [PR #3220](https://github.com/CrocSwap/integer-mult-bounds/pull/3220), -which prices additive phase-child repairs. This package contributes one concrete global rank-only -incumbent using partially hosted donors (children 14 and 15) and its exact operator counterexample; -it does not duplicate or replace those broader results. A later overlap refresh could not reach -GitHub, so these counts are a dated snapshot, not a novelty certificate. +which prices additive phase-child repairs. This package contributes exact replays of its frozen +global rank-only incumbent and the source-pinned PR #3251 per-group candidate. These are +candidate-specific rejections, not replacements for those broader results. Counts are dated +snapshots, not novelty certificates. ## Reproduce -The frozen rank-only result and exact rejection use standard-library replay; no OR-Tools dependency -is needed for verification: +The frozen OR-Tools result and both exact rejections use standard-library replay; no OR-Tools +dependency is needed for verification: ```sh python3.12 -B research/t740-joint-axis-optimization/verify.py @@ -87,8 +110,8 @@ only the independent exact replay determines whether a move list preserves the o - **Can operator-preserving exchanges involving partially hosted donors create a net rank gain?** First derive exact per-character constraints for the whole eight-child T740 port pattern and screen a small source-bound domain before another moment optimization. Blocker: the current - CP-SAT model checks only rank/commutation/orthogonality, while the physical identity couples - all streams. + CP-SAT model checks rank/commutation/orthogonality, while the physical identity couples all + streams; exact replay rejects the two saved candidates. - **Can a global rank-only search be made cheaper once exact operator constraints are added?** First incorporate the operator-derived phase tables on the four fully idle children and one partially hosted donor in a single representative group. Blocker: the current joint model is @@ -100,6 +123,6 @@ The T740 baseline BINS, moves and exact verifier are preserved byte-for-byte fro blobs and hashes are recorded in the source archive. The physical operator replay comes from the merged `idle-star-paired-axis-census` package, with its source lineage and notices retained there. PR #3199's broader four-child screen is acknowledged as the nearest overlap; this package adds a -concrete rank-only candidate that also uses partially hosted donors and an exact operator -counterexample for that candidate. New work is Apache-2.0 and uses substantial OpenAI Codex -assistance under the user's research direction. +concrete global rank-only candidate using partially hosted donors and a source-pinned exact +counterexample for PR #3251's higher per-group headline. New work is Apache-2.0 and uses substantial +OpenAI Codex assistance under the user's research direction. diff --git a/research/t740-joint-axis-optimization/SOURCES.json b/research/t740-joint-axis-optimization/SOURCES.json index 17df6780e5..b759ccb3c2 100644 --- a/research/t740-joint-axis-optimization/SOURCES.json +++ b/research/t740-joint-axis-optimization/SOURCES.json @@ -127,6 +127,27 @@ "usage": "input", "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c", "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc" + }, + { + "path": "research/rank7-idle-donors-exact-r438/BINS.json.gz", + "usage": "provenance", + "git_blob": "fc2446437c8ba8b5f10aa4cefd5290927c64dc26", + "sha256": "fee514002092bdbe0874d8c1f6b355340fca621a39c2aa77281a6a4fca266606", + "pin": "head:d7d6254416f0b3ffe659079cca42fd152df63a36:research/rank7-idle-donors-exact-r438/BINS.json.gz" + }, + { + "path": "research/rank7-idle-donors-exact-r438/MOVES.json.gz", + "usage": "provenance", + "git_blob": "d2b8831feb9dd56b5a92aee70401b97f779b1764", + "sha256": "ec9c11b924e4ab9de4f66cb42cc914fb7eb8c80c0f16f7a34d1dcf51f73ad52e", + "pin": "head:d7d6254416f0b3ffe659079cca42fd152df63a36:research/rank7-idle-donors-exact-r438/MOVES.json.gz" + }, + { + "path": "research/rank7-idle-donors-exact-r438/RESULT.json", + "usage": "provenance", + "git_blob": "e20225791d140383404496879103e1a849722d95", + "sha256": "151aa6b7e5d6c13f07028c14cf17568ccb62b496ba21467725b5588a4b323578", + "pin": "head:d7d6254416f0b3ffe659079cca42fd152df63a36:research/rank7-idle-donors-exact-r438/RESULT.json" } ] } diff --git a/research/t740-joint-axis-optimization/TASK.json b/research/t740-joint-axis-optimization/TASK.json index 1d2898d95c..cdd691234f 100644 --- a/research/t740-joint-axis-optimization/TASK.json +++ b/research/t740-joint-axis-optimization/TASK.json @@ -52,13 +52,13 @@ ] }, "scope_status": "changed", - "actual_scope": "A joint rank-only CP-SAT search over the pinned PR #3200 T740 idle-axis domain, followed by an exact eight-stream operator replay of its best frozen candidate.", - "scope_change_reason": "The donor explicitly assigned the goal of improving the best available kappa and asked to continue with OR-Tools. PR #3200 lists exact per-group optimization as an open question. A rank-only model found a numerically better hypothetical profile, but direct exact replay rejects this candidate. Cached related work includes PR #3199's four-idle-child exact-coordinate CP-SAT screen, PR #3204's broader four-site rigidity result, and PR #3220's additive repair-cost bound. This package contributes a concrete global rank-only false positive involving partially hosted donors, not a new supplier or kappa.", - "bottleneck_link": "The rank-only histogram improves the conditional complex moment, but the exact physical operator changes at one T740 group. This establishes why the operator-equality gate must enter any optimization before a numerical profile can count as a kappa improvement.", + "actual_scope": "A joint rank-only CP-SAT search over the pinned PR #3200 T740 idle-axis domain, followed by source-bound exact eight-stream operator replays of its best frozen candidate and the newer PR #3251 per-group candidate.", + "scope_change_reason": "The donor explicitly assigned the goal of improving the best available kappa and asked to continue with OR-Tools. A rank-only model found a better hypothetical profile than PR #3200, but exact replay rejects it. A fresh overlap refresh then found PR #3251's still-higher per-group headline; its pinned candidate also fails exact replay in owner replica 0 / port 0. Cached related work includes PR #3199's four-idle-child exact-coordinate CP-SAT screen, PR #3204's broader four-site rigidity result, and PR #3220's additive repair-cost bound. This package contributes two candidate-specific physical counterexamples, not a new supplier or kappa.", + "bottleneck_link": "Both saved numerical profiles pass rank, commute and moment checks, but their exact physical operators change in a T740 group. Operator equality must enter the optimization or act as an exact post-search filter before a numerical profile can count as a kappa improvement.", "budget_minutes": 60, - "stop_rule": "Stop when the exact operator replay rejects the best saved rank-only candidate; do not continue rank-only seed or runtime searches. Preserve the counterexample and make the next search include exact operator constraints.", + "stop_rule": "Stop after replaying the saved global rank-only candidate and the current higher PR #3251 per-group candidate against the exact operator. Do not continue rank-only seed or runtime searches; require exact operator constraints or a certified exact filter before further moment optimization.", "outcome": "negative-result", - "evidence": "RANK-ONLY-MOVES.json.gz and RANK-ONLY-RESULT.json retain the OR-Tools FEASIBLE candidate and hypothetical moment/root. verify.py first authenticates and checks the PR #3200 baseline and rank-only move rules, then uses the merged source-bound eight-stream replay to reproduce a matrix mismatch at character 2^53 for owner replica 0 / port 0. The cached overlap snapshot was complete as of 2026-10-17 18:40 UTC and exposed related PRs #3199, #3204 and #3220; a fresh network query failed, so the snapshot is dated. No new admissible kappa is claimed; the selected record is unchanged. A repeat with the same seed/time limit/workers returned only the baseline rank profile, so parallel incumbent discovery is nondeterministic.", + "evidence": "RANK-ONLY-MOVES.json.gz and RANK-ONLY-RESULT.json retain the OR-Tools FEASIBLE candidate and hypothetical moment/root. The package also pins the PR #3251 BINS/MOVES/RESULT artifacts to exact head d7d6254416f0b3ffe659079cca42fd152df63a36. The inherited PR #3200 verifier accepts that conditional profile, while the merged source-bound eight-stream replay reproduces matrix mismatches at 2^53 for the OR-Tools candidate and 2^52 for the higher PR #3251 candidate, both at owner replica 0 / port 0. A fresh overlap snapshot at 2026-10-17 19:46 UTC covered 309 open PRs and 2,095 discussions without warnings. No new admissible kappa is claimed; the selected record is unchanged. A repeat of the parallel CP-SAT run returned only the baseline rank profile, so incumbent discovery is nondeterministic.", "author": "Codex (OpenAI), under the user’s explicit research direction", "ai_assistance": "Substantial OpenAI Codex assistance, including the OR-Tools rank-only model, exact source-bound replay integration and package preparation.", "open_questions": [ diff --git a/research/t740-joint-axis-optimization/VERIFY.json b/research/t740-joint-axis-optimization/VERIFY.json index a84fb853d3..d2287e5f92 100644 --- a/research/t740-joint-axis-optimization/VERIFY.json +++ b/research/t740-joint-axis-optimization/VERIFY.json @@ -33,7 +33,7 @@ "{package}/verify.py" ], "timeout_seconds": 240, - "checks": "Authenticate PR #3200 and the merged operator-audit sources; verify the hypothetical rank-only profile/root; positive-control the exact baseline; replay all six owner-zero port-zero transfers; check equality at coordinate characters 2^0 through 2^52 and reproduce the exact Gaussian-integer matrix mismatch at 2^53; reject profile and foreign-axis controls. No OR-Tools is needed for this verification." + "checks": "Authenticate PR #3200 and PR #3251 artifacts plus the merged operator-audit sources; verify the rank-only and PR #3251 numerical profiles; positive-control the exact baseline; replay all six owner-zero port-zero moves for each candidate; reproduce the rank-only mismatch at 2^53 and the higher PR #3251 candidate mismatch at 2^52; reject profile and foreign-axis controls. No OR-Tools is needed for verification." } ] } diff --git a/research/t740-joint-axis-optimization/vendor/pr3251/BINS.json.gz b/research/t740-joint-axis-optimization/vendor/pr3251/BINS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..fc2446437c8ba8b5f10aa4cefd5290927c64dc26 GIT binary patch literal 239829 zcmd431z1$w->8jJgLFtYQc6ln3J6Gts0auWQqm&Q2n-=1Qi60yS%83~zznT4DBUeJ zbPwO2q4aq;|MR}*JLi0#*S_u*dj@b_d#$ziTK8|$1%pr!|1KVW{MO=NBI=Z}!*yf2 z`ohA9>#L*;i}uW`^IUw-lrk+te@}^$~}Ib-3xZ zzgU$at`FbLJ%rmHZXE7c9nRYxE-riRwH>a|9d1e@>IQy{z$Zoy*ADl9+#$T!>!9jz zrs`me?l9nR*WhrX>TuBjK4k#>6t9Dss>2?yiZ_P`E34ZYM%-oxKYol%EJ|*yZm&r8 z0GYi-$(cpTs;e*Vl5bxDZz`6?%PQ2IM(qw3PVL;tncy4nud zx;9cytFik+jjFVLO-!OLiZ)WTtSU~OCJ4M5^bu2yTX@%WiXWgI^*UL@5w>`z4b7Pwd`$y4Ya!00kt^OKKN9)E4?o3;oRGxQF)e9vX5trF_9SZl|L}rz| zV(pA5*^0dHQK>&PSkC2+t}^_=NnMH_sry=1kKqvatO+?qOCPfqFHF8k1pYh7rUcrR zQ`E(THEdxrJW=dRq`cGWN%J8p|7fnWhC}9dcOAY}RgzThlpHr=`Cuf&*1MyENu#R& 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