From ec8ae9f06b91d4c23c9e2f94b5ead1cb8914f0c9 Mon Sep 17 00:00:00 2001 From: rohanarun Date: Wed, 14 Oct 2026 12:25:55 -0400 Subject: [PATCH 1/3] Draft strict positive-slack refinement of PR1928 with independent endpoint binding --- research/fine-prime-slack10030/CLAIM.json | 8 + .../DEPENDENCY-MANIFEST.json | 383 + .../fine-prime-slack10030/DEPENDENCY.json | 8 + research/fine-prime-slack10030/MANIFEST.json | 33 + research/fine-prime-slack10030/NOTICE | 14 + .../fine-prime-slack10030/PARAMETERS.json | 8 + research/fine-prime-slack10030/PROOF.md | 11 + research/fine-prime-slack10030/README.md | 17 + .../fine-prime-slack10030/SOURCE-FETCH.json | 26 + research/fine-prime-slack10030/TASK.md | 1 + .../fine-prime-slack10030/certify_endpoint.py | 19 + .../fine-prime-slack10030/check_ledger.py | 196 + .../independent_check.py | 56 + research/fine-prime-slack10030/inputs/B.json | 15 + .../inputs/CLAIM1800.json | 17 + .../inputs/LEADER1839.json | 9 + .../inputs/LEADER1875.json | 7 + .../inputs/LEADER1928.json | 4 + .../inputs/OUTER-CLAIM1800.json | 9 + .../inputs/SOURCE-SPEC.json | 7300 +++++++++++++++++ .../fine-prime-slack10030/inputs/SPEC.json | 7300 +++++++++++++++++ .../fine-prime-slack10030/moment_interval.py | 19 + .../reference/check_ledger.py | 217 + .../reference/fine_mercator.py | 49 + .../reference/fine_moment.py | 36 + .../reference/independent_check.py | 51 + .../reference1982/INPUTS.json | 110 + .../reference1982/README.md | 78 + .../reference1982/SOURCES.json | 30 + .../reference1982/verify.py | 320 + .../fine-prime-slack10030/replay_outer.py | 27 + research/fine-prime-slack10030/verify.py | 68 + 32 files changed, 16446 insertions(+) create mode 100644 research/fine-prime-slack10030/CLAIM.json create mode 100644 research/fine-prime-slack10030/DEPENDENCY-MANIFEST.json create mode 100644 research/fine-prime-slack10030/DEPENDENCY.json create mode 100644 research/fine-prime-slack10030/MANIFEST.json create mode 100644 research/fine-prime-slack10030/NOTICE create mode 100644 research/fine-prime-slack10030/PARAMETERS.json create mode 100644 research/fine-prime-slack10030/PROOF.md create mode 100644 research/fine-prime-slack10030/README.md create mode 100644 research/fine-prime-slack10030/SOURCE-FETCH.json create mode 100644 research/fine-prime-slack10030/TASK.md create mode 100644 research/fine-prime-slack10030/certify_endpoint.py create mode 100644 research/fine-prime-slack10030/check_ledger.py create mode 100644 research/fine-prime-slack10030/independent_check.py create mode 100644 research/fine-prime-slack10030/inputs/B.json create mode 100644 research/fine-prime-slack10030/inputs/CLAIM1800.json create mode 100644 research/fine-prime-slack10030/inputs/LEADER1839.json create mode 100644 research/fine-prime-slack10030/inputs/LEADER1875.json create mode 100644 research/fine-prime-slack10030/inputs/LEADER1928.json create mode 100644 research/fine-prime-slack10030/inputs/OUTER-CLAIM1800.json create mode 100644 research/fine-prime-slack10030/inputs/SOURCE-SPEC.json create mode 100644 research/fine-prime-slack10030/inputs/SPEC.json create mode 100644 research/fine-prime-slack10030/moment_interval.py create mode 100644 research/fine-prime-slack10030/reference/check_ledger.py create mode 100644 research/fine-prime-slack10030/reference/fine_mercator.py create mode 100644 research/fine-prime-slack10030/reference/fine_moment.py create mode 100644 research/fine-prime-slack10030/reference/independent_check.py create mode 100644 research/fine-prime-slack10030/reference1982/INPUTS.json create mode 100644 research/fine-prime-slack10030/reference1982/README.md create mode 100644 research/fine-prime-slack10030/reference1982/SOURCES.json create mode 100644 research/fine-prime-slack10030/reference1982/verify.py create mode 100644 research/fine-prime-slack10030/replay_outer.py create mode 100644 research/fine-prime-slack10030/verify.py diff --git a/research/fine-prime-slack10030/CLAIM.json b/research/fine-prime-slack10030/CLAIM.json new file mode 100644 index 0000000000..9dc107bbc8 --- /dev/null +++ b/research/fine-prime-slack10030/CLAIM.json @@ -0,0 +1,8 @@ +{ + "status": "PASS_ARITHMETIC_FULL_REPLAY_PENDING", + "kappa": 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"vendor/pr1673/capped-phase-fusion/target002_upstream/pr1661/research/gmx-t74-p566-ep400/NOTICE": "3918a42010a435782de0fe8c38fab8f7df5d48a375ecf603c2bad1b818a16d6f", + "vendor/pr1673/capped-phase-fusion/TASK.json": "47b82ef23e20991010fae838ad4da9bdac3f947a8fea916a028fd6260f95f5f8", + "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md": "4d3b8466598a864a234b978e25976648d4e761840aad9153dd18d73d3dfe4d15", + "vendor/pr1673/capped-phase-fusion/VERIFIER-NEGATIVE-CONTROLS.json": "eeb887cdc0c76426c75ddbfc3d4af7ccbbe19d17962c6ad7a1549dafe8dabb5a", + "vendor/pr1673/capped-phase-fusion/VERIFY.json": "cb50aa523a0863a457181ca815e69a1b3b4d91ed1006a79263f4a8f18457c669", + "vendor/pr1673/capped-phase-fusion/verify.py": "93ef0f46e132485da6194587199b8f039e25b1b9f099f93bbdaeac5c0d66de7f", + "vendor/pr1786/FINE-PRIME-PADDING.md": "47d1b1b4df28aadda3cd6bdeb1fbc47290595e9208cd09c1a1f338520d33fdce", + "vendor/pr1786/NOTICE.md": "dcc1adb2461aa93ca62b6a912dbd8b215599e6af8053dfbacb7423b544dd659a", + "verify.py": "b8c6883e2403c60bb64a5bbdcb227d9fbba29e6742d7c1546e4a7b4729bb9c6b", + "verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b", + "verify_release.py": "f2c29886c93f21ef2448eadd4387f1a7c17159b237c5b13f227c5ae5a2f3e08e" +} diff --git a/research/fine-prime-slack10030/DEPENDENCY.json b/research/fine-prime-slack10030/DEPENDENCY.json new file mode 100644 index 0000000000..c98bf9b828 --- /dev/null +++ b/research/fine-prime-slack10030/DEPENDENCY.json @@ -0,0 +1,8 @@ +{ + "pr": 1800, + "head": "46d865ab92e58098538b8c5348b6a131c99abf45", + "repository": "jeremykothe2/integer-mult-bounds", + "package": "research/capped-fusion-t74-k554", + "manifest_sha256": "b8dba5524f8603e1848c73a8dd675404a0d3d9eed3b0285e9f0cfccde38fd15f", + "scope": "Unchanged supplier and analytic construction; refine positive free slack parameters only." +} diff --git a/research/fine-prime-slack10030/MANIFEST.json b/research/fine-prime-slack10030/MANIFEST.json new file mode 100644 index 0000000000..f8bdba92a1 --- /dev/null +++ b/research/fine-prime-slack10030/MANIFEST.json @@ -0,0 +1,33 @@ +{ + "CLAIM.json": "26be93d654314d45648184b8e1f5a0b139ea91bc5cc8eaae86f637f5ebe74e87", + "DEPENDENCY-MANIFEST.json": "b8dba5524f8603e1848c73a8dd675404a0d3d9eed3b0285e9f0cfccde38fd15f", + "DEPENDENCY.json": "57b6fe18ea819cca8860e65b1f9d7de83438dd3f1a309661ea5aad6932ef8213", + "NOTICE": "85873634c64b16b1799c78147f91397d73bcccd5788359a21eb1e13a7b5f235c", + "PARAMETERS.json": "562c18285feebe4c64ae163d1ab090fef55eb1ae4cb3cb4e2daee023f6fb51a4", + "PROOF.md": "49cc2fa36015e7a21d8b2334f7d444e7ae57d54acbaba7f76c10bd1235863b16", + "README.md": "1020602b20608dade528287e1dbad01238125d9afb740f5bf0a5064377a34eb4", + "SOURCE-FETCH.json": "91fd5398dadfab18778516ad53774beef78e31dc9bd9cf0fb044a01118d1b29f", + "TASK.md": "0af3d0fd294c06818f2877132764f629dd63d79c4b960b7cfd3964784f9ecdbc", + "certify_endpoint.py": "1094730778c8b25256c635b9aabb850d92258550a5a6af263b8115673fba2724", + "check_ledger.py": "c081b7df35ce5f8797190adce63e906d7d35b5303c297e3e66a0c82258593906", + "independent_check.py": "9434771a3f73ebb7a58e7bf162aba2eef05e380ebd6a40a2f67273a32df4c9ee", + "inputs/B.json": "3786841ba498af359e3e5920eb2ccdb39a1005021e99f3e29a9ffae66fbbfa6d", + "inputs/CLAIM1800.json": "1dd5490597ead36a31634f6008b1cd5ce0b51c4acd48a541b13306212e3f52f1", + "inputs/LEADER1839.json": "1cc459f3c79046a2dc025f7e004958d178b886a3b541d64d886e4628f77fc252", + "inputs/LEADER1875.json": "c85b80237dfad16c46d590363060341ff358e83de008cd1df44d7198a166e9c0", + "inputs/LEADER1928.json": "7ae7276da85eafbeb29591ff8d8196f24f90182867349a045886cf38fd6b703d", + "inputs/OUTER-CLAIM1800.json": "c10ff0673ee9152d2efee792fb3532ca25a5edee0bf52c5b700bf86735752779", + "inputs/SOURCE-SPEC.json": "41d7bd51c18eb354c6a785780ddefd35b3a8e2513daa2c4f585b236b7173e943", + "inputs/SPEC.json": "07b368b62dd9dbac61d9d6a91a682b2710a724c600c20a9d1ad1e9de3cc68103", + "moment_interval.py": "a4561baac4a5a2f8066f278b43739b6bc6e1f4c5329fd8ca2b747cdcd9b5e681", + "reference/check_ledger.py": "58162da8e9e7c02de50a9e63649c05ddc4fc5026b7f9173c9058018d093b9603", + "reference/fine_mercator.py": "c0bbb95baff4f301413778c6c595049a0f3fca4ca2cdc86351898137c53e1658", + "reference/fine_moment.py": "feaf1d3b6bf0e3b8eaeb22c40bea3a04ca63a98c08534fa5c28ae913c8ed70c2", + "reference/independent_check.py": "791c0bd5b1b634e20952914c8946bd8402415f4b1163ed83e94e7881fb657a5e", + "reference1982/INPUTS.json": "609c486efb1fe1e03ff2c84ba11085b231b9372e81fb2650bda821ce84e6e1ae", + "reference1982/README.md": "d1c74bccb238aaed7b6512a202f18424ed6d8330b11ad23d60a907ed2b2f7d88", + "reference1982/SOURCES.json": "9297601e0b659319b43f1bb9cde36e4aa04a545b7257f5f5c08a83e67ec00369", + "reference1982/verify.py": "93b65b1ed0aff0f766fa9ae304041e9e79d385b074339289023a11e11cf53098", + "replay_outer.py": "f3bef0ca5139984faf357861283f7ed914f236d5a31b9f0dfcf88dcd93183026", + "verify.py": "871b39cc0cdf73a9618a7383f18326e347e6fd7b36cbd4b22d714684876df950" +} diff --git a/research/fine-prime-slack10030/NOTICE b/research/fine-prime-slack10030/NOTICE new file mode 100644 index 0000000000..c7b32a87db --- /dev/null +++ b/research/fine-prime-slack10030/NOTICE @@ -0,0 +1,14 @@ +New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained. +Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance. + +T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance. + +PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged. + +Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance. + +This refinement also credits Jeremy Kothe and PR1839 contributors for the finer endpoint recertification, and Rohan Arun PR1828 for parameterized positive-slack replay. Original retained enclosure engines and predecessor files are unchanged in reference/. New endpoint, parameters, binding checker and documentation prepared by Rohan Arun with substantial OpenAI Codex assistance. No independent human review is claimed. + +400-digit extension credits the concurrent PR1875 comparison by Rohan Arun with Anthropic Claude assistance. Exact conditional arithmetic extension and verification package prepared with OpenAI Codex assistance. + +PR1982 independent moment checker: Aaron Wang with opencode assistance, Apache-2.0; retained unchanged. PR1928 endpoint and ledger: Jeremy Kothe and contributors. Slack10030 arithmetic adaptation: Rohan Arun with substantial OpenAI Codex assistance. diff --git a/research/fine-prime-slack10030/PARAMETERS.json b/research/fine-prime-slack10030/PARAMETERS.json new file mode 100644 index 0000000000..5949e368b0 --- /dev/null +++ b/research/fine-prime-slack10030/PARAMETERS.json @@ -0,0 +1,8 @@ +{ + "root_digits": 10000, + "slack_digits": 10030, + "zeta_digits": 10032, + "stop_digits": 10036, + "backoff_digits": 10042, + "kappa_grid_digits": 10070 +} diff --git a/research/fine-prime-slack10030/PROOF.md b/research/fine-prime-slack10030/PROOF.md new file mode 100644 index 0000000000..ba37883eec --- /dev/null +++ b/research/fine-prime-slack10030/PROOF.md @@ -0,0 +1,11 @@ +# Finer endpoint with fixed positive slacks + +The physical supplier and paid rank profile are unchanged from PR1800 at its pinned head. This package re-certifies that profile's moment root on the same 10^-10000 rational grid certified in PR1928. The input source specification is preserved byte for byte as inputs/SOURCE-SPEC.json. The derived SPEC differs only in expected.complex_lower. The unchanged independent PR1982 checker proves M(B)<10; the membership gap is delta>0; the Gaussian gap is delta*(1-2q)>0; the effective-router gap is h/2>0. The stopping condition stop*b r0 = 1e-64; beta = 1 - 3 DELTA_E lies in the admissible window +# [1 - DELTA_E (1 + 1/q), 1 - 2 DELTA_E). DELTA_E = 2e-64 is the smallest round value above r0. +DELTA_E=2*R0 +EPS=1-DELTA_E +BETA=1-3*DELTA_E +THETA_POWER=Q(2) +HALO_POWER=48 +CORE_POWER=128 +STRASSEN_TAU=Q(45,16) +KAPPA_1786=Q('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # exact kappa of chafreaky's PR1786 ledger (EXPECTED-BALANCE.json), headline 0.001679754788150048 +KAPPA_PKG5=Q('0.001677992607205282520732088774830808372222877897034109604209719298829805473412451530867883424937597') # previous package (rectangular k=2, tau_eff=2.2500351) +KAPPA_PKG4=Q('0.0016778199023144364336310551358776001013829401215770658599799349282716974076737897457922714197448847') # previous package (radix union schedule, square boundary tau=2.372864) +KAPPA_1712=Q('0.0016776417313433545642517275958639984231708545722735432722117400060454625429077941422798526440584702') # pkg of PR1712 (Le Gall tau=12/5, old union row) +KAPPA_1699=Q('0.001677641731343354564251058287063644749065568493') # exact kappa of PR1699's ledger (Chafik Boukhalfa), same supplier profile +certified_complex=Q(spec['expected']['complex_lower']) +bit=Q('0.001733427039589844234749') +# Keep short independently checkable decimals strictly inside both endpoints. +b=certified_complex-B_GAP # strictly inside the certified supplier endpoint; B.json carries the same exact value +assert b==Q(BJ['b']) +q=b-GAP +a=(q+b)/2 +online=Q(spec['expected']['kappa']) +old=Q('0.001673360105405778') +assert bcertified_complex and moment(b_up)[0]>1 # a larger test endpoint is rejected + +def ledger(kind, *, q_=q, zeta=ZETA, slack=SLACK, + old_scan=False, full_gauge=False, full_key=False, old_union=False, old_theta=False, old_linear=False, old_tag=False, + eps_=EPS, beta_=BETA, tau_eff=STRASSEN_TAU, halo_power=HALO_POWER, core_power=CORE_POWER): + r=R0; stop=STOP + # Existing explicit Strassen format, 7^16<2^45; c=3/32. + # Union: radix-distributed schedule (outer/UNION-SCHEDULE.md, new in this package): row exponent eps+1/2-xi. The boundary row binds with main; the Gaussian row has slack at this explicit point. + c=(3-tau_eff)/2 + eps=eps_; beta=beta_ + xi=eps*(1+q_)-c+slack + saving=eps*q_ + # Deliberate strict gap (BACKOFF) after decimal truncation to the FLOOR grid. + kappa=Q((saving*FLOOR).__floor__(),FLOOR)-BACKOFF + # kappa is derived, not silently asserted to equal an expected decimal. + tau=1-a; sigma=1-b + internal=tau+(1-stop)*max(sigma-tau,Q(0)) + leaf=sigma+stop*(1-sigma) + lam=1-(q_+a)/2 + key=beta+1-eps + margins={ + 'main_transform':saving, + 'global_coordinate_router':a, + 'fused_gaussian':1-eps+q_*beta, + 'group_bit_router':1-eps+a*beta, + 'group_scans':1-eps+beta, + 'boundary_algebraic_matrix':c+xi-eps, + 'sparse_union_movement':xi+Q(1,2)-eps, + 'polynomial_products':eps, + 'microbox_face_corrections':1-(eps+beta+halo_power-core_power+2), + } + if old_union:margins['old_g_factor_union_row']=1-eps-beta-Q(1,2)+xi + if old_scan:margins['old_per_axis_scan']=1-eps + if full_key:margins['unnecessary_full_key_sort']=margins['sparse_union_movement']-key + checks={ + 'actual_bit_above_effective':bit-a, + 'complex_above_effective':b-a, + 'q_positive':q_, 'complex_endpoint':b-q_, + 'q_below_effective':a-q_, 'stop_positive':stop, + 'stop_below_one':1-stop, + 'leaf_saving_above_effective':(1-stop)*b-a, + 'q_below_internal':1-internal-q_, 'q_below_leaf':1-leaf-q_, + 'lambda_above_tau':lam-tau, 'lambda_above_sigma':lam-sigma, + 'lambda_above_internal':lam-internal, + 'lambda_prime_above_lambda':1-q_-lam, + 'lambda_prime_above_leaf':1-q_-leaf, + 'epsilon_positive':eps,'epsilon_below_one':1-eps, + 'cap_above_band':xi-Q(1,2),'cap_below_cell':eps-xi, + 'group_positive':beta,'group_below_dimension':eps-beta, + 'support_router_span':1-beta, + 'group_gauge_power_slack':1-(2*xi-THETA_POWER)-r-beta, + 'actual_logarithmic_group_guard':1-(2*xi-THETA_POWER)-beta, + 'global_gamma_power_slack':1-eps-r, + 'actual_logarithmic_gamma_guard':1-eps, + 'alpha_logarithm_absorption':r, + 'group_key_fits_record':1-key, + 'membership_arithmetic_fits_record':1-beta-2*(1-eps), + 'microbox_halo_volume':core_power-halo_power-beta, + 'positive_layout_slack':slack, + 'short_record_fallback':eps-a, + 'improvement_over_online_final':kappa-online, + 'improvement_over_previous_local_final':kappa-old, + 'complex_below_one_over_32':Q(1,32)-b, + } + checks['strassen_integer_power_gap']=Q(2**tau_eff.numerator-7**tau_eff.denominator) + checks['theta_positive_polynomial_power']=THETA_POWER + checks['cap_below_phase_cell_power']=THETA_POWER-xi + checks['halo_covers_generic_inverse_radius']=Q(halo_power-43) + checks['union_tag_work_per_visit_fits_record']=1-beta + checks['union_header_fits_record']=1-beta + checks['source_axis_superpolynomial']=1-eps + checks['improvement_over_pr1786']=kappa-KAPPA_1786 + checks['improvement_over_pr1758']=kappa-Q('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') + checks['improvement_over_pr1699']=kappa-KAPPA_1699 + checks['improvement_over_pr1712']=kappa-KAPPA_1712 + checks['improvement_over_previous_package']=kappa-KAPPA_PKG4 + checks['improvement_over_pkg_k2']=kappa-KAPPA_PKG5 + if full_gauge:checks['unrecentered_group_gauge']=1-THETA_POWER-r-beta + if old_theta:checks['old_theta_chirp_guard']=1-(2*xi-eps)-r-beta + if old_linear:checks['old_linear_guard']=1-xi-r-beta + if old_tag:checks['old_union_tag_2beta']=1-2*beta + checks.update({n+'_above_kappa':v-kappa for n,v in margins.items()}) + assert margins['boundary_algebraic_matrix']==saving+slack + assert margins['sparse_union_movement']==saving+slack+(tau_eff-2)/2 + return {'kind':kind,'kappa':kappa,'epsilon':eps,'xi':xi,'beta':beta, + 'q':q_,'a':a,'r0':r,'zeta':zeta,'slack':slack, + 'margins':margins,'strict_checks':checks} + +def encode(x): + if isinstance(x,Q): + with localcontext() as c: + c.prec=PARAM['kappa_grid_digits']+20 + return {'rational':str(x),'decimal':str(Decimal(x.numerator)/Decimal(x.denominator))} + if isinstance(x,dict):return {str(k):encode(v) for k,v in x.items()} + if isinstance(x,(list,tuple)):return [encode(v) for v in x] + return x + +rows={};controls={} +for kind in ['struct_boundary_radix_union']: + row=ledger(kind) + assert all(v>0 for v in row['strict_checks'].values()) + assert min(row['margins'].values())==row['margins']['main_transform'] + rows[kind]=row + variants=[('endpoint_equality',{'q_':b}),('zero_layout_slack',{'slack':Q(0)}), + ('old_per_axis_scan',{'old_scan':True}),('full_cell_gauge',{'full_gauge':True}), + ('full_key_sort',{'full_key':True}),('old_g_factor_union_row',{'old_union':True}), + ('old_theta_chirp_guard',{'old_theta':True}),('old_linear_guard',{'old_linear':True}), + ('old_union_tag_2beta',{'old_tag':True}),('matrix_below_strassen',{'tau_eff':Q(14,5)}), + ('halo_too_short',{'halo_power':40}),('core_too_small',{'core_power':48}), + ('group_equals_dimension',{'beta_':EPS}),('epsilon_equals_one',{'eps_':Q(1)}),('epsilon_not_above_r0_slack',{'eps_':1-R0}),('beta_below_gaussian_window',{'beta_':1-700*DELTA_E}),('beta_above_membership_window',{'beta_':1-2*DELTA_E})] + controls[kind]={} + for name,kwargs in variants: + bad=ledger(kind,**kwargs) + failed={n:v for n,v in bad['strict_checks'].items() if v<=0} + assert failed,(kind,name) + controls[kind][name]=failed + assert 'old_g_factor_union_row_above_kappa' in controls[kind]['old_g_factor_union_row'] and 'unnecessary_full_key_sort_above_kappa' in controls[kind]['full_key_sort'] +out={'status':'PASS_FINE_PRIME_PADDING_EXACT_ARITHMETIC', + 'scope':'Conditional fine-prime padding composition. Fresh native admission is required by verify.py. The cited prime theorem, written gauge-free theorem and inherited all-size interfaces are not proved by this arithmetic. No independent human review is claimed.', + 'geometry_changes':{'theta_power':THETA_POWER,'halo_power':HALO_POWER,'core_power':CORE_POWER,'matrix_exponent':STRASSEN_TAU}, + 'complex_lower_short':b,'complex_lower_pinned':certified_complex, + 'native_moment':native,'profile':profile,'m':m,'W':W, + 'online_final_kappa':online,'rows':rows,'rejecting_controls':controls, + 'pr1673_kappa':Q('0.001677160151714381'),'improvement_over_pr1673':rows['struct_boundary_radix_union']['kappa']-Q('0.001677160151714381'), + 'source_sha256':{p.relative_to(WORK).as_posix():hashlib.sha256(p.read_bytes()).hexdigest() for p in [SPEC,CLAIM]}} +(HERE/'LEDGER.json').write_text(json.dumps(encode(out),indent=2)+'\n') +print(out['status']) +for name,row in rows.items(): + print(name,'FINAL KAPPA',encode(row['kappa'])['decimal'], + 'positive checks',len(row['strict_checks']), + 'gain over online',encode(row['kappa']-online)['decimal']) diff --git a/research/fine-prime-slack10030/independent_check.py b/research/fine-prime-slack10030/independent_check.py new file mode 100644 index 0000000000..f697b892f4 --- /dev/null +++ b/research/fine-prime-slack10030/independent_check.py @@ -0,0 +1,56 @@ +# Derived from Jeremy Kothe and contributors, PR1800 exact head +# 46d865ab92e58098538b8c5348b6a131c99abf45; original retained in reference/. +# Only numerical parameters, input/output paths and decimal display precision change. +# Historical comments below describe predecessor settings; PARAMETERS.json is authoritative. +"""Independent balance-equation check (PR1673, adapted: this package's supplier b and SPEC), not an execution of the ledger in check_ledger.py.""" +from fractions import Fraction as F +from pathlib import Path +from decimal import Decimal,localcontext +import json,hashlib,sys +W=Path(__file__).resolve().parent;D=Path(sys.argv[1]).resolve();D.mkdir(parents=True,exist_ok=True) +P=json.loads((W/'PARAMETERS.json').read_text());G=10**P['slack_digits'] +src=W/'inputs/SPEC.json' +BJ=json.loads((W/'inputs/B.json').read_text()) +spec=json.loads(src.read_text());pinned=F(spec['expected']['complex_lower']) +b=F(BJ['b']);q=b-F(1,G);eff=(q+b)/2;actual_bit=F('0.001733427039589844234749') +r=F(1,G);z=F(1,10**P['zeta_digits']);s=F(1,G) +assert 0eff +rows={} +# FINE-PRIME PADDING (outer/FINE-PADDING-COMPOSITION.md): explicit point epsilon=1-delta, beta=1-3 delta, delta=2e-64, Strassen boundary tau=45/16 (7^16<2^45), c=3/32, +# theta in (1/(4p^2),1/(2p^2-1)], chirp guard beta+2xi-2<1, halo power 48, core power 128. Derived here WITHOUT the ledger code; the structured boundary is not used. +delta=F(2,G);E=1-delta;B=1-3*delta +assert 7**16<2**45;tau=F(45,16);c=(3-tau)/2;assert c==F(3,32) +nu=2;halo=48;core=128 +X=E+E*q+s-c # boundary saving c+X-E = E q + s +assert c+X-E==E*q+s +# the Gaussian row has slack: 1-E+qB-Eq = delta(1-2q) +assert 1-E+q*B-E*q==delta*(1-2*q)>0 +# admissible beta window for this epsilon: Gaussian row needs beta >= 1-delta(1+1/q); membership needs beta < 1-2 delta +assert 1-delta*(1+1/q)<=B<1-2*delta +assert F(1,2)z>0 and 1-E-r>0 and core-halo-B>0 and halo>43 +assert 1-B>0 and 1-B-2*(1-E)==delta>0 +costs={'transform':1-E*q,'global_router':1-eff,'gaussian':E-q*B,'group_router':E-eff*B,'group_scans':E-B,'boundary':E-X+(tau-1)/2,'sparse_union':E+F(1,2)-X,'polynomials':1-E,'microfaces':E+B+halo-core+2} +K=F((E*q*10**P['kappa_grid_digits']).__floor__(),10**P['kappa_grid_digits'])-F(1,10**P['backoff_digits']) +assert max(costs.values())==costs['transform'] and all(v<1-K for v in costs.values()) +# earlier packages' guards fail at this point (they are rejecting controls in the ledger): linear guard 1-X-r-B<0, old theta chirp guard 1-(2X-E)-r-B<0, 2B<1 test fails +assert 1-X-r-B<0 and 1-(2*X-E)-r-B<0 and 1-2*B<0 +assert K>F('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # PR1786 exact kappa +assert K>F('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') # PR1758 +assert K r0 (beta = 1-3 delta); only kappa moves, kappa = (1-delta) q - O(1e-76) +sweep=[] +for dd in [F(1,10**7),F(1,10**12),F(1,10**30),F(1,10**60),F(2,G),F(11,10**65)]: + Ed=1-dd;Bd=1-3*dd;Xd=Ed+Ed*q+s-c + assert 1-Ed-r>0 and 1-dd*(1+1/q)<=Bd<1-2*dd and 1-Ed+q*Bd-Ed*q>0 and Ed-Bd>0 and 1-Bd-2*(1-Ed)>0 + assert F(1,2)0 and core-halo-Bd>0 + assert 1-Ed+eff*Bd>Ed*q and eff>Ed*q and 1-Ed+Bd>Ed*q and Ed>Ed*q and 1-(Ed+Bd+halo-core+2)>Ed*q + sweep.append((str(dd),str(float(q-Ed*q)))) +assert 1-F(1,G)<=1-r # delta=r0 itself is rejected by 1-eps-r0>0 +assert not (1-(1-r)-r>0) +rows['struct_boundary_radix_union']={'epsilon':str(E),'cap':str(X),'beta':str(B),'kappa':str(K),'margin_above_kappa':str(E*q-K),'checked_cost_powers':len(costs),'gap_to_q':str(q-K),'epsilon_free_sweep_delta_gap_to_q':sweep} +report={'status':'PASS_INDEPENDENT_BALANCE_DERIVATION','source_sha256':hashlib.sha256(src.read_bytes()).hexdigest(),'b':str(b),'rows':rows,'scope':'Independent balance derivation and margin comparisons for this package\'s supplier endpoint; the supplier native admission is bound by verify_release.py; inherited all-size assumptions remain.'} +(D/'INDEPENDENT.json').write_text(json.dumps(report,indent=2)+'\n') +print(json.dumps(report,indent=2)) diff --git a/research/fine-prime-slack10030/inputs/B.json b/research/fine-prime-slack10030/inputs/B.json new file mode 100644 index 0000000000..7b80c11f90 --- /dev/null +++ b/research/fine-prime-slack10030/inputs/B.json @@ -0,0 +1,15 @@ +{ + "b": 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+ "profile": { + "1": 1560432, + "2": 336336, + "3": 278724, + "4": 84912, + "48": 22748, + "5": 54612, + "8": 5328 + }, + "live": 66304, + "note": "Strictly interior slack refinement of the unchanged PR1928 native endpoint." +} diff --git a/research/fine-prime-slack10030/inputs/CLAIM1800.json b/research/fine-prime-slack10030/inputs/CLAIM1800.json new file mode 100644 index 0000000000..ee6eeb0df2 --- /dev/null +++ b/research/fine-prime-slack10030/inputs/CLAIM1800.json @@ -0,0 +1,17 @@ +{ + "status": "PASS_T74_PIVOT566_KERNEL_WITH_ENDPOINT_AND_OUTER_REFINEMENT_COMPLETE_FINITE_ADMISSION", + "kappa": "1676938111022438771190100017020725032555691674761792047536039179/1000000000000000000000000000000000000000000000000000000000000000000", + "kappa_decimal": "0.001676938111022438771190100017020725032555691674761792047536039179", + "baseline_pr": 1644, + "baseline_kappa": "0.00167689666902129930775071099726796267", + "construction_improvement": false, + "outer_refinement": { + "grid_digits": 66, + "margin_digits": 76, + "bootstrap_steps": 30, + "endpoint_digits": 70 + }, + "scope": "Conditional finite construction only. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global packing claim.", + "verification": "Exact discovery using verified PR1319 owner/invoice receipts passes both moment engines and 47 outer inequalities. Full new-package finite replay and independent outer checks pending. Native providers are unchanged and will be explicitly source-bound reused.", + "gain_over_claimed_leader": "5.8464055E-59" +} diff --git a/research/fine-prime-slack10030/inputs/LEADER1839.json b/research/fine-prime-slack10030/inputs/LEADER1839.json new file mode 100644 index 0000000000..84d422de25 --- /dev/null +++ b/research/fine-prime-slack10030/inputs/LEADER1839.json @@ -0,0 +1,9 @@ +{ + "kappa": "0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263049999999997996640490086748910957328658012158594", + "kappa_rational": "8398774780627722606678354969603512884991557192512901477301637600814322741301628194131524999999998998320245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "branch": "fine source-prime padding (PR1786, chafreaky; Trudgian's prime theorem; vendor/pr1786) with the gauge-free interiors (PR1758), the radix-distributed union schedule with per-visit tag work and the explicit Strassen boundary (tau=45/16); epsilon=1-2e-100 is a free parameter (outer/FINE-PADDING-COMPOSITION.md): kappa = epsilon q - 1e-112, 3.4e-103 below q; the structured boundary of the previous package is not used; omega_C<=9/4 not used; slack refinement and recertified endpoint: the supplier native endpoint is recertified to 1e-90 (accept at the endpoint, reject at endpoint+1e-90, repaired fine engines), 6.45e-71 above the previous 1e-70 pin, and all free slacks are 1e-100 or below", + "b": "certified complex_lower - 1e-100 (see outer/B.json)", + "outer": "PR1673 capped phase-cell fusion (Vlado Vojdanovski)", + "supplier": "PR1661 T74 pivot-566 stack plus the pivot-554 helper-donor kernel (PR1672 lineage)", + "retuned_slacks": "b = certified complex endpoint - 1e-100, q = b - 1e-100, r0=1e-100, zeta=1e-102, layout slack=1e-100, stop=1e-106, floor grid 1e-136, backoff 1e-112 (outer/RETUNED-SLACKS.md)" +} diff --git a/research/fine-prime-slack10030/inputs/LEADER1875.json b/research/fine-prime-slack10030/inputs/LEADER1875.json new file mode 100644 index 0000000000..4724fd6ca7 --- /dev/null +++ b/research/fine-prime-slack10030/inputs/LEADER1875.json @@ -0,0 +1,7 @@ +{ + "pr": 1875, + "head": "5b06a3fd5f80a6ca3d62f28e04cd650897a5b47a", + "kappa_rational": 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+} diff --git a/research/fine-prime-slack10030/inputs/OUTER-CLAIM1800.json b/research/fine-prime-slack10030/inputs/OUTER-CLAIM1800.json new file mode 100644 index 0000000000..d8ca9c20fe --- /dev/null +++ b/research/fine-prime-slack10030/inputs/OUTER-CLAIM1800.json @@ -0,0 +1,9 @@ +{ + "kappa": "0.0016797549561255445213356709939207025769983114385025802954603273198268490086748910957328658012158594", + "kappa_rational": "8398774780627722606678354969603512884991557192512901477301636599134245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "branch": "fine source-prime padding (PR1786, chafreaky; Trudgian's prime theorem; vendor/pr1786) with the gauge-free interiors (PR1758), the radix-distributed union schedule with per-visit tag work and the explicit Strassen boundary (tau=45/16); epsilon=1-2e-64 is a free parameter (outer/FINE-PADDING-COMPOSITION.md): kappa = epsilon q - 1e-76, 3.4e-67 below q; the structured boundary of the previous package is not used; omega_C<=9/4 not used", + "b": "certified complex_lower - 1e-64 (see outer/B.json)", + "outer": "PR1673 capped phase-cell fusion (Vlado Vojdanovski)", + "supplier": "PR1661 T74 pivot-566 stack plus the pivot-554 helper-donor kernel (PR1672 lineage)", + "retuned_slacks": "b = certified complex endpoint - 1e-64, q = b - 1e-64, r0=1e-64, zeta=1e-66, layout slack=1e-64, stop=1e-70, floor grid 1e-100, backoff 1e-76 (outer/RETUNED-SLACKS.md)" +} diff --git a/research/fine-prime-slack10030/inputs/SOURCE-SPEC.json b/research/fine-prime-slack10030/inputs/SOURCE-SPEC.json new file mode 100644 index 0000000000..2989f666c7 --- /dev/null +++ b/research/fine-prime-slack10030/inputs/SOURCE-SPEC.json @@ -0,0 +1,7300 @@ +{ + "call_order": [ + [ + 0, + 0 + ], + [ + 0, + 37 + ], + [ + 0, + 1 + ], + [ + 0, + 38 + ], + [ + 0, + 2 + ], + [ + 0, + 39 + ], + [ + 0, + 3 + ], + [ + 0, + 40 + ], + [ + 0, + 4 + ], + [ + 0, + 41 + ], + [ + 1, + 0 + ], + [ + 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"3e003abf2aff6127002c1d352867bf51aacda5713a197dcbdac749a1c673c8f6", + "CLIFFORD-RECIPES.json": "3eaf9e1fbce086198d4904767036dfc5d85eef76a332408f042c05d99abcf9e3", + "CLIFFORD-REVIEW.json": "bd380ca1cb9c43ba67bfc093e579a992d902a1b42cd5dbeec7ddff475d761cad", + "RESIDUAL-ADAPTERS.json": "df5afb8969525b20e7eb4cf572270b724a9427f8d16f78edbd014c5005191133" + } + }, + "semantic_phase_sha256": "bd380ca1cb9c43ba67bfc093e579a992d902a1b42cd5dbeec7ddff475d761cad", + "wrappers": 240 + } + }, + "schema": "witness-spec/1", + "width_spot_helpers": [ + 258, + 270, + 282, + 294 + ], + "outer_refinement": { + "grid_digits": 66, + "margin_digits": 76, + "bootstrap_steps": 30, + "endpoint_digits": 70 + } +} diff --git a/research/fine-prime-slack10030/moment_interval.py b/research/fine-prime-slack10030/moment_interval.py new file mode 100644 index 0000000000..74ee030d63 --- /dev/null +++ b/research/fine-prime-slack10030/moment_interval.py @@ -0,0 +1,19 @@ +"""Directed integer moment intervals using Aaron Wang / PR1982, retained unchanged.""" +import importlib.util,json +from pathlib import Path +from fractions import Fraction as Q +P=Path(__file__).resolve().parent +s=importlib.util.spec_from_file_location('root1982',P/'reference1982/verify.py') +v=importlib.util.module_from_spec(s);s.loader.exec_module(v) +v.check_inputs_pin();v.check_log_identities() +src=v.load_inputs()['sources']['pr1928'] +BITS=v.default_bits(int(src['grid_digits'])) +def moment(x,profile,m,live): + assert m==73 and profile=={int(k):int(n) for k,n in src['global_profile'].items()} and live==int(src['live']) + logs=v.log_table(m,sorted(profile),BITS) + lo=hi=0 + for rank,count in profile.items(): + elo,ehi=v.exp_interval(*v.scaled_product(x,logs[rank]),BITS) + lo+=rank*count*elo;hi+=rank*count*ehi + target=(m*live)< 0. +R0=Q(1,10**64); ZETA=Q(1,10**66); SLACK=Q(1,10**64); GAP=Q(1,10**64); STOP=Q(1,10**70) +FLOOR=10**100; BACKOFF=Q(1,10**76); B_GAP=Q(1,10**64) +# Fine prime padding: theta is between 1/(4p^2) and 1/(2p^2-1). +# Online chirp guard beta+2*xi-2<1; coefficient setup uses O(p^2 log p) bits. +# epsilon = 1 - DELTA_E is a FREE parameter (outer/FINE-PADDING-COMPOSITION.md sec. 2): every row is strictly satisfied for every DELTA_E > r0 = 1e-64; beta = 1 - 3 DELTA_E lies in the admissible window +# [1 - DELTA_E (1 + 1/q), 1 - 2 DELTA_E). DELTA_E = 2e-64 is the smallest round value above r0. +DELTA_E=Q(2,10**64) +EPS=1-DELTA_E +BETA=1-3*DELTA_E +THETA_POWER=Q(2) +HALO_POWER=48 +CORE_POWER=128 +STRASSEN_TAU=Q(45,16) +KAPPA_1786=Q('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # exact kappa of chafreaky's PR1786 ledger (EXPECTED-BALANCE.json), headline 0.001679754788150048 +KAPPA_PKG5=Q('0.001677992607205282520732088774830808372222877897034109604209719298829805473412451530867883424937597') # previous package (rectangular k=2, tau_eff=2.2500351) +KAPPA_PKG4=Q('0.0016778199023144364336310551358776001013829401215770658599799349282716974076737897457922714197448847') # previous package (radix union schedule, square boundary tau=2.372864) +KAPPA_1712=Q('0.0016776417313433545642517275958639984231708545722735432722117400060454625429077941422798526440584702') # pkg of PR1712 (Le Gall tau=12/5, old union row) +KAPPA_1699=Q('0.001677641731343354564251058287063644749065568493') # exact kappa of PR1699's ledger (Chafik Boukhalfa), same supplier profile +certified_complex=Q(spec['expected']['complex_lower']) +bit=Q('0.001733427039589844234749') +# Keep short independently checkable decimals strictly inside both endpoints. +b=certified_complex-B_GAP # strictly inside the certified supplier endpoint; B.json carries the same exact value +assert b==Q(BJ['b']) +q=b-GAP +a=(q+b)/2 +online=Q(spec['expected']['kappa']) +old=Q('0.001673360105405778') +assert b=2:x/=2;k+=1 + lo,hi=unit_log(x) + return down(lo+k*ln2[0]),up(hi+k*ln2[1]) +def exp(x): + assert 0<=x<1 + N=45 + lo=sum((x**j/factorial(j) for j in range(N)),Q(0)) + hi=lo+x**N/factorial(N)/(1-x/(N+1)) + return down(lo),up(hi) +def moment(endpoint): + lo=hi=Q(0) + for r,n in profile.items(): + l,h=log(Q(m,r)); weight=Q(n*r,m*W) + lo+=weight*exp(endpoint*l)[0] + hi+=weight*exp(endpoint*h)[1] + return down(lo),up(hi) + +native=moment(b) +assert native[1]<1 +b_up=Q(BJ['b_above_endpoint']) +assert b_up>certified_complex and moment(b_up)[0]>1 # a larger test endpoint is rejected + +def ledger(kind, *, q_=q, zeta=ZETA, slack=SLACK, + old_scan=False, full_gauge=False, full_key=False, old_union=False, old_theta=False, old_linear=False, old_tag=False, + eps_=EPS, beta_=BETA, tau_eff=STRASSEN_TAU, halo_power=HALO_POWER, core_power=CORE_POWER): + r=R0; stop=STOP + # Existing explicit Strassen format, 7^16<2^45; c=3/32. + # Union: radix-distributed schedule (outer/UNION-SCHEDULE.md, new in this package): row exponent eps+1/2-xi. The boundary row binds with main; the Gaussian row has slack at this explicit point. + c=(3-tau_eff)/2 + eps=eps_; beta=beta_ + xi=eps*(1+q_)-c+slack + saving=eps*q_ + # Deliberate strict gap (BACKOFF) after decimal truncation to the FLOOR grid. + kappa=Q((saving*FLOOR).__floor__(),FLOOR)-BACKOFF + # kappa is derived, not silently asserted to equal an expected decimal. + tau=1-a; sigma=1-b + internal=tau+(1-stop)*max(sigma-tau,Q(0)) + leaf=sigma+stop*(1-sigma) + lam=1-(q_+a)/2 + key=beta+1-eps + margins={ + 'main_transform':saving, + 'global_coordinate_router':a, + 'fused_gaussian':1-eps+q_*beta, + 'group_bit_router':1-eps+a*beta, + 'group_scans':1-eps+beta, + 'boundary_algebraic_matrix':c+xi-eps, + 'sparse_union_movement':xi+Q(1,2)-eps, + 'polynomial_products':eps, + 'microbox_face_corrections':1-(eps+beta+halo_power-core_power+2), + } + if old_union:margins['old_g_factor_union_row']=1-eps-beta-Q(1,2)+xi + if old_scan:margins['old_per_axis_scan']=1-eps + if full_key:margins['unnecessary_full_key_sort']=margins['sparse_union_movement']-key + checks={ + 'actual_bit_above_effective':bit-a, + 'complex_above_effective':b-a, + 'q_positive':q_, 'complex_endpoint':b-q_, + 'q_below_effective':a-q_, 'stop_positive':stop, + 'stop_below_one':1-stop, + 'leaf_saving_above_effective':(1-stop)*b-a, + 'q_below_internal':1-internal-q_, 'q_below_leaf':1-leaf-q_, + 'lambda_above_tau':lam-tau, 'lambda_above_sigma':lam-sigma, + 'lambda_above_internal':lam-internal, + 'lambda_prime_above_lambda':1-q_-lam, + 'lambda_prime_above_leaf':1-q_-leaf, + 'epsilon_positive':eps,'epsilon_below_one':1-eps, + 'cap_above_band':xi-Q(1,2),'cap_below_cell':eps-xi, + 'group_positive':beta,'group_below_dimension':eps-beta, + 'support_router_span':1-beta, + 'group_gauge_power_slack':1-(2*xi-THETA_POWER)-r-beta, + 'actual_logarithmic_group_guard':1-(2*xi-THETA_POWER)-beta, + 'global_gamma_power_slack':1-eps-r, + 'actual_logarithmic_gamma_guard':1-eps, + 'alpha_logarithm_absorption':r, + 'group_key_fits_record':1-key, + 'membership_arithmetic_fits_record':1-beta-2*(1-eps), + 'microbox_halo_volume':core_power-halo_power-beta, + 'positive_layout_slack':slack, + 'short_record_fallback':eps-a, + 'improvement_over_online_final':kappa-online, + 'improvement_over_previous_local_final':kappa-old, + 'complex_below_one_over_32':Q(1,32)-b, + } + checks['strassen_integer_power_gap']=Q(2**tau_eff.numerator-7**tau_eff.denominator) + checks['theta_positive_polynomial_power']=THETA_POWER + checks['cap_below_phase_cell_power']=THETA_POWER-xi + checks['halo_covers_generic_inverse_radius']=Q(halo_power-43) + checks['union_tag_work_per_visit_fits_record']=1-beta + checks['union_header_fits_record']=1-beta + checks['source_axis_superpolynomial']=1-eps + checks['improvement_over_pr1786']=kappa-KAPPA_1786 + checks['improvement_over_pr1758']=kappa-Q('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') + checks['improvement_over_pr1699']=kappa-KAPPA_1699 + checks['improvement_over_pr1712']=kappa-KAPPA_1712 + checks['improvement_over_previous_package']=kappa-KAPPA_PKG4 + checks['improvement_over_pkg_k2']=kappa-KAPPA_PKG5 + if full_gauge:checks['unrecentered_group_gauge']=1-THETA_POWER-r-beta + if old_theta:checks['old_theta_chirp_guard']=1-(2*xi-eps)-r-beta + if old_linear:checks['old_linear_guard']=1-xi-r-beta + if old_tag:checks['old_union_tag_2beta']=1-2*beta + checks.update({n+'_above_kappa':v-kappa for n,v in margins.items()}) + assert margins['boundary_algebraic_matrix']==saving+slack + assert margins['sparse_union_movement']==saving+slack+(tau_eff-2)/2 + return {'kind':kind,'kappa':kappa,'epsilon':eps,'xi':xi,'beta':beta, + 'q':q_,'a':a,'r0':r,'zeta':zeta,'slack':slack, + 'margins':margins,'strict_checks':checks} + +def encode(x): + if isinstance(x,Q): + with localcontext() as c: + c.prec=140 + return {'rational':str(x),'decimal':str(Decimal(x.numerator)/Decimal(x.denominator))} + if isinstance(x,dict):return {str(k):encode(v) for k,v in x.items()} + if isinstance(x,(list,tuple)):return [encode(v) for v in x] + return x + +rows={};controls={} +for kind in ['struct_boundary_radix_union']: + row=ledger(kind) + assert all(v>0 for v in row['strict_checks'].values()) + assert min(row['margins'].values())==row['margins']['main_transform'] + rows[kind]=row + variants=[('endpoint_equality',{'q_':b}),('zero_layout_slack',{'slack':Q(0)}), + ('old_per_axis_scan',{'old_scan':True}),('full_cell_gauge',{'full_gauge':True}), + ('full_key_sort',{'full_key':True}),('old_g_factor_union_row',{'old_union':True}), + ('old_theta_chirp_guard',{'old_theta':True}),('old_linear_guard',{'old_linear':True}), + ('old_union_tag_2beta',{'old_tag':True}),('matrix_below_strassen',{'tau_eff':Q(14,5)}), + ('halo_too_short',{'halo_power':40}),('core_too_small',{'core_power':48}), + ('group_equals_dimension',{'beta_':EPS}),('epsilon_equals_one',{'eps_':Q(1)}),('epsilon_not_above_r0_slack',{'eps_':1-R0}),('beta_below_gaussian_window',{'beta_':1-700*DELTA_E}),('beta_above_membership_window',{'beta_':1-2*DELTA_E})] + controls[kind]={} + for name,kwargs in variants: + bad=ledger(kind,**kwargs) + failed={n:v for n,v in bad['strict_checks'].items() if v<=0} + assert failed,(kind,name) + controls[kind][name]=failed + assert 'old_g_factor_union_row_above_kappa' in controls[kind]['old_g_factor_union_row'] and 'unnecessary_full_key_sort_above_kappa' in controls[kind]['full_key_sort'] +out={'status':'PASS_FINE_PRIME_PADDING_EXACT_ARITHMETIC', + 'scope':'Conditional fine-prime padding composition. Fresh native admission is required by verify.py. The cited prime theorem, written gauge-free theorem and inherited all-size interfaces are not proved by this arithmetic. No independent human review is claimed.', + 'geometry_changes':{'theta_power':THETA_POWER,'halo_power':HALO_POWER,'core_power':CORE_POWER,'matrix_exponent':STRASSEN_TAU}, + 'complex_lower_short':b,'complex_lower_pinned':certified_complex, + 'native_moment':native,'profile':profile,'m':m,'W':W, + 'online_final_kappa':online,'rows':rows,'rejecting_controls':controls, + 'pr1673_kappa':Q('0.001677160151714381'),'improvement_over_pr1673':rows['struct_boundary_radix_union']['kappa']-Q('0.001677160151714381'), + 'source_sha256':{p.relative_to(WORK).as_posix():hashlib.sha256(p.read_bytes()).hexdigest() for p in [SPEC,CLAIM]}} +(HERE/'LEDGER.json').write_text(json.dumps(encode(out),indent=2)+'\n') +print(out['status']) +for name,row in rows.items(): + print(name,'FINAL KAPPA',encode(row['kappa'])['decimal'], + 'positive checks',len(row['strict_checks']), + 'gain over online',encode(row['kappa']-online)['decimal']) diff --git a/research/fine-prime-slack10030/reference/fine_mercator.py b/research/fine-prime-slack10030/reference/fine_mercator.py new file mode 100644 index 0000000000..4b0e214522 --- /dev/null +++ b/research/fine-prime-slack10030/reference/fine_mercator.py @@ -0,0 +1,49 @@ +"""Finer-constant copy of the retained Mercator moment engine (engines/moment.py): identical algorithm and enclosure logic, +DYAD 2^320 outward rounding, 320 (even) Mercator terms (tail bounded by the next term), 40 exponential terms.""" +from fractions import Fraction as F +from functools import lru_cache +DYAD = 1 << 320 +LOGN = 321 # the loop sums n = 1..LOGN-1 = 320 terms: an EVEN alternating partial sum lies BELOW log(1+z), as the retained engine (n = 1..224) does +EXPN = 40 +def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) +def ceil(x): return -floor(-x) +def mercator(y): + """Enclosure [s, s + next term] of log(y) for 1 <= y <= 3/2 by the alternating Mercator series in z = y-1.""" + z=y-1 + assert 0 <= z <= F(1,2) + assert (LOGN - 1) % 2 == 0, 'an even number of terms is required: an odd partial sum lies above the log' + t=z; s=F(0) + for n in range(1, LOGN): + s += (t if n & 1 else -t)/n + t *= z + return s, s+t/LOGN + +@lru_cache(None) +def logarithm(x): + assert x >= 1 + k = 0 + while x >= 2: x /= 2; k += 1 + j = int(x >= F(3, 2)) + if j: x /= F(3, 2) + a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3)) + return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f) + +def exponential(l,u): + assert 0 <= l <= u < F(1,10) + def poly(x): + s=t=F(1) + for j in range(1,EXPN): t=t*x/j; s+=t + return s,t + lo,_=poly(l);hi,last=poly(u) + return floor(lo),ceil(hi+last*u/EXPN/(1-u/(EXPN+1))) +def moment(H,m,W,a,bad=False): + lo=hi=F(0) + for r,n in H.items(): + assert 0 < r < m and n > 0 + l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u) + p=F(r*n,m*W);lo+=p*e;hi+=p*f + if bad: + l,u=logarithm(F(m));e,f=exponential(a*l,a*u) + p=F(32*m*sum(H.values()),10**16*W) + lo+=p*e;hi+=p*f + return floor(lo),ceil(hi) diff --git a/research/fine-prime-slack10030/reference/fine_moment.py b/research/fine-prime-slack10030/reference/fine_moment.py new file mode 100644 index 0000000000..3f3f810e8e --- /dev/null +++ b/research/fine-prime-slack10030/reference/fine_moment.py @@ -0,0 +1,36 @@ +"""Higher-precision independent base-two moment enclosure (same algorithm as base_two_moment.py, finer constants).""" +from fractions import Fraction as Q +GRID = 10**100 +LOG_TERMS = 110 +EXP_TERMS = 40 +def require(c, msg): + if not c: raise ValueError(msg) +def log_unit(x): + require(1 <= x <= 2, "logarithm range") + z = (x-1)/(x+1) + lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(LOG_TERMS)), Q(0)) + return lo, lo+2*z**(2*LOG_TERMS+1)/((2*LOG_TERMS+1)*(1-z*z)) +def log_bounds(x): + k = 0 + while x > 2: + x /= 2; k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) +def exp_bounds(x): + require(0 <= x < 1, "exponential range") + term = total = Q(1) + for j in range(1, EXP_TERMS): + term *= x/j; total += term + tail = term*x/EXP_TERMS/(1-x/(EXP_TERMS+1)) + return total, total+tail +def moment(m, W, entries, saving): + lo = hi = Q(0) + for t, count in entries: + t, count = int(t), int(count) + require(0 < t < m and count > 0, "improper child") + l, u = log_bounds(Q(m, t)) + lo += Q(t*count, m*W)*exp_bounds(saving*l)[0] + hi += Q(t*count, m*W)*exp_bounds(saving*u)[1] + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) diff --git a/research/fine-prime-slack10030/reference/independent_check.py b/research/fine-prime-slack10030/reference/independent_check.py new file mode 100644 index 0000000000..402a320cc3 --- /dev/null +++ b/research/fine-prime-slack10030/reference/independent_check.py @@ -0,0 +1,51 @@ +"""Independent balance-equation check (PR1673, adapted: this package's supplier b and SPEC), not an execution of the ledger in check_ledger.py.""" +from fractions import Fraction as F +from pathlib import Path +from decimal import Decimal,localcontext +import json,hashlib +D=Path(__file__).resolve().parent;W=D.parent +src=W/'new/SPEC.json' +BJ=json.loads((D/'B.json').read_text()) +spec=json.loads(src.read_text());pinned=F(spec['expected']['complex_lower']) +b=F(BJ['b']);q=b-F(1,10**64);eff=(q+b)/2;actual_bit=F('0.001733427039589844234749') +r=F(1,10**64);z=F(1,10**66);s=F(1,10**64) +assert 0eff +rows={} +# FINE-PRIME PADDING (outer/FINE-PADDING-COMPOSITION.md): explicit point epsilon=1-delta, beta=1-3 delta, delta=2e-64, Strassen boundary tau=45/16 (7^16<2^45), c=3/32, +# theta in (1/(4p^2),1/(2p^2-1)], chirp guard beta+2xi-2<1, halo power 48, core power 128. Derived here WITHOUT the ledger code; the structured boundary is not used. +delta=F(2,10**64);E=1-delta;B=1-3*delta +assert 7**16<2**45;tau=F(45,16);c=(3-tau)/2;assert c==F(3,32) +nu=2;halo=48;core=128 +X=E+E*q+s-c # boundary saving c+X-E = E q + s +assert c+X-E==E*q+s +# the Gaussian row has slack: 1-E+qB-Eq = delta(1-2q) +assert 1-E+q*B-E*q==delta*(1-2*q)>0 +# admissible beta window for this epsilon: Gaussian row needs beta >= 1-delta(1+1/q); membership needs beta < 1-2 delta +assert 1-delta*(1+1/q)<=B<1-2*delta +assert F(1,2)z>0 and 1-E-r>0 and core-halo-B>0 and halo>43 +assert 1-B>0 and 1-B-2*(1-E)==delta>0 +costs={'transform':1-E*q,'global_router':1-eff,'gaussian':E-q*B,'group_router':E-eff*B,'group_scans':E-B,'boundary':E-X+(tau-1)/2,'sparse_union':E+F(1,2)-X,'polynomials':1-E,'microfaces':E+B+halo-core+2} +K=F((E*q*10**100).__floor__(),10**100)-F(1,10**76) +assert max(costs.values())==costs['transform'] and all(v<1-K for v in costs.values()) +# earlier packages' guards fail at this point (they are rejecting controls in the ledger): linear guard 1-X-r-B<0, old theta chirp guard 1-(2X-E)-r-B<0, 2B<1 test fails +assert 1-X-r-B<0 and 1-(2*X-E)-r-B<0 and 1-2*B<0 +assert K>F('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # PR1786 exact kappa +assert K>F('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') # PR1758 +assert K r0 (beta = 1-3 delta); only kappa moves, kappa = (1-delta) q - O(1e-76) +sweep=[] +for dd in [F(1,10**7),F(1,10**12),F(1,10**30),F(1,10**60),F(2,10**64),F(11,10**65)]: + Ed=1-dd;Bd=1-3*dd;Xd=Ed+Ed*q+s-c + assert 1-Ed-r>0 and 1-dd*(1+1/q)<=Bd<1-2*dd and 1-Ed+q*Bd-Ed*q>0 and Ed-Bd>0 and 1-Bd-2*(1-Ed)>0 + assert F(1,2)0 and core-halo-Bd>0 + assert 1-Ed+eff*Bd>Ed*q and eff>Ed*q and 1-Ed+Bd>Ed*q and Ed>Ed*q and 1-(Ed+Bd+halo-core+2)>Ed*q + sweep.append((str(dd),str(float(q-Ed*q)))) +assert 1-F(1,10**64)<=1-r # delta=r0 itself is rejected by 1-eps-r0>0 +assert not (1-(1-r)-r>0) +rows['struct_boundary_radix_union']={'epsilon':str(E),'cap':str(X),'beta':str(B),'kappa':str(K),'margin_above_kappa':str(E*q-K),'checked_cost_powers':len(costs),'gap_to_q':str(q-K),'epsilon_free_sweep_delta_gap_to_q':sweep} +report={'status':'PASS_INDEPENDENT_BALANCE_DERIVATION','source_sha256':hashlib.sha256(src.read_bytes()).hexdigest(),'b':str(b),'rows':rows,'scope':'Independent balance derivation and margin comparisons for this package\'s supplier endpoint; the supplier native admission is bound by verify_release.py; inherited all-size assumptions remain.'} +(D/'INDEPENDENT.json').write_text(json.dumps(report,indent=2)+'\n') +print(json.dumps(report,indent=2)) diff --git a/research/fine-prime-slack10030/reference1982/INPUTS.json b/research/fine-prime-slack10030/reference1982/INPUTS.json new file mode 100644 index 0000000000..51fd7b007c --- /dev/null +++ b/research/fine-prime-slack10030/reference1982/INPUTS.json @@ -0,0 +1,110 @@ +{ + "m": 73, + "schema_version": 1, + "sources": { + "pr1672": { + "complex_lower": "4199387390313861303339177484801756442495778596256450738650818800407/2500000000000000000000000000000000000000000000000000000000000000000000", + "conservative_complex_lower": "8398774766397181318443389806932001359929734105781555583223880640081/5000000000000000000000000000000000000000000000000000000000000000000000", + "git_blob": "bcff1fe102ce25b852011497a00949461d14e6d7", + "global_profile": { + "1": 1560432, + "2": 336336, + "3": 278724, + "4": 84912, + "48": 22748, + "5": 54612, + "8": 5328 + }, + "grid_digits": 70, + "head": "b8ab040dbb7638e79249e763c60e877765d9d3b7", + "headline_kappa": "1676938111022438771190100017020725032555691674761792047536039179/1000000000000000000000000000000000000000000000000000000000000000000", + "headline_kappa_field": "expected/kappa", + "headline_kappa_file_sha256": "41d7bd51c18eb354c6a785780ddefd35b3a8e2513daa2c4f585b236b7173e943", + "headline_kappa_git_blob": "bcff1fe102ce25b852011497a00949461d14e6d7", + "headline_kappa_path": "research/gmx-t74-k554-signed-001/new/SPEC.json", + "idle_remainder_profile": { + "48": 22748 + }, + "live": 66304, + "path": "research/gmx-t74-k554-signed-001/new/SPEC.json", + "pr": 1672, + "provider_counts": { + "extra": 417, + "gauge44": 249 + }, + "provider_profiles": { + "extra": { + "1": 2340, + "2": 508, + "3": 420, + "4": 126, + "5": 82, + "8": 8 + }, + "gauge44": { + "1": 2348, + "2": 500, + "3": 416, + "4": 130, + "5": 82, + "8": 8 + } + }, + "rank_mass": 4816512, + "sha256": "41d7bd51c18eb354c6a785780ddefd35b3a8e2513daa2c4f585b236b7173e943", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1672" + }, + "pr1928": { + "complex_lower": 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+ "headline_kappa_field": "kappa_rational", + "headline_kappa_file_sha256": "d72b5053ceea907bfb23befc0b73024c8b03d5128ac95f9a50462827ff8d6c09", + "headline_kappa_git_blob": "881309466b325073e16e110a2e74a2fc117f82cb", + "headline_kappa_path": "research/capped-fusion-t74-k554/outer/OUTER-CLAIM.json", + "idle_remainder_profile": { + "48": 22748 + }, + "live": 66304, + "path": "research/capped-fusion-t74-k554/new/SPEC.json", + "pr": 1928, + "provider_counts": { + "extra": 417, + "gauge44": 249 + }, + "provider_profiles": { + "extra": { + "1": 2340, + "2": 508, + "3": 420, + "4": 126, + "5": 82, + "8": 8 + }, + "gauge44": { + "1": 2348, + "2": 500, + "3": 416, + "4": 130, + "5": 82, + "8": 8 + } + }, + "rank_mass": 4816512, + "sha256": "75510fe5113baa42468c5835ebc9728bdc204acd6e07b898b3bc300e453d3443", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1928" + } + } +} diff --git a/research/fine-prime-slack10030/reference1982/README.md b/research/fine-prime-slack10030/reference1982/README.md new file mode 100644 index 0000000000..dccf9230ba --- /dev/null +++ b/research/fine-prime-slack10030/reference1982/README.md @@ -0,0 +1,78 @@ +# Independent enclosure of the pivot-566+554 T74 complex root + +**Independent verification of a pending supplier number. No new κ, no change to the selected record, and no check of the outer reduction.** + +The open claims from https://github.com/CrocSwap/integer-mult-bounds/pull/1800 to https://github.com/CrocSwap/integer-mult-bounds/pull/1928 all price the same pending complex supplier: the pivot-566 stack with the pivot-554 helper-donor kernel (lineage https://github.com/CrocSwap/integer-mult-bounds/pull/1625 and https://github.com/CrocSwap/integer-mult-bounds/pull/1672). At their "free ε → 1" point, κ approaches this supplier's complex moment root b. https://github.com/CrocSwap/integer-mult-bounds/pull/1928 takes b as its certified native endpoint minus 10^-10010. Up to now, the only certificates of that endpoint came from the authors' own engines. + +This package checks the endpoint with code that shares no algorithm with those engines. + +## Object + +Both pinned PR heads record the same data in `new/SPEC.json`: + +- global profile `{1:1560432, 2:336336, 3:278724, 4:84912, 5:54612, 8:5328, 48:22748}`, m = 73, live W = 66304; +- native and conservative endpoints on a 10^-70 grid (https://github.com/CrocSwap/integer-mult-bounds/pull/1672, head `b8ab040d`) and on a 10^-10000 grid (https://github.com/CrocSwap/integer-mult-bounds/pull/1928, head `07e4e423`). + +`extract_inputs.py` copies these fields, the two provider profiles, the provider counts, the idle remainder and each PR's headline κ into [INPUTS.json](INPUTS.json), with the Git blob and SHA-256 of each source file. With the pull refs fetched, `extract_inputs.py --check` rebuilds the file byte for byte. + +The moment definitions come from the repository's written review, not from code. The native moment is `sum_r H[r] (r/m)^(1-x) / W` ([native-complex-moment552/PROOF.md](../native-complex-moment552/PROOF.md)). The conservative model adds the inherited fallback of `32 m^2 N` rank-one children on a 10^-16 fraction, N = number of children ([three-stage-cover-assembly.tex](../../notes/three-stage-cover-assembly.tex), line 24). An endpoint e on a 10^-d grid is certified when M(e) < 1 < M(e + 10^-d). + +## Method + +`verify.py` uses only the standard library and imports nothing from the repository or from either PR. + +- **Logs.** Write A = ln(16/15), B = ln(25/24), C = ln(81/80); each is 2 atanh(1/31), 2 atanh(1/49) or 2 atanh(1/161). Then ln 2 = 7A + 5B + 3C, ln 3 = 11A + 8B + 5C and ln 5 = 16A + 12B + 7C. The verifier checks these identities exactly from the prime factorizations. ln 73 = 3 ln 2 + 2 ln 3 + 2 atanh(1/145). Every rank here is 5-smooth, so each ln(73/r) is a nonnegative integer combination of four atanh series. +- **Exp.** Halve the argument s times, sum a Taylor polynomial with an explicit tail bound, then square s times. +- **Rounding.** Every quantity is an integer multiple of 2^-bits rounded outward. The final test compares two exact integers. A sign that the enclosure cannot decide counts as failure; precision is raised at most twice and never turns an undecided sign into a pass. + +The authors' engines use a Mercator series and binary range reduction with atanh((x-1)/(x+1)) (`code/fine_mercator.py`, `code/fine_moment.py`). Earlier independent audits used a prime-by-prime log chain (pending-claims-independent-pricing) or binary reduction (pr1407-complex-moment-audit-seed39). This package uses neither. + +## Result + +`PASS_T74_K554_ROOT_ENCLOSURE_INDEPENDENT`, about 15 s on Python 3.12. + +- **Brackets.** All four pass: native and conservative, at both grids. The 10^-70 cases decide at 360 bits and the 10^-10000 cases at 33,347 bits, without precision refinement. +- **Nesting.** For both models, the 10^-70 endpoint of https://github.com/CrocSwap/integer-mult-bounds/pull/1672 equals the 10^-70 floor of the 10^-10000 endpoint of https://github.com/CrocSwap/integer-mult-bounds/pull/1928. +- **Profile composition.** At both heads, 249 gauge44 calls and 417 extra calls with their recorded per-call profiles, plus 22,748 idle rank-48 children, sum to the global profile. Rank mass is 4,816,512 and the deficit is 73 × 66,304 − 4,816,512 = 23,680. +- **Headline κ.** The κ of https://github.com/CrocSwap/integer-mult-bounds/pull/1928 (`outer/OUTER-CLAIM.json`) lies 2.003 × 10^-10010 below the native endpoint, as its stated choice of b implies. The κ of https://github.com/CrocSwap/integer-mult-bounds/pull/1672 (`new/SPEC.json`, 47-inequality outer) lies 2.817 × 10^-6 below. +- **Controls.** All ten are rejected. At 10^-70: next grid point as endpoint, previous grid point as endpoint, one child moved from rank 1 to rank 2, m = 72, W − 1, conservative endpoint without the surcharge, native endpoint with the surcharge. At 10^-10000: the first two and the surcharge-omission control again. + +The optional `crosscheck_decimal.py` (about 4 to 5 minutes) repeats the 10^-10000 case with Python's `decimal` ln and exp at 10,060 digits. It finds all seven log values inside the enclosures and the same four signs. `decimal` rounds to nearest, so this corroborates the result but does not certify it. + +## Reproduce + +From the repository root: + +```sh +python3 scripts/research_package.py --package research/t74-k554-root-enclosure --check-only +python3.12 scripts/research_package.py --package research/t74-k554-root-enclosure +python3.12 -B research/t74-k554-root-enclosure/crosscheck_decimal.py # optional, slow +git fetch origin pull/1672/head pull/1928/head +python3 research/t74-k554-root-enclosure/extract_inputs.py --check # optional, needs the pull refs +``` + +`verify.py --write` regenerates [RESULT.json](RESULT.json); without it the run must reproduce the file byte for byte. + +## Scope + +This checks one number per model and grid, plus the arithmetic that composes the profile. The following are taken as given: + +- the global profile and the per-call provider profiles (no replay of words, owners or hosting); +- the moment model and the native, surcharge-free complex recurrence, from the review of CrocSwap/integer-mult-bounds#552 and CrocSwap/integer-mult-bounds#559; +- the outer reduction from b to κ, the fine source-prime padding and the ε → 1 transfer (see https://github.com/CrocSwap/integer-mult-bounds/pull/1797 for an audit of the CrocSwap/integer-mult-bounds#1786 lemmas on a different supplier); +- all inherited all-size/compiler, realization, hosting, precision/tape, exact-recovery, analytic and bit H1-H5 assumptions. + +It is a finite check of recorded endpoints, not a proof of any multiplication theorem. + +## Open next questions + +The structured list is in [TASK.json](TASK.json). + +1. **Outer ledger of https://github.com/CrocSwap/integer-mult-bounds/pull/1928.** Does `outer/LEDGER.json` follow from the endpoint certified here, checked by code that does not import `outer/*.py`? This package certifies b only. A first step is to re-derive the slack list from `outer/RETUNED-SLACKS.md` and the CrocSwap/integer-mult-bounds#1673 note and compare each slack exactly. Nothing blocks it. +2. **Profile against the emitted program.** Does the global profile equal the one emitted by the T74 hosted template and owner map? The seed78 emitted-ledger rebuild could be adapted to the two-provider layout (249 + 417 calls). The PR's template and owner archives are reproduced externally, so a maintainer replay capsule would make this cheap. + +## Credit + +Supplier construction: mdumitrean (https://github.com/CrocSwap/integer-mult-bounds/pull/1625, pivot-566 kernel), Jeremy Kothe (https://github.com/CrocSwap/integer-mult-bounds/pull/1672 and the refinement chain to https://github.com/CrocSwap/integer-mult-bounds/pull/1928), Rohan Arun (https://github.com/CrocSwap/integer-mult-bounds/pull/1319, T74 fill) and the lineage credited in those PRs. Outer: Vlado Vojdanovski (https://github.com/CrocSwap/integer-mult-bounds/pull/1673) and chafreaky (https://github.com/CrocSwap/integer-mult-bounds/pull/1786). The moment definitions are from the review of CrocSwap/integer-mult-bounds#552 and CrocSwap/integer-mult-bounds#559 and `notes/three-stage-cover-assembly.tex`. The audit pattern follows Sagar Thakrar's frontier1094-emitted-ledger-seed78 and the selected-suppliers-de-diagnostic and pr1407-complex-moment-audit-seed39 packages. + +Prepared by Aaron Wang, with help from opencode. New material is Apache-2.0. diff --git a/research/fine-prime-slack10030/reference1982/SOURCES.json b/research/fine-prime-slack10030/reference1982/SOURCES.json new file mode 100644 index 0000000000..a9a8b3ccd7 --- /dev/null +++ b/research/fine-prime-slack10030/reference1982/SOURCES.json @@ -0,0 +1,30 @@ +{ + "schema_version": 1, + "base_commit": "ae95f60feec79897b153dba6459bb3f9fd4d7b8e", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1", + "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075" + }, + { + "path": "research/native-complex-moment552/PROOF.md", + "usage": "provenance", + "git_blob": "9adf304048b62c6db9250a611a8d4b0b60ed8276", + "sha256": "d5d498edc56fdef8c5798af7f5ec66948bd2f66c553b9efe366cdaab01bd3453" + }, + { + "path": "notes/three-stage-cover-assembly.tex", + "usage": "provenance", + "git_blob": "983ffb6ac8fb9117360cd0797c00c05dfa071c9d", + "sha256": "ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d" + } + ] +} diff --git a/research/fine-prime-slack10030/reference1982/verify.py b/research/fine-prime-slack10030/reference1982/verify.py new file mode 100644 index 0000000000..55481742f6 --- /dev/null +++ b/research/fine-prime-slack10030/reference1982/verify.py @@ -0,0 +1,320 @@ +#!/usr/bin/env python3 +"""Independent exact enclosure of the pivot-566+554 T74 complex moment root. + +For a profile H, dimension m and live stock W, the native complex moment is + M(x) = sum_r H[r] (r/m)^(1-x) / W = sum_r (r H[r] / (m W)) * exp(x ln(m/r)) +(research/native-complex-moment552/PROOF.md). The conservative model adds the +inherited fallback 32 m^2 N / 10^16 children of rank one, N = sum_r H[r] +(notes/three-stage-cover-assembly.tex), i.e. 32 m N exp(x ln m) / (10^16 W). +An endpoint e on a 10^-d grid is certified when M(e) < 1 < M(e + 10^-d). + +Method, chosen to share no algorithm with the authors' engines (Mercator series +and binary range reduction with atanh((x-1)/(x+1))) or with earlier audits: + ln 2, ln 3, ln 5 are fixed integer combinations of A = ln(16/15), + B = ln(25/24), C = ln(81/80); ln 73 = ln 72 + ln(73/72); each ln(p/q) with + p - q = 1 is 2 atanh(1/(p+q)). exp uses argument halving, a Taylor + polynomial and repeated squaring. Every quantity is an integer multiple of + 2^-bits rounded outward, and the final comparisons are exact integer + comparisons. Inconclusive signs fail closed. + +Standard library only; imports and executes nothing from the repository or +from either source package. Aaron Wang, with help from opencode. Apache-2.0. +""" +import argparse +import hashlib +import json +import math +import sys +import time +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +sys.set_int_max_str_digits(0) # the PR1928 endpoints have about 10,000 digits +INPUTS_SHA256 = '609c486efb1fe1e03ff2c84ba11085b231b9372e81fb2650bda821ce84e6e1ae' + +# ln(p/q) = 2 atanh(1/(p+q)) for these unit-gap ratios; exponent vectors over (2, 3, 5). +RATIOS = {'A': ((16, 15), (4, -1, -1)), 'B': ((25, 24), (-3, -1, 2)), 'C': ((81, 80), (-4, 4, -1))} +# ln p = sum coefficient * ratio log, for p = 2, 3, 5. +PRIME_LOGS = {2: (7, 5, 3), 3: (11, 8, 5), 5: (16, 12, 7)} + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def cdiv(a, b): + return -((-a) // b) + + +def check_log_identities(): + """Exact check that PRIME_LOGS inverts the exponent vectors of RATIOS.""" + for i, (p, coeff) in enumerate(PRIME_LOGS.items()): + vec = [sum(c * RATIOS[k][1][j] for c, k in zip(coeff, 'ABC')) for j in range(3)] + require(vec == [int(i == j) for j in range(3)], 'log identity for %d' % p) + for (num, den), vec in RATIOS.values(): + require(num - den == 1 and num * 2 ** max(0, -vec[0]) * 3 ** max(0, -vec[1]) * 5 ** max(0, -vec[2]) + == den * 2 ** max(0, vec[0]) * 3 ** max(0, vec[1]) * 5 ** max(0, vec[2]), 'ratio factorization') + + +def atanh_inv(k, bits): + """Integer interval [lo, hi] containing 2^bits * atanh(1/k), k >= 2.""" + one, k2 = 1 << bits, k * k + terms = int(bits / (2 * math.log2(k))) + 2 + plo, phi = one // k, cdiv(one, k) + lo = hi = 0 + for j in range(terms): + lo += plo // (2 * j + 1) + hi += cdiv(phi, 2 * j + 1) + plo, phi = plo // k2, cdiv(phi, k2) + # remaining terms: sum_{j>=terms} k^-(2j+1)/(2j+1) <= k^-(2 terms+1) * k^2/((2 terms+1)(k^2-1)); phi bounds 2^bits k^-(2 terms+1) + hi += cdiv(phi * k2, (2 * terms + 1) * (k2 - 1)) + return lo, hi + + +def combine(parts, coeffs): + lo = sum(c * (p[0] if c > 0 else p[1]) for p, c in zip(parts, coeffs)) + hi = sum(c * (p[1] if c > 0 else p[0]) for p, c in zip(parts, coeffs)) + return lo, hi + + +def factor235(n): + e = [] + for p in (2, 3, 5): + k = 0 + while n % p == 0: + n //= p + k += 1 + e.append(k) + require(n == 1, 'rank is not 5-smooth') + return e + + +def log_table(m, ranks, bits): + """Integer intervals for 2^bits ln(m/r); requires m = 73 (so m - 1 = 72 is 5-smooth).""" + require(m == 73, 'this enclosure is written for m = 73') + base = [tuple(2 * v for v in atanh_inv(num + den, bits)) for (num, den), _ in RATIOS.values()] + d73 = tuple(2 * v for v in atanh_inv(73 + 72, bits)) + out = {} + for r in ranks: + require(0 < r < m, 'child rank range') + e = [a - b for a, b in zip(factor235(72), factor235(r))] # 72/r over (2, 3, 5) + coeff = [sum(e[i] * PRIME_LOGS[p][j] for i, p in enumerate((2, 3, 5))) for j in range(3)] + lo, hi = combine(base, coeff) + out[r] = (lo + d73[0], hi + d73[1]) + return out + + +def exp_interval(ylo, yhi, bits): + """Integer interval containing 2^bits exp(y) for 2^bits y in [ylo, yhi], 0 <= y < 1/2.""" + one = 1 << bits + require(0 <= ylo <= yhi < one // 2, 'exp range') + s = int(math.isqrt(bits)) + 1 + guard = s + 32 + w = bits + guard + xlo, xhi = (ylo << guard) >> s, cdiv(yhi << guard, 1 << s) + W1 = 1 << w + slo = shi = tlo = thi = W1 + n = 0 + while True: + n += 1 + tlo = ((tlo * xlo) >> w) // n + thi = cdiv(cdiv(thi * xhi, W1), n) + slo += tlo + shi += thi + if thi <= 1: + break + shi += thi + 1 # tail after term n is at most term n since x/(n+1) <= 1/2 + for _ in range(s): + slo = (slo * slo) >> w + shi = cdiv(shi * shi, W1) + return slo >> guard, cdiv(shi, 1 << guard) + + +def scaled_product(x, lohi): + """Interval of 2^bits * x * L for exact x > 0 and L given by an integer interval.""" + return (x.numerator * lohi[0]) // x.denominator, cdiv(x.numerator * lohi[1], x.denominator) + + +def side(src, x, surcharge, bits, m=None, profile=None, live=None): + """-1 if M(x) < 1, +1 if M(x) > 1, 0 if the enclosure at this precision cannot decide.""" + m = m or 73 + profile = profile or {int(r): int(n) for r, n in src['global_profile'].items()} + live = live or int(src['live']) + logs = log_table(m, tuple(sorted(set(profile) | {1})), bits) + lo_sum = hi_sum = 0 + for r, n in profile.items(): + if r == m: + elo = ehi = 1 << bits + else: + elo, ehi = exp_interval(*scaled_product(x, logs[r]), bits) + lo_sum += r * n * elo + hi_sum += r * n * ehi + target = m * live << bits + if surcharge: + N = sum(profile.values()) + elo, ehi = exp_interval(*scaled_product(x, logs[1]), bits) + lo_sum, hi_sum, target = (10 ** 16 * lo_sum + 32 * m * m * N * elo, + 10 ** 16 * hi_sum + 32 * m * m * N * ehi, 10 ** 16 * target) + if hi_sum < target: + return -1 + if lo_sum > target: + return 1 + return 0 + + +def default_bits(digits): + return int(digits * math.log2(10)) + 128 + + +def bracket(src, surcharge, endpoint=None, bits=None, **model): + d = int(src['grid_digits']) + grid = Q(1, 10 ** d) + e = Q(endpoint if endpoint is not None else src['conservative_complex_lower' if surcharge else 'complex_lower']) + bits = bits or default_bits(d) + at, nxt = side(src, e, surcharge, bits, **model), side(src, e + grid, surcharge, bits, **model) + for _ in range(2): # refine only an undecided sign; never accept an undecided one + if at and nxt: + break + bits *= 2 + at, nxt = side(src, e, surcharge, bits, **model), side(src, e + grid, surcharge, bits, **model) + on_grid = (e * 10 ** d).denominator == 1 + return {'on_grid': on_grid, 'endpoint_side': at, 'next_side': nxt, 'bits': bits, + 'pass': on_grid and at == -1 and nxt == 1} + + +def ledger(src): + m, live = 73, int(src['live']) + total = {} + for p, cnt in src['provider_counts'].items(): + for r, n in src['provider_profiles'][p].items(): + total[int(r)] = total.get(int(r), 0) + int(cnt) * int(n) + for r, n in src['idle_remainder_profile'].items(): + total[int(r)] = total.get(int(r), 0) + int(n) + glob = {int(r): int(n) for r, n in src['global_profile'].items()} + require(total == glob, 'provider profiles and idle remainder do not sum to the global profile') + mass = sum(r * n for r, n in glob.items()) + require(mass == int(src['rank_mass']), 'rank mass') + require(max(glob) < m, 'child rank range') + return dict(calls=sum(int(c) for c in src['provider_counts'].values()), children=sum(glob.values()), + rank_mass=mass, deficit=m * live - mass) + + +def controls(src, names=None): + """Each semantic mutation must make the bracket fail; True means rejected.""" + d = int(src['grid_digits']) + g = Q(1, 10 ** d) + nat, con = Q(src['complex_lower']), Q(src['conservative_complex_lower']) + prof = {int(r): int(n) for r, n in src['global_profile'].items()} + moved = {**prof, 1: prof[1] - 1, 2: prof[2] + 1} + cases = { + 'next_grid_as_endpoint': lambda: bracket(src, False, endpoint=nat + g), + 'previous_grid_as_endpoint': lambda: bracket(src, False, endpoint=nat - g), + 'one_child_rank1_to_rank2': lambda: bracket(src, False, profile=moved), + 'dimension_72': lambda: _m72(src), + 'live_minus_one': lambda: bracket(src, False, live=int(src['live']) - 1), + 'conservative_endpoint_without_surcharge': lambda: bracket(src, False, endpoint=con), + 'native_endpoint_with_surcharge': lambda: bracket(src, True, endpoint=nat), + } + out = {} + for name, run in cases.items(): + if names is None or name in names: + out[name] = not run()['pass'] + return out + + +def _m72(src): + """m = 72 cannot use the m = 73 log table; evaluate it with ln(72/r) = ln(73/r) - ln(73/72).""" + d = int(src['grid_digits']) + bits = default_bits(d) + e, g = Q(src['complex_lower']), Q(1, 10 ** d) + prof = {int(r): int(n) for r, n in src['global_profile'].items()} + logs = log_table(73, tuple(sorted(set(prof) | {1})), bits) + d73 = tuple(2 * v for v in atanh_inv(145, bits)) + + def sgn(x): + lo_sum = hi_sum = 0 + for r, n in prof.items(): + l = (logs[r][0] - d73[1], logs[r][1] - d73[0]) + elo, ehi = exp_interval(*scaled_product(x, l), bits) + lo_sum += r * n * elo + hi_sum += r * n * ehi + t = 72 * int(src['live']) << bits + return -1 if hi_sum < t else (1 if lo_sum > t else 0) + return {'pass': sgn(e) == -1 and sgn(e + g) == 1} + + +def load_inputs(): + return json.loads((HERE / 'INPUTS.json').read_text(encoding='utf-8')) + + +def check_inputs_pin(): + require(hashlib.sha256((HERE / 'INPUTS.json').read_bytes()).hexdigest() == INPUTS_SHA256, 'INPUTS.json pin') + + +def run(): + check_inputs_pin() + check_log_identities() + inputs = load_inputs() + coarse, fine = inputs['sources']['pr1672'], inputs['sources']['pr1928'] + result = dict(status=None, inputs_sha256=INPUTS_SHA256, m=inputs['m'], ledgers={}, brackets={}, nesting={}, controls={}) + for key, src in inputs['sources'].items(): + result['ledgers'][key] = ledger(src) + for model, surcharge in (('native', False), ('conservative', True)): + b = bracket(src, surcharge) + result['brackets']['%s/%s' % (key, model)] = b + for model, field in (('native', 'complex_lower'), ('conservative', 'conservative_complex_lower')): + e70, e10k = Q(coarse[field]), Q(fine[field]) + floor70 = Q((e10k * 10 ** 70).__floor__(), 10 ** 70) + result['nesting'][model] = dict(coarse_equals_floor_of_fine=(floor70 == e70)) + result['controls']['pr1672'] = controls(coarse) + result['controls']['pr1928'] = controls(fine, ('next_grid_as_endpoint', 'previous_grid_as_endpoint', + 'conservative_endpoint_without_surcharge')) + result['headline_kappa_below_native_endpoint'] = { + key: dict(below=Q(src['headline_kappa']) < Q(src['complex_lower']), + endpoint_minus_kappa=_sci(Q(src['complex_lower']) - Q(src['headline_kappa']))) + for key, src in inputs['sources'].items()} + result['scope'] = ('Native and conservative complex moment brackets and the profile composition only. The outer ' + 'reduction that turns the endpoint into each headline kappa is not checked here.') + ok = (all(b['pass'] for b in result['brackets'].values()) and all(n['coarse_equals_floor_of_fine'] for n in result['nesting'].values()) + and all(all(c.values()) for c in result['controls'].values()) + and all(h['below'] for h in result['headline_kappa_below_native_endpoint'].values())) + require(ok, 'enclosure failed: ' + json.dumps(result, default=str)[:2000]) + result['status'] = 'PASS_T74_K554_ROOT_ENCLOSURE_INDEPENDENT' + return result + + +def _sci(x): + sign = '-' if x < 0 else '' + x = abs(x) + if x == 0: + return '0' + e = math.floor(math.log10(x.numerator) - math.log10(x.denominator)) + mant = x / Q(10) ** e + while mant >= 10: + mant, e = mant / 10, e + 1 + while mant < 1: + mant, e = mant * 10, e - 1 + return '%s%se%d' % (sign, str(Q((mant * 10 ** 9).__floor__(), 10 ** 9).__float__()), e) + + +def main(): + ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument('--write', action='store_true', help='rewrite RESULT.json instead of comparing with it') + a = ap.parse_args() + t0 = time.perf_counter() + result = run() + text = json.dumps(result, indent=1, sort_keys=True) + '\n' + path = HERE / 'RESULT.json' + if a.write: + path.write_text(text, encoding='utf-8', newline='\n') + else: + require(path.read_text(encoding='utf-8') == text, 'RESULT.json differs from this run') + n_ctl = sum(len(c) for c in result['controls'].values()) + print('%s | brackets %d | nesting %d | controls %d rejected | %.1f s' % ( + result['status'], len(result['brackets']), len(result['nesting']), n_ctl, time.perf_counter() - t0)) + + +if __name__ == '__main__': + main() diff --git a/research/fine-prime-slack10030/replay_outer.py b/research/fine-prime-slack10030/replay_outer.py new file mode 100644 index 0000000000..2e5617ba70 --- /dev/null +++ b/research/fine-prime-slack10030/replay_outer.py @@ -0,0 +1,27 @@ +# Derived from PR1800 run_outer.py; only paths and explicit CRLF transport handling differ. +"""Regenerates the two ledger artifacts in a temporary copy (the package stays immutable), compares them with the committed ones and +replays PR1673's supplier-independent evidence. Usage: run_outer.py TMPDIR""" +import json, shutil, subprocess, sys +from pathlib import Path +P = Path(sys.argv[1]).resolve() +tmp = Path(sys.argv[2]); (tmp / 'new').mkdir(parents=True) +shutil.copytree(P / 'outer', tmp / 'outer', ignore=shutil.ignore_patterns('__pycache__')) +shutil.copy2(P / 'new/SPEC.json', tmp / 'new/SPEC.json'); shutil.copy2(P / 'CLAIM.json', tmp / 'CLAIM.json') +for art in ('LEDGER.json', 'INDEPENDENT.json'): + (tmp / 'outer' / art).unlink() +for script in ('check_ledger.py', 'independent_check.py'): + subprocess.run([sys.executable, '-B', str(tmp / 'outer' / script)], check=True, stdout=subprocess.DEVNULL) +for art in ('LEDGER.json', 'INDEPENDENT.json'): + # Committed PR1800 artifacts use CRLF; fresh Python output uses LF. + # Normalize only CRLF bytes, preserving every other byte and every JSON value. + generated=(tmp / 'outer' / art).read_bytes(); committed=(P / 'outer' / art).read_bytes() + assert json.loads(generated)==json.loads(committed), art + if generated.replace(b'\r\n',b'\n') != committed.replace(b'\r\n',b'\n'): + raise SystemExit('regenerated artifact differs from committed: ' + art) +subprocess.run([sys.executable, '-B', str(P / 'outer/sched_test.py')], check=True) +subprocess.run([sys.executable, '-B', str(P / 'outer/sched_review.py')], check=True, stdout=subprocess.DEVNULL) +subprocess.run([sys.executable, '-B', str(P / 'outer/struct_check.py')], check=True, stdout=subprocess.DEVNULL) +subprocess.run([sys.executable, '-B', str(P / 'outer/check_gaugefree.py')], check=True, stdout=subprocess.DEVNULL) +subprocess.run([sys.executable, '-B', str(P / 'outer/check_fine_padding.py'), '--out', str(tmp / 'fine-padding.json')], check=True, stdout=subprocess.DEVNULL) +subprocess.run([sys.executable, '-B', str(P / 'outer/replay_evidence.py')], check=True) +print('PASS_OUTER') diff --git a/research/fine-prime-slack10030/verify.py b/research/fine-prime-slack10030/verify.py new file mode 100644 index 0000000000..07a7fea353 --- /dev/null +++ b/research/fine-prime-slack10030/verify.py @@ -0,0 +1,68 @@ +"""Source-bound PR1800 composition replay; assertions must be enabled. + +Fetches the exact immutable dependency when --dependency is omitted. All downloads, +replay outputs and dependency copies stay under --work. No predecessor is edited. +""" +import argparse, concurrent.futures, hashlib, json, os, shutil, subprocess, sys, time, urllib.request +from pathlib import Path +from fractions import Fraction as Q +P=Path(__file__).resolve().parent + +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +def read(p):return json.loads(p.read_text()) +def main(): + if not __debug__:raise RuntimeError('Assertions required') + ap=argparse.ArgumentParser();ap.add_argument('--work',type=Path,required=True);ap.add_argument('--dependency',type=Path);ap.add_argument('--arithmetic-only',action='store_true');a=ap.parse_args() + work=a.work.resolve();assert not work.exists() and not work.is_relative_to(P);work.mkdir(parents=True) + pins=read(P/'MANIFEST.json') + for n,h in pins.items():assert sha(P/n)==h,n + info=read(P/'DEPENDENCY.json');dpins=read(P/'DEPENDENCY-MANIFEST.json');stages=[] + env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0',OPENBLAS_NUM_THREADS='1',OMP_NUM_THREADS='1',TMPDIR=str(work)) + env.pop('PYTHONOPTIMIZE',None) + def run(name,script,*args): + t=time.monotonic();log=work/(name+'.log') + with log.open('w') as out:r=subprocess.run([sys.executable,'-B',str(script),*map(str,args)],cwd=work,env=env,stdout=out,stderr=subprocess.STDOUT) + stages.append(dict(name=name,exit_code=r.returncode,seconds=time.monotonic()-t,log_sha256=sha(log)));(work/'STAGES.json').write_text(json.dumps(stages,indent=2)) + assert r.returncode==0,(name,log.read_text()[-3000:]);print('PASS',name,flush=True) + run('endpoint',P/'certify_endpoint.py',work/'ENDPOINT-REPLAY.json');run('ledger',P/'check_ledger.py',work/'arithmetic');run('balance',P/'independent_check.py',work/'arithmetic') + ledger=read(work/'arithmetic/LEDGER.json');balance=read(work/'arithmetic/INDEPENDENT.json');claim=read(P/'CLAIM.json') + row=ledger['rows']['struct_boundary_radix_union'];k=Q(row['kappa']['rational']) + assert k==Q(balance['rows']['struct_boundary_radix_union']['kappa'])==Q(claim['kappa']) + assert k>Q(read(P/'inputs/LEADER1839.json')['kappa_rational']) + assert k>Q(read(P/'inputs/LEADER1875.json')['kappa_rational']) + assert k>Q(read(P/'inputs/LEADER1928.json')['kappa_rational']) + assert len(row['strict_checks'])==57 and all(Q(x['rational'])>0 for x in row['strict_checks'].values()) + assert len(ledger['rejecting_controls']['struct_boundary_radix_union'])==17 + if a.arithmetic_only: + (work/'RESULT.json').write_text(json.dumps(dict(status='PASS_ARITHMETIC_ONLY',kappa=str(k),full_admission=False,stages=stages),indent=2));return + dependency=work/'dependency' + if a.dependency: + src=a.dependency.resolve() + assert sha(src/'MANIFEST.json')==info['manifest_sha256'] + for n,h in dpins.items():assert sha(src/n)==h,n + shutil.copytree(src,dependency) + else: + dependency.mkdir() + base='https://raw.githubusercontent.com/'+info['repository']+'/'+info['head']+'/'+info['package']+'/' + def fetch(n): + f=dependency/n;assert f.resolve().is_relative_to(dependency.resolve()) + raw=urllib.request.urlopen(base+n,timeout=120).read();assert hashlib.sha256(raw).hexdigest()==dpins[n],n + f.parent.mkdir(parents=True,exist_ok=True);f.write_bytes(raw) + with concurrent.futures.ThreadPoolExecutor(max_workers=6) as ex:list(ex.map(fetch,dpins)) + raw=urllib.request.urlopen(base+'MANIFEST.json').read();assert hashlib.sha256(raw).hexdigest()==info['manifest_sha256'];(dependency/'MANIFEST.json').write_bytes(raw) + for n,h in dpins.items():assert sha(dependency/n)==h,n + assert sha(P/'inputs/SOURCE-SPEC.json')==sha(dependency/'new/SPEC.json') + run('inherited-outer',P/'replay_outer.py',dependency,work/'inherited-outer') + run('supplier',dependency/'verify.py','--work',work/'supplier','--audit-shards','1') + result=read(work/'supplier/RESULT.json');asm=read(work/'supplier/strict/ASSEMBLY.json');spec=read(P/'inputs/SPEC.json');bj=read(P/'inputs/B.json') + assert result['status']=='PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION' + assert asm['status']=='PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY' and len(asm['outer'])==47 + assert Q(asm['complex_lower'])==Q(read(P/'inputs/SOURCE-SPEC.json')['expected']['complex_lower']) + assert Q(asm['complex_lower']) Date: Wed, 14 Oct 2026 12:26:30 -0400 Subject: [PATCH 2/3] Preserve exact CRLF bytes of pinned predecessor references --- .../inputs/CLAIM1800.json | 34 +- .../inputs/LEADER1839.json | 18 +- .../inputs/OUTER-CLAIM1800.json | 18 +- .../inputs/SOURCE-SPEC.json | 14600 ++++++++-------- .../reference/check_ledger.py | 434 +- .../reference/fine_mercator.py | 96 +- .../reference/independent_check.py | 102 +- 7 files changed, 7651 insertions(+), 7651 deletions(-) diff --git a/research/fine-prime-slack10030/inputs/CLAIM1800.json b/research/fine-prime-slack10030/inputs/CLAIM1800.json index ee6eeb0df2..6752dfbeca 100644 --- a/research/fine-prime-slack10030/inputs/CLAIM1800.json +++ b/research/fine-prime-slack10030/inputs/CLAIM1800.json @@ -1,17 +1,17 @@ -{ - "status": "PASS_T74_PIVOT566_KERNEL_WITH_ENDPOINT_AND_OUTER_REFINEMENT_COMPLETE_FINITE_ADMISSION", - "kappa": "1676938111022438771190100017020725032555691674761792047536039179/1000000000000000000000000000000000000000000000000000000000000000000", - "kappa_decimal": "0.001676938111022438771190100017020725032555691674761792047536039179", - "baseline_pr": 1644, - "baseline_kappa": "0.00167689666902129930775071099726796267", - "construction_improvement": false, - "outer_refinement": { - "grid_digits": 66, - "margin_digits": 76, - "bootstrap_steps": 30, - "endpoint_digits": 70 - }, - "scope": "Conditional finite construction only. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global packing claim.", - "verification": "Exact discovery using verified PR1319 owner/invoice receipts passes both moment engines and 47 outer inequalities. Full new-package finite replay and independent outer checks pending. Native providers are unchanged and will be explicitly source-bound reused.", - "gain_over_claimed_leader": "5.8464055E-59" -} +{ + "status": "PASS_T74_PIVOT566_KERNEL_WITH_ENDPOINT_AND_OUTER_REFINEMENT_COMPLETE_FINITE_ADMISSION", + "kappa": "1676938111022438771190100017020725032555691674761792047536039179/1000000000000000000000000000000000000000000000000000000000000000000", + "kappa_decimal": "0.001676938111022438771190100017020725032555691674761792047536039179", + "baseline_pr": 1644, + "baseline_kappa": "0.00167689666902129930775071099726796267", + "construction_improvement": false, + "outer_refinement": { + "grid_digits": 66, + "margin_digits": 76, + "bootstrap_steps": 30, + "endpoint_digits": 70 + }, + "scope": "Conditional finite construction only. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global packing claim.", + "verification": "Exact discovery using verified PR1319 owner/invoice receipts passes both moment engines and 47 outer inequalities. Full new-package finite replay and independent outer checks pending. Native providers are unchanged and will be explicitly source-bound reused.", + "gain_over_claimed_leader": "5.8464055E-59" +} diff --git a/research/fine-prime-slack10030/inputs/LEADER1839.json b/research/fine-prime-slack10030/inputs/LEADER1839.json index 84d422de25..008785f257 100644 --- a/research/fine-prime-slack10030/inputs/LEADER1839.json +++ b/research/fine-prime-slack10030/inputs/LEADER1839.json @@ -1,9 +1,9 @@ -{ - "kappa": "0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263049999999997996640490086748910957328658012158594", - "kappa_rational": "8398774780627722606678354969603512884991557192512901477301637600814322741301628194131524999999998998320245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", - "branch": "fine source-prime padding (PR1786, chafreaky; Trudgian's prime theorem; vendor/pr1786) with the gauge-free interiors (PR1758), the radix-distributed union schedule with per-visit tag work and the explicit Strassen boundary (tau=45/16); epsilon=1-2e-100 is a free parameter (outer/FINE-PADDING-COMPOSITION.md): kappa = epsilon q - 1e-112, 3.4e-103 below q; the structured boundary of the previous package is not used; omega_C<=9/4 not used; slack refinement and recertified endpoint: the supplier native endpoint is recertified to 1e-90 (accept at the endpoint, reject at endpoint+1e-90, repaired fine engines), 6.45e-71 above the previous 1e-70 pin, and all free slacks are 1e-100 or below", - "b": "certified complex_lower - 1e-100 (see outer/B.json)", - "outer": "PR1673 capped phase-cell fusion (Vlado Vojdanovski)", - "supplier": "PR1661 T74 pivot-566 stack plus the pivot-554 helper-donor kernel (PR1672 lineage)", - "retuned_slacks": "b = certified complex endpoint - 1e-100, q = b - 1e-100, r0=1e-100, zeta=1e-102, layout slack=1e-100, stop=1e-106, floor grid 1e-136, backoff 1e-112 (outer/RETUNED-SLACKS.md)" -} +{ + "kappa": "0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263049999999997996640490086748910957328658012158594", + "kappa_rational": "8398774780627722606678354969603512884991557192512901477301637600814322741301628194131524999999998998320245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "branch": "fine source-prime padding (PR1786, chafreaky; Trudgian's prime theorem; vendor/pr1786) with the gauge-free interiors (PR1758), the radix-distributed union schedule with per-visit tag work and the explicit Strassen boundary (tau=45/16); epsilon=1-2e-100 is a free parameter (outer/FINE-PADDING-COMPOSITION.md): kappa = epsilon q - 1e-112, 3.4e-103 below q; the structured boundary of the previous package is not used; omega_C<=9/4 not used; slack refinement and recertified endpoint: the supplier native endpoint is recertified to 1e-90 (accept at the endpoint, reject at endpoint+1e-90, repaired fine engines), 6.45e-71 above the previous 1e-70 pin, and all free slacks are 1e-100 or below", + "b": "certified complex_lower - 1e-100 (see outer/B.json)", + "outer": "PR1673 capped phase-cell fusion (Vlado Vojdanovski)", + "supplier": "PR1661 T74 pivot-566 stack plus the pivot-554 helper-donor kernel (PR1672 lineage)", + "retuned_slacks": "b = certified complex endpoint - 1e-100, q = b - 1e-100, r0=1e-100, zeta=1e-102, layout slack=1e-100, stop=1e-106, floor grid 1e-136, backoff 1e-112 (outer/RETUNED-SLACKS.md)" +} diff --git a/research/fine-prime-slack10030/inputs/OUTER-CLAIM1800.json b/research/fine-prime-slack10030/inputs/OUTER-CLAIM1800.json index d8ca9c20fe..d1b384e263 100644 --- a/research/fine-prime-slack10030/inputs/OUTER-CLAIM1800.json +++ b/research/fine-prime-slack10030/inputs/OUTER-CLAIM1800.json @@ -1,9 +1,9 @@ -{ - "kappa": "0.0016797549561255445213356709939207025769983114385025802954603273198268490086748910957328658012158594", - "kappa_rational": "8398774780627722606678354969603512884991557192512901477301636599134245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", - "branch": "fine source-prime padding (PR1786, chafreaky; Trudgian's prime theorem; vendor/pr1786) with the gauge-free interiors (PR1758), the radix-distributed union schedule with per-visit tag work and the explicit Strassen boundary (tau=45/16); epsilon=1-2e-64 is a free parameter (outer/FINE-PADDING-COMPOSITION.md): kappa = epsilon q - 1e-76, 3.4e-67 below q; the structured boundary of the previous package is not used; omega_C<=9/4 not used", - "b": "certified complex_lower - 1e-64 (see outer/B.json)", - "outer": "PR1673 capped phase-cell fusion (Vlado Vojdanovski)", - "supplier": "PR1661 T74 pivot-566 stack plus the pivot-554 helper-donor kernel (PR1672 lineage)", - "retuned_slacks": "b = certified complex endpoint - 1e-64, q = b - 1e-64, r0=1e-64, zeta=1e-66, layout slack=1e-64, stop=1e-70, floor grid 1e-100, backoff 1e-76 (outer/RETUNED-SLACKS.md)" -} +{ + "kappa": "0.0016797549561255445213356709939207025769983114385025802954603273198268490086748910957328658012158594", + "kappa_rational": "8398774780627722606678354969603512884991557192512901477301636599134245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "branch": "fine source-prime padding (PR1786, chafreaky; Trudgian's prime theorem; vendor/pr1786) with the gauge-free interiors (PR1758), the radix-distributed union schedule with per-visit tag work and the explicit Strassen boundary (tau=45/16); epsilon=1-2e-64 is a free parameter (outer/FINE-PADDING-COMPOSITION.md): kappa = epsilon q - 1e-76, 3.4e-67 below q; the structured boundary of the previous package is not used; omega_C<=9/4 not used", + "b": "certified complex_lower - 1e-64 (see outer/B.json)", + "outer": "PR1673 capped phase-cell fusion (Vlado Vojdanovski)", + "supplier": "PR1661 T74 pivot-566 stack plus the pivot-554 helper-donor kernel (PR1672 lineage)", + "retuned_slacks": "b = certified complex endpoint - 1e-64, q = b - 1e-64, r0=1e-64, zeta=1e-66, layout slack=1e-64, stop=1e-70, floor grid 1e-100, backoff 1e-76 (outer/RETUNED-SLACKS.md)" +} diff --git a/research/fine-prime-slack10030/inputs/SOURCE-SPEC.json b/research/fine-prime-slack10030/inputs/SOURCE-SPEC.json index 2989f666c7..bcff1fe102 100644 --- a/research/fine-prime-slack10030/inputs/SOURCE-SPEC.json +++ b/research/fine-prime-slack10030/inputs/SOURCE-SPEC.json @@ -1,7300 +1,7300 @@ -{ - "call_order": [ - [ - 0, - 0 - ], - [ - 0, - 37 - ], - [ - 0, - 1 - ], - [ - 0, - 38 - ], - [ - 0, - 2 - ], - [ - 0, - 39 - ], - [ - 0, - 3 - ], - [ - 0, - 40 - ], - [ - 0, - 4 - ], - [ - 0, - 41 - ], - [ - 1, - 0 - ], - [ - 1, - 37 - ], - [ - 0, - 5 - ], - [ - 0, - 42 - 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"bootstrap_steps": 30, + "endpoint_digits": 70 + } +} diff --git a/research/fine-prime-slack10030/reference/check_ledger.py b/research/fine-prime-slack10030/reference/check_ledger.py index 568d5978d7..590a8395cb 100644 --- a/research/fine-prime-slack10030/reference/check_ledger.py +++ b/research/fine-prime-slack10030/reference/check_ledger.py @@ -1,217 +1,217 @@ -#!/usr/bin/env python3 -"""Exact ledger for fine-prime padding (PR1786, chafreaky / Chafik Boukhalfa, with Tim Trudgian's prime theorem) at the free point epsilon = 1 - 2e-64, explicit Strassen boundary. - -Adapted from PR1786's ledger, itself adapted from PR1731's cost ledger, credited to Jeremy Kothe et al. and -Vlado Vojdanovski (PR1673); uses PR1758's gauge-free chirp and per-visit tag -accounting. New source-prime, coefficient-setup and halo lemmas are in -FINE-PRIME-PADDING.md. Finite arithmetic does not prove the all-size theorem. -""" -from fractions import Fraction as Q -from decimal import Decimal, localcontext -from pathlib import Path -from math import factorial -import hashlib, json - -if not __debug__: raise RuntimeError('Assertions must be enabled') -HERE=Path(__file__).resolve().parent -WORK=HERE.parent -SPEC=WORK/'new/SPEC.json' -CLAIM=WORK/'CLAIM.json' -BJ=json.loads((HERE/'B.json').read_text()) -spec=json.loads(SPEC.read_text()) -# Free strict slacks of the PR1673 proof (retuned in this package, see RETUNED-SLACKS.md); every one only needs to be > 0. -R0=Q(1,10**64); ZETA=Q(1,10**66); SLACK=Q(1,10**64); GAP=Q(1,10**64); STOP=Q(1,10**70) -FLOOR=10**100; BACKOFF=Q(1,10**76); B_GAP=Q(1,10**64) -# Fine prime padding: theta is between 1/(4p^2) and 1/(2p^2-1). -# Online chirp guard beta+2*xi-2<1; coefficient setup uses O(p^2 log p) bits. -# epsilon = 1 - DELTA_E is a FREE parameter (outer/FINE-PADDING-COMPOSITION.md sec. 2): every row is strictly satisfied for every DELTA_E > r0 = 1e-64; beta = 1 - 3 DELTA_E lies in the admissible window -# [1 - DELTA_E (1 + 1/q), 1 - 2 DELTA_E). DELTA_E = 2e-64 is the smallest round value above r0. -DELTA_E=Q(2,10**64) -EPS=1-DELTA_E -BETA=1-3*DELTA_E -THETA_POWER=Q(2) -HALO_POWER=48 -CORE_POWER=128 -STRASSEN_TAU=Q(45,16) -KAPPA_1786=Q('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # exact kappa of chafreaky's PR1786 ledger (EXPECTED-BALANCE.json), headline 0.001679754788150048 -KAPPA_PKG5=Q('0.001677992607205282520732088774830808372222877897034109604209719298829805473412451530867883424937597') # previous package (rectangular k=2, tau_eff=2.2500351) -KAPPA_PKG4=Q('0.0016778199023144364336310551358776001013829401215770658599799349282716974076737897457922714197448847') # previous package (radix union schedule, square boundary tau=2.372864) -KAPPA_1712=Q('0.0016776417313433545642517275958639984231708545722735432722117400060454625429077941422798526440584702') # pkg of PR1712 (Le Gall tau=12/5, old union row) -KAPPA_1699=Q('0.001677641731343354564251058287063644749065568493') # exact kappa of PR1699's ledger (Chafik Boukhalfa), same supplier profile -certified_complex=Q(spec['expected']['complex_lower']) -bit=Q('0.001733427039589844234749') -# Keep short independently checkable decimals strictly inside both endpoints. -b=certified_complex-B_GAP # strictly inside the certified supplier endpoint; B.json carries the same exact value -assert b==Q(BJ['b']) -q=b-GAP -a=(q+b)/2 -online=Q(spec['expected']['kappa']) -old=Q('0.001673360105405778') -assert b=2:x/=2;k+=1 - lo,hi=unit_log(x) - return down(lo+k*ln2[0]),up(hi+k*ln2[1]) -def exp(x): - assert 0<=x<1 - N=45 - lo=sum((x**j/factorial(j) for j in range(N)),Q(0)) - hi=lo+x**N/factorial(N)/(1-x/(N+1)) - return down(lo),up(hi) -def moment(endpoint): - lo=hi=Q(0) - for r,n in profile.items(): - l,h=log(Q(m,r)); weight=Q(n*r,m*W) - lo+=weight*exp(endpoint*l)[0] - hi+=weight*exp(endpoint*h)[1] - return down(lo),up(hi) - -native=moment(b) -assert native[1]<1 -b_up=Q(BJ['b_above_endpoint']) -assert b_up>certified_complex and moment(b_up)[0]>1 # a larger test endpoint is rejected - -def ledger(kind, *, q_=q, zeta=ZETA, slack=SLACK, - old_scan=False, full_gauge=False, full_key=False, old_union=False, old_theta=False, old_linear=False, old_tag=False, - eps_=EPS, beta_=BETA, tau_eff=STRASSEN_TAU, halo_power=HALO_POWER, core_power=CORE_POWER): - r=R0; stop=STOP - # Existing explicit Strassen format, 7^16<2^45; c=3/32. - # Union: radix-distributed schedule (outer/UNION-SCHEDULE.md, new in this package): row exponent eps+1/2-xi. The boundary row binds with main; the Gaussian row has slack at this explicit point. - c=(3-tau_eff)/2 - eps=eps_; beta=beta_ - xi=eps*(1+q_)-c+slack - saving=eps*q_ - # Deliberate strict gap (BACKOFF) after decimal truncation to the FLOOR grid. - kappa=Q((saving*FLOOR).__floor__(),FLOOR)-BACKOFF - # kappa is derived, not silently asserted to equal an expected decimal. - tau=1-a; sigma=1-b - internal=tau+(1-stop)*max(sigma-tau,Q(0)) - leaf=sigma+stop*(1-sigma) - lam=1-(q_+a)/2 - key=beta+1-eps - margins={ - 'main_transform':saving, - 'global_coordinate_router':a, - 'fused_gaussian':1-eps+q_*beta, - 'group_bit_router':1-eps+a*beta, - 'group_scans':1-eps+beta, - 'boundary_algebraic_matrix':c+xi-eps, - 'sparse_union_movement':xi+Q(1,2)-eps, - 'polynomial_products':eps, - 'microbox_face_corrections':1-(eps+beta+halo_power-core_power+2), - } - if old_union:margins['old_g_factor_union_row']=1-eps-beta-Q(1,2)+xi - if old_scan:margins['old_per_axis_scan']=1-eps - if full_key:margins['unnecessary_full_key_sort']=margins['sparse_union_movement']-key - checks={ - 'actual_bit_above_effective':bit-a, - 'complex_above_effective':b-a, - 'q_positive':q_, 'complex_endpoint':b-q_, - 'q_below_effective':a-q_, 'stop_positive':stop, - 'stop_below_one':1-stop, - 'leaf_saving_above_effective':(1-stop)*b-a, - 'q_below_internal':1-internal-q_, 'q_below_leaf':1-leaf-q_, - 'lambda_above_tau':lam-tau, 'lambda_above_sigma':lam-sigma, - 'lambda_above_internal':lam-internal, - 'lambda_prime_above_lambda':1-q_-lam, - 'lambda_prime_above_leaf':1-q_-leaf, - 'epsilon_positive':eps,'epsilon_below_one':1-eps, - 'cap_above_band':xi-Q(1,2),'cap_below_cell':eps-xi, - 'group_positive':beta,'group_below_dimension':eps-beta, - 'support_router_span':1-beta, - 'group_gauge_power_slack':1-(2*xi-THETA_POWER)-r-beta, - 'actual_logarithmic_group_guard':1-(2*xi-THETA_POWER)-beta, - 'global_gamma_power_slack':1-eps-r, - 'actual_logarithmic_gamma_guard':1-eps, - 'alpha_logarithm_absorption':r, - 'group_key_fits_record':1-key, - 'membership_arithmetic_fits_record':1-beta-2*(1-eps), - 'microbox_halo_volume':core_power-halo_power-beta, - 'positive_layout_slack':slack, - 'short_record_fallback':eps-a, - 'improvement_over_online_final':kappa-online, - 'improvement_over_previous_local_final':kappa-old, - 'complex_below_one_over_32':Q(1,32)-b, - } - checks['strassen_integer_power_gap']=Q(2**tau_eff.numerator-7**tau_eff.denominator) - checks['theta_positive_polynomial_power']=THETA_POWER - checks['cap_below_phase_cell_power']=THETA_POWER-xi - checks['halo_covers_generic_inverse_radius']=Q(halo_power-43) - checks['union_tag_work_per_visit_fits_record']=1-beta - checks['union_header_fits_record']=1-beta - checks['source_axis_superpolynomial']=1-eps - checks['improvement_over_pr1786']=kappa-KAPPA_1786 - checks['improvement_over_pr1758']=kappa-Q('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') - checks['improvement_over_pr1699']=kappa-KAPPA_1699 - checks['improvement_over_pr1712']=kappa-KAPPA_1712 - checks['improvement_over_previous_package']=kappa-KAPPA_PKG4 - checks['improvement_over_pkg_k2']=kappa-KAPPA_PKG5 - if full_gauge:checks['unrecentered_group_gauge']=1-THETA_POWER-r-beta - if old_theta:checks['old_theta_chirp_guard']=1-(2*xi-eps)-r-beta - if old_linear:checks['old_linear_guard']=1-xi-r-beta - if old_tag:checks['old_union_tag_2beta']=1-2*beta - checks.update({n+'_above_kappa':v-kappa for n,v in margins.items()}) - assert margins['boundary_algebraic_matrix']==saving+slack - assert margins['sparse_union_movement']==saving+slack+(tau_eff-2)/2 - return {'kind':kind,'kappa':kappa,'epsilon':eps,'xi':xi,'beta':beta, - 'q':q_,'a':a,'r0':r,'zeta':zeta,'slack':slack, - 'margins':margins,'strict_checks':checks} - -def encode(x): - if isinstance(x,Q): - with localcontext() as c: - c.prec=140 - return {'rational':str(x),'decimal':str(Decimal(x.numerator)/Decimal(x.denominator))} - if isinstance(x,dict):return {str(k):encode(v) for k,v in x.items()} - if isinstance(x,(list,tuple)):return [encode(v) for v in x] - return x - -rows={};controls={} -for kind in ['struct_boundary_radix_union']: - row=ledger(kind) - assert all(v>0 for v in row['strict_checks'].values()) - assert min(row['margins'].values())==row['margins']['main_transform'] - rows[kind]=row - variants=[('endpoint_equality',{'q_':b}),('zero_layout_slack',{'slack':Q(0)}), - ('old_per_axis_scan',{'old_scan':True}),('full_cell_gauge',{'full_gauge':True}), - ('full_key_sort',{'full_key':True}),('old_g_factor_union_row',{'old_union':True}), - ('old_theta_chirp_guard',{'old_theta':True}),('old_linear_guard',{'old_linear':True}), - ('old_union_tag_2beta',{'old_tag':True}),('matrix_below_strassen',{'tau_eff':Q(14,5)}), - ('halo_too_short',{'halo_power':40}),('core_too_small',{'core_power':48}), - ('group_equals_dimension',{'beta_':EPS}),('epsilon_equals_one',{'eps_':Q(1)}),('epsilon_not_above_r0_slack',{'eps_':1-R0}),('beta_below_gaussian_window',{'beta_':1-700*DELTA_E}),('beta_above_membership_window',{'beta_':1-2*DELTA_E})] - controls[kind]={} - for name,kwargs in variants: - bad=ledger(kind,**kwargs) - failed={n:v for n,v in bad['strict_checks'].items() if v<=0} - assert failed,(kind,name) - controls[kind][name]=failed - assert 'old_g_factor_union_row_above_kappa' in controls[kind]['old_g_factor_union_row'] and 'unnecessary_full_key_sort_above_kappa' in controls[kind]['full_key_sort'] -out={'status':'PASS_FINE_PRIME_PADDING_EXACT_ARITHMETIC', - 'scope':'Conditional fine-prime padding composition. Fresh native admission is required by verify.py. The cited prime theorem, written gauge-free theorem and inherited all-size interfaces are not proved by this arithmetic. No independent human review is claimed.', - 'geometry_changes':{'theta_power':THETA_POWER,'halo_power':HALO_POWER,'core_power':CORE_POWER,'matrix_exponent':STRASSEN_TAU}, - 'complex_lower_short':b,'complex_lower_pinned':certified_complex, - 'native_moment':native,'profile':profile,'m':m,'W':W, - 'online_final_kappa':online,'rows':rows,'rejecting_controls':controls, - 'pr1673_kappa':Q('0.001677160151714381'),'improvement_over_pr1673':rows['struct_boundary_radix_union']['kappa']-Q('0.001677160151714381'), - 'source_sha256':{p.relative_to(WORK).as_posix():hashlib.sha256(p.read_bytes()).hexdigest() for p in [SPEC,CLAIM]}} -(HERE/'LEDGER.json').write_text(json.dumps(encode(out),indent=2)+'\n') -print(out['status']) -for name,row in rows.items(): - print(name,'FINAL KAPPA',encode(row['kappa'])['decimal'], - 'positive checks',len(row['strict_checks']), - 'gain over online',encode(row['kappa']-online)['decimal']) +#!/usr/bin/env python3 +"""Exact ledger for fine-prime padding (PR1786, chafreaky / Chafik Boukhalfa, with Tim Trudgian's prime theorem) at the free point epsilon = 1 - 2e-64, explicit Strassen boundary. + +Adapted from PR1786's ledger, itself adapted from PR1731's cost ledger, credited to Jeremy Kothe et al. and +Vlado Vojdanovski (PR1673); uses PR1758's gauge-free chirp and per-visit tag +accounting. New source-prime, coefficient-setup and halo lemmas are in +FINE-PRIME-PADDING.md. Finite arithmetic does not prove the all-size theorem. +""" +from fractions import Fraction as Q +from decimal import Decimal, localcontext +from pathlib import Path +from math import factorial +import hashlib, json + +if not __debug__: raise RuntimeError('Assertions must be enabled') +HERE=Path(__file__).resolve().parent +WORK=HERE.parent +SPEC=WORK/'new/SPEC.json' +CLAIM=WORK/'CLAIM.json' +BJ=json.loads((HERE/'B.json').read_text()) +spec=json.loads(SPEC.read_text()) +# Free strict slacks of the PR1673 proof (retuned in this package, see RETUNED-SLACKS.md); every one only needs to be > 0. +R0=Q(1,10**64); ZETA=Q(1,10**66); SLACK=Q(1,10**64); GAP=Q(1,10**64); STOP=Q(1,10**70) +FLOOR=10**100; BACKOFF=Q(1,10**76); B_GAP=Q(1,10**64) +# Fine prime padding: theta is between 1/(4p^2) and 1/(2p^2-1). +# Online chirp guard beta+2*xi-2<1; coefficient setup uses O(p^2 log p) bits. +# epsilon = 1 - DELTA_E is a FREE parameter (outer/FINE-PADDING-COMPOSITION.md sec. 2): every row is strictly satisfied for every DELTA_E > r0 = 1e-64; beta = 1 - 3 DELTA_E lies in the admissible window +# [1 - DELTA_E (1 + 1/q), 1 - 2 DELTA_E). DELTA_E = 2e-64 is the smallest round value above r0. +DELTA_E=Q(2,10**64) +EPS=1-DELTA_E +BETA=1-3*DELTA_E +THETA_POWER=Q(2) +HALO_POWER=48 +CORE_POWER=128 +STRASSEN_TAU=Q(45,16) +KAPPA_1786=Q('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # exact kappa of chafreaky's PR1786 ledger (EXPECTED-BALANCE.json), headline 0.001679754788150048 +KAPPA_PKG5=Q('0.001677992607205282520732088774830808372222877897034109604209719298829805473412451530867883424937597') # previous package (rectangular k=2, tau_eff=2.2500351) +KAPPA_PKG4=Q('0.0016778199023144364336310551358776001013829401215770658599799349282716974076737897457922714197448847') # previous package (radix union schedule, square boundary tau=2.372864) +KAPPA_1712=Q('0.0016776417313433545642517275958639984231708545722735432722117400060454625429077941422798526440584702') # pkg of PR1712 (Le Gall tau=12/5, old union row) +KAPPA_1699=Q('0.001677641731343354564251058287063644749065568493') # exact kappa of PR1699's ledger (Chafik Boukhalfa), same supplier profile +certified_complex=Q(spec['expected']['complex_lower']) +bit=Q('0.001733427039589844234749') +# Keep short independently checkable decimals strictly inside both endpoints. +b=certified_complex-B_GAP # strictly inside the certified supplier endpoint; B.json carries the same exact value +assert b==Q(BJ['b']) +q=b-GAP +a=(q+b)/2 +online=Q(spec['expected']['kappa']) +old=Q('0.001673360105405778') +assert b=2:x/=2;k+=1 + lo,hi=unit_log(x) + return down(lo+k*ln2[0]),up(hi+k*ln2[1]) +def exp(x): + assert 0<=x<1 + N=45 + lo=sum((x**j/factorial(j) for j in range(N)),Q(0)) + hi=lo+x**N/factorial(N)/(1-x/(N+1)) + return down(lo),up(hi) +def moment(endpoint): + lo=hi=Q(0) + for r,n in profile.items(): + l,h=log(Q(m,r)); weight=Q(n*r,m*W) + lo+=weight*exp(endpoint*l)[0] + hi+=weight*exp(endpoint*h)[1] + return down(lo),up(hi) + +native=moment(b) +assert native[1]<1 +b_up=Q(BJ['b_above_endpoint']) +assert b_up>certified_complex and moment(b_up)[0]>1 # a larger test endpoint is rejected + +def ledger(kind, *, q_=q, zeta=ZETA, slack=SLACK, + old_scan=False, full_gauge=False, full_key=False, old_union=False, old_theta=False, old_linear=False, old_tag=False, + eps_=EPS, beta_=BETA, tau_eff=STRASSEN_TAU, halo_power=HALO_POWER, core_power=CORE_POWER): + r=R0; stop=STOP + # Existing explicit Strassen format, 7^16<2^45; c=3/32. + # Union: radix-distributed schedule (outer/UNION-SCHEDULE.md, new in this package): row exponent eps+1/2-xi. The boundary row binds with main; the Gaussian row has slack at this explicit point. + c=(3-tau_eff)/2 + eps=eps_; beta=beta_ + xi=eps*(1+q_)-c+slack + saving=eps*q_ + # Deliberate strict gap (BACKOFF) after decimal truncation to the FLOOR grid. + kappa=Q((saving*FLOOR).__floor__(),FLOOR)-BACKOFF + # kappa is derived, not silently asserted to equal an expected decimal. + tau=1-a; sigma=1-b + internal=tau+(1-stop)*max(sigma-tau,Q(0)) + leaf=sigma+stop*(1-sigma) + lam=1-(q_+a)/2 + key=beta+1-eps + margins={ + 'main_transform':saving, + 'global_coordinate_router':a, + 'fused_gaussian':1-eps+q_*beta, + 'group_bit_router':1-eps+a*beta, + 'group_scans':1-eps+beta, + 'boundary_algebraic_matrix':c+xi-eps, + 'sparse_union_movement':xi+Q(1,2)-eps, + 'polynomial_products':eps, + 'microbox_face_corrections':1-(eps+beta+halo_power-core_power+2), + } + if old_union:margins['old_g_factor_union_row']=1-eps-beta-Q(1,2)+xi + if old_scan:margins['old_per_axis_scan']=1-eps + if full_key:margins['unnecessary_full_key_sort']=margins['sparse_union_movement']-key + checks={ + 'actual_bit_above_effective':bit-a, + 'complex_above_effective':b-a, + 'q_positive':q_, 'complex_endpoint':b-q_, + 'q_below_effective':a-q_, 'stop_positive':stop, + 'stop_below_one':1-stop, + 'leaf_saving_above_effective':(1-stop)*b-a, + 'q_below_internal':1-internal-q_, 'q_below_leaf':1-leaf-q_, + 'lambda_above_tau':lam-tau, 'lambda_above_sigma':lam-sigma, + 'lambda_above_internal':lam-internal, + 'lambda_prime_above_lambda':1-q_-lam, + 'lambda_prime_above_leaf':1-q_-leaf, + 'epsilon_positive':eps,'epsilon_below_one':1-eps, + 'cap_above_band':xi-Q(1,2),'cap_below_cell':eps-xi, + 'group_positive':beta,'group_below_dimension':eps-beta, + 'support_router_span':1-beta, + 'group_gauge_power_slack':1-(2*xi-THETA_POWER)-r-beta, + 'actual_logarithmic_group_guard':1-(2*xi-THETA_POWER)-beta, + 'global_gamma_power_slack':1-eps-r, + 'actual_logarithmic_gamma_guard':1-eps, + 'alpha_logarithm_absorption':r, + 'group_key_fits_record':1-key, + 'membership_arithmetic_fits_record':1-beta-2*(1-eps), + 'microbox_halo_volume':core_power-halo_power-beta, + 'positive_layout_slack':slack, + 'short_record_fallback':eps-a, + 'improvement_over_online_final':kappa-online, + 'improvement_over_previous_local_final':kappa-old, + 'complex_below_one_over_32':Q(1,32)-b, + } + checks['strassen_integer_power_gap']=Q(2**tau_eff.numerator-7**tau_eff.denominator) + checks['theta_positive_polynomial_power']=THETA_POWER + checks['cap_below_phase_cell_power']=THETA_POWER-xi + checks['halo_covers_generic_inverse_radius']=Q(halo_power-43) + checks['union_tag_work_per_visit_fits_record']=1-beta + checks['union_header_fits_record']=1-beta + checks['source_axis_superpolynomial']=1-eps + checks['improvement_over_pr1786']=kappa-KAPPA_1786 + checks['improvement_over_pr1758']=kappa-Q('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') + checks['improvement_over_pr1699']=kappa-KAPPA_1699 + checks['improvement_over_pr1712']=kappa-KAPPA_1712 + checks['improvement_over_previous_package']=kappa-KAPPA_PKG4 + checks['improvement_over_pkg_k2']=kappa-KAPPA_PKG5 + if full_gauge:checks['unrecentered_group_gauge']=1-THETA_POWER-r-beta + if old_theta:checks['old_theta_chirp_guard']=1-(2*xi-eps)-r-beta + if old_linear:checks['old_linear_guard']=1-xi-r-beta + if old_tag:checks['old_union_tag_2beta']=1-2*beta + checks.update({n+'_above_kappa':v-kappa for n,v in margins.items()}) + assert margins['boundary_algebraic_matrix']==saving+slack + assert margins['sparse_union_movement']==saving+slack+(tau_eff-2)/2 + return {'kind':kind,'kappa':kappa,'epsilon':eps,'xi':xi,'beta':beta, + 'q':q_,'a':a,'r0':r,'zeta':zeta,'slack':slack, + 'margins':margins,'strict_checks':checks} + +def encode(x): + if isinstance(x,Q): + with localcontext() as c: + c.prec=140 + return {'rational':str(x),'decimal':str(Decimal(x.numerator)/Decimal(x.denominator))} + if isinstance(x,dict):return {str(k):encode(v) for k,v in x.items()} + if isinstance(x,(list,tuple)):return [encode(v) for v in x] + return x + +rows={};controls={} +for kind in ['struct_boundary_radix_union']: + row=ledger(kind) + assert all(v>0 for v in row['strict_checks'].values()) + assert min(row['margins'].values())==row['margins']['main_transform'] + rows[kind]=row + variants=[('endpoint_equality',{'q_':b}),('zero_layout_slack',{'slack':Q(0)}), + ('old_per_axis_scan',{'old_scan':True}),('full_cell_gauge',{'full_gauge':True}), + ('full_key_sort',{'full_key':True}),('old_g_factor_union_row',{'old_union':True}), + ('old_theta_chirp_guard',{'old_theta':True}),('old_linear_guard',{'old_linear':True}), + ('old_union_tag_2beta',{'old_tag':True}),('matrix_below_strassen',{'tau_eff':Q(14,5)}), + ('halo_too_short',{'halo_power':40}),('core_too_small',{'core_power':48}), + ('group_equals_dimension',{'beta_':EPS}),('epsilon_equals_one',{'eps_':Q(1)}),('epsilon_not_above_r0_slack',{'eps_':1-R0}),('beta_below_gaussian_window',{'beta_':1-700*DELTA_E}),('beta_above_membership_window',{'beta_':1-2*DELTA_E})] + controls[kind]={} + for name,kwargs in variants: + bad=ledger(kind,**kwargs) + failed={n:v for n,v in bad['strict_checks'].items() if v<=0} + assert failed,(kind,name) + controls[kind][name]=failed + assert 'old_g_factor_union_row_above_kappa' in controls[kind]['old_g_factor_union_row'] and 'unnecessary_full_key_sort_above_kappa' in controls[kind]['full_key_sort'] +out={'status':'PASS_FINE_PRIME_PADDING_EXACT_ARITHMETIC', + 'scope':'Conditional fine-prime padding composition. Fresh native admission is required by verify.py. The cited prime theorem, written gauge-free theorem and inherited all-size interfaces are not proved by this arithmetic. No independent human review is claimed.', + 'geometry_changes':{'theta_power':THETA_POWER,'halo_power':HALO_POWER,'core_power':CORE_POWER,'matrix_exponent':STRASSEN_TAU}, + 'complex_lower_short':b,'complex_lower_pinned':certified_complex, + 'native_moment':native,'profile':profile,'m':m,'W':W, + 'online_final_kappa':online,'rows':rows,'rejecting_controls':controls, + 'pr1673_kappa':Q('0.001677160151714381'),'improvement_over_pr1673':rows['struct_boundary_radix_union']['kappa']-Q('0.001677160151714381'), + 'source_sha256':{p.relative_to(WORK).as_posix():hashlib.sha256(p.read_bytes()).hexdigest() for p in [SPEC,CLAIM]}} +(HERE/'LEDGER.json').write_text(json.dumps(encode(out),indent=2)+'\n') +print(out['status']) +for name,row in rows.items(): + print(name,'FINAL KAPPA',encode(row['kappa'])['decimal'], + 'positive checks',len(row['strict_checks']), + 'gain over online',encode(row['kappa']-online)['decimal']) diff --git a/research/fine-prime-slack10030/reference/fine_mercator.py b/research/fine-prime-slack10030/reference/fine_mercator.py index 4b0e214522..0570a37b8c 100644 --- a/research/fine-prime-slack10030/reference/fine_mercator.py +++ b/research/fine-prime-slack10030/reference/fine_mercator.py @@ -1,49 +1,49 @@ -"""Finer-constant copy of the retained Mercator moment engine (engines/moment.py): identical algorithm and enclosure logic, -DYAD 2^320 outward rounding, 320 (even) Mercator terms (tail bounded by the next term), 40 exponential terms.""" -from fractions import Fraction as F -from functools import lru_cache -DYAD = 1 << 320 +"""Finer-constant copy of the retained Mercator moment engine (engines/moment.py): identical algorithm and enclosure logic, +DYAD 2^320 outward rounding, 320 (even) Mercator terms (tail bounded by the next term), 40 exponential terms.""" +from fractions import Fraction as F +from functools import lru_cache +DYAD = 1 << 320 LOGN = 321 # the loop sums n = 1..LOGN-1 = 320 terms: an EVEN alternating partial sum lies BELOW log(1+z), as the retained engine (n = 1..224) does -EXPN = 40 -def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) -def ceil(x): return -floor(-x) -def mercator(y): - """Enclosure [s, s + next term] of log(y) for 1 <= y <= 3/2 by the alternating Mercator series in z = y-1.""" - z=y-1 - assert 0 <= z <= F(1,2) - assert (LOGN - 1) % 2 == 0, 'an even number of terms is required: an odd partial sum lies above the log' - t=z; s=F(0) - for n in range(1, LOGN): - s += (t if n & 1 else -t)/n - t *= z - return s, s+t/LOGN - -@lru_cache(None) -def logarithm(x): - assert x >= 1 - k = 0 - while x >= 2: x /= 2; k += 1 - j = int(x >= F(3, 2)) - if j: x /= F(3, 2) - a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3)) - return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f) - -def exponential(l,u): - assert 0 <= l <= u < F(1,10) - def poly(x): - s=t=F(1) - for j in range(1,EXPN): t=t*x/j; s+=t - return s,t - lo,_=poly(l);hi,last=poly(u) - return floor(lo),ceil(hi+last*u/EXPN/(1-u/(EXPN+1))) -def moment(H,m,W,a,bad=False): - lo=hi=F(0) - for r,n in H.items(): - assert 0 < r < m and n > 0 - l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u) - p=F(r*n,m*W);lo+=p*e;hi+=p*f - if bad: - l,u=logarithm(F(m));e,f=exponential(a*l,a*u) - p=F(32*m*sum(H.values()),10**16*W) - lo+=p*e;hi+=p*f - return floor(lo),ceil(hi) +EXPN = 40 +def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) +def ceil(x): return -floor(-x) +def mercator(y): + """Enclosure [s, s + next term] of log(y) for 1 <= y <= 3/2 by the alternating Mercator series in z = y-1.""" + z=y-1 + assert 0 <= z <= F(1,2) + assert (LOGN - 1) % 2 == 0, 'an even number of terms is required: an odd partial sum lies above the log' + t=z; s=F(0) + for n in range(1, LOGN): + s += (t if n & 1 else -t)/n + t *= z + return s, s+t/LOGN + +@lru_cache(None) +def logarithm(x): + assert x >= 1 + k = 0 + while x >= 2: x /= 2; k += 1 + j = int(x >= F(3, 2)) + if j: x /= F(3, 2) + a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3)) + return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f) + +def exponential(l,u): + assert 0 <= l <= u < F(1,10) + def poly(x): + s=t=F(1) + for j in range(1,EXPN): t=t*x/j; s+=t + return s,t + lo,_=poly(l);hi,last=poly(u) + return floor(lo),ceil(hi+last*u/EXPN/(1-u/(EXPN+1))) +def moment(H,m,W,a,bad=False): + lo=hi=F(0) + for r,n in H.items(): + assert 0 < r < m and n > 0 + l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u) + p=F(r*n,m*W);lo+=p*e;hi+=p*f + if bad: + l,u=logarithm(F(m));e,f=exponential(a*l,a*u) + p=F(32*m*sum(H.values()),10**16*W) + lo+=p*e;hi+=p*f + return floor(lo),ceil(hi) diff --git a/research/fine-prime-slack10030/reference/independent_check.py b/research/fine-prime-slack10030/reference/independent_check.py index 402a320cc3..7542b25073 100644 --- a/research/fine-prime-slack10030/reference/independent_check.py +++ b/research/fine-prime-slack10030/reference/independent_check.py @@ -1,51 +1,51 @@ -"""Independent balance-equation check (PR1673, adapted: this package's supplier b and SPEC), not an execution of the ledger in check_ledger.py.""" -from fractions import Fraction as F -from pathlib import Path -from decimal import Decimal,localcontext -import json,hashlib -D=Path(__file__).resolve().parent;W=D.parent -src=W/'new/SPEC.json' -BJ=json.loads((D/'B.json').read_text()) -spec=json.loads(src.read_text());pinned=F(spec['expected']['complex_lower']) -b=F(BJ['b']);q=b-F(1,10**64);eff=(q+b)/2;actual_bit=F('0.001733427039589844234749') -r=F(1,10**64);z=F(1,10**66);s=F(1,10**64) -assert 0eff -rows={} -# FINE-PRIME PADDING (outer/FINE-PADDING-COMPOSITION.md): explicit point epsilon=1-delta, beta=1-3 delta, delta=2e-64, Strassen boundary tau=45/16 (7^16<2^45), c=3/32, -# theta in (1/(4p^2),1/(2p^2-1)], chirp guard beta+2xi-2<1, halo power 48, core power 128. Derived here WITHOUT the ledger code; the structured boundary is not used. -delta=F(2,10**64);E=1-delta;B=1-3*delta -assert 7**16<2**45;tau=F(45,16);c=(3-tau)/2;assert c==F(3,32) -nu=2;halo=48;core=128 -X=E+E*q+s-c # boundary saving c+X-E = E q + s -assert c+X-E==E*q+s -# the Gaussian row has slack: 1-E+qB-Eq = delta(1-2q) -assert 1-E+q*B-E*q==delta*(1-2*q)>0 -# admissible beta window for this epsilon: Gaussian row needs beta >= 1-delta(1+1/q); membership needs beta < 1-2 delta -assert 1-delta*(1+1/q)<=B<1-2*delta -assert F(1,2)z>0 and 1-E-r>0 and core-halo-B>0 and halo>43 -assert 1-B>0 and 1-B-2*(1-E)==delta>0 -costs={'transform':1-E*q,'global_router':1-eff,'gaussian':E-q*B,'group_router':E-eff*B,'group_scans':E-B,'boundary':E-X+(tau-1)/2,'sparse_union':E+F(1,2)-X,'polynomials':1-E,'microfaces':E+B+halo-core+2} -K=F((E*q*10**100).__floor__(),10**100)-F(1,10**76) -assert max(costs.values())==costs['transform'] and all(v<1-K for v in costs.values()) -# earlier packages' guards fail at this point (they are rejecting controls in the ledger): linear guard 1-X-r-B<0, old theta chirp guard 1-(2X-E)-r-B<0, 2B<1 test fails -assert 1-X-r-B<0 and 1-(2*X-E)-r-B<0 and 1-2*B<0 -assert K>F('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # PR1786 exact kappa -assert K>F('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') # PR1758 -assert K r0 (beta = 1-3 delta); only kappa moves, kappa = (1-delta) q - O(1e-76) -sweep=[] -for dd in [F(1,10**7),F(1,10**12),F(1,10**30),F(1,10**60),F(2,10**64),F(11,10**65)]: - Ed=1-dd;Bd=1-3*dd;Xd=Ed+Ed*q+s-c - assert 1-Ed-r>0 and 1-dd*(1+1/q)<=Bd<1-2*dd and 1-Ed+q*Bd-Ed*q>0 and Ed-Bd>0 and 1-Bd-2*(1-Ed)>0 - assert F(1,2)0 and core-halo-Bd>0 - assert 1-Ed+eff*Bd>Ed*q and eff>Ed*q and 1-Ed+Bd>Ed*q and Ed>Ed*q and 1-(Ed+Bd+halo-core+2)>Ed*q - sweep.append((str(dd),str(float(q-Ed*q)))) -assert 1-F(1,10**64)<=1-r # delta=r0 itself is rejected by 1-eps-r0>0 -assert not (1-(1-r)-r>0) -rows['struct_boundary_radix_union']={'epsilon':str(E),'cap':str(X),'beta':str(B),'kappa':str(K),'margin_above_kappa':str(E*q-K),'checked_cost_powers':len(costs),'gap_to_q':str(q-K),'epsilon_free_sweep_delta_gap_to_q':sweep} -report={'status':'PASS_INDEPENDENT_BALANCE_DERIVATION','source_sha256':hashlib.sha256(src.read_bytes()).hexdigest(),'b':str(b),'rows':rows,'scope':'Independent balance derivation and margin comparisons for this package\'s supplier endpoint; the supplier native admission is bound by verify_release.py; inherited all-size assumptions remain.'} -(D/'INDEPENDENT.json').write_text(json.dumps(report,indent=2)+'\n') -print(json.dumps(report,indent=2)) +"""Independent balance-equation check (PR1673, adapted: this package's supplier b and SPEC), not an execution of the ledger in check_ledger.py.""" +from fractions import Fraction as F +from pathlib import Path +from decimal import Decimal,localcontext +import json,hashlib +D=Path(__file__).resolve().parent;W=D.parent +src=W/'new/SPEC.json' +BJ=json.loads((D/'B.json').read_text()) +spec=json.loads(src.read_text());pinned=F(spec['expected']['complex_lower']) +b=F(BJ['b']);q=b-F(1,10**64);eff=(q+b)/2;actual_bit=F('0.001733427039589844234749') +r=F(1,10**64);z=F(1,10**66);s=F(1,10**64) +assert 0eff +rows={} +# FINE-PRIME PADDING (outer/FINE-PADDING-COMPOSITION.md): explicit point epsilon=1-delta, beta=1-3 delta, delta=2e-64, Strassen boundary tau=45/16 (7^16<2^45), c=3/32, +# theta in (1/(4p^2),1/(2p^2-1)], chirp guard beta+2xi-2<1, halo power 48, core power 128. Derived here WITHOUT the ledger code; the structured boundary is not used. +delta=F(2,10**64);E=1-delta;B=1-3*delta +assert 7**16<2**45;tau=F(45,16);c=(3-tau)/2;assert c==F(3,32) +nu=2;halo=48;core=128 +X=E+E*q+s-c # boundary saving c+X-E = E q + s +assert c+X-E==E*q+s +# the Gaussian row has slack: 1-E+qB-Eq = delta(1-2q) +assert 1-E+q*B-E*q==delta*(1-2*q)>0 +# admissible beta window for this epsilon: Gaussian row needs beta >= 1-delta(1+1/q); membership needs beta < 1-2 delta +assert 1-delta*(1+1/q)<=B<1-2*delta +assert F(1,2)z>0 and 1-E-r>0 and core-halo-B>0 and halo>43 +assert 1-B>0 and 1-B-2*(1-E)==delta>0 +costs={'transform':1-E*q,'global_router':1-eff,'gaussian':E-q*B,'group_router':E-eff*B,'group_scans':E-B,'boundary':E-X+(tau-1)/2,'sparse_union':E+F(1,2)-X,'polynomials':1-E,'microfaces':E+B+halo-core+2} +K=F((E*q*10**100).__floor__(),10**100)-F(1,10**76) +assert max(costs.values())==costs['transform'] and all(v<1-K for v in costs.values()) +# earlier packages' guards fail at this point (they are rejecting controls in the ledger): linear guard 1-X-r-B<0, old theta chirp guard 1-(2X-E)-r-B<0, 2B<1 test fails +assert 1-X-r-B<0 and 1-(2*X-E)-r-B<0 and 1-2*B<0 +assert K>F('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # PR1786 exact kappa +assert K>F('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') # PR1758 +assert K r0 (beta = 1-3 delta); only kappa moves, kappa = (1-delta) q - O(1e-76) +sweep=[] +for dd in [F(1,10**7),F(1,10**12),F(1,10**30),F(1,10**60),F(2,10**64),F(11,10**65)]: + Ed=1-dd;Bd=1-3*dd;Xd=Ed+Ed*q+s-c + assert 1-Ed-r>0 and 1-dd*(1+1/q)<=Bd<1-2*dd and 1-Ed+q*Bd-Ed*q>0 and Ed-Bd>0 and 1-Bd-2*(1-Ed)>0 + assert F(1,2)0 and core-halo-Bd>0 + assert 1-Ed+eff*Bd>Ed*q and eff>Ed*q and 1-Ed+Bd>Ed*q and Ed>Ed*q and 1-(Ed+Bd+halo-core+2)>Ed*q + sweep.append((str(dd),str(float(q-Ed*q)))) +assert 1-F(1,10**64)<=1-r # delta=r0 itself is rejected by 1-eps-r0>0 +assert not (1-(1-r)-r>0) +rows['struct_boundary_radix_union']={'epsilon':str(E),'cap':str(X),'beta':str(B),'kappa':str(K),'margin_above_kappa':str(E*q-K),'checked_cost_powers':len(costs),'gap_to_q':str(q-K),'epsilon_free_sweep_delta_gap_to_q':sweep} +report={'status':'PASS_INDEPENDENT_BALANCE_DERIVATION','source_sha256':hashlib.sha256(src.read_bytes()).hexdigest(),'b':str(b),'rows':rows,'scope':'Independent balance derivation and margin comparisons for this package\'s supplier endpoint; the supplier native admission is bound by verify_release.py; inherited all-size assumptions remain.'} +(D/'INDEPENDENT.json').write_text(json.dumps(report,indent=2)+'\n') +print(json.dumps(report,indent=2)) From 3a42e3010c188b30287f576d1ec5f0e80193c671 Mon Sep 17 00:00:00 2001 From: rohanarun Date: Wed, 14 Oct 2026 12:35:33 -0400 Subject: [PATCH 3/3] Bind completed native replay and exact source receipts for slack refinement --- research/fine-prime-slack10030/CLAIM.json | 5 +- research/fine-prime-slack10030/MANIFEST.json | 15 +- research/fine-prime-slack10030/README.md | 8 +- .../RELEASE-BINDING.json | 10 ++ .../evidence/ENDPOINT-REPLAY.json | 85 ++++++++++ .../evidence/FULL-RESULT.json | 43 +++++ .../evidence/FULL-STAGES.json | 32 ++++ .../evidence/SUPPLIER-RESULT.json | 98 +++++++++++ .../evidence/SUPPLIER-STAGES.json | 74 +++++++++ .../evidence/VERIFIED-SOURCE-MANIFEST.json | 33 ++++ .../packing-context/RESULT.json | 21 +++ .../packing-context/SOURCE.json | 7 + .../packing-context/ceiling.py | 152 ++++++++++++++++++ .../packing-context/verify.py | 17 ++ 14 files changed, 594 insertions(+), 6 deletions(-) create mode 100644 research/fine-prime-slack10030/RELEASE-BINDING.json create mode 100644 research/fine-prime-slack10030/evidence/ENDPOINT-REPLAY.json create mode 100644 research/fine-prime-slack10030/evidence/FULL-RESULT.json create mode 100644 research/fine-prime-slack10030/evidence/FULL-STAGES.json create mode 100644 research/fine-prime-slack10030/evidence/SUPPLIER-RESULT.json create mode 100644 research/fine-prime-slack10030/evidence/SUPPLIER-STAGES.json create mode 100644 research/fine-prime-slack10030/evidence/VERIFIED-SOURCE-MANIFEST.json create mode 100644 research/fine-prime-slack10030/packing-context/RESULT.json create mode 100644 research/fine-prime-slack10030/packing-context/SOURCE.json create mode 100644 research/fine-prime-slack10030/packing-context/ceiling.py create mode 100644 research/fine-prime-slack10030/packing-context/verify.py diff --git a/research/fine-prime-slack10030/CLAIM.json b/research/fine-prime-slack10030/CLAIM.json index 9dc107bbc8..e9706f3a48 100644 --- a/research/fine-prime-slack10030/CLAIM.json +++ b/research/fine-prime-slack10030/CLAIM.json @@ -1,8 +1,9 @@ { - "status": "PASS_ARITHMETIC_FULL_REPLAY_PENDING", + "status": "VERIFIED_CONDITIONAL_FINITE_ADMISSION", "kappa": 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"improvement_scientific": "2.0033595099133E-10010", - "scope": "Conditional arithmetic slack refinement only; unchanged native supplier and inherited all-size compiler, hosting, semantic precision, fixed-tape prime-packing, interchange, recovery and analytic hypotheses. No unconditional theorem, practical speedup or independent human review." + "scope": "Conditional arithmetic slack refinement only; unchanged native supplier and inherited all-size compiler, hosting, semantic precision, fixed-tape prime-packing, interchange, recovery and analytic hypotheses. No unconditional theorem, practical speedup or independent human review.", + "verification_receipt": "evidence/FULL-RESULT.json" } diff --git a/research/fine-prime-slack10030/MANIFEST.json b/research/fine-prime-slack10030/MANIFEST.json index f8bdba92a1..09379ba258 100644 --- a/research/fine-prime-slack10030/MANIFEST.json +++ b/research/fine-prime-slack10030/MANIFEST.json @@ -1,15 +1,22 @@ { - "CLAIM.json": "26be93d654314d45648184b8e1f5a0b139ea91bc5cc8eaae86f637f5ebe74e87", + "CLAIM.json": "f8a49b6a98be4f9f223e409a6d176570650f95339faafa700e7d2cf1a269f667", "DEPENDENCY-MANIFEST.json": "b8dba5524f8603e1848c73a8dd675404a0d3d9eed3b0285e9f0cfccde38fd15f", "DEPENDENCY.json": "57b6fe18ea819cca8860e65b1f9d7de83438dd3f1a309661ea5aad6932ef8213", "NOTICE": "85873634c64b16b1799c78147f91397d73bcccd5788359a21eb1e13a7b5f235c", "PARAMETERS.json": "562c18285feebe4c64ae163d1ab090fef55eb1ae4cb3cb4e2daee023f6fb51a4", "PROOF.md": "49cc2fa36015e7a21d8b2334f7d444e7ae57d54acbaba7f76c10bd1235863b16", - "README.md": "1020602b20608dade528287e1dbad01238125d9afb740f5bf0a5064377a34eb4", + "README.md": "e48cf3c96387f50fd43038d830c1e7b969b3c20467c1c721c0034080d458b0ac", + "RELEASE-BINDING.json": "9408672b3abc76a95b106ca0298efe8a185da62a36107e9c86e9c303b33f264e", "SOURCE-FETCH.json": "91fd5398dadfab18778516ad53774beef78e31dc9bd9cf0fb044a01118d1b29f", "TASK.md": "0af3d0fd294c06818f2877132764f629dd63d79c4b960b7cfd3964784f9ecdbc", "certify_endpoint.py": "1094730778c8b25256c635b9aabb850d92258550a5a6af263b8115673fba2724", "check_ledger.py": "c081b7df35ce5f8797190adce63e906d7d35b5303c297e3e66a0c82258593906", + "evidence/ENDPOINT-REPLAY.json": "8ccd4b4921a726aa45fd39751322a13dceab387c69359d7a8e834386b08ea18f", + "evidence/FULL-RESULT.json": "ae76c2129e08f6a389fe5a3f6b856136ae1ecab8566bb3a2742a69dd42f7c7e0", + "evidence/FULL-STAGES.json": "5e4b828eeabdbb4777a3564bf0eee35f16fbff853441d4f5e0103692a5e75b33", + "evidence/SUPPLIER-RESULT.json": "584591297ec988547b77b4e0cda678f85d55b05b31bb62f356c3d4f586f857ca", + "evidence/SUPPLIER-STAGES.json": "e9ca6fdba6f2d4c49a0c60970b96fa5fa77297a11d2eed5f103782df32417a2b", + "evidence/VERIFIED-SOURCE-MANIFEST.json": "ef0aa7c086679de44ef1d19d525928a87fc8e984facd9cc7d0ec76791b8c199c", "independent_check.py": "9434771a3f73ebb7a58e7bf162aba2eef05e380ebd6a40a2f67273a32df4c9ee", "inputs/B.json": "3786841ba498af359e3e5920eb2ccdb39a1005021e99f3e29a9ffae66fbbfa6d", "inputs/CLAIM1800.json": "1dd5490597ead36a31634f6008b1cd5ce0b51c4acd48a541b13306212e3f52f1", @@ -20,6 +27,10 @@ "inputs/SOURCE-SPEC.json": "41d7bd51c18eb354c6a785780ddefd35b3a8e2513daa2c4f585b236b7173e943", "inputs/SPEC.json": "07b368b62dd9dbac61d9d6a91a682b2710a724c600c20a9d1ad1e9de3cc68103", "moment_interval.py": "a4561baac4a5a2f8066f278b43739b6bc6e1f4c5329fd8ca2b747cdcd9b5e681", + "packing-context/RESULT.json": "c2e1cd26b567d21027b4fdce0d90d9573d64c555be9f0992e317aed3c4f4bfcf", + "packing-context/SOURCE.json": "f3a748fd2db4d60cd0fd56db9cd7de1955e48079dc3b033aaf5e0518f9acbc6d", + "packing-context/ceiling.py": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc", + "packing-context/verify.py": "c467556892990101b613a92e2bde875bc26e1244571a1968ccb9a61666df9968", "reference/check_ledger.py": "58162da8e9e7c02de50a9e63649c05ddc4fc5026b7f9173c9058018d093b9603", "reference/fine_mercator.py": "c0bbb95baff4f301413778c6c595049a0f3fca4ca2cdc86351898137c53e1658", "reference/fine_moment.py": "feaf1d3b6bf0e3b8eaeb22c40bea3a04ca63a98c08534fa5c28ae913c8ed70c2", diff --git a/research/fine-prime-slack10030/README.md b/research/fine-prime-slack10030/README.md index bde28cafb8..b419ebd3aa 100644 --- a/research/fine-prime-slack10030/README.md +++ b/research/fine-prime-slack10030/README.md @@ -1,10 +1,10 @@ -Draft conditional refinement of PR #1928 at head `07e4e4231459e36b1055396306dcbd950248df62`. +Locally verified conditional refinement of PR #1928 at head `07e4e4231459e36b1055396306dcbd950248df62`. The exact candidate exceeds that ledger by approximately **2.0033595099133e-10010**. Its decimal prefix remains `0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561328`. Exact rationals and the full decimal are in CLAIM.json; the comparison uses rational arithmetic, not rounded displays. This is an extremely small positive-slack improvement of the same supplier, not a structural construction or practical speedup. It retains the PR1928 10,000-digit native endpoint B and uses h=10^-10030, b=B-h, q=B-2h, epsilon=1-2h, beta=1-6h. The kappa is floor(epsilon*q*10^10070)/10^10070 - 10^-10042. -Local checks completed: the unchanged independent PR1982 endpoint checker, including its four brackets, nesting checks and ten rejecting controls; 57 strict rational outer inequalities; 17 rejecting controls; and a separate nine-cost balance derivation agreeing exactly. Fresh complete supplier replay is PENDING. No hosted CI pass or independent human review is claimed. +Local checks completed: the unchanged independent PR1982 endpoint checker, including its four brackets, nesting checks and ten rejecting controls; 57 strict rational outer inequalities; 17 rejecting controls; and a separate nine-cost balance derivation agreeing exactly. Fresh complete supplier replay PASSED locally, including inherited outer replay, both native supplier variants, parent and strict T74 admission, and final assembly-to-endpoint-to-ledger bindings. No hosted CI pass or independent human review is claimed. Reproduce arithmetic with Python 3.11+: `PYTHONINTMAXSTRDIGITS=0 python3 -B research/fine-prime-slack10030/verify.py --work /absolute/new/work --arithmetic-only`. For complete replay omit `--arithmetic-only`; optionally pass `--dependency /path/to/immutable/PR1800/package`. Outputs and fetched dependency files stay under the fresh work directory. Full replay binds the unchanged PR1800 native assembly to the new separately enclosed endpoint and ledger. @@ -15,3 +15,7 @@ Conditional on all inherited PR1800/1786/1758/1673 compiler, common-label/mutabl Open next questions: Can a complete P104 low-rank channel and compatible side correction reduce the actual paid moment? This matters for a material gain; first price and replay one complete frame-compatible local word. The unresolved side correction, native compilation and chronological hosting are blockers for that separate structural route. Further precision-only changes have negligible practical significance. Credits: Jeremy Kothe and PR1928/1800 contributors; Aaron Wang with opencode assistance for the independently derived PR1982 moment checker (retained unchanged at b10c1a196cf5fbbdedc43c9fd26ff2e834849600); Chafik Boukhalfa / PR1786, Tim Trudgian, Vlado Vojdanovski / PR1673, PR1758 contributors, LeverRank, mdumitrean, midhatn and all inherited supplier authors. Retained original sources and notices accompany the derived checkers. Prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. + +Fixed-mixture packing context: native saving ceiling bracket ['843830269237/500000000000000', '67506421539/40000000000000']. This candidate realizes approximately 99.53156560995382% of that native upper ceiling. This uses the exact 249-A/417-B average profile, rank cap51 and retained coverage identity; it is not a universal bound or the older balanced a/(1+a) transfer. Reproduce the supplement with `PYTHONINTMAXSTRDIGITS=0 python3 -B research/fine-prime-slack10030/packing-context/verify.py research/fine-prime-slack10030`. Credit Douglas Colkitt with Claude assistance for the retained ceiling engine. + +Full verification: PASS_CONDITIONAL_SLACK_REFINEMENT_FINITE_ADMISSION. Evidence includes the exact replayed source manifest and stage/log hashes. Only status prose and claim metadata change after replay; mathematical inputs, parameters, verifier code and the exact candidate rational are unchanged. This is local AI-assisted finite verification, not a full unconditional proof or hosted CI acceptance. diff --git a/research/fine-prime-slack10030/RELEASE-BINDING.json b/research/fine-prime-slack10030/RELEASE-BINDING.json new file mode 100644 index 0000000000..8baf682c51 --- /dev/null +++ b/research/fine-prime-slack10030/RELEASE-BINDING.json @@ -0,0 +1,10 @@ +{ + "replayed_head": "4f0093ad905e3229472a44177f910064fda86c01", + "replayed_manifest": "ef0aa7c086679de44ef1d19d525928a87fc8e984facd9cc7d0ec76791b8c199c", + "changed_existing_files": [ + "CLAIM.json", + "README.md" + ], + "unchanged_code_parameters_inputs": true, + "full_receipt_sha256": "ae76c2129e08f6a389fe5a3f6b856136ae1ecab8566bb3a2742a69dd42f7c7e0" +} diff --git a/research/fine-prime-slack10030/evidence/ENDPOINT-REPLAY.json b/research/fine-prime-slack10030/evidence/ENDPOINT-REPLAY.json new file mode 100644 index 0000000000..9b2377413c --- /dev/null +++ b/research/fine-prime-slack10030/evidence/ENDPOINT-REPLAY.json @@ -0,0 +1,85 @@ +{ + "status": "PASS_INDEPENDENT_ENDPOINT_BRACKET_AND_BINDING", + "inputs_sha256": "609c486efb1fe1e03ff2c84ba11085b231b9372e81fb2650bda821ce84e6e1ae", + "m": 73, + "ledgers": { + "pr1672": { + "calls": 666, + "children": 2343092, + "rank_mass": 4816512, + "deficit": 23680 + }, + "pr1928": { + "calls": 666, + "children": 2343092, + "rank_mass": 4816512, + "deficit": 23680 + } + }, + "brackets": { + "pr1672/native": { + "on_grid": true, + "endpoint_side": -1, + "next_side": 1, + "bits": 360, + "pass": true + }, + "pr1672/conservative": { + "on_grid": true, + "endpoint_side": -1, + "next_side": 1, + "bits": 360, + "pass": true + }, + "pr1928/native": { + "on_grid": true, + "endpoint_side": -1, + "next_side": 1, + "bits": 33347, + "pass": true + }, + "pr1928/conservative": { + "on_grid": true, + "endpoint_side": -1, + "next_side": 1, + "bits": 33347, + "pass": true + } + }, + "nesting": { + "native": { + "coarse_equals_floor_of_fine": true + }, + "conservative": { + "coarse_equals_floor_of_fine": true + } + }, + "controls": { + "pr1672": { + "next_grid_as_endpoint": true, + "previous_grid_as_endpoint": true, + "one_child_rank1_to_rank2": true, + "dimension_72": true, + "live_minus_one": true, + "conservative_endpoint_without_surcharge": true, + "native_endpoint_with_surcharge": true + }, + "pr1928": { + "next_grid_as_endpoint": true, + "previous_grid_as_endpoint": true, + "conservative_endpoint_without_surcharge": true + } + }, + "headline_kappa_below_native_endpoint": { + "pr1672": { + "below": true, + "endpoint_minus_kappa": "2.816845103e-6" + }, + "pr1928": { + "below": true, + "endpoint_minus_kappa": "2.003359509e-10010" + } + }, + "scope": "Native and conservative complex moment brackets and the profile composition only. The outer reduction that turns the endpoint into each headline kappa is not checked here.", + "source_spec_sha256": "41d7bd51c18eb354c6a785780ddefd35b3a8e2513daa2c4f585b236b7173e943" +} diff --git a/research/fine-prime-slack10030/evidence/FULL-RESULT.json b/research/fine-prime-slack10030/evidence/FULL-RESULT.json new file mode 100644 index 0000000000..ba77ef9fe2 --- /dev/null +++ b/research/fine-prime-slack10030/evidence/FULL-RESULT.json @@ -0,0 +1,43 @@ +{ + "status": "PASS_CONDITIONAL_SLACK_REFINEMENT_FINITE_ADMISSION", + "kappa": 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+ "dependency_head": "46d865ab92e58098538b8c5348b6a131c99abf45", + "dependency_manifest": "b8dba5524f8603e1848c73a8dd675404a0d3d9eed3b0285e9f0cfccde38fd15f", + "package_manifest": "ef0aa7c086679de44ef1d19d525928a87fc8e984facd9cc7d0ec76791b8c199c", + "assembly_sha256": "d43caa6859768878f5ad1cc4c8765197d4b760ed27b3370df428215631309e00", + "full_admission": true, + "stages": [ + { + "name": "endpoint", + "exit_code": 0, + "seconds": 14.205085833993508, + "log_sha256": "6774c67eac73e6454dff144c507a53a73c790cf2e561395729bec0aebe6cf530" + }, + { + "name": "ledger", + "exit_code": 0, + "seconds": 5.075438625004608, + "log_sha256": "6a3cde30325bfbd92b8b58f5aba5db15ad0e94e139f3c62b7a1527b8429d9a06" + }, + { + "name": "balance", + "exit_code": 0, + "seconds": 0.2177864999976009, + "log_sha256": "bbde4ea41cb3b070f7f0c2030ad36b0535dbceeda38892ac60847c4a37ea08ad" + }, + { + "name": "inherited-outer", + "exit_code": 0, + "seconds": 17.589301958010765, + "log_sha256": "670f60ee3ecc7e2d7fc4b23b468d4cdb8cfab9edaf252cd2410c1cabcb0318dc" + }, + { + "name": "supplier", + "exit_code": 0, + "seconds": 513.196323458018, + "log_sha256": "720a899b01ce3a986cb42fe28763992c05313b85697be3c6bd4d0ed571e2dfcf" + } + ], + "scope": "Conditional arithmetic slack refinement only; unchanged native supplier and inherited all-size compiler, hosting, semantic precision, fixed-tape prime-packing, interchange, recovery and analytic hypotheses. No unconditional theorem, practical speedup or independent human review." +} diff --git a/research/fine-prime-slack10030/evidence/FULL-STAGES.json b/research/fine-prime-slack10030/evidence/FULL-STAGES.json new file mode 100644 index 0000000000..a74a2ed1a8 --- /dev/null +++ b/research/fine-prime-slack10030/evidence/FULL-STAGES.json @@ -0,0 +1,32 @@ +[ + { + "name": "endpoint", + "exit_code": 0, + "seconds": 14.205085833993508, + "log_sha256": "6774c67eac73e6454dff144c507a53a73c790cf2e561395729bec0aebe6cf530" + }, + { + "name": "ledger", + "exit_code": 0, + "seconds": 5.075438625004608, + "log_sha256": "6a3cde30325bfbd92b8b58f5aba5db15ad0e94e139f3c62b7a1527b8429d9a06" + }, + { + "name": "balance", + "exit_code": 0, + "seconds": 0.2177864999976009, + "log_sha256": "bbde4ea41cb3b070f7f0c2030ad36b0535dbceeda38892ac60847c4a37ea08ad" + }, + { + "name": "inherited-outer", + "exit_code": 0, + "seconds": 17.589301958010765, + "log_sha256": "670f60ee3ecc7e2d7fc4b23b468d4cdb8cfab9edaf252cd2410c1cabcb0318dc" + }, + { + "name": "supplier", + "exit_code": 0, + "seconds": 513.196323458018, + "log_sha256": "720a899b01ce3a986cb42fe28763992c05313b85697be3c6bd4d0ed571e2dfcf" + } +] \ No newline at end of file diff --git a/research/fine-prime-slack10030/evidence/SUPPLIER-RESULT.json b/research/fine-prime-slack10030/evidence/SUPPLIER-RESULT.json new file mode 100644 index 0000000000..bc3ae13232 --- /dev/null +++ b/research/fine-prime-slack10030/evidence/SUPPLIER-RESULT.json @@ -0,0 +1,98 @@ +{ + "status": "PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION", + "kappa": "1676938111022438771190100017020725032555691674761792047536039179/1000000000000000000000000000000000000000000000000000000000000000000", + "kappa_decimal": "0.001676938111022438771190100017020725032555691674761792047536039179", + "manifest_sha256": "b8dba5524f8603e1848c73a8dd675404a0d3d9eed3b0285e9f0cfccde38fd15f", + "native_reuse": { + "base": false, + "extra": false + }, + "provider_verification": "PASS_GLOBAL_MIXED_X54_FUSIONS_NATIVE_AND_STRICT_ADMISSION", + "roles": 319680, + "prefix_bits": 1441, + "charged_prefix_bits": 2048, + "physical_row_coefficient": 19545, + "row_limit": 20161, + "controls": { + "admission": 114, + "bit": 12, + "controller": 15, + "independent_owner": 8, + "geometry": 6 + }, + "stages": [ + { + "name": "fine-engine-oracle", + "exit_code": 0, + "seconds": 7.608319999999367, + "log_sha256": "ea6df7be568d6461ac54e0d56754797de0f70f2f1ecc335114791445b75795d3" + }, + { + "name": "retained-provider-and-parent-admission", + "exit_code": 0, + "seconds": 325.6333786660107, + "log_sha256": "a84cbfcd6ad1a9a2f8279939fcbcec5457b8b55d3dc9971e3407491a82c1c57e" + }, + { + "name": "reconstruct-owners", + "exit_code": 0, + "seconds": 6.626985999988392, + "log_sha256": "363a74def2d33de399e70eab63d987832b079286cb7c58f9ffa87e186ae761f5" + }, + { + "name": "lift-parent", + "exit_code": 0, + "seconds": 4.587185332988156, + "log_sha256": "9578ab17094f120d54af46f9e0601714c09a2978faa0d7949823099d06d931d4" + }, + { + "name": "native-new-extra", + "exit_code": 0, + "seconds": 105.55226616701111, + "log_sha256": "5ca9f310247cb601c905ff30597baa4634847395d7826e9ab926a9876ced2514" + }, + { + "name": "native-new-base", + "exit_code": 0, + "seconds": 106.16056729099364, + "log_sha256": "5ca9f310247cb601c905ff30597baa4634847395d7826e9ab926a9876ced2514" + }, + { + "name": "rebuild-words-566", + "exit_code": 0, + "seconds": 1.6947345829976257, + "log_sha256": "dcbcbeda80423df29ef008bfac58409378f1fd0a3b9b23fc31ab9f03659dd86f" + }, + { + "name": "audit-local-566-base", + "exit_code": 0, + "seconds": 0.6279997090168763, + "log_sha256": "3de42e5930b250cc0a61558e23fe7fb9f0495d6be77189b1f022dcfb2e0cbada" + }, + { + "name": "audit-local-566-extra", + "exit_code": 0, + "seconds": 0.6317510840017349, + "log_sha256": "29883a84a7cfe5f776761591bb74ad6cd19e703e26b2e477158853141af2255c" + }, + { + "name": "rebind-566", + "exit_code": 0, + "seconds": 0.26311120798345655, + "log_sha256": "14c50afb24394dadd2bf0f7210a8ea64798abce4d1b295cbaf36405bc979ae14" + }, + { + "name": "strict-t74", + "exit_code": 0, + "seconds": 69.30408279199037, + "log_sha256": "93aace5a404d4b42bebd4a51d2c3e06ad600e533efbaebf966a94edc2eb74def" + }, + { + "name": "geometry-controls", + "exit_code": 0, + "seconds": 0.3360467080201488, + "log_sha256": "0a3ecf05cfa2bebb61fffd2fbb4b244c03d742069e2705d02512699bbf4b01f9" + } + ], + "scope": "Conditional finite construction only. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global packing claim." +} diff --git a/research/fine-prime-slack10030/evidence/SUPPLIER-STAGES.json b/research/fine-prime-slack10030/evidence/SUPPLIER-STAGES.json new file mode 100644 index 0000000000..04557ce955 --- /dev/null +++ b/research/fine-prime-slack10030/evidence/SUPPLIER-STAGES.json @@ -0,0 +1,74 @@ +[ + { + "name": "fine-engine-oracle", + "exit_code": 0, + "seconds": 7.608319999999367, + "log_sha256": "ea6df7be568d6461ac54e0d56754797de0f70f2f1ecc335114791445b75795d3" + }, + { + "name": "retained-provider-and-parent-admission", + "exit_code": 0, + "seconds": 325.6333786660107, + "log_sha256": "a84cbfcd6ad1a9a2f8279939fcbcec5457b8b55d3dc9971e3407491a82c1c57e" + }, + { + "name": "reconstruct-owners", + "exit_code": 0, + "seconds": 6.626985999988392, + "log_sha256": "363a74def2d33de399e70eab63d987832b079286cb7c58f9ffa87e186ae761f5" + }, + { + "name": "lift-parent", + "exit_code": 0, + "seconds": 4.587185332988156, + 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+ ], + "scope": "Fixed 249-A/417-B mixture, nine stages, 896 live families per replica, centre64, retained coverage law and rank51 halving guard. Native saving ceiling, not the historical balanced a/(1+a) transfer. Current outer ledger has kappa 1 is a what-if for a changed coverage law only); + * the local word fixes its own paid child profile `local` (per call); + * every remaining unit of mass is an idle/remainder child of rank at most R, where the outer + recipe's halving guard m^2 > 2 R^2 bounds R (R = 51 for m = 73). + +Lemma. For a >= 0, a child of rank r costs (r/m)^(1-a) = r * c(r), with c(r) = r^(-a) m^(a-1) +non-increasing in r. Hence, with idle mass M fixed and idle ranks <= R, every idle histogram has +moment >= the relaxation that puts all of M into (possibly fractional) rank-R children: + + relax(a) = [ sum_local n_r (r/m)^(1-a) + (M/R) (R/m)^(1-a) ] / w (per call). + +The moment is increasing in a. So relax(a*) > 1 certifies that no hosting, owner packing or +idle-remainder change of the given local word, template and outer recipe certifies a saving +>= a*. Under the retained reduction kappa < a/(1+a) when the complex side binds, so +a*/(1+a*) also bounds kappa. This is a bound for the stated model, not for other local words, +templates, coverage laws or outer recipes. + +Exact rational intervals: ln k from atanh chains, exp by Taylor with Lagrange remainder, +outward rounding to 2^-PREC. Standard library only. Douglas Colkitt, with Claude (Anthropic) +assistance. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import isqrt + +PREC = 256 + + +def require(ok, why): + if not ok: + raise ValueError(why) + + +def down(x): + return Q((x.numerator << PREC) // x.denominator, 1 << PREC) + + +def up(x): + return -down(-x) + + +@lru_cache(None) +def atanh(t): + """Enclosure of atanh(t) for rational 0 < t <= 1/3.""" + require(0 < t <= Q(1, 3), 'atanh range') + s, p, k = Q(0), t, 0 + while True: + term = p / (2 * k + 1) + s += term + p *= t * t + k += 1 + tail = p / ((2 * k + 1) * (1 - t * t)) + if tail < Q(1, 1 << (PREC + 8)): + return down(s), up(s + tail) + + +@lru_cache(None) +def ln(k): + """Enclosure of ln k for an integer k >= 1: ln k = ln(k-1) + 2 atanh(1/(2k-1)).""" + require(isinstance(k, int) and k >= 1, 'ln domain') + if k == 1: + return Q(0), Q(0) + lo, hi = ln(k - 1) + a, b = atanh(Q(1, 2 * k - 1)) + return down(lo + 2 * a), up(hi + 2 * b) + + +def exp(lo, hi): + """Enclosure of exp([lo, hi]) for 0 <= lo <= hi <= 1/2.""" + require(0 <= lo <= hi <= Q(1, 2), 'exp range') + def series(y, upper): + s, t, k = Q(1), Q(1), 0 + while True: + k += 1 + t = t * y / k + s += t + if t * y < Q(1, 1 << (PREC + 8)): + return up(s + 2 * t * y / (k + 1)) if upper else down(s) + return series(lo, False), series(hi, True) + + +def child_cost(r, m, a): + """Enclosure of (r/m)^(1-a) = (r/m) exp(a ln(m/r)).""" + lm, um = ln(m) + lr, ur = ln(r) + e = exp(max(Q(0), a * (lm - ur)), a * (um - lr)) + return down(Q(r, m) * e[0]), up(Q(r, m) * e[1]) + + +def max_idle_rank(m): + """Largest R with m^2 > 2 R^2 (outer halving guard).""" + R = isqrt((m * m - 1) // 2) + while 2 * (R + 1) ** 2 < m * m: + R += 1 + while 2 * R * R >= m * m: + R -= 1 + return R + + +def model(local, m, families, stages, centre, R=None, unpaid=1): + """Per-call quantities. local: {rank: count per call (Fraction ok)}.""" + R = max_idle_rank(m) if R is None else R + require(2 * R * R < m * m, 'idle rank cap violates the halving guard') + require(all(0 < r < m for r in local) and all(n >= 0 for n in local.values()), 'local profile') + w = Q(families, stages) + require(1 <= unpaid < m, 'unpaid coordinates per family') + total = (m - unpaid) * w + centre + local_mass = sum(r * Q(n) for r, n in local.items()) + idle = total - local_mass + require(idle >= 0, 'local word pays more mass than the coverage law allows') + return dict(R=R, w=w, total_mass=total, local_mass=local_mass, idle_mass=idle, deficit=unpaid * w - centre) + + +def relax(local, m, families, stages, centre, a, R=None, unpaid=1): + """Enclosure of the per-call relaxation moment at saving a.""" + q = model(local, m, families, stages, centre, R, unpaid) + lo = hi = Q(0) + for r, n in local.items(): + c = child_cost(r, m, a) + lo, hi = lo + Q(n) * c[0], hi + Q(n) * c[1] + c = child_cost(q['R'], m, a) + k = q['idle_mass'] / q['R'] + lo, hi = lo + k * c[0], hi + k * c[1] + return down(lo / q['w']), up(hi / q['w']) + + +def ceiling(local, m, families, stages, centre, grid=Q(1, 10 ** 15), R=None, unpaid=1): + """Grid bracket [a_lo, a_hi]: relax(a_lo) < 1 < relax(a_hi), certified. a_hi is the ceiling.""" + lo, hi = Q(0), Q(1, 20) + require(relax(local, m, families, stages, centre, hi, R, unpaid)[0] > 1, 'search window too small') + require(relax(local, m, families, stages, centre, lo, R, unpaid)[1] < 1, 'relaxation has no positive saving') + while hi - lo > grid: + mid = Q(int((lo + hi) / 2 / grid)) * grid + if mid <= lo: + mid = lo + grid + v = relax(local, m, families, stages, centre, mid, R, unpaid) + if v[1] < 1: + lo = mid + elif v[0] > 1: + hi = mid + else: + raise ValueError('enclosure too wide to separate the grid point') + return lo, hi diff --git a/research/fine-prime-slack10030/packing-context/verify.py b/research/fine-prime-slack10030/packing-context/verify.py new file mode 100644 index 0000000000..17b70c7a64 --- /dev/null +++ b/research/fine-prime-slack10030/packing-context/verify.py @@ -0,0 +1,17 @@ +"""Supplementary fixed-mixture packing ceiling, not a supplier construction.""" +import json,sys +from pathlib import Path +from fractions import Fraction as Q +import ceiling +P=Path(__file__).resolve().parent +spec=json.loads((Path(sys.argv[1])/'inputs/SOURCE-SPEC.json').read_text()) +claim=json.loads((Path(sys.argv[1])/'CLAIM.json').read_text()) +h={int(k):int(v) for k,v in spec['expected']['global_profile'].items()} +assert spec['expected']['live']==74*896 and spec['geometry']['dimension']==73 +local={k:Q(v,666) for k,v in h.items() if k!=48} +assert sum(k*v for k,v in h.items())==72*66304+64*666 +lo,hi=ceiling.ceiling(local,73,896,9,64) +k=Q(claim['kappa']) +r=dict(status='PASS_FIXED_MIXTURE_PACKING_CEILING',native_saving_ceiling_bracket=[str(lo),str(hi)],rank_cap=51,local_profile={str(k):str(v) for k,v in local.items()},kappa_over_native_cap_interval=[str(k/hi),str(k/lo)],scope='Fixed 249-A/417-B mixture, nine stages, 896 live families per replica, centre64, retained coverage law and rank51 halving guard. Native saving ceiling, not the historical balanced a/(1+a) transfer. Current outer ledger has kappa