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b/research/rank-sector-async/NOTICE.md @@ -0,0 +1,13 @@ +# Scoped attribution + +Prepared with OpenAI Codex assistance. Apache-2.0; see LICENSE. Original authorship notices in included vendor code are retained. + +PR507 directly supplies the partial-own factory, 84-pivot reference and its retiming map. PR484 supplies the gauge/kernel construction and wrappers; PR496 supplies whole-owner pooling and invoice ancestry. PR493 supplies the unchanged cited bit operator. PR495 supplies body-frame retiming, with PR501 and PR502 integrating it. PR473's single-gauge proposal inspired our coordinated four-gauge collapse; its updated schedule was also considered. PR505 contains our prior asynchronous complete-invocation scheduling. PR506 supplies a related public comparison and portability feedback. PR477's experiment log informed bounded route selection. + +Earlier retained ancestry includes PR433/425/370 for geometry and the scalar/phase compiler, PR458 for whole-owner spectator wrappers, PR361/315 for exact moments and outer arithmetic, and PR434/417/435/440/401/408/416 for response-kernel and gauge methods. SOURCES.json separates direct ingredients, ancestry, comparisons and excluded interfaces; credits do not mean their gains were added independently. + +Our contribution here is the actual combined reconstructed 99-pivot word and literal whole-owner allocation, with complete fresh checks of the changed complex program. OpenAI math, the Problem 1.8 implementation and the installed machine compiler sources informed the documented research adaptations. No fresh Lean certification is claimed. + +Additional direct inspiration: OpenAI math sparse interpolation, unit-flow/matching, rational Schur history and exact pruning. The source and adaptation ledgers distinguish these roles. Recent PR509-513 were inspected as context, not counted as additional numerical gains. + +This derivative changes the coordinate-total factory by a rank-factor construction, retaining the99-pivot pair35 ancestry and unchanged whole-owner witness. Additional OpenAI source families this round: Cotype rank factors, UniformKServer rounding, SwitchChain switches and DukePrimeDegree root commutators. See their exact hashes and scope in research-notes/. PR514-517 and the updatedPR511 are acknowledged as described in SOURCES.json. diff --git a/research/rank-sector-async/PORTABILITY.md b/research/rank-sector-async/PORTABILITY.md new file mode 100644 index 0000000000..b6e9671200 --- /dev/null +++ b/research/rank-sector-async/PORTABILITY.md @@ -0,0 +1,11 @@ +# Portable replay and browser uploads + +No hidden file is required. MANIFEST.json binds every included file except itself. Each entry declares either exact raw-byte hashing (gzip and other binary inputs) or SHA-256 after converting CRLF to LF (recognized text files). This accepts only the platform newline distinction; it does not ignore whitespace, JSON values, source code or any other content. An omitted file or changed token still fails. + +verify.py copies static work inputs into its new output directory, canonicalizes recognized text there, and creates an LF copy of the frozen asynchronous plan. Only those canonical copies enter runtime raw-byte template hashes. Each child executes through code/run_portable.py, which preserves argv, import path and working directory while forcing generated Path.write_text output to UTF-8/LF. Generated adapter JSON therefore has the same embedded hash on Windows and Linux. + +Gzip transport bytes are manifest-bound. Newly generated gzip container headers can vary across Python versions; the expected final template hash binds decompressed canonical content instead. Mathematical input fields are checked independently. The normalized local word omits only two irrelevant inherited display floats and a checked redundant dimension field. + +The package is tested locally with assertions enabled. Optimized Python is rejected. The final portability test changes every recognized package text file to CRLF and runs the complete verifier against the frozen expected result. This is a Windows line-ending test, not a claim that Linux or Python 3.14 ran locally. + +Upload batches contain at most 40 files each, have no hidden files, and reproduce the same research/rank-sector-async directory. Upload each batch's research folder at your fork's repository root, on one fresh branch. Do not upload the part folder itself. After all batches are committed, open one PR from that branch. Nothing in the verifier publishes, deletes files or modifies a fork. diff --git a/research/rank-sector-async/PROOF.md b/research/rank-sector-async/PROOF.md new file mode 100644 index 0000000000..647ef2c1dc --- /dev/null +++ b/research/rank-sector-async/PROOF.md @@ -0,0 +1,13 @@ +# Sufficient rank-sector construction + +In each of fourteen blocks, the twelve retired rows have clean source rank eight. Choose eight independent rows. Their coefficient matrix on the eight source coordinates is invertible. Let A be that matrix. Extend the four desired coordinate-sum rows to an invertible eight-row output matrix M, then emit the elementary factorization of M A^-1 at the existing legal rank-four frame. On the clean source sector this gives (M A^-1) A x=Mx. The remaining four physical rows are kept, not deleted or cleared. + +The clean calculation is not the arbitrary-input certificate. The new factory's complete dirty response is recomputed; the exact 99-pivot compensation, frame checks and inverse cleanup are rebuilt. Every independent dirty/source/target column is checked in both forward and inverse-transpose orientations. All 99 omitted-correction controls reject. All scalar coefficients satisfy the existing dyadic compiler contract, and all nonlinear precision consequences are included in the actual prefix invoice. + +Four unused retired rows in each block stay at rank three until full-frame cleanup. Their old rank-one rise to four followed by a rank-five rise to nine is replaced by one rank-six rise. Hence the local delta is -56 rank-one children, -56 rank-five children and +56 rank-six children. Rank mass is unchanged. For every exponent p in (0,1), strict concavity gives 6^p < 1+5^p, so this is a universal strict improvement of the local moment in that range. No entropy approximation is needed for this comparison. + +The normalized selected word is SHA-256 d966e1481e0c09e4b7a0607429411046c6b3663ee83e6b8833958a745b82e337. Its residual inventory is unchanged in order: 18 width-seven, 161 width-eight and 381 width-nine helpers. Therefore the previous complete-owner assignment is a concrete feasible witness without a new allocation oracle. Every emitted physical chart and residual wrapper is nevertheless regenerated from this new provider and independently checked. + +Eight replicas execute nine complete calls in order (7*stage+6*replica,stage,replica), finishing each before the next. Each helper has one whole owner whose idle interval contains the invocation, and every complementary residual is paid before the owner's next touch. Induction using the inherited complete invocation contract preserves the original endpoint and restores spectators. No helper is split across families and no scalar gate crosses an unfinished invocation. + +The full profile is {1: 178128, 2: 13104, 3: 40196, 4: 6336, 5: 21032, 6: 8928, 7: 164, 8: 1224, 48: 796}; its rank sum is 73*7680-2496. Maximum recursive rank is 48 and 73^2>2*48^2. The fresh invoice derives the prefix from the actual new scalar program, not the previous provider's fixture. Two exact rational moment engines and all 47 strict outer inequalities establish conditional kappa=1402213284556683/1000000000000000000, b=1404182247558147721001/1000000000000000000000000, c=391360506745414227149/250000000000000000000000. Adjacent-price and malformed-assembly controls reject. All-size and analytic interfaces remain stated dependencies. diff --git a/research/rank-sector-async/README.md b/research/rank-sector-async/README.md new file mode 100644 index 0000000000..157bd44860 --- /dev/null +++ b/research/rank-sector-async/README.md @@ -0,0 +1,23 @@ +# Rank-factor coordinate totals with asynchronous whole owners + +Conditional kappa = **0.001402213284556683**, exactly `1402213284556683/1000000000000000000`: **0.613517% above our preceding checked construction**, 0.001393662920776407. The complex supplier binds at b = `1404182247558147721001/1000000000000000000000000`; the unchanged cited PR493 bit supplier has c = `391360506745414227149/250000000000000000000000`. + +The new local construction computes each block's four coordinate totals inside an independent eight-row sector. The preceding factory raised all twelve retired rows to the rank-four frame. Four rows per block can instead remain untouched until cleanup, fusing 56 rank-one/rank-five recursive pairs into 56 rank-six children. All 560 helper registers, all 99 response cancellations and the entire ordered width inventory remain. Arbitrary dirty inputs are retained and compensated, not erased. + +The actual local paid profile is {1:2474,2:182,3:516,4:88,5:242,6:124,7:1,8:17}. The global profile, including all idle remainders, is `{1: 178128, 2: 13104, 3: 40196, 4: 6336, 5: 21032, 6: 8928, 7: 164, 8: 1224, 48: 796}`. The existing literal allocation of 40,320 whole helper uses is preserved, then re-emitted and independently checked against the new provider. Rank deficit 2,496, ambient dimension 73, live stock 7,680 and physical stock 8,258 are unchanged. + +## Reproduce + +Python 3.11 or later, standard library only: + +```text +python -B verify.py --work /absolute/path/to/a-new-output-directory +``` + +Choose a new directory outside this package and keep assertions enabled. No network, optimizer, C++ compiler or Lean is needed. Fifteen stages reconstruct the factory, check 800 arbitrary-dirt columns in both orientations plus 99 omitted-correction controls, audit exact Gaussian phases and physical wrappers, independently verify every owner and remainder, recount the scalar-prefix/row invoice, and run two rational moment engines and all 47 strict outer constraints. The bit operator is a cited dependency, not reverified here. + +## Four new source-inspired routes + +The selected gain comes from the Cotype rank-factor adaptation. Three other distinct OpenAI-source techniques were concretely screened: UniformKServer correlated owner repairs, SwitchChain degree-preserving output-pair switches, and DukePrimeDegree paid root-commutator rewrites. They did not add savings. Their sufficient transformation rules, source hashes and bounded outcomes are preserved in RESEARCH.md and research-notes/. Four techniques tested does not mean four numerical gains, four imported Lean theorems or a claim of global novelty. + +This remains a finite conditional construction. All-size compilation, common-label/mutable-basis transport, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer interfaces remain dependencies. No unconditional multiplication theorem or new Lean certification is claimed. The snapshot was frozen through PR517 before packaging; see SOURCES.json and NOTICE.md. No publication is performed by the verifier. diff --git a/research/rank-sector-async/RESEARCH.md b/research/rank-sector-async/RESEARCH.md new file mode 100644 index 0000000000..96d49a32cc --- /dev/null +++ b/research/rank-sector-async/RESEARCH.md @@ -0,0 +1,18 @@ +# Four new OpenAI-source adaptations + +OpenAI math source snapshot: adc7f1241b42e322a6451854ab7e4b4c146bf78a. These sources were inspected, not freshly compiled or instantiated in Lean. + +| Source family | Concrete sufficient construction | Outcome | +| --- | --- | --- | +| Analysis/Cotype/RankFactors | Extract an independent sector, reconstruct the exact requested row map there, retain arbitrary-dirt rows outside it | Selected construction; 56 pairs of recursive calls fused, full replay passed | +| UniformKServer/TreeRounding and RoundingKernel | Jointly repair several owner bins while preserving role identities, invocation marginals, capacities and explicitly charged parked mass | 200,000 strict-repair triples plus a bounded neutral sweep found no improved full leftover profile | +| Probability/SwitchChain/FourVertexSwitch and PairTradeSwitch | Switch Y-borrowing output matchings and reconstruct their inverse basis/scatter | Inherited retiming was incompatible; 27 raw-frame candidates were legal but lost the paid moment | +| DukePrimeDegree/Geometry/RootCommutator | Reorder elementary shears with the explicit product-coefficient correction and pay every gate/frame change | Adjacent and 128-event windows found no lower-cost nominee; 603 candidate profiles on pair35 and 547 on the new provider | + +The Cotype source proves exact rank-pairing factors and their contraction identity. Our coordinate-total construction is a separate finite row-sector adaptation; the source theorem itself is not a multiplication speedup. The initial displacement-kernel/telescoping idea was also screened and helped identify the small requested output space, but is not relabeled as the winning rank-factor theorem. + +The minimum-retained-subset screen found that each block requires eight selected retired rows in the tested subset model, using modular exact rank checks. This does not rule out new linear combinations, altered packet construction or different interfaces. The successful universal moment inequality and full finite witness, not a barrier, are the result delivered here. + +The other screens are bounded discovery evidence, not universal no-go results. Floating moment screens nominate or reject research candidates; only the selected full rational replay certifies the reported exponent. No approximate quantum operation, unconstructed decomposition, unpaid scalar correction or hypothetical solver is assumed. + +PR517's exact packing ceiling freezes a different 84-pivot word and does not bound this 99-pivot rank-sector word. It usefully distinguishes a small allocation gap from a genuinely changed local construction. PR515 is an alternative bit-side method, not substituted for the stronger retained supplier. PR516 is draft formal realization context and does not remove our stated conditional assumptions automatically. PR511 updates provenance, not kappa. All are credited in SOURCES.json; unchanged public verifiers were not rerun. diff --git a/research/rank-sector-async/SOURCES.json b/research/rank-sector-async/SOURCES.json new file mode 100644 index 0000000000..08cf67b4ad --- /dev/null +++ b/research/rank-sector-async/SOURCES.json @@ -0,0 +1,146 @@ +{ + "snapshot": "79 recent/updated PR conversations; frozen through PR517 before packaging.", + "direct": [ + { + "pr": 496, + "head": "00cf70efd6a8637531deafef698157ca83e249ee", + "role": "whole-owner parent, invoice and assembly ancestry" + }, + { + "pr": 484, + "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f", + "role": "PR496 pinned gauge80-kernel42 parent, not newer moving head" + }, + { + "pr": 493, + "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7", + "role": "unchanged cited R489 bit supplier" + }, + { + "pr": 502, + "head": "4d30b8322184598e65e90a92389e17e1baedd9eb", + "role": "retiming transfer constructor and PR495 schedule fixture" + }, + { + "pr": 501, + "head": "1dc056496fdbbc74073ed26d948a2dc235dbf356", + "role": "parallel retiming integration; credited, no duplicated gain" + }, + { + "pr": 473, + "head": "628b454d3df00367d2d4f78de7d4eb9cbcbd47ca", + "role": "single-helper gauge withdrawal inspiration" + }, + { + "pr": 507, + "head": "8d4444cf8a16d500cbb94add6e4fa8bcfb9c7d5e", + "role": "partial-own factory, 84-pivot reference and retiming map" + }, + { + "pr": 505, + "head": "4ee769c8e28837482272b5f4742497da8e2fc9d4", + "role": "our prior complete-invocation asynchronous scheduling" + }, + { + "pr": 506, + "head": "a4948baee6c7ea35323db74ff636620c6af2925a", + "role": "public asynchronous retiming comparison and portability feedback" + } + ], + "openai_math": { + "repository": "https://github.com/openai/math", + "revision": "adc7f1241b42e322a6451854ab7e4b4c146bf78a", + "status": "source inspection and mathematical adaptation; no new Lean audit" + }, + "other_inspirations": [ + 497, + 458, + 442, + 434, + 433, + 425, + 417, + 435, + 440, + 401, + 408, + 416, + 370, + 361, + 315, + 495, + 503, + 504 + ], + "excluded": { + "494": "under-review split-residual interface not used", + "491": "withdrawn GL sampling argument not used", + "499": "larger claim inherits disputed split-residual interface; not used" + }, + "related_updated": [ + { + "pr": 473, + "head": "94b3c908fb7628142817d995155368aba2eae841", + "role": "new nonuniform scheduling comparison; earlier pinned gauge proposal remains a separate source" + }, + { + "pr": 477, + "head": "2f23f46f1f9e4599168d40096fbacce4973a2978", + "role": "experiment log consulted to avoid repeating old searches" + } + ], + "recent_context": [ + { + "pr": 509, + "head": "7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59", + "role": "abstract Lemma G proof; no new numerical ingredient" + }, + { + "pr": 510, + "head": "64edee18af02aab0c1696b677a0287dd0146381b", + "role": "nonbinding bit improvement; not substituted" + }, + { + "pr": 511, + "head": "79f7c03c7f820ab89955b75ef239cbaccc627e6e", + "role": "formal dispatcher context" + }, + { + "pr": 512, + "head": "73d367fe754cf5921cd954221133b20ac752f932", + "role": "asynchronous partial-own comparison" + }, + { + "pr": 513, + "head": "005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73", + "role": "formal completed-bank context" + } + ], + "this_round": [ + { + "pr": 514, + "head": "246bfacd4cb4072836ae3147099f548bb728229f", + "role": "publication of earlier92-pivot baseline; inherited ancestry" + }, + { + "pr": 515, + "head": "6590606e733768f6a7004b3f55ae35f988ba515f", + "role": "alternative bit copy deletion and chain optimization; comparison only" + }, + { + "pr": 516, + "head": "871b1c51e53918c5e6c945dfe8ef45546c17da56", + "role": "draft paid-wrapper/asynchronous formal realization; not recompiled or instantiated here" + }, + { + "pr": 517, + "head": "65518fcff5a7bd490365273ae5469a82aac14853", + "role": "old84-pivot coordinated witness and restricted packing ceiling; route-selection context" + }, + { + "pr": 511, + "head": "9a20ad04be54b1c0fa26bd4ceb689f9ea220eab5", + "role": "provenance update; no new numerical ingredient" + } + ] +} diff --git a/research/rank-sector-async/code/assemble.py b/research/rank-sector-async/code/assemble.py new file mode 100644 index 0000000000..de2a375d13 --- /dev/null +++ b/research/rank-sector-async/code/assemble.py @@ -0,0 +1,42 @@ +"""Two exact moment engines and strict outer composition of a new PR484 rehosting +with the unchanged published PR493 bit supplier. Prepared by OpenAI Codex; arithmetic +engines are pinned inherited PR361/Mercator and independent base-two code. +Usage: assemble_candidate.py AUDIT_OUT PARENT_VARIANT HOSTED BIT_RESULT +""" +from pathlib import Path +from fractions import Fraction as Q +import json,gzip,sys,hashlib,importlib.util +O,V,H,B=map(Path,sys.argv[1:5]);sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +def load(n): + p=V/'work/pr361/code/engines'/(n+'.py');s=importlib.util.spec_from_file_location('candidate_'+n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +M,Other,Outer=[load(n)for n in ['moment','base_two_moment','outer']] +owner=json.loads((O/'OWNERS-AND-PROFILE.json').read_text());inv=json.loads((O/'PREFIX-AND-INVOICE.json').read_text());host=json.loads((H/'HOSTED.json').read_text());bit=json.loads(B.read_text())["eleven"];P={int(r):n for r,n in owner['paid_profile'].items()};m,W=73,owner['live'];assert m*W-sum(r*n for r,n in P.items())==2496 +rc=M.certify(P,m,W,True);b=Q(rc['lower']);bp=Q(rc['upper']);assert bp-b==Q(1,10**24) +fallback=32*m*m*sum(P.values());receipts=[] +for z,accept in[(b,True),(bp,False)]: + ml,mh=M.moment(P,m,W,z,True);a,c=Other.moment(m,W,list(P.items()),z);d,e=Other.moment(m,W,[(1,fallback)],z);a+=d/10**16;c+=e/10**16 + assert (mh<1 and c<1)if accept else(ml>1 and a>1) + receipts.append(dict(endpoint=str(z),mercator=[str(ml-1),str(mh-1)],base_two=[str(a-1),str(c-1)],accept=accept)) +# Reprice the cited unchanged bit histogram, clearly separate from bit operator verification. +bitP={int(r):n for r,n in bit['profile'].items()};bitc=Q(bit['bit_lower']);bitnext=bitc+Q(1,10**24) +for zz,accepted in [(bitc,True),(bitnext,False)]: + bl,bh=M.moment(bitP,78,9600,zz,True) + ol,oh=Other.moment(78,9600,list(bitP.items()),zz) + fl,fh=Other.moment(78,9600,[(1,32*78*78*sum(bitP.values()))],zz) + assert (bh<1 and oh+fh/10**16<1) if accepted else (bl>1 and ol+fl/10**16>1) +c=Q(bit['bit_lower']);eta=beta=Q(1,10**18);grid=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24) +assert 00 + cut=max(ceil(36/gap**2),ceil(2*(4+coeff)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+coeff);cuts.append(dict(gap=str(gap),cutoff_log2=str(cut)));chain.append(a) +q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;kap=grid*((ticks.numerator-1)//ticks.denominator) +bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*row,25)}} +a=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta);assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values());controls=[] +for name,k,e,be in [('next_grid',kap+grid,eta,beta),('zero_eta',kap,Q(0),beta),('zero_beta',kap,eta,Q(0)),('unit_beta',kap,eta,Q(1))]: + try:Outer.assembly(chain[-1],b,bridge,k,eta=e,beta=be) + except AssertionError:controls.append(name) + else:raise AssertionError(name) +res=dict(status='PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY',complex_lower=str(b),complex_decimal=rc['lower'],next_b_rejected=str(bp),exact_moment_receipts=receipts,bit_lower=str(c),bit_result_sha256=sha(B),bit_template_sha256=bit['emitted_program_sha256'],bit_prefix_bits=bit['bit']['charged_prefix_bits'],bit_charged_three_level_coefficient_bits=coeff,external_row_allowance=row,kappa=str(kap),kappa_decimal=f'{float(kap):.18f}',binding_component='bit'if c<(1-beta)*b else'complex',strict_outer_constraints={k:str(v)for k,v in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cuts,complex_template_sha256=host['template_sha256'],owner_audit_sha256=sha(O/'OWNERS-AND-PROFILE.json'),invoice_sha256=sha(O/'PREFIX-AND-INVOICE.json'),bit_scope='PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.',scope='Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately.') +(O/'EXACT-ASSEMBLY.json').write_text(json.dumps(res,indent=2)+'\n');print(res['status'],'b',res['complex_decimal'],'kappa',res['kappa_decimal'],flush=True) diff --git a/research/rank-sector-async/code/audit_async.py b/research/rank-sector-async/code/audit_async.py new file mode 100644 index 0000000000..43642d1aa0 --- /dev/null +++ b/research/rank-sector-async/code/audit_async.py @@ -0,0 +1,149 @@ +"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit. +Imports no emitter, optimizer, expander, edge-coloring, or source hosting code. +CLI: VERIFIED_VARIANT POOLED_HOSTED OUT.json +The local provider is read from VERIFIED_VARIANT, never from a baseline width histogram. +""" +import sys,json,gzip,hashlib,copy +from pathlib import Path +from collections import Counter,defaultdict +BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json');V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers']);assert V==120 and canon['h']==9; width=[9-len(canon['frames'][canon['start'][2*V+h]])for h in range(R)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=7680;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R + +def orthobasis(port): + q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<>i&1 else 0)for i in order]+[1<2*max(paid)**2 + return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72) + +r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256'] +assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items()) +controls=[] +def reject(name,mut): + q=copy.deepcopy(ct);mut(q) + try:audit(q) + except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name) + else:raise AssertionError('ACCEPTED '+name) +reject('wrong call time',lambda q:q['calls'][0].__setitem__('time',71)) +enter=lambda q:next(o for c in q['calls']for o in c['owners'][240:]if o[1][0]==4) +reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240])) +reject('helper on active data family',lambda q:q['calls'][0]['owners'][240].__setitem__(0,q['calls'][0]['owners'][0][0])) +reject('owner in private namespace',lambda q:q['calls'][0]['owners'][240].__setitem__(0,7680)) +reject('unbound change of owner replica',lambda q:q['calls'][0]['owners'][240].__setitem__(0,(q['calls'][0]['owners'][240][0]+960)%7680)) +reject('omit complete invocation',lambda q:q['calls'].pop()) +reject('reorder invocation replicas',lambda q:q['calls'].__setitem__(0,q['calls'][1])) +reject('interleave local invocations',lambda q:q.__setitem__('loop_order','interleaved local instructions')) +reject('change local instruction stream',lambda q:q['local_programs']['forward'].pop()) +reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1)) +reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72)) +reject('omit spectator route',lambda q:enter(q).__setitem__(1,enter(q)[1][:3])) +reject('overlap residual footprint',lambda q:q['calls'][0]['owners'][240][1].__setitem__(2,100)) +reject('omit idle remainder',lambda q:q['idle_children'].pop()) +reject('underpay idle remainder',lambda q:q['idle_children'][0].__setitem__('rank',0)) +reject('omit bridge touch',lambda q:q['execution_schedule'].pop(next(i for i,e in enumerate(q['execution_schedule'])if e['kind']=='bridge'))) +reject('remove one-owner rule',lambda q:q['hosting'].pop('max_helpers_per_physical_family_per_call')) +reject('duplicate frozen role',lambda q:q['hosting']['pooled_slots'].__setitem__(1,q['hosting']['pooled_slots'][0])) +reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1)) +report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=7680,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2496,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,widths=dict(sorted(Counter(width).items())),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations.') +REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2)) + +owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=7680,physical=PHYSICAL,rank_mass=r['mass'],deficit=2496,hosted_residuals=HOSTED,banked_residuals=0,all_800_owners_per_call_distinct=True,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest()) +(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n') + diff --git a/research/rank-sector-async/code/audit_async_invoice.py b/research/rank-sector-async/code/audit_async_invoice.py new file mode 100644 index 0000000000..baca4c6dbb --- /dev/null +++ b/research/rank-sector-async/code/audit_async_invoice.py @@ -0,0 +1,100 @@ +"""Async PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex. +Reads emitted programs, canonical word and raw routes, importing no supplier code. +Inherited all-size compiler admissibility is a condition, not inferred here. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter +import gzip,json,math,hashlib +import sys +O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3]) +def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json') +VV=w['v'];R=w['R'];N=2*VV+R;M=73;L=9;T=8;K=4 +assert VV==120 and w['h']==9 +PAYLOAD=512 +control=read(O/'ASYNC-AUDIT.json') +raw=gzip.decompress((HOSTED/'GLOBAL-TEMPLATE.json.gz').read_bytes());th=hashlib.sha256(raw).hexdigest() +assert th==control['complex_template_sha256']==owners['template_sha256'] +assert control['one_owner_per_complete_invocation'] and control['complete_invocations']==72 +assert new['local_programs']==old['local_programs'] and new['recipe']==old['recipe'] +assert Counter(c['orientation']for c in new['calls'])==Counter(c['orientation']for c in old['calls']) +local={} +for ori,evs in p.items(): + rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0 + for e in evs: + if e[0]=='climb':paid[e[5]]+=1 + elif e[0]=='center':paid[e[4]]+=1 + elif e[0]=='scalar': + macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0 + if op=='clear':rows[a]={};env[a]=F(0);count=1 + elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1 + elif op=='scale': + q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator + assert num and num&(num-1)==0 and den&(den-1)==0 + rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q) + count=abs(num.bit_length()-den.bit_length())+int(q<0) + elif op=='add': + b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator + assert a!=b and num>0 and den&(den-1)==0 + # Lower actual coefficient to cleared Horner work. Every intermediate + # magnitude envelope is explicitly included, before denominator halvings. + acc=0;count=1 + for i,ch in enumerate(bin(num)[2:]): + if i:acc*=2;count+=1;peak=max(peak,acc*env[b]) + if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b]) + v=F(acc) + for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b]) + assert v==abs(q);count+=2 # signed accumulation and private work clear + env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{}) + for j,z in list(rows[b].items()): + value=rr.get(j,F(0))+q*z + if value:rr[j]=value + else:rr.pop(j,None) + workops+=count + else:raise AssertionError(op) + real+=2*count;peak=max(peak,env[a]) + assert all(not row for reg,row in rows.items()if reg[0]=='C') + for i in range(N): + expected={i:F(1)} + if ori=='forward'and 120<=i<240:expected[i-120]=F(1) + if ori=='backward'and i<120:expected[i+120]=F(-1) + assert rows['L',i]==expected + assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192 + assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros'] + assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()} + local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True) +centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][240:]];enter=sum(x<9 for x in widths) +children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3 +adapters=16*(macros+children+N+centres)+64*M +primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler +bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;assert sum(e['kind']=='bridge'for e in new['execution_schedule'])==T*bridges +shifts=K*VV*T;moves=2*K*VV*T +oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L +scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls']) +nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144 +outside=8*nonlocal_items+64*M +pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP +invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler']) +# Independent hosted stock rebase, retaining the larger unhosted operation +# overcharge; only the stock and mass in the common router/literal change. +W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile'] +assert M*W-mass==2496 and P==W+R+centres+2 +rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex) +r=M//2;group=2**(r*r) +for i in range(1,r+1):group*=2**(2*i)-1 +stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2 +G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252+2*PAYLOAD;maxchild=max(map(int,profile)) +ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router2*maxchild*maxchild) +assert all(ineq.values()) +localbits=max(x['prefix_bits']for x in local.values());input_l2_bits=(M+1)//2 +bridge_sweeps=sum(e['kind']=='bridge'for e in new['execution_schedule']) +required_prefix=localbits+input_l2_bits+len(new['calls'])+bridge_sweeps+4 +assert 0 < localbits <= 192 and len(new['calls']) == 72 and bridge_sweeps == 72 and required_prefix < PAYLOAD +assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged'] +assert new['physical']<=old['physical'] and new['live']<=old['live'] and not new['bank_padding']['families'] +out=dict(status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',template_sha256=th,global_prefix_bits=required_prefix,charged_prefix_bits=PAYLOAD,complete_invocation_sweeps=72,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*PAYLOAD,local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound.') +(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True) + +prefix=dict(status='PASS_ASYNC_GLOBAL_PREFIX',template_sha256=th,global_prefix_bits=required_prefix,retained_payload_bits=PAYLOAD,complete_invocation_cover_sweeps=len(new['calls']),bridge_factor_two_sweeps=bridge_sweeps,local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,primitive_arithmetic_margin_bits=4,controller_audit_sha256=hashlib.sha256((O/'ASYNC-AUDIT.json').read_bytes()).hexdigest(),proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Distinct full orthogonal owner charts act by right-translation bijections on the retained cover group. Thus the maximum full-stream L2 norm grows by at most2per complete local cover sweep and individual bridge. All72local sweeps and72individual bridge sweeps are counted. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently replayed scalar/Horner envelope costs {localbits} bits, initial sup-to-L2 conversion {input_l2_bits} bits, primitive margin 4 bits: total {required_prefix} < {PAYLOAD}. All-size child/compiler and precision/tape interfaces remain inherited.') +(O/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n') diff --git a/research/rank-sector-async/code/audit_kernel_scalar.py b/research/rank-sector-async/code/audit_kernel_scalar.py new file mode 100644 index 0000000000..4373bb9bd5 --- /dev/null +++ b/research/rank-sector-async/code/audit_kernel_scalar.py @@ -0,0 +1,55 @@ +"""Independent exact scalar witness for a selected complex kernel word. +Uses immutable correct-word compensation for omission controls; no repaired +compensation is silently supplied to a mutant. No physical-hosting claim. +""" +import sys,json,gzip,hashlib,copy +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +p=Path(__file__).resolve().parent +path=Path(sys.argv[1]);selection=Path(sys.argv[2]);out=Path(sys.argv[3]);w=json.loads(gzip.decompress(path.read_bytes()));sel=json.loads(selection.read_text());n=240+w['report']['R'] +def ident():return[{r:Q(1)}for r in range(n)] +def apply(e,rows): + if e[0]=='scale': + _,t,a,b,*_=e;q=Q(a,b);rows[t]={j:q*x for j,x in rows[t].items()};return + _,t,s,a,b,*_=e;q=Q(a,b) + for j,x in list(rows[s].items()): + z=rows[t].get(j,Q(0))+q*x + if z:rows[t][j]=z + else:rows[t].pop(j,None) +def inv(e,dual=False): + e=copy.deepcopy(e) + if e[0]=='add': + e[3]*=-1 + if dual:e[1],e[2]=e[2],e[1] + else:e[2],e[3]=e[3],e[2] + return e +def replay(es): + rows=ident() + for e in es:apply(e,rows) + return rows +main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(n)] +for r in range(120,240):dirty[r]={j:x for j,x in mx[r].items()if j>=240} +for e in w['precondition']:apply(e,dirty) +comp=[] +for r in range(120,240): + for j,x in sorted(dirty[r].items()): + assert not w.get('start_extra',{}).get(str(j)),('nonzero-frame compensation',j) + comp.append(['add',r,j,-x.numerator,x.denominator,[]]) +cleanup=[inv(e)for e in reversed(w['A']+w['B'])if not 120<=e[1]<240] +assert[e[:-1]for e in cleanup]==[e[:-1]for e in w['cleanup']] +program=w['precondition']+comp+main+cleanup;expected=ident() +for t in range(120):expected[120+t][t]=Q(1) +assert replay(program)==expected +back=ident() +for t in range(120):back[t][120+t]=Q(-1) +assert replay([inv(e,True)for e in program])==back +controls={} +for cl in sel['kernel']: + for h in cl['pivots']: + aa=[e for e in w['A']if not(e[0]=='add'and e[2]==240+h and e[1]>=240 and e[-1]==cl['E'])] + assert len(aa)0 and abs(q.numerator)&(abs(q.numerator)-1)==0,(part,e) +norm=copy.deepcopy(w);assert norm.get('R',560)==norm['report']['R']==560;norm.pop('R',None) +for k in ['complex_coarse_float','gain_percent_float']:norm['report'].pop(k,None) +semantic=hashlib.sha256(json.dumps(norm,sort_keys=True,separators=(',',':')).encode()).hexdigest() +assert semantic=='bf26b8c3709039eb027430218f8b9bd3c369eb9c584e4ebfc2f9e350bab93f19' +(out/'FULL-WORD.json.gz').write_bytes(g.dump(w));(out/'RETIMED-BASE.json.gz').write_bytes(g.dump(b));(out/'SELECTION.json').write_bytes(selfile.read_bytes()) +receipt=dict(status='PASS_SOURCE_BOUND_PAIR35_CONSTRUCTION_AND_DYADIC_GATE',sources={label:sha(f)for label,f in [('public_constructor',source),('prototype',hamming/'PROTOTYPE.json'),('packet_programs',hamming/'PACKET-PROGRAMS.json.gz'),('old_partial',oldfile),('retimed_partial',retfile),('pair_spec',specfile),('selection',selfile),('gk_word.py',code/'gk_word.py'),('gk_common.py',code/'gk_common.py')]},normalized_word_sha256=semantic,word_sha256=sha(out/'FULL-WORD.json.gz'),profile=dict(profile),widths=dict(Counter(widths)),widths_ordered=widths,pivots=99,transferred_frames=transferred,dyadic_event_counts=counts,scope='Exact local source, relation, frame and scalar compiler compatibility; complete arbitrary-dirt and physical provider replay remain separate.') +(out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n');print(receipt['status']) diff --git a/research/rank-sector-async/code/build_ranksector.py b/research/rank-sector-async/code/build_ranksector.py new file mode 100644 index 0000000000..a53740c2ee --- /dev/null +++ b/research/rank-sector-async/code/build_ranksector.py @@ -0,0 +1,56 @@ +"""Reconstruct the rank-sector coordinate-total supplier from frozen sources. +Apache-2.0. Prepared with OpenAI Codex assistance; retain inherited PR507/484 notices. +Usage: python -B build_ranksector.py HAMMING GK_CODE OLD_PAIR_BASE + RETIMED_PAIR_BASE PAIR_SPEC KERNEL_SELECTION NEW_OUT +The adjacent construct_ranksector.py is a pinned source file, not an optimizer. +""" +from pathlib import Path +from fractions import Fraction +from collections import Counter +import sys,json,gzip,copy,hashlib,difflib,subprocess +if not __debug__:raise RuntimeError('Assertions must remain enabled') +hamming,code,oldfile,retfile,specfile,selfile,out=map(Path,sys.argv[1:]);assert not out.exists() +source=Path(__file__).resolve().with_name('construct_ranksector.py') +rawsha=lambda f:hashlib.sha256(f.read_bytes()).hexdigest() +lf=lambda f:f.read_bytes().replace(b'\r\n',b'\n').replace(b'\r',b'\n') +textsha=lambda f:hashlib.sha256(lf(f)).hexdigest() +assert textsha(source)=='0b535b717ea3d15cf7e86b096a9a95fc92d71748cd5f937d1989001a3d2ec996' +assert textsha(specfile)=='751fad3214c819635216df2dab77b682c6a1798d1d71a959ba4e7392aab9b8c0' +assert textsha(selfile)=='e818377083be1b581da718ae4cdb0741f074df313c0813e4239377b3754f25a5' +read=lambda f:json.loads(gzip.decompress(f.read_bytes())if f.suffix=='.gz'else f.read_bytes()) +old=read(oldfile);ret=read(retfile);selection=read(selfile) +assert old['report']['R']==ret['report']['R']==560 +out.mkdir(parents=True) +with(out/'factory-construction.log').open('w')as log: + subprocess.run([sys.executable,'-B',str(Path(__file__).with_name('run_portable.py')),str(source),str(hamming),str(out/'factory'),str(specfile)],stdout=log,stderr=subprocess.STDOUT,check=True) +sys.dont_write_bytecode=True;sys.path.insert(0,str(code));import gk_word as g +b=read(out/'factory/FULL-WORD.json.gz');assert b['report']['R']==560 +transferred={} +for part in ['A','B']: + assert [e[:-1]for e in old[part]]==[e[:-1]for e in ret[part]] + aa=[tuple(e[:-1])for e in old[part]];bb=[tuple(e[:-1])for e in b[part]];count=0 + for ia,ib,n in difflib.SequenceMatcher(a=aa,b=bb,autojunk=False).get_matching_blocks(): + for d in range(n): + assert old[part][ia+d][:-1]==b[part][ib+d][:-1] + if old[part][ia+d][-1]!=ret[part][ia+d][-1]:b[part][ib+d][-1]=copy.deepcopy(ret[part][ia+d][-1]);count+=1 + transferred[part]=count +b['cleanup']=[g.inverse(e,g.FULL)for e in reversed(b['A']+b['B'])if not 120<=e[1]<240] +w=g.build(b,selection);profile=g.profile(w);widths=g.widths_of(w) +assert profile=={1:2474,2:182,3:516,4:88,5:242,6:124,7:1,8:17} +assert Counter(widths)=={7:18,8:161,9:381} +assert sum(len(c['pivots'])for c in selection['kernel'])==99 +counts={} +for part in ['A','B','cut','cleanup','precondition']: + counts[part]=len(w.get(part,[])) + for e in w.get(part,[]): + assert e[0]in['add','scale'] + q=Fraction(e[3],e[4])if e[0]=='add'else Fraction(e[2],e[3]);n=abs(q.numerator);d=q.denominator + assert not d&(d-1),(part,e) + if e[0]=='scale':assert n>0 and not n&(n-1),(part,e) +norm=copy.deepcopy(w);assert norm.get('R',560)==norm['report']['R']==560;norm.pop('R',None) +for k in ['complex_coarse_float','gain_percent_float']:norm['report'].pop(k,None) +semantic=hashlib.sha256(json.dumps(norm,sort_keys=True,separators=(',',':')).encode()).hexdigest() +assert semantic=='d966e1481e0c09e4b7a0607429411046c6b3663ee83e6b8833958a745b82e337' +(out/'FULL-WORD.json.gz').write_bytes(g.dump(w));(out/'RETIMED-BASE.json.gz').write_bytes(g.dump(b));(out/'SELECTION.json').write_bytes(lf(selfile)) +receipt=dict(status='PASS_SOURCE_BOUND_RANKSECTOR_AND_DYADIC_GATE',sources={label:rawsha(f)for label,f in [('prototype',hamming/'PROTOTYPE.json'),('packet_programs',hamming/'PACKET-PROGRAMS.json.gz'),('old_pair_base',oldfile),('retimed_pair_base',retfile)]},lf_source_hashes={label:textsha(f)for label,f in [('ranksector_constructor',source),('pair_spec',specfile),('selection',selfile),('gk_word.py',code/'gk_word.py'),('gk_common.py',code/'gk_common.py')]},normalized_word_sha256=semantic,word_sha256=rawsha(out/'FULL-WORD.json.gz'),profile=dict(profile),widths=dict(Counter(widths)),widths_ordered=widths,pivots=99,transferred_frames=transferred,dyadic_event_counts=counts,scope='Exact local source, rank-factor decoder, response relations, frame chains and dyadic contract; independent all-column, physical and outer replay remain separate.') +(out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n');print(receipt['status']) diff --git a/research/rank-sector-async/code/construct_partial.py b/research/rank-sector-async/code/construct_partial.py new file mode 100644 index 0000000000..69500f6513 --- /dev/null +++ b/research/rank-sector-async/code/construct_partial.py @@ -0,0 +1,309 @@ +# Adapted by OpenAI Codex for isolated structural research. +# Modified from PR425 by icekylinx with Codex assistance. +"""Full discovery word for Hamming packets with borrowed X and Y registers. + +This changes the scalar architecture. It is not accepted by the old restricted +gx interface: source bases may change until full-frame cleanup, and targets use +an explicitly inverted output basis. No supplier admission is asserted. +""" +import copy,gzip,json,math,time +import itertools as it +from collections import Counter,defaultdict +from fractions import Fraction as Q +from pathlib import Path + +import sys +INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text()) +P=D['binary_ports'];R=D['root_lines'];v=120;h=9 +modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz')) + +def basis(vectors): + b={} + for x in vectors: + for p in sorted(b,reverse=True): + if x>>p&1:x^=b[p] + if x: + p=x.bit_length()-1 + for q in b: + if b[q]>>p&1:b[q]^=x + b[p]=x + return tuple(b[p] for p in sorted(b,reverse=True)) +def inside(a,b):return basis(a+b)==b +def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0]) +FULL=basis([1<>p&1:x^=b[p] + if x: + p=x.bit_length()-1 + for q in b: + if b[q]>>p&1:b[q]^=x + b[p]=x + return tuple(b[p] for p in sorted(b,reverse=True)) +def inside(a,b):return basis(a+b)==b +def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0]) +FULL=basis([1<len(T):chosen.append(r);T.append(t) + assert len(chosen)==8 + U=[[Q(R[s][i])for s in ids]for i in c];assert rowrank(U)==4 + for j in range(8): + t=[Q(k==j)for k in range(8)] + if rowrank(U+[t])>len(U):U.append(t) + assert len(U)==8 + V=invmat(T);M=[[sum(U[i][k]*V[k][j]for k in range(8))for j in range(8)]for i in range(8)] + linear(chosen,M,F) + for i,r in zip(c,chosen[:4]): + assert rows[r]=={s:Q(R[s][i])for s in ids};block_totals[c,i]=r + +# Eight global coordinate sums, with a single copy each for the centers. The +# other copy is exactly the correction needed by the eight frame-line targets. +global_totals={};centers=[] +for i in range(8): + regs=[block_totals[c,i] for c in sorted(blocks) if i in c] + F=hyper(P[frame[i]]);a=regs[0] + for b in regs[1:]:add(a,b,1,F) + global_totals[i]=a + centers.append(a) +centers += [frame[i] for i in range(8)] +center_frames=[cur[r] for r in centers] +assert list(map(len,center_frames))==[8]*8+[1]*8 + +# Own-block and coordinate-frame corrections, one stream per code target. +own_out={};tetrads={} +for c,z in sorted(blocks.items()): + ids=z['receipt']['source_lines'] + tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)] + tetrads[c]=tet + for parity,targets in enumerate(tet): + sources=tet[1-parity];xs=[own[s] for s in sources] + F=basis([P[s] for s in sources]) + # Current own registers are an invertible pair-partial basis T*x. + T=[[rows[x].get(s,Q(0)) for s in sources] for x in xs] + n=len(T);aug=[r+[Q(i==j) for j in range(n)] for i,r in enumerate(T)] + for col in range(n): + k=next(i for i in range(col,n) if aug[i][col]);aug[k],aug[col]=aug[col],aug[k] + q=aug[col][col];aug[col]=[x/q for x in aug[col]] + for i in range(n): + if i!=col: + q=aug[i][col];aug[i]=[a-q*b for a,b in zip(aug[i],aug[col])] + inv=[r[n:] for r in aug] + M=[[sum(Q(G[t][s])*inv[k][j] for k,s in enumerate(sources)) for j in range(n)] for t in targets] + assert all(q.denominator&(q.denominator-1)==0 for row in M for q in row) + linear(xs,M,F) + for t,x in zip(targets,xs):own_out[t]=x + +# Cross-block M packets, shared by four targets, then two-output pair transforms. +Ms={};consumers=defaultdict(list);pairs=[] +for c in sorted(blocks): + for p in it.combinations(c,2): + ds=sorted(d for d in blocks if d!=c and set(p)<=set(d)) + for epsilon in (-1,1): + (a,alpha),(b,beta)=[packets[d,p,epsilon,c] for d in ds] + F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F) + Ms[c,p,epsilon]=(a,alpha) + i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))] + for parity,tet in enumerate(tetrads[c]): + for pi,(p,q) in enumerate(partitions): + groups=defaultdict(list) + for t in tet:groups[R[t][p[0]]*R[t][p[1]]].append(t) + for eps,ts in sorted(groups.items()): + assert len(ts)==2;a,b=sorted(ts) + e2=R[a][q[0]]*R[a][q[1]] + assert e2==R[b][q[0]]*R[b][q[1]] + keys=[(c,p,eps),(c,q,e2)];pid=len(pairs) + selected=(pi==parity) # different first partitions in the two tetrads + pairs.append({'targets':(a,b),'keys':keys,'selected':selected, + 'matrix':[[R[t][p[0]],R[t][q[0]]] for t in (a,b)]}) + for key in keys:consumers[key].append(pid) +slots={} +for key,uses in sorted(consumers.items()): + assert len(uses)==2 + a,alpha=Ms[key];ordinary=[i for i in uses if not pairs[i]['selected']] + for j,pid in enumerate(ordinary): + if j==0:r=a + else:r=alloc();add(r,a,1,cur[a]) + slots[pid,key]=(r,alpha) + +assert len(cur)-240==560,(len(cur)-240) + +# The selected target pairs borrow Y as the first packet destination. Their +# two-shear output basis is compensated at frame zero and in the scatter table. +phase=B;selected=[];output_basis=[] +for pid,pair in enumerate(pairs): + if not pair['selected']:continue + (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix'] + (a,alpha),(b,beta)=Ms[key1],Ms[key2] + add(v+t,a,-Q(mat[0][0],2)*alpha,cur[a]) + add(v+u,b,-Q(mat[0][1],2)*beta,cur[b]) + selected.append((pid,t,u,mat)) +for pid,t,u,mat in selected: + F=basis(cur[v+t]+cur[v+u]);assert all((P[s]&p).bit_count()%2==0 for s in (t,u) for p in F) + add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F) + z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F) + output_basis.append((t,u,z)) + +for pid,pair in enumerate(pairs): + if pair['selected']:continue + (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix'] + (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2] + F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta + ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta + add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F) + add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u])) +for t,r in own_out.items():add(v+t,r,-Q(1,2),hyper(P[t])) + +side=[dict(rows[v+t]) for t in range(v)] +for t in range(v): + expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {} + assert side[t]==expected,('side identity',t) + +# Correct the eight-center scatter through the inverse two-output basis. +scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)] +precondition=[] +for t,u,z in output_basis: + a,b=scatter[t].copy(),scatter[u].copy() + scatter[t]=[x/2-y/z for x,y in zip(a,b)] + scatter[u]=[x/2+y/z for x,y in zip(a,b)] + precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]], + ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]]) + +for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL) +H[8]+=8;H[1]+=8;by['c'][8]+=8;by['c'][1]+=8 +n=len(cur);Rcount=n-240 +assert sum(r*z for r,z in H.items())==9*Rcount+240*8+72 + +def apply(event,matrix): + if event[0]=='add': + _,t,s,a,b,*_=event;q=Q(a,b) + for j,x in list(matrix[s].items()): + z=matrix[t].get(j,Q(0))+q*x + if z:matrix[t][j]=z + else:matrix[t].pop(j,None) + else: + _,t,a,b,*_=event;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()} +def inverse(e,F=None): + e=copy.deepcopy(e) + if e[0]=='add':e[3]*=-1 + else:e[2],e[3]=e[3],e[2] + if F is not None:e[-1]=list(F) + return e +cut=[] +for t,rr in enumerate(scatter): + for i,q in enumerate(rr): + if q:cut.append(['add',v+t,centers[i],q.numerator,q.denominator,None]) +cleanup=[inverse(e,FULL) for e in reversed(A+B) if not v<=e[1]<2*v] + +# Exact clean replay checks the changed decoder and restored source basis. +matrix=[{r:Q(1)} if r=0 and off+w<=rank[i] + assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1] + B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i] + occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[] + order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M + sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma + route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9 + cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells + digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n') +for c in t['calls']: + k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R)) + c['owners']=c['owners'][:240]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==800 and all(f2*max(paid)**2 + +assert t['local_programs']==parent['local_programs'] +raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0)) +res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=2496,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.') +(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2)) diff --git a/research/rank-sector-async/code/run_portable.py b/research/rank-sector-async/code/run_portable.py new file mode 100644 index 0000000000..dcfe7128e1 --- /dev/null +++ b/research/rank-sector-async/code/run_portable.py @@ -0,0 +1,15 @@ +"""Run one retained verifier with UTF-8/LF text outputs on every platform. +This changes output serialization only; no mathematical operation is replaced. +""" +from pathlib import Path +import runpy,sys +if not __debug__: + raise RuntimeError('Assertions must remain enabled') +original_write_text=Path.write_text +def write_text_lf(self,data,encoding=None,errors=None,newline=None): + return original_write_text(self,data,encoding=encoding or 'utf-8',errors=errors,newline='\n') +Path.write_text=write_text_lf +script=Path(sys.argv[1]).resolve() +sys.argv=sys.argv[1:] +sys.path.insert(0,str(script.parent)) +runpy.run_path(str(script),run_name='__main__') diff --git a/research/rank-sector-async/evidence/EXACT-ASSEMBLY.json b/research/rank-sector-async/evidence/EXACT-ASSEMBLY.json new file mode 100644 index 0000000000..63368d7a04 --- /dev/null +++ b/research/rank-sector-async/evidence/EXACT-ASSEMBLY.json @@ -0,0 +1,127 @@ +{ 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"PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.", + "scope": "Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately." +} diff --git a/research/rank-sector-async/evidence/INDEPENDENT-FINAL-REVIEW.json b/research/rank-sector-async/evidence/INDEPENDENT-FINAL-REVIEW.json new file mode 100644 index 0000000000..b754ecc708 --- /dev/null +++ b/research/rank-sector-async/evidence/INDEPENDENT-FINAL-REVIEW.json @@ -0,0 +1,43 @@ +{ + "status": "PASS_INDEPENDENT_CHANGED_CONSTRUCTION_AND_COMPLETED_REPLAY_REVIEW", + "kappa": "1402213284556683/1000000000000000000", + "kappa_decimal": "0.001402213284556683", + "complex_lower": "1404182247558147721001/1000000000000000000000000", + "template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11", + "completed_stages": 15, + "columns_each_orientation": 800, + "kernel_negative_controls": 99, + "whole_family_roles": 40320, + "complete_invocations": 72, + "actual_73_column_maps": 2842, + "asynchronous_negative_controls": 19, + "strict_outer_constraints": 47, + "required_prefix_bits": 210, + "charged_prefix_bits": 512, + "physical_row_coefficient": 16467, + "normalized_word_sha256": "d966e1481e0c09e4b7a0607429411046c6b3663ee83e6b8833958a745b82e337", + "fresh_source_and_receipt_bindings": { + "RESULT.json": "b4202a5c53b933bfb82f747978dd296fad80e291a6f95ea2c233d8853995bbf0", + "audit/ASYNC-AUDIT.json": "88c53e113fcbb28f9335374eadb42409c5d6719a57de65d6a3061af68cb52868", + "audit/OWNERS-AND-PROFILE.json": "43fa819bd814d1ae36a3c35e46f8a2e9884427927b93c79431534945bfa2420f", + "audit/PREFIX-AND-INVOICE.json": "b4379c3dcafdae3afa0370cfc0c1e01b30470147bf42beb16e6a836ef9870347", + "audit/EXACT-ASSEMBLY.json": "de523955c6389eaa3b04b1c1b148cd4fbd3f571ae4c099a22229082300ffd2e5", + "audit/KERNEL-SCALAR.json": "b205d2df68f6bfdeb39ed713a12a10cd02a25d240ee2c68f13c123c666e39e29", + "base/split-centres/CONSTRUCTION.json": "c9e42e607f162c950ffd4427a7fe50fcdc12a29965f81a0f8546cdc427357404", + "hosted/HOSTED.json": "7fa5eb4d8cdef206d01fb308b327e6e36f2a22634c7505a69e2003a623575547" + }, + "independent_work": [ + "Reviewed invertible U*T^-1 construction and retained arbitrary-dirt storage", + "Recomputed all literal owner windows, distinctness, residual intervals, remainders and paid profile", + "Independently reinterpreted exact scalar/Horner envelopes", + "Checked emitted template, source, constructor and final invoice/assembly receipt bindings", + "Package builder differs from research builder only by documented run_portable.py subprocess launcher; actual constructor identical" + ], + "limitations": [ + "Inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain conditional", + "PR493 bit supplier is unchanged and cited, not freshly reverified", + "No new Lean formalization or kernel certification", + "Package manifest and final CRLF staging replay are parent-owned finalization, not executed by this reviewer" + ], + "own_processes_running": 0 +} diff --git a/research/rank-sector-async/evidence/INDEPENDENT-NOMINATION.json b/research/rank-sector-async/evidence/INDEPENDENT-NOMINATION.json new file mode 100644 index 0000000000..30a545b25d --- /dev/null +++ b/research/rank-sector-async/evidence/INDEPENDENT-NOMINATION.json @@ -0,0 +1,29 @@ +{ + "status": "PASS_INDEPENDENT_LITERAL_OWNER_AND_PROFILE_REVIEW", + "calls": 72, + "roles": 40320, + "remainder_profile": { + "3": 3044, + "5": 3608, + "7": 92, + "48": 796 + }, + "profile": { + "1": 178128, + "2": 13104, + "3": 40196, + "4": 6336, + "5": 21032, + "6": 8928, + "7": 164, + "8": 1224, + "48": 796 + }, + "deficit": 2496, + "source_hashes": { + "RANKSECTOR-PLAN.json": "9b4b8f125a19ec5741050ca62167c0a4ea2e7f80880f4635c1b6e6c99ea506e8", + "RANKSECTOR-OWNERS.json.gz": "5e1ac46a2390c8355ad4b05a154c8c95ed4dd47e87f620d549c5deb26bfa95f7", + "RANKSECTOR-SCREEN.json": "0c4ba24edb7ca709948583d8eae89010daba71ad8a5aabca486d88e97401aa9e" + }, + "scope": "Exact nomination-level chronology, original child lifetimes, complete-family uniqueness, disjoint pending-coordinate offsets, source-bound widths, all remainders. Full physical maps, phases and scalar invoice remain separate checks." +} diff --git a/research/rank-sector-async/evidence/INDEPENDENT-PREFIX.json b/research/rank-sector-async/evidence/INDEPENDENT-PREFIX.json new file mode 100644 index 0000000000..f163d6100e --- /dev/null +++ b/research/rank-sector-async/evidence/INDEPENDENT-PREFIX.json @@ -0,0 +1,15 @@ +{ + "status": "PASS_INDEPENDENT_SCALAR_HORNER_ENVELOPE", + "source_sha256": "b758341ac6c0b7f44570a30f20eca841003b69db67a98a1eefa0fd0248fc480f", + "backward": { + "peak": "57889301/2", + "bits": 25 + }, + "forward": { + "peak": "737611", + "bits": 20 + }, + "global_required_bits": 210, + "charged_bits": 512, + "method": "Separate positive-envelope interpreter. Unsigned binary Horner accumulator never exceeds numerator times source envelope; denominator halvings do not increase it. Every scalar update, copy and clear is included; whole stream adds37inputbits,72invocations,72bridges,4primitive margin." +} diff --git a/research/rank-sector-async/evidence/PAIR35-COMMUTATOR-SCREEN.json b/research/rank-sector-async/evidence/PAIR35-COMMUTATOR-SCREEN.json new file mode 100644 index 0000000000..fe51488c70 --- /dev/null +++ b/research/rank-sector-async/evidence/PAIR35-COMMUTATOR-SCREEN.json @@ -0,0 +1 @@ +[] diff --git a/research/rank-sector-async/evidence/PORTABLE-REPLAY.json b/research/rank-sector-async/evidence/PORTABLE-REPLAY.json new file mode 100644 index 0000000000..cbf913479e --- /dev/null +++ b/research/rank-sector-async/evidence/PORTABLE-REPLAY.json @@ -0,0 +1,88 @@ +{ + "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE", + "kappa": "1402213284556683/1000000000000000000", + "kappa_decimal": "0.001402213284556683", + "complex_lower": "1404182247558147721001/1000000000000000000000000", + "bit_lower": "391360506745414227149/250000000000000000000000", + "template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11", + "strict_constraints": 47, + "scope": "New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.", + "stages": [ + { + "stage": "partial-factory", + "exit": 0, + "seconds": 0.6090000000258442 + }, + { + "stage": "construct-kernel92", + "exit": 0, + "seconds": 2.062999999994645 + }, + { + "stage": "construct-pair35", + "exit": 0, + "seconds": 1.6559999999881256 + }, + { + "stage": "construct-ranksector", + "exit": 0, + "seconds": 1.6719999999913853 + }, + { + "stage": "kernel-scalar-controls", + "exit": 0, + "seconds": 27.90600000001723 + }, + { + "stage": "scalar", + "exit": 0, + "seconds": 2.1710000000020955 + }, + { + "stage": "emit-local", + "exit": 0, + "seconds": 1.187000000005355 + }, + { + "stage": "phases", + "exit": 0, + "seconds": 198.46899999998277 + }, + { + "stage": "adapters", + "exit": 0, + "seconds": 1.2030000000086147 + }, + { + "stage": "parent-integration", + "exit": 0, + "seconds": 1.1400000000139698 + }, + { + "stage": "parent-replay", + "exit": 0, + "seconds": 8.187999999994645 + }, + { + "stage": "emit-async", + "exit": 0, + "seconds": 4.280999999988126 + }, + { + "stage": "independent-async", + "exit": 0, + "seconds": 23.453000000008615 + }, + { + "stage": "invoice", + "exit": 0, + "seconds": 1.8280000000086147 + }, + { + "stage": "two-moments-assembly", + "exit": 0, + "seconds": 0.5779999999795109 + } + ], + "package_manifest_sha256": "8d86cb4990686bc00ca28b7759ab29db55b81875de31f97c7246caccdc21a7eb" +} diff --git a/research/rank-sector-async/evidence/PREFIX-AND-INVOICE.json b/research/rank-sector-async/evidence/PREFIX-AND-INVOICE.json new file mode 100644 index 0000000000..25d48f5a6c --- /dev/null +++ b/research/rank-sector-async/evidence/PREFIX-AND-INVOICE.json @@ -0,0 +1,69 @@ +{ + "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE", + "template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11", + "global_prefix_bits": 210, + "charged_prefix_bits": 512, + "complete_invocation_sweeps": 72, + "bridge_sweeps": 72, + "row_prefix_extra": 1024, + "local": { + "backward": { + "events": 22124, + "macros": 16692, + "real_component_primitives": 169838, + "prefix_l1": "57889301/2", + "prefix_bits": 25, + "coefficient_work_primitive_count": 83983, + "all_exact_columns": 800, + "all_560_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true + }, + "forward": { + "events": 22124, + "macros": 16692, + "real_component_primitives": 169742, + "prefix_l1": "737611", + "prefix_bits": 20, + "coefficient_work_primitive_count": 83919, + "all_exact_columns": 800, + "all_560_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true + } + }, + "entering_helpers": 179, + "entrance_rank": 197, + "local_adapters": 343104, + "local_primitive_bound": 8898174588782, + "wrapper_elementary_factors_charged": 3711744, + "compiler": 25934336, + "unhosted_pervertex": 1454373093983904, + "hosted_rebased_pervertex": 1454373093651264, + "conservative_pervertex_used": 1454373093983904, + "finite": { + "physical_stock_bits": 2641, + "router_bits": 7984, + "literal_bits": 35282, + "physical_row_coefficient": 16467, + "retained_row_coefficient": 20161, + "required_C0_bits": 200012, + "halving_integer_inequality": [ + 5329, + 4608 + ], + "G_exponent": 30000, + "E_exponent": 100000, + "C0_exponent": 210000 + }, + "strict_checks": { + "local_primitive_bound": true, + "logical": true, + "router": true, + "literal": true, + "mass": true, + "precision": true, + "tape": true, + "row": true, + "halving": true + }, + "scope": "Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound." +} diff --git a/research/rank-sector-async/evidence/RANKSECTOR-COMMUTATOR-SCREEN.json b/research/rank-sector-async/evidence/RANKSECTOR-COMMUTATOR-SCREEN.json new file mode 100644 index 0000000000..fe51488c70 --- /dev/null +++ b/research/rank-sector-async/evidence/RANKSECTOR-COMMUTATOR-SCREEN.json @@ -0,0 +1 @@ +[] diff --git a/research/rank-sector-async/evidence/TRANSPORT-CONTROLS.json b/research/rank-sector-async/evidence/TRANSPORT-CONTROLS.json new file mode 100644 index 0000000000..ac2797863a --- /dev/null +++ b/research/rank-sector-async/evidence/TRANSPORT-CONTROLS.json @@ -0,0 +1,17 @@ +[ + { + "control": "tampered-token", + "exit": 1, + "rejected_before_output": true + }, + { + "control": "missing-file", + "exit": 1, + "rejected_before_output": true + }, + { + "control": "optimized-python", + "exit": 1, + 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147573952589676412928, + 295147905179352825856, + 590295810358705651712, + 1180591620717411303424, + 2361183241434822606848, + 4722366482869645213696 + ], + "translation_after": 0 + }, + { + "rank": 16, + "orthogonal_axes": [ + 144115188075855872, + 288230376151711744, + 576460752303423488, + 1152921504606846976, + 2305843009213693952, + 4611686018427387904, + 9223372036854775808, + 18446744073709551616, + 36893488147419103232, + 73786976294838206464, + 147573952589676412928, + 295147905179352825856, + 590295810358705651712, + 1180591620717411303424, + 2361183241434822606848, + 4722366482869645213696 + ], + "translation_after": 0 + }, + { + "rank": 0, + "orthogonal_axes": [], + "translation_after": 0 + }, + { + "rank": 0, + "orthogonal_axes": [], + "translation_after": 0 + } + ], + "terminal_Y_translation": 127 + } + ], + "cover_correction": { + "formula": "delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.", + "reason": "P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector.", + "mandatory": true, + "complete_small_cover_checks": [ + { + "n": 1, + "orthogonal_matrices": 1, + "nonzero_full_kernel_corrections": 0 + }, + { + "n": 2, + "orthogonal_matrices": 2, + "nonzero_full_kernel_corrections": 0 + }, + { + "n": 3, + "orthogonal_matrices": 6, + "nonzero_full_kernel_corrections": 0 + }, + { + "n": 4, + "orthogonal_matrices": 48, + "nonzero_full_kernel_corrections": 24 + }, + { + "n": 5, + "orthogonal_matrices": 720, + "nonzero_full_kernel_corrections": 600 + } + ] + }, + "global_phase_argument": "Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as well.", + "scope": "All compressed data boundary operators, idle children, terminal X_q and all-live cover correction. Internal arbitrary-subspace canonical labels are checked separately." +} \ No newline at end of file diff --git a/research/rank-sector-async/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz b/research/rank-sector-async/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz new file mode 100644 index 0000000000..975ce5c0df Binary files /dev/null and b/research/rank-sector-async/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz differ diff --git a/research/rank-sector-async/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz b/research/rank-sector-async/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz new file mode 100644 index 0000000000..ccbdc0596c Binary files /dev/null and b/research/rank-sector-async/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz differ diff --git a/research/rank-sector-async/inputs/work/odd-stages/clifford_exact.py b/research/rank-sector-async/inputs/work/odd-stages/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/rank-sector-async/inputs/work/odd-stages/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1< 2: + x /= 2 + k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + # Outward rational rounding keeps later certificates compact. + 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, 13): + term *= x/j + total += term + tail = term*x/13/(1-x/14) + 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)) + lower = exp_bounds(saving*l)[0] + upper = exp_bounds(saving*u)[1] + lo += Q(t*count, m*W)*lower + hi += Q(t*count, m*W)*upper + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + diff --git a/research/rank-sector-async/inputs/work/pr361/code/engines/moment.py b/research/rank-sector-async/inputs/work/pr361/code/engines/moment.py new file mode 100644 index 0000000000..7d697cb452 --- /dev/null +++ b/research/rank-sector-async/inputs/work/pr361/code/engines/moment.py @@ -0,0 +1,113 @@ +"""Independent prospective ordinary five-stage cost, never supplier admission. + +Consumes a raw one-invocation ledger made from the actual source/internal/target +paths. No packed profile is used as an input. Missing physical/finite/compiler +obligations must remain explicit in the accompanying report. +""" +from collections import Counter +from decimal import Decimal, localcontext, ROUND_FLOOR +from fractions import Fraction as F +from functools import lru_cache +from math import factorial +import hashlib, json, sys +from pathlib import Path + +DYAD = 1 << 224 + +def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) +def ceil(x): return -floor(-x) + +@lru_cache(None) +def logarithm(x): + """Mercator bounds after binary reduction; ln(2) via two Mercator sums. + + For 1 <= y < 2, log(y) is an alternating series in z=y-1. + We instead reduce to 1 <= y < 3/2, and bound log(3/2) and + log(2) by the same alternating series at z=1/2 and z=1/3, + using log(2)=log(3/2)+log(4/3). All sums are exact rationals. + """ + assert x >= 1 + k = 0 + while x >= 2: x /= 2; k += 1 + j = int(x >= F(3, 2)) + if j: x /= F(3, 2) + def mercator(y): + z=y-1 + assert 0 <= z <= F(1,2) + # An even partial sum is below log; the next term bounds its tail. + t=z; s=F(0) + for n in range(1, 225): + s += (t if n & 1 else -t)/n + t *= z + return s, s+t/225 + 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(1,25): t=t*x/j; s+=t + return s,t + lo,_=poly(l);hi,last=poly(u) + return floor(lo),ceil(hi+last*u/25/(1-u/26)) + +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: + # Existing envelope shape, only conditionally portable to the new cover. + 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) + +def decimal(x): + with localcontext() as c: + c.prec=70 + return str(Decimal(x.numerator)/Decimal(x.denominator)) + +def certify(H,m,W,bad=False): + with localcontext() as c: + c.prec=70 + terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()] + fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0) + lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003') + for _ in range(210): + a=(lo+hi)/2 + if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a + else:hi=a + q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR)) + lo=F(q,10**24);hi=lo+F(1,10**24) + lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad) + assert lv[1]<10 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2 + assert 1-eps*(1+c)==eta-eps*eta/4 + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/rank-sector-async/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz b/research/rank-sector-async/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz new file mode 100644 index 0000000000..8bec1751f7 Binary files /dev/null and b/research/rank-sector-async/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz differ diff --git a/research/rank-sector-async/references/PR493-NOTICE.md b/research/rank-sector-async/references/PR493-NOTICE.md new file mode 100644 index 0000000000..ac7d789262 --- /dev/null +++ b/research/rank-sector-async/references/PR493-NOTICE.md @@ -0,0 +1,11 @@ +# Attribution for the included PR493 material + +Apache-2.0. Prepared by eumemic with substantial Anthropic Claude assistance. +The only copied PR493 payload in this package is its published EXPECTED.json. +Its R489 bit operator is cited, not vendored or freshly reconstructed here. + +The original complete notice is available with the pinned source: +https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/NOTICE.md + +This attribution excerpt omits sections for code and historical receipt files +that are not included in this package. It does not modify any upstream file. diff --git a/research/rank-sector-async/research-notes/CORRELATED-REPAIR.md b/research/rank-sector-async/research-notes/CORRELATED-REPAIR.md new file mode 100644 index 0000000000..52e2ab8ab3 --- /dev/null +++ b/research/rank-sector-async/research-notes/CORRELATED-REPAIR.md @@ -0,0 +1,13 @@ +# Correlated owner repair + +The new source family is the OpenAI UniformKServer tree-rounding construction. TreeRounding.park keeps unassigned mass explicit, Rounded constrains both subtree totals and parked mass, and extended_star preserves old observables while coupling new choices. RoundingKernel.kernel_next and kernel_rounded state support and transition guarantees. These were read as source, not compiled or instantiated in the multiplication proof. The borrowed idea is to repair several assignments jointly while preserving exact marginals and charging parked mass; our deterministic finite repair is a separate construction, not the source randomized rounding theorem. + +Sufficient finite repair rule: choose a set of complete pending-child bins and remove only the helper roles assigned to them. Reassign exactly those role identities among those bins. Each role keeps its invocation, local register and width. Require the new pending interval to contain that invocation, total width in each bin to remain within its rank, and every physical family in an invocation to have at most one whole helper and no active data wire. Repack all selected supports contiguously and charge the exact leftover rank. Then the resulting map satisfies the same abstract complete-owner allocation contract. Full physical charts still have to be regenerated and independently replayed against the selected local provider before this becomes a deliverable. + +The executable screen enumerates simultaneous assignments of all roles of three selected bins, checks capacity, timeline and per-call collision constraints, and minimizes the complete contribution of the changed leftover ranks at the baseline exponent. No leftover rank is erased. Neutral-face moves are allowed in a separately recorded bounded screen to avoid mistaking a strict local minimum for a complete result. + +The first native scan examined 200,000 bin triples and 225,394,867 recursion nodes. It accepted no strictly improving repair. This is only a bounded discovery outcome. The separate aggregate capacity screen leaves about 0.044 percent supplier headroom in this fixed architecture, which directs further effort toward genuinely changed local providers. Neither screen proves optimality or supplies a new kappa claim. + +The separate 40-second neutral-face sweep accepted 120,911 cost-neutral moves and visited 2,135,369,213 recursive assignment nodes. Its final leftover histogram was unchanged: 3:3044, 5:3608, 7:92, 48:796. No new physical certificate was packaged from these neutral research maps. + +The selected improvement instead comes from the kernel lane's rank-sector factorization. Its ordered residual widths are byte-for-byte equal as integers to the pair35 list. Thus the original literal owner map is reused unchanged, with a fresh source-bound operator replay. The local profile delta is -56 rank-1 calls -56 rank-5 calls +56 rank-6 calls, preserving rank mass and improving every moment with exponent strictly between zero and one, since 6^a < 1 + 5^a. The measured complete-profile supplier root is about 0.0014041822501567602 before exact assembly. This actual gain must not be attributed to our unsuccessful correlated repair route. diff --git a/research/rank-sector-async/research-notes/PORTABLE-REPLAY.md b/research/rank-sector-async/research-notes/PORTABLE-REPLAY.md new file mode 100644 index 0000000000..59228e00c2 --- /dev/null +++ b/research/rank-sector-async/research-notes/PORTABLE-REPLAY.md @@ -0,0 +1,7 @@ +# Fresh transport replay + +All 15 stages passed on a new copy with every recognized text source and input converted to CRLF. Nested factory subprocesses use the portable launcher so generated text is UTF-8/LF before raw source hashes are embedded. Static binary inputs are hashed byte-for-byte; generated gzip header bytes are distinguished from the canonical mathematical template hash. No Linux or Python 3.14 run is claimed from this Windows test. + +The manifest rejects changed tokens and missing files before output creation; optimized Python is explicitly rejected. No hidden file is required. No mathematical source changed after the complete portability replay: only evidence and this note were added, followed by manifest reconstruction and byte-exact upload reassembly. + +The new scalar program has a larger exact envelope than the preceding word. Its independent review gives forward 737611 and backward 57889301/2, requiring 25 local bits and 210 overall bits. This fits the retained 512-bit charge. The invoice derives its bound from the actual new scalar events, rather than copying the preceding 206-bit result. The physical row coefficient remains explicitly checked against its allowance. diff --git a/research/rank-sector-async/research-notes/RANKSECTOR-PROOF.md b/research/rank-sector-async/research-notes/RANKSECTOR-PROOF.md new file mode 100644 index 0000000000..e0b10841d5 --- /dev/null +++ b/research/rank-sector-async/research-notes/RANKSECTOR-PROOF.md @@ -0,0 +1,56 @@ +# Coordinate-total reconstruction on an independent row sector + +## The implemented improvement + +The old partial-own factory has twelve retired registers in each of fourteen code blocks. Their clean source rows span only eight dimensions. It raises all twelve registers from their rank-three frames to the common rank-four block frame, reduces the twelve-by-eight row matrix, and forms four coordinate totals. The extra four raised rows are unnecessary for those outputs. + +The new factory chooses eight independent retired rows, changes basis on those eight registers so that the first four contain the required coordinate totals, and leaves the other four registers untouched until the ordinary cleanup. All 560 helpers remain present. No dirty register is erased, identified with another register, or treated as clean storage. + +This removes four intermediate climbs in each block. Each affected register previously paid a rank-one climb followed by a rank-five climb; it now pays one rank-six climb. The exact local delta is + + -56 rank-one calls -56 rank-five calls +56 rank-six calls. + +The selected 99 kernel pivots, gauge selection and ordered whole-residual inventory are unchanged. The inventory is eighteen width-seven, 161 width-eight and 381 width-nine helpers. The new local profile is: + + rank: 1 2 3 4 5 6 7 8 + count: 2474 182 516 88 242 124 1 17. + +For every 0 < b < 1, strict subadditivity of x^(1-b) gives 6^(1-b) < 1 + 5^(1-b). Thus this change strictly reduces the recursive moment while preserving rank mass. Across the existing seventy-two invocations, the complete global child profile has the corresponding factor-seventy-two delta. The same whole-owner allocation can be retained because the ordered widths agree exactly. The final finite arithmetic replay also charges the actual scalar program and is the authority for the published supplier bound and kappa. + +## Sufficient algebraic construction + +Write the eight independent clean rows as an invertible matrix T in the eight source coordinates. Let L be the four-by-eight matrix of required coordinate sums. The four rows of L are independent. Extend them to an eight-row basis U, and form + + M = U T^(-1). + +The emitted elementary operations apply M to precisely the eight selected physical registers at their admitted common block frame. Their clean output rows are M T = U, so the first four are exactly L. M is invertible on arbitrary physical register contents, and all unselected registers are literally unchanged by this stage. The inverse cleanup is reconstructed from the new actual word. + +Dirty-state correctness is not inferred from the clean row equation alone. The complete helper response matrix is recomputed, the actual target compensations and kernel prefix are reconstructed, and all scalar basis columns are checked in both orientations. For this frozen word, all 800 forward columns, all 800 inverse-transpose columns, and 99 independent omitted-kernel-correction controls pass. Every scalar denominator is a power of two and every scaling operation is a signed power of two, matching the existing finite scalar compiler. + +The constructor uses deterministic finite row reduction to select T and extend L. This is part of reconstruction, not an optimizer or an assumed gadget. The exact common-frame containment tests, final scalar identity, dirty-data compensation, dyadic compatibility and physical global replay remain explicit checks in the package. + +## OpenAI proof source and precise transfer + +The direct source is `lean/OAI/Analysis/Cotype/RankFactors.lean`, from the corpus's cotype-cotype project (catalogue item 326). In namespace `OAI.Cotype`, `exists_rank_pairing_matrix` constructs rectangular factors for an arbitrary square matrix P over a field: + + I.transpose * P * J = identity_on_rank(P). + +Its proof selects the independent block in `Matrix.exists_rank_normal_form`. The following theorem, `rank_pairing_contract`, proves that these factors preserve the desired bilinear contraction exactly. We transferred the constructive principle: restrict to the independent sector needed by the output pairing instead of normalizing every redundant row. Here the independent sector has dimension eight, the requested total map has four rows, and the preserved ambient registers carry the unused dirty coordinates. + +This is a different construction from the preceding package's Newton-inspired pair-cover selection. The pair covers are fixed throughout this change. It is also not a claim that the Banach-space theorem automatically certifies our circuit. The file and its proof were inspected; the new rational circuit has separate finite checks. No fresh Lean compilation was performed in this round. + +The initially inspected alternative source, `Computability/FourierCircuit/DisplacementKernel.lean`, gives the exact `reconstruct` identity for an interior outer-product recurrence and its explicit boundary terms. This motivated a packet-to-total telescoping gate. All fifty-six coordinate totals were found in the admissible retired/packet row spans, but the winning construction is the independent rank sector described above, not a claim that a displacement factorization itself improved the final bound. + +## Bounded search and reproducibility + +The clean checkpoint, rowspace tests and frames are retained in `TOTALS-CHECKPOINT.json` and `TOTALS-GATE.json`. After the positive eight-row construction, one bounded native C++ pass enumerated the 4096 subsets of the twelve retired rows in each block over the prime 1000003. Within that modular gate, each block required at least eight independent rows to span the four coordinate totals, with 63 choices of eight rows. This is a bounded search record, not a global optimality theorem or an exclusion of redesigned factories. + +`construct_ranksector.py` contains the actual factory and its exact decoder assertions. `build_ranksector.py` reconstructs it, transfers only matching inherited scalar-event frames, rebuilds the existing 99-pivot selection, checks the dyadic contract and binds the complete normalized word. It invokes no discovery search. Text-source pins normalize only line endings to avoid platform-dependent CRLF failures. Whole-word normalization removes only the two established stale floating display annotations and an asserted redundant register-count field; mathematical operations, coefficients, frames and the rest of the word remain hash-bound. + +Normalized selected-word SHA-256: + + d966e1481e0c09e4b7a0607429411046c6b3663ee83e6b8833958a745b82e337 + +The local scalar receipt is `ranksector/SCALAR-AUDIT.json`; the source reconstruction receipt is `rebuilt-ranksector/CONSTRUCTION.json`. Physical owner maps, local complex phases, normalized spectators and the final two-engine arithmetic receipt are checked independently by the package replay. + +Inherited public mechanisms remain credited: PR507 supplies the partial-own factory; PR484 the gauge/kernel compiler; PR496 the pooled whole-owner interface; PR495/501/502 the frame retiming; and PR473 inspired the coordinated gauge reductions. The preceding package supplies the two-block pair cover and its 99-pivot selection, as well as the asynchronous controller and literal allocation. The improvement here is specifically the rank-sector coordinate-total reconstruction. diff --git a/research/rank-sector-async/research-notes/RANKSECTOR-SOURCES.json b/research/rank-sector-async/research-notes/RANKSECTOR-SOURCES.json new file mode 100644 index 0000000000..0e3b1d30f7 --- /dev/null +++ b/research/rank-sector-async/research-notes/RANKSECTOR-SOURCES.json @@ -0,0 +1,25 @@ +{ + "snapshot": "adc7f1241b42e322a6451854ab7e4b4c146bf78a", + "sources": [ + { + "path": "lean/OAI/Analysis/Cotype/RankFactors.lean", + "sha256": "dca9d3a06e6b1d9fa3e53c9423bf41b6a192a9946f36284920d322c90b9bce55", + "declarations": [ + "OAI.Cotype.exists_rank_pairing_matrix", + "OAI.Cotype.rank_pairing_contract" + ], + "role": "winning independent-sector construction", + "evidence": "Direct source/proof inspection, no fresh Lean compilation" + }, + { + "path": "lean/OAI/Computability/FourierCircuit/DisplacementKernel.lean", + "sha256": "6663fc0dd25d18e0541f5328aead03e3bfd1c40e02fbaa7c171f8e6e35043b55", + "declarations": [ + "OAI.ExactFourier.Displacement.reconstruct", + "OAI.ExactFourier.Displacement.kernel_eq_mul" + ], + "role": "screened telescoping source, not a separate numerical gain", + "evidence": "Direct source/proof inspection, no fresh Lean compilation" + } + ] +} diff --git a/research/rank-sector-async/research-notes/ROOT-WORD-PROOF.md b/research/rank-sector-async/research-notes/ROOT-WORD-PROOF.md new file mode 100644 index 0000000000..a8c3ac6795 --- /dev/null +++ b/research/rank-sector-async/research-notes/ROOT-WORD-PROOF.md @@ -0,0 +1,29 @@ +# Paid commutator rewrites of scalar words + +Source: the OpenAI DukePrimeDegree root-coordinate proof. RootCommutator.adjacent_root_conjugation gives an exact three-root transvection identity; EliminationChain.param_val identifies the actual ordered product, and EliminationWordEntries.word_val_eq_sum_single gives the compatible triangular special case. These sources were inspected, not newly compiled. No ergodic or limiting argument is imported into a finite algorithm. + +For three distinct registers a,b,c and rational q,r, replace the execution sequence + + a += q*b; b += r*c + +by + + b += r*c; a += q*b; a -= q*r*c. + +Substitution shows that both produce (a+q*b,b+r*c,c) from arbitrary initial values. Likewise, a+=q*b; c+=r*a equals c+=r*a; a+=q*b; c+=r*q*b. No zero-initialized helper is assumed. Dyadic coefficients remain dyadic under multiplication. The extra correction is an actual paid scalar gate. + +If the original first and second gates have frames F contained in G, put all three replacement gates at G only when every preceding register frame lies inside G and every subsequent register frame still contains G. Recompute the entire frame chain and actual prefix envelope. When gates lie farther apart, move the first past intervening gates only if their elementary operators commute; our structural gate checks that neither target occurs as the other's source and handles scales conservatively. Then apply the same identity and retain every correction. An exact all-input and physical replay is required before claiming any accepted word. + +For adjacent gates, let d_s and d_o be the dimensions of the shared and other first-gate registers beforehand; let f=dim(F), g=dim(G), and h the other register's next frame dimension. The old affected recursive costs at exponent a are + + (f-d_s)^a + (g-f)^a + (f-d_o)^a + (h-f)^a, + +and the new costs are + + (g-d_s)^a + (g-d_o)^a + (h-g)^a, + +omitting zero increments. Other registers' equal charges cancel. This gives a sufficient cost gate, but it is not assumed positive. A finite scan must also charge scalar precision and restoration. + +On the checked pair35 provider, the adjacent scan found no improving legal window. A larger native C++ scan inspected up to 128 following events, respecting exact commutation, and evaluated603 complete candidate frame profiles. None passed its floating discovery-price gate. GF(2) frame legality was exact; the discovery price used ordinary floating arithmetic and is not a rational nonexistence certificate. No changed word or kappa gain is claimed from this route. This is a bounded test of a sufficient transformation, not a universal barrier. + +The same native window test was then applied to the selected rank-sector provider: 547 full candidate profiles, no nominee passing the discovery cost gate. This follow-up is distinct from the 603-window pair35 screen above. diff --git a/research/rank-sector-async/research-notes/ROOT-WORD-SOURCES.json b/research/rank-sector-async/research-notes/ROOT-WORD-SOURCES.json new file mode 100644 index 0000000000..81d64db053 --- /dev/null +++ b/research/rank-sector-async/research-notes/ROOT-WORD-SOURCES.json @@ -0,0 +1,23 @@ +{ + "revision": "adc7f1241b42e322a6451854ab7e4b4c146bf78a", + "evidence": "source-only inspection; no fresh Lean kernel audit", + "sources": [ + { + "path": "lean/OAI/NumberTheory/DukePrimeDegree/Geometry/RootCommutator.lean", + "sha256": "02e98ff42087d4b8ea7ed45338a024dd154c3aacdc585b1d6e06e137bb5e9d40" + }, + { + "path": "lean/OAI/NumberTheory/DukePrimeDegree/Geometry/EliminationWordEntries.lean", + "sha256": "5d1be438e824ebc60b1845554aa07cfbd5f4a7bb1e424bcff2fe41c9bed0ba0e" + }, + { + "path": "lean/OAI/NumberTheory/DukePrimeDegree/Geometry/EliminationChain.lean", + "sha256": 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gate.", + "uniform_attempted": 9, + "uniform_saved_records": 8 +} \ No newline at end of file diff --git a/research/rank-sector-async/research-notes/SWITCH-SOURCES.json b/research/rank-sector-async/research-notes/SWITCH-SOURCES.json new file mode 100644 index 0000000000..2b9207922a --- /dev/null +++ b/research/rank-sector-async/research-notes/SWITCH-SOURCES.json @@ -0,0 +1,22 @@ +{ + "family": "Problem315 SwitchChain", + "sources": [ + { + "path": "openai-math/lean\\OAI\\Probability\\SwitchChain\\FourVertexSwitch.lean", + "sha256": "07cc53158c1970dd75cbc2f7bf5d83c6ffc59e22d0484aaa6e17417e4bc818e3", + "scope": "Read source; no fresh Lean compilation or axiom audit." + }, + { + "path": "openai-math/lean\\OAI\\Probability\\SwitchChain\\PairTradeSwitch.lean", + "sha256": "1357424dee22e34e6bdb86013a7e441854edf0d14874c04d9b993c5c6f3362a9", + "scope": "Read source; no fresh Lean compilation or axiom audit." + } + ], + "declarations": [ + "fourVertexState_agrees_outside", + "switchStep_fourVertexState", + "PairFiber.fourVertexState_key", + "PairFiber.trade_exchange_eq_fourVertexState", + "PairFiber.switchStep_of_key_leftSet_exchange" + ] +} \ No newline at end of file diff --git a/research/rank-sector-async/research-notes/Y-SWITCH-PROOF.md b/research/rank-sector-async/research-notes/Y-SWITCH-PROOF.md new file mode 100644 index 0000000000..433d3f6539 --- /dev/null +++ b/research/rank-sector-async/research-notes/Y-SWITCH-PROOF.md @@ -0,0 +1,11 @@ +# Degree-preserving Y-borrowing switches + +A new source family was read: OpenAI Problem315 SwitchChain, FourVertexSwitch and PairTradeSwitch. The exact source files and hashes are in OPENAI-SOURCE.json. Those Lean declarations construct a four-vertex edge switch preserving the relevant degrees and outside adjacency; PairTradeSwitch identifies the resulting fiber exchange. These sources were read, not freshly kernel-audited. + +The adaptation changes the selected output matching which borrows Y in each parity tetrad. It is distinct from the earlier own-snapshot pair-cover choice: the own snapshots stay fixed to pair35. The switch keeps one selected incident pair at each target. The scalar output change is compensated by the explicitly inverted two-output basis and recomputed scatter, rather than assuming graph degree preservation implies circuit equivalence. Every altered packet copy is retained, and the actual constructor checks its clean scalar identity. + +Sufficient transfer: choose a matching on each four-target tetrad; rebuild the selected target-pair transform, its inverse at the input, and its inverse-transformed scatter. If all elementary operations occur at common nested legal frames, every coefficient is in the accepted scalar compiler, and the complete dirty-column and physical-normalization audits pass, this constructs the same whole-cover endpoint. Degree preservation alone proves only the matching incidence invariant, not those additional facts. The implementation explicitly rebuilds the word; no existence of a missing gadget is assumed. + +Bounded results: 9 uniform selectors, 28 single-block switched selectors with inherited retiming, and 28 exact raw-frame rebuilds were screened. The unchanged uniform selector reproduces pair35. All 28 retimed local switches fail a real frame or centre chain. Raw rebuilding produces 27 legal relation/frame candidates and one centre-chain rejection. Every legal raw candidate has a strictly worse sampled paid moment at a=0.0014, unchanged99 entrance pivots and unchanged ordered helper widths. Hence none was nominated for expensive physical replay or numerical improvement. This does not rule out other switch schedules or a jointly reoptimized frame system. + +All scripts and failed witnesses are preserved in this directory. Heavy candidate selection uses the existing native C++ response-census engine; exact reconstruction uses rational arithmetic. No Lean formalization, publication, or new kappa claim is made for this lane. diff --git a/research/rank-sector-async/research-notes/transvection-window.cpp b/research/rank-sector-async/research-notes/transvection-window.cpp new file mode 100644 index 0000000000..95accecda3 --- /dev/null +++ b/research/rank-sector-async/research-notes/transvection-window.cpp @@ -0,0 +1,24 @@ +#include +#include +#include +#include +#include +using namespace std;using B=array; +int dim(B b){int n=0;for(int x:b)n+=x!=0;return n;} +B joinb(B a,B b){for(int x:b)for(int j=8;j>=0;j--)if(x>>j&1){if(a[j])x^=a[j];else{a[j]=x;break;}}return a;} +bool sub(B a,B b){return dim(joinb(b,a))==dim(b);} +struct E{int typ,t,s;B f;}; +bool commute(E a,E b){if(a.typ)return a.t!=b.t&&(b.typ||a.t!=b.s);if(b.typ)return b.t!=a.t&&b.t!=a.s;return a.t!=b.s&&b.t!=a.s;} +double p(int n){return n?pow(double(n),1.-.001396):0.;} +double eval(const vector&es,vectorcur,const vector&finish){double cost=0;for(auto&e:es){for(int r:{e.t,e.typ?-1:e.s})if(r>=0){if(!sub(cur[r],e.f))return 1e30;cost+=p(dim(e.f)-dim(cur[r]));cur[r]=e.f;}}for(int i=0;i>parts;bool first=true;cout<<"[";long long tested=0; +for(int part=0;part>n>>r;vectorinitial(r),finish(r);for(auto&v:initial)for(int&x:v)cin>>x;for(auto&v:finish)for(int&x:v)cin>>x;vectores(n);for(auto&e:es){cin>>e.typ>>e.t>>e.s;for(int&x:e.f)cin>>x;}double base=eval(es,initial,finish); +for(int i=0;ia(es.begin(),es.begin()+i);a.insert(a.end(),es.begin()+i+1,es.begin()+j);a.push_back(z);E ee=e;ee.f=z.f;a.push_back(ee);E corr={0,kind==1?e.t:z.t,kind==1?z.s:e.s,z.f};a.push_back(corr);a.insert(a.end(),es.begin()+j+1,es.end());tested++; + double gain=base-eval(a,initial,finish);if(gain>1e-10){if(!first)cout<<",";first=false;cout<<"{\"part\":"<0 and den&(den-1)==0 + # Lower actual coefficient to cleared Horner work. Every intermediate + # magnitude envelope is explicitly included, before denominator halvings. + acc=0;count=1 + for i,ch in enumerate(bin(num)[2:]): + if i:acc*=2;count+=1;peak=max(peak,acc*env[b]) + if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b]) + v=F(acc) + for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b]) + assert v==abs(q);count+=2 # signed accumulation and private work clear + env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{}) + for j,z in list(rows[b].items()): + value=rr.get(j,F(0))+q*z + if value:rr[j]=value + else:rr.pop(j,None) + workops+=count + else:raise AssertionError(op) + real+=2*count;peak=max(peak,env[a]) + assert all(not row for reg,row in rows.items()if reg[0]=='C') + for i in range(N): + expected={i:F(1)} + if ori=='forward'and 120<=i<240:expected[i-120]=F(1) + if ori=='backward'and i<120:expected[i+120]=F(-1) + assert rows['L',i]==expected + assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192 + assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros'] + assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()} + local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True) +centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][240:]];enter=sum(x<9 for x in widths) +children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3 +adapters=16*(macros+children+N+centres)+64*M +primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler +bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;shifts=K*VV*T;moves=2*K*VV*T +oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L +scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls']) +nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144 +outside=8*nonlocal_items+64*M +pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP +invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler']) +# Independent hosted stock rebase, retaining the larger unhosted operation +# overcharge; only the stock and mass in the common router/literal change. +W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile'] +assert M*W-mass==2496 and P==W+R+centres+2 +rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex) +r=M//2;group=2**(r*r) +for i in range(1,r+1):group*=2**(2*i)-1 +stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2 +G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252;maxchild=max(map(int,profile)) +ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router2*maxchild*maxchild) +assert all(ineq.values()) +out=dict(status='PASS_INDEPENDENT_SCALAR_PREFIX_AND_HOSTED_FINITE_INVOICE',local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention.') +(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True) diff --git a/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py new file mode 100644 index 0000000000..252ca9393d --- /dev/null +++ b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py @@ -0,0 +1,59 @@ +"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding. Apache-2.0. +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. The wrapper construction follows PR #458 +(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first); +S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers R_E^-1 before the whole local invocation and L_E^-1 after its +full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically. +usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json +Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive +constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that L_E^-1 S_E R_E^-1 has exactly the +tableau and zero-state vector (global phase included) of fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong +translation, wrong width) must be rejected.""" +import copy, gzip, json, sys +from pathlib import Path +R = Path(__file__).resolve().parent.parent.parent +sys.path.insert(0, str(R / 'split-centres-global/vendor')) +from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity +n = 9; FULL = tuple(1 << i for i in range(n)) +def monomial_op(rec): + """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)""" + out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset'])) + return out.then(Op(n, identity(n), [('phase', rec['phase'])])) +def S_of(U): + return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, FULL)) +def wrapped_ok(U, rec): + """exactly: L^-1 S R^-1 = C_[w] x I (apply order: R^-1, S, L^-1)""" + w = n - len(U); S = S_of(U); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left']) + net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w)) + return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state() +def main(): + c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v'] + starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0}) + recipes = {} + for f in starts: + U = frames[f]; rec, compiled = lower_child(S_of(U)) + recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right']) + Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes), sort_keys=True, separators=(',', ':')) + '\n') + # ---- independent decode of the serialized file + data = json.loads(Path(sys.argv[2]).read_text())['recipes'] + dot = lambda a, b: bin(a & b).count('1') & 1 + detail = [] + for f in starts: + rec = data[str(f)]; U = frames[f] + assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f) + detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U), + totally_isotropic=all(dot(a, b) == 0 for a in U for b in U))) + controls = [] + def reject(name, fn): + f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec) + if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name) + controls.append(name) + reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4)) + reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1)) + reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4)) + reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left']))) + reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1)) + res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail), + all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail) + Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n') + print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight']) +if __name__ == '__main__': main() diff --git a/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py new file mode 100644 index 0000000000..e80ca6b8b3 --- /dev/null +++ b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py @@ -0,0 +1,189 @@ +# GK: modified copy of PR #433's complex_audit.py (icekylinx with Codex; PR #425) by DreamingOfClouds with Claude Opus 5.5 +# (Anthropic), via Claude Code. Every change is marked "GK:"; with a word that has no start_extra / target_levels the +# behaviour and the written files are PR #433's. +# Modified from PR425 by icekylinx with Codex assistance. +"""Read-back audit, independent of the Hamming producer and its row state.""" +import copy,gzip,hashlib,importlib.util,json,math,time +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +OUT=Path('split-centres');p=OUT/'FULL-WORD.json.gz' +word=json.load(gzip.open(p));v=120;n=240+word['report']['R'];start=time.monotonic() +def apply(e,rows): + if e[0]=='scale': + _,t,a,b,*_=e;q=Q(a,b);assert q + rows[t]={j:q*x for j,x in rows[t].items()} + else: + _,t,s,a,b,*_=e;q=Q(a,b);assert t!=s + for j,x in list(rows[s].items()): + z=rows[t].get(j,Q(0))+q*x + if z:rows[t][j]=z + else:rows[t].pop(j,None) +def ident():return [{r:Q(1)} for r in range(n)] +def inv(e): + e=copy.deepcopy(e) + if e[0]=='add':e[3]*=-1 + else:e[2],e[3]=e[3],e[2] + return e +def dual(e): + e=inv(e) + if e[0]=='add':e[1],e[2]=e[2],e[1] + return e + +main=word['A']+word['cut']+word['B'] +assert all(not 120<=e[2]<240 for e in word['A']+word['B'] if e[0]=='add' and not 120<=e[1]<240) +matrix=ident() +for e in main:apply(e,matrix) +print('full main columns',n,'replayed',flush=True) +# Compute -A_Y^-1 B_S using only rows of the explicit main operator. +dirty=[{} for r in range(n)] +for r in range(v,2*v):dirty[r]={j:x for j,x in matrix[r].items() if j>=2*v} +for e in word['precondition']:apply(e,dirty) +comp=[] +for r in range(v,2*v): + for j,q in sorted(dirty[r].items()):comp.append(['add',r,j,-q.numerator,q.denominator,[]]) + +cleanup=[inv(e) for e in reversed(word['A']+word['B']) if not v<=e[1]<2*v] +assert [e[:-1] for e in cleanup]==[e[:-1] for e in word['cleanup']] +program=word['precondition']+comp+main+cleanup +actual=ident() +for e in program:apply(e,actual) +expected=ident() +for t in range(v):expected[v+t][t]=Q(1) +assert actual==expected +print('PASS exact arbitrary dirt and restored sources/helpers',flush=True) +back=ident() +for e in program:apply(dual(e),back) +expected_back=ident() +for t in range(v):expected_back[t][v+t]=Q(-1) +assert back==expected_back +print('PASS exact inverse-transpose on every column',flush=True) +# Independent sparse vector controls avoid repeating a dense full replay. +def vector(es,x): + x=list(map(Q,x)) + for e in es: + if e[0]=='scale':x[e[1]]*=Q(e[2],e[3]) + else:x[e[1]]+=Q(e[3],e[4])*x[e[2]] + return x +sample=[((i*137+13)%101)-50 for i in range(n)] +want=vector(program,sample) +controls={ + 'missing_dirty_compensation':word['precondition']+main+cleanup, + 'missing_Y_inverse_basis':comp+main+cleanup, + 'missing_source_cleanup':word['precondition']+comp+main, + 'wrong_dual_event_order':[dual(e) for e in reversed(program)], +} +for name,es in controls.items(): + expected_sample=vector([dual(e) for e in program],sample) if name=='wrong_dual_event_order' else want + assert vector(es,sample)!=expected_sample,name + +# Orthogonal transvection and a port permutation bring the new geometry onto +# the already fixed 120-port routing family. Every incidence is transformed. +old=json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz')) +def tau(x):return x^(43 if (x&43).bit_count()%2 else 0) +assert 43 .bit_count()%2==0 +assert set(map(tau,word['ports']))==set(old['ports']) +mapping={i:old['ports'].index(tau(q)) for i,q in enumerate(word['ports'])} +mapping.update({v+i:v+mapping[i] for i in range(v)}) +mapping.update({r:r for r in range(2*v,n)}) +def basis(vs): + b={} + for x in vs: + for k in sorted(b,reverse=True): + if x>>k&1:x^=b[k] + if x: + k=x.bit_length()-1 + for j in b: + if b[j]>>k&1:b[j]^=x + b[k]=x + return tuple(b[k] for k in sorted(b,reverse=True)) +def perp(x):return basis([z for z in range(1,512) if not (x&z).bit_count()%2]) +full=tuple(1<0 + edges.add((old,f));paid[delta]+=1;cur[r]=f +for part in ('A','B'): + if part=='B': + assert all(cur[r]==f for r,f in zip(can['centers'],can['center_frames'])) + assert all(cur[r]==tlev.get(r-v,0) for r in range(v,2*v)) # GK: targets sit at their level + for r_c,f in zip(can['centers'],can['center_frames']): + # GK: a centre copy descends cf -> served levels (descending chain) -> lowest served level; at the defaults the + # only served level is 0 and this is PR #433's single child of rank |cf| + served={tlev.get(e[1]-v,0) for e in can['cut'] if e[2]==r_c} + o=f + for Lv in sorted(served,key=lambda x:-len(frames[x])): + assert basis(frames[Lv]+frames[o])==tuple(frames[o]),('centre level outside the previous frame',r_c) + if Lv!=o: + paid[len(frames[o])-len(frames[Lv])]+=1 + if not(o==f and Lv==0):edges.add((o,Lv));edges.add((Lv,o)) # (cf,0),(0,cf) are added by the phase script + o=Lv + for e in can[part]: + rs=[e[1]]+([e[2]] if e[0]=='add' else []) + for r in rs:climb(r,e[-1]);incidences+=1 +for r,f in enumerate(can['final']):climb(r,f) +assert dict(paid)=={int(r):x for r,x in word['report']['local_profile'].items()} +# GK: entrances lower the helper climb by their rank; centre descents may stop above frame zero +if not word.get('start_extra') and not word.get('target_levels'):assert sum(r*x for r,x in paid.items())==9*can['R']+240*8+72 +else:assert sum(r*x for r,x in paid.items())==sum(int(r)*x for r,x in word['report']['local_profile'].items()) +can['local_profile']=dict(sorted(paid.items()));can['edges']=sorted(edges) +cp=OUT/'CANONICAL-WORD.json.gz';cp.write_bytes(gzip.compress(json.dumps(can,sort_keys=True,separators=(',',':')).encode(),mtime=0)) + +def engine(name): + p=Path('work/pr361/code/engines')/(name+'.py');s=importlib.util.spec_from_file_location('hamming_'+name,p) + m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +M,M2=engine('moment'),engine('base_two_moment');m,W=73,word['report'].get('live',12720) # GK: unhosted stock of the word +HG={int(r):z for r,z in word['report']['global_profile'].items()} +root=M.certify(HG,m,W,True);b=Q(int(Q(root['lower'])*10**18),10**18);grid=Q(1,10**18) +assert M.moment(HG,m,W,b,True)[1]<1>p&1:x^=b[p] + if x: + p=x.bit_length()-1 + for q in b: + if b[q]>>p&1:b[q]^=x + b[p]=x + return tuple(b[p] for p in sorted(b,reverse=True)) +def dual(e): + e=list(e) + if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1 + else:e[2],e[3]=e[3],e[2] + return e +def scalar(e,back): + e=dual(e) if back else list(e) + if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]] + return ['scale',['L',e[1]],e[2],e[3]] +def primitive_bound(e): + if e[0] in ('clear','copy'):return 1 + q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3]) + a,b=abs(q.numerator),q.denominator + assert b&(b-1)==0 + if e[0]=='scale': + assert a&(a-1)==0 + return abs(a.bit_length()-b.bit_length())+int(q<0) + # Exact binary Horner multiplication on a cleared private stream, repeated + # halving, signed accumulation into the target, then clear the private stream. + return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1) + +def emit(back): + out=[];cur=c['start'].copy() + def event(e):out.append(e) + def scal(e,f):event(['scalar',e,f]) + event(['phase','zero_frame_precondition']) + for e in c['precondition']+c['compensation']: + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + assert all(c['start'][r]==0 for r in regs) + scal(scalar(e,back),0) + event(['phase','entry_adapters']) + # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate + # that touches it and L_E^-1 follows the full-frame cleanup. Words without entrances emit PR #433's events. + entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0] + for r,f in enumerate(c['start']): + if r in entering:event(['residual_adapter','pre',r,f]) + else:event(['adapter','old_to_new',r,f]) + def climb(r,f,part): + old=cur[r] + if old==f:return + assert basis(frames[old]+frames[f])==tuple(frames[f]) + rank=len(frames[f])-len(frames[old]);assert rank>0 + event(['climb',part,r,old,f,rank]);cur[r]=f + for part in ('A','centers','B','final'): + event(['phase',part]) + if part in ('A','B'): + for e in c[part]: + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + for r in regs:climb(r,e[-1],part) + scal(scalar(e,back),e[-1]) + elif part=='centers': + # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends + # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level + lv=lambda r:c.get('target_levels',{}).get(str(r-v),0) + assert all(cur[r]==lv(r) for r in range(v,2*v)) + for k,r in enumerate(c['centers']): + cf=c['center_frames'][k];assert cur[r]==cf + terms=[e for e in c['cut'] if e[2]==r] + path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x])) + C=['C',k] + if not back: + scal(['clear',C],cf);scal(['copy',C,['L',r]],cf) + for a in range(len(path)): + if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])]) + for e in terms: + if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a]) + scal(['clear',C],path[-1]) + else: + scal(['clear',C],path[-1]) + for a in range(len(path)-1,-1,-1): + for e in terms: + if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a]) + if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])]) + scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf) + else: + for r,f in enumerate(c['final']):climb(r,f,part) + event(['phase','exit_adapters']) + for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f]) + event(['phase','full_frame_cleanup']) + for e in c['cleanup']: + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + assert all(c['final'][r]==1 for r in regs) + scal(scalar(e,back),1) + for r in entering:event(['residual_adapter','post',r,c['start'][r]]) # GK: L_E^-1 after the full-frame cleanup + event(['phase','done']) + return out + +def check_local(events,back): + # Literal scalar replay of the emitted stream, including center lifetimes. + state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0 + for e in events: + if e[0]=='climb':assert not live;paid[e[5]]+=1 + elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1 + elif e[0]=='scalar': + op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op) + if tag=='clear': + state[t]={} + if t[0]=='C' and t[1] in live:live.remove(t[1]) + elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1]) + elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()} + else: + s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{}) + if t[0]=='C' and t[1] not in live:live.append(t[1]) + for j,x in list(state.get(s,{}).items()): + z=row.get(j,Q(0))+q*x + if z:row[j]=z + else:row.pop(j,None) + assert not live and all(not row for r,row in state.items() if r[0]=='C') + for r in range(n): + expected={r:Q(1)} + if back and r> p & 1: x ^= b[p] + if x: + p = x.bit_length() - 1 + for q in b: + if b[q] >> p & 1: b[q] ^= x + b[p] = x + return tuple(b[p] for p in sorted(b, reverse=True)) + + +def widths_of(word): + """residual width of every helper: 9 - dim(entrance frame); 9 when the word has no extension""" + R = word['report']['R'] if 'R' not in word else word['R'] + w = [L] * R + for r, E in word.get('start_extra', {}).items(): + assert 2 * V <= int(r) < 2 * V + R + w[int(r) - 2 * V] = L - len(basis(E)) + return w + + +def split_pad(p): + """a pad of rank p is paid as nested commuting children of rank <= 51 (so that 73^2 > 2*child^2); rank 1 stays 1""" + if p == 0: return [] + n = -(-p // 51); return [p // n + (1 if i < p % n else 0) for i in range(n)] + + +def tile(items): + """Bank tiling of unhosted residuals. items: list of (rep, helper, width); a bank has M = 73 cells. + * width-9 residuals (no wrapper acts on them): first fit in the given order, packed from offset 0, eight per bank, pad rank 1 + (PR #433/#442's tiling and routes [2, slot]); + * ENTERING residuals (width w < 9, paid wrappers, e = 9 - w spectators): banks of their own in which every entering helper is the ONLY + owner of its bank family in its invocation (the one-helper rule of PR #458 extended to banks): bank j holds the j-th entering + helper of each replica, residuals packed from offset 0 in replica order (at most one helper per replica, hence per invocation). + The spectators of an entering helper are the first e cells of the bank beyond every residual cell of the bank (the pad, which no call + uses for a residual, is paid as before: rank 73 - sum of widths; the spectators are borrowed inside it and not deducted). + Returns (assign, banks, pads): assign[(rep, helper)] = (bank, offset, width, pure, spectators) with pure = the bank holds only width-9 + residuals and spectators = () for width 9; pads = Counter of pad ranks (split into children of rank <= 51).""" + assign = {}; pads = Counter(); fill = [] + for z, (rep, h, w) in enumerate(items): # width 9: first fit, as PR #433 (all widths 9 reproduces it exactly) + if w != L: continue + for b, f in enumerate(fill): + if f + w <= M: break + else: + b = len(fill); fill.append(0) + assign[(rep, h)] = (b, fill[b], w, True, ()); fill[b] += w + nwide = len(fill); byrep = {} + for rep, h, w in items: + if w < L: byrep.setdefault(rep, []).append((h, w)) + cells = [0] * max((len(v) for v in byrep.values()), default=0); emax = [0] * len(cells); place = {} + for rep in sorted(byrep): # the j-th entering helper of every replica goes to entering bank j + for j, (h, w) in enumerate(byrep[rep]): + place[(rep, h)] = (nwide + j, cells[j], w); cells[j] += w; emax[j] = max(emax[j], L - w) + for j in range(len(cells)): assert cells[j] + emax[j] <= M, ('entering bank without room for its spectators', j) + for (rep, h), (b, off, w) in place.items(): + assign[(rep, h)] = (b, off, w, False, tuple(range(cells[b - nwide], cells[b - nwide] + L - w))) + fill += cells + for f in fill: + for part in split_pad(M - f): pads[part] += 1 + return assign, len(fill), pads + + +def route(off, w, pure, sp=()): + """owner route of a banked helper residual: PR #433's [2, slot] for width 9 (pure width-9 bank); an entering helper (w < 9) is + [2, offset, width, [spectator cells]] with e = 9 - w spectators""" + if w == L: assert pure and not sp; return [2, off // L] + assert not pure and len(sp) == L - w; return [2, off, w, list(sp)] + + +def unhosted_stock(widths): + """live stock and padding histogram of the unhosted (parent) template, per stage x nine""" + R = len(widths) + _, nb, pads = tile([(rep, h, widths[h]) for rep in range(T) for h in range(R)]) + return DATA + L * nb, Counter({r: z * L for r, z in pads.items()}) diff --git a/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py new file mode 100644 index 0000000000..15782ba625 --- /dev/null +++ b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py @@ -0,0 +1,194 @@ +"""Apply a frozen selection (shared-donor kernel + entrance gauges) to PR #433's complex word. Apache-2.0. +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +usage: gk_word.py BASE_FULL-WORD.json.gz SELECTION.json OUT_FULL-WORD.json.gz +An empty selection ({}) copies the input byte for byte (regression anchor). + +selection = {"kernel": [{"E": [x], "donors": [h..], "pivots": [h..]}..], "gauge": {"h": [x..]}} (h = helper index 0..R-1) +Kernel (PR #417/#435/#434/#440): a pivot starts at E; every donor receives donor += -q * pivot at frame E before the main +word, where col(pivot) = sum q_d col(d) are the exact dirty-response columns; the pivot's frame-zero compensation vanishes. +Gauge (#401/#408-#416): the compensation target += -C[t,h] * helper of helper h is executed at frame E_h as the first gates +of the main word; h starts at E_h and its targets climb to the level L_t = largest E over their entering helpers. +The exact verification is the arbitrary-dirt replay of audit_gk.py; this module also checks the structural conditions.""" +import copy, gzip, hashlib, json, sys +from collections import Counter, defaultdict +from fractions import Fraction as Q +from pathlib import Path +sys.path.insert(0, str(Path(__file__).resolve().parent)) +from gk_common import * + + +def apply_op(e, rows): + if e[0] == 'scale': + _, t, a, b, *_ = e; q = Q(a, b); rows[t] = {j: q * x for j, x in rows[t].items()} + else: + _, t, s, a, b, *_ = e; q = Q(a, b) + for j, x in list(rows[s].items()): + z = rows[t].get(j, Q(0)) + q * x + if z: rows[t][j] = z + else: rows[t].pop(j, None) + + +def inverse(e, F): + e = copy.deepcopy(e) + if e[0] == 'add': e[3] *= -1 + else: e[2], e[3] = e[3], e[2] + e[-1] = list(F); return e + + +def responses(word): + """dirty-response columns col[h] = {target: coefficient} of the unmodified word (after the frame-zero preconditioner)""" + R = word['report']['R']; n = 2 * V + R + rows = [{r: Q(1)} for r in range(n)] + for e in word['A'] + word['cut'] + word['B']: apply_op(e, rows) + dirty = [{} for _ in range(n)] + for r in range(V, 2 * V): dirty[r] = {j: x for j, x in rows[r].items() if j >= 2 * V} + for e in word['precondition']: apply_op(e, dirty) + col = [{} for _ in range(R)] + for r in range(V, 2 * V): + for j, x in dirty[r].items(): col[j - 2 * V][r - V] = x + return col + + +def first_frames(word): + first = {} + for seq in (word['A'], word['B']): + for e in seq: + F = basis(e[-1]) + for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): + if r >= 2 * V: first.setdefault(r - 2 * V, F) + return first + + +def solve_relation(col, donors, p): + """exact rational c with col[p] = sum_d c_d col[d]; None if p is not in the span""" + ts = sorted({t for d in donors for t in col[d]} | set(col[p])) + idx = {t: i for i, t in enumerate(ts)} + Mx = [[Q(0)] * (len(donors) + 1) for _ in ts] + for ci, d in enumerate(donors): + for t, x in col[d].items(): Mx[idx[t]][ci] = x + for t, x in col[p].items(): Mx[idx[t]][-1] = x + piv = []; r = 0 + for c in range(len(donors)): + pr = next((i for i in range(r, len(Mx)) if Mx[i][c]), None) + if pr is None: continue + Mx[r], Mx[pr] = Mx[pr], Mx[r]; q = Mx[r][c]; Mx[r] = [x / q for x in Mx[r]] + for i in range(len(Mx)): + if i != r and Mx[i][c]: + f = Mx[i][c]; Mx[i] = [a - f * b for a, b in zip(Mx[i], Mx[r])] + piv.append(c); r += 1 + if any(Mx[i][-1] for i in range(r, len(Mx))): return None + assert r == len(donors), 'donors must have independent response columns' + return {donors[c]: Mx[i][-1] for i, c in enumerate(piv) if Mx[i][-1]} + + +def span(U): + s = {0} + for b in U: s |= {x ^ b for x in s} + return s + + +def perp(x): return basis([z for z in range(1, 512) if not (x & z).bit_count() % 2]) + + +def profile(word): + """local paid profile of a gk word by direct simulation of the frame chains (second implementation: audit_gk.py)""" + R = word['report']['R']; n = 2 * V + R; P = word['ports'] + cur = {} + for r in range(n): + cur[r] = (P[r],) if r < V else ((basis(word['start_extra'][str(r)]) if str(r) in word.get('start_extra', {}) else ()) if r >= 2 * V else ()) + paid = Counter() + def climb(r, F): + F = basis(F); o = cur[r] + assert basis(list(o) + list(F)) == F, ('frame violation', r, o, F) + if o != F: paid[len(F) - len(o)] += 1; cur[r] = F + lev = {int(t): basis(E) for t, E in word.get('target_levels', {}).items()} + for seq, part in ((word['A'], 'A'), (word['B'], 'B')): + if part == 'B': + for r, f in zip(word['centers'], word['center_frames']): + assert cur[r] == basis(f), 'centre frame' + served = sorted({lev.get(e[1] - V, ()) for e in word['cut'] if e[2] == r}, key=lambda E: -len(E)) + o = basis(f) + for Lv in served: + assert span(Lv) <= span(o), 'served levels must descend inside the centre frame' + if Lv != o: paid[len(o) - len(Lv)] += 1; o = Lv + for t in range(V): assert cur[V + t] == lev.get(t, ()), 'target level at the centre scatter' + for e in seq: + for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): climb(r, e[-1]) + for r in range(n): climb(r, FULL if (r < V or r >= 2 * V) else perp(P[r - V])) + return paid + + +def global_profile(local, widths): + """unhosted nine-stage profile: local x (stages*replicas) + the 240*8 idle children per rank + bank pads""" + live, pads = unhosted_stock(widths) + g = Counter({r: z * L * T for r, z in local.items()}) + for r in (16, 8, 32, 8, 48, 8, 48, 32, 16): g[r] += 240 * T + g.update(pads) + return live, g + + +def build(word, sel, check=True): # check=False only for the mutation controls that must be caught by the certifying scripts + if not sel: return word + w = copy.deepcopy(word); R = w['report']['R'] + col = responses(word); first = first_frames(word) + gauge = {int(h): basis(E) for h, E in sel.get('gauge', {}).items()} + classes = sel.get('kernel', []) + pivots = {p for c in classes for p in c['pivots']}; donors = {d for c in classes for d in c['donors']} + assert not (pivots & donors) and not (pivots | donors) & set(gauge) and len(pivots) == sum(len(c['pivots']) for c in classes) + # --- structural conditions ------------------------------------------------------------------------------------- + for h, E in gauge.items(): + assert not check or span(E) <= span(first[h]), ('gauge entrance outside the first frame', h) + levels = defaultdict(list) + for h, E in gauge.items(): + for t in col[h]: levels[t].append(E) + for t, Es in levels.items(): # pairwise nested comps per target + for a in Es: + for b in Es: assert not check or span(a) <= span(b) or span(b) <= span(a), ('non-nested gauges at target', t) + lev = {t: max(Es, key=len) for t, Es in levels.items()} + for k, r in enumerate(w['centers']): # chain per centre, inside the centre frame + served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == r} + for a in served: + for b in served: assert not check or span(a) <= span(b) or span(b) <= span(a), ('centre chain', k) + top = max(served, key=len) + assert not check or span(top) <= span(basis(w['center_frames'][k])), ('level outside centre frame', k) + # --- gates ---------------------------------------------------------------------------------------------------------- + gates = [] + for h, E in sorted(gauge.items(), key=lambda kv: (len(kv[1]), kv[0])): + for t, x in sorted(col[h].items()): + c = -x; gates.append(['add', V + t, 2 * V + h, c.numerator, c.denominator, list(E)]) + pre = [] + start = {2 * V + h: list(E) for h, E in gauge.items()} + for cl in sorted(classes, key=lambda c: (len(c['E']), c['E'])): + E = basis(cl['E']) + for x in [*cl['donors'], *cl['pivots']]: assert span(E) <= span(first[x]), ('kernel entrance outside the first frame', x) + for p in cl['pivots']: + rel = solve_relation(col, cl['donors'], p) + assert rel is not None, ('pivot response not in the donor span', p) + start[2 * V + p] = list(E) + for d, c in rel.items(): + q = -c; pre.append(['add', 2 * V + d, 2 * V + p, q.numerator, q.denominator, list(E)]) + w['A'] = gates + pre + w['A'] + w['cleanup'] = [inverse(e, FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V] + w['start_extra'] = {str(r): list(E) for r, E in sorted(start.items())} + w['target_levels'] = {str(t): list(E) for t, E in sorted(lev.items()) if E} + if not check: return w + prof = profile(w); widths = widths_of(w) + live, g = global_profile(prof, widths) + w['report']['local_profile'] = {str(k): z for k, z in sorted(prof.items())} + w['report']['global_profile'] = {str(k): z for k, z in sorted(g.items())} + w['report']['live'] = live + w['report']['entrance_rank'] = sum(L - x for x in widths); w['report']['entering_helpers'] = sum(1 for x in widths if x < L) + w['report']['selection_sha256'] = hashlib.sha256(json.dumps(sel, sort_keys=True).encode()).hexdigest() + return w + + +def dump(w): return gzip.compress(json.dumps(w, sort_keys=True, separators=(',', ':')).encode(), mtime=0) + + +if __name__ == '__main__': + src, selp, out = map(Path, sys.argv[1:4]) + sel = json.loads(selp.read_text()) + if not sel: out.write_bytes(src.read_bytes()); print('empty selection: copied byte for byte'); sys.exit(0) + word = json.load(gzip.open(src)); w = build(word, sel); out.write_bytes(dump(w)) + print('gk word: entering helpers', w['report']['entering_helpers'], 'entrance rank', w['report']['entrance_rank'], + 'local profile', w['report']['local_profile'], 'unhosted live', w['report']['live']) diff --git a/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py new file mode 100644 index 0000000000..df261063e1 --- /dev/null +++ b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py @@ -0,0 +1,123 @@ +# GK: modified copy of PR #433's complex_integrate.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5 +# (Anthropic), via Claude Code. Every change is marked "GK:". On a word without start_extra / target_levels the behaviour +# and every written file equal PR #433's (regression anchor in verify.py). +import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__))) +# Adapted from PR425 for heterogeneous centres by icekylinx, with Codex assistance. +import copy,gzip,hashlib,importlib.util,json,math +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz' +c=json.load(gzip.open(cp));audit=json.loads((OUT/'SCALAR-FRAME-AUDIT.json').read_text()) +phase=json.loads((OUT/'CLIFFORD-REVIEW.json').read_text());sha=lambda p:hashlib.sha256(Path(p).read_bytes()).hexdigest() +assert phase['canonical_word_sha256']==audit['canonical_word_sha256']==sha(cp) +assert phase['all_child_equalities_include_global_phase'] +programs=json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'));checks=json.loads((OUT/'LOCAL-CHECKS.json').read_text()) +frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R;private_centres=len(c['centers']) +for z in checks.values():z['paid_profile']={int(r):n for r,n in z['paid_profile'].items()} +old=Path('work/complex-nine-native');template=json.load(gzip.open(old/'GLOBAL-TEMPLATE.json.gz')) +data_phase=json.loads((old/'DATA-PHASES.json').read_text()) +assert template['exact_data_phase_recipe_sha256']==sha(old/'DATA-PHASES.json') +assert data_phase['status']=='PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES' +m,T,L,k=73,8,9,4 +# GK: residual widths 9 - dim(start frame); banks tile per width class (all 9: PR #433's eight residuals + one pad) +from gk_common import tile,route +widths=[h-len(frames[c['start'][2*v+i]]) for i in range(R)] +assign,nb,pads=tile([(rep,i,widths[i]) for rep in range(T) for i in range(R)]);entering0=any(w_2*maxchild**depth +assert local_bound<1<<48 and logical<1<<6050 and router0 + bound=max(math.ceil(36/gap**2),math.ceil(2*(4+512)/gap)) + assert bound*gap**2>=36 and bound*gap>=2*(4+512) + cutoffs.append(str(bound));chain.append(z) +bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1}, + 'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}} +q=chain[-1]*(1-2*eta);ticks=(1-eta)*q/(1+q)/grid;kap=Q((ticks.numerator-1)//ticks.denominator,10**18) +assembly=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta) +try:Outer.assembly(chain[-1],b,bridge,kap+grid,eta=eta,beta=beta) +except AssertionError:pass +else:raise AssertionError('next kappa grid accepted') +result={'status':'PASS_NEW_STRUCTURAL_PROGRAM_AND_FINITE_ASSEMBLY_PENDING_REPLAY', + 'canonical_word_sha256':sha(cp),'scalar_audit_sha256':sha(OUT/'SCALAR-FRAME-AUDIT.json'), + 'exact_phase_receipt_sha256':sha(OUT/'CLIFFORD-REVIEW.json'),'global_template_sha256':hashlib.sha256(blob).hexdigest(), + 'local_program_checks':checks,'R':R,'m':m,'live':W,'physical':physical, + 'bank_assignments':len(assignments),'rank_mass':mass,'deficit':2496, + 'global_profile':dict(sorted(paid.items())),'emitted_local_events_all_calls':event_count, + 'finite_invoice':{'local_primitive_bound':local_bound,'local_adapters':adapters, + 'pervertex':pervertex,'physical_stock_bits':stock.bit_length(), + 'router_bits':router.bit_length(),'literal_bits':literal.bit_length(), + 'physical_row_coefficient':row,'retained_row_coefficient':20161, + 'compiler':compiler,'G_exponent':30000,'E_exponent':100000,'C0_exponent':210000, + 'required_C0_bits':(32*m*BB*BB).bit_length(),'halving_degree':depth, + 'halving_integer_inequality':[m**depth,2*maxchild**depth]}, + 'complex_b':str(b),'bit_c':str(bit),'prospective_kappa':str(kap),'kappa_float':float(kap), + 'log2_kappa':math.log2(float(kap)), + 'kappa_gain_percent':float(100*(kap/Q(998390813251625,10**18)-1)), + 'strict_outer_constraints':{name:str(z) for name,z in assembly['strict_constraints'].items()}, + 'next_kappa_grid_rejected':True,'bootstrap_cutoffs_log2':cutoffs, + 'scope':'New finite scalar interface with a written conjugation proof, conditional on inherited all-size compiler, precision/tape and analytic transfer. Independent emitted-program replay and fresh package replay still required before final promotion.'} +(OUT/'INTEGRATION.json').write_text(json.dumps(result,indent=2)+'\n') +print('PASS prospective kappa',float(kap),'gain',result['kappa_gain_percent'],'percent',flush=True) diff --git a/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py new file mode 100644 index 0000000000..220cc7a2f5 --- /dev/null +++ b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py @@ -0,0 +1,111 @@ +"""Whole-residual idle-axis hosting with at most ONE helper per physical family per invocation (the rule of PR #458), plus the exact +host chart with explicit spectator coordinates. Apache-2.0. Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +A copy (port) of an idle child hosts a PATTERN: residuals of pairwise distinct stages inside the child's window, offsets 0, w1, w1+w2, ... +(a residual is whole: one slot in one family). The children of one (pair, side) have pairwise disjoint windows (checked), so the +families they share never host two helpers of one invocation, and the integer programme needs only the distinct-stage condition. +Chart: for the host's port q the parent's idle basis is B_q = U_q (+) I (PR #433 geometry; the construction is that of PR #458). A hosted +residual of width w occupies the pending vectors b_off..b_(off+w-1) of its child; the other e = 9 - w coordinates of the local nine are +SPECTATORS: the first e basis indices of B_q not occupied by the residual, in increasing order. The paid wrappers (adapters_gk.py) act on +these nine coordinates and restore the spectators identically.""" +import math +from collections import Counter + +H, M = 9, 73 + + +def cost(r, m): return r * math.log(m / r) if r else 0.0 + + +def patterns(rank, stages, widths): + out = [()] + ws = sorted(widths, reverse=True) + def rec(i, cur, tot): + for j in range(i, len(stages)): + for w in ws: + if tot + w <= rank: + c = cur + [(stages[j], w)]; out.append(tuple(c)); rec(j + 1, c, tot + w) + rec(0, [], 0) + return out + + +def solve(win, copies, avail, m, pad_value, time_limit=600): + """win {idx: (pair, rank, stages)}, avail {(stage, width): helpers per replica}. Maximise saved idle cost (+ pad_value per hosted residual).""" + import numpy as np + from scipy.optimize import milp, LinearConstraint, Bounds + widths = sorted({w for (_, w) in avail}); var = [] + for idx, (p, r, st) in sorted(win.items()): + for pat in patterns(r, sorted(st), widths): var.append((idx, pat)) + n = len(var); c = np.zeros(n) + for j, (idx, pat) in enumerate(var): + r = win[idx][1]; c[j] = -(cost(r, m) - cost(r - sum(w for _, w in pat), m) + pad_value * len(pat)) + rows, lo, hi = [], [], [] + by = {} + for j, (idx, pat) in enumerate(var): by.setdefault(idx, []).append(j) + for idx, js in by.items(): + row = np.zeros(n); row[js] = 1; rows.append(row); lo.append(copies); hi.append(copies) + for (s, w), a in sorted(avail.items()): + row = np.zeros(n) + for j, (idx, pat) in enumerate(var): row[j] = sum(1 for sw in pat if sw == (s, w)) + rows.append(row); lo.append(0); hi.append(a) + res = milp(c, constraints=LinearConstraint(np.array(rows), lo, hi), integrality=np.ones(n), bounds=Bounds(np.zeros(n), np.full(n, np.inf)), + options=dict(time_limit=time_limit, disp=False)) + assert res.x is not None, res.message + x = [int(round(t)) for t in res.x] + return [[idx, [list(sw) for sw in pat], x[j]] for j, (idx, pat) in enumerate(var) if x[j]], -res.fun + + +def save(path, key, sel, val): + import json + from pathlib import Path + p = Path(path); d = json.loads(p.read_text()) if p.exists() else {} + d[key] = dict(rule='one-helper-per-family', patterns=sorted(sel), proxy_saving=val) + p.write_text(json.dumps(d, indent=1, sort_keys=True) + '\n') + + +def load(path, key): + import json + from pathlib import Path + d = json.loads(Path(path).read_text())[key]; assert d['rule'] == 'one-helper-per-family' + return d['patterns'], d['proxy_saving'] + + +def check_disjoint_groups(win, pair_of, side_of): + """children of one (pair, side) share their physical families; their windows must be disjoint""" + seen = {} + for idx, (p, r, st) in win.items(): + for s in st: + k = (pair_of[idx], side_of[idx], s); assert k not in seen, ('windows of two children of one family group overlap', idx, seen[k], k); seen[k] = idx + + +def expand(win, sel, widths, V): + """-> slots [idx, port, off, w, s, h] (one replica), rem {(idx, port): remaining pending rank}""" + R = len(widths); pool = {} + for h in sorted(range(R)): pool.setdefault(widths[h], []).append(h) + pool = {(s, w): list(hs) for s in range(9) for w, hs in pool.items()} + slots = []; rem = {}; used = Counter() + for idx, pat, copies in sorted(sel, key=lambda e: (e[0], e[1])): + r = win[idx][1] + for _ in range(copies): + cp = used[idx]; used[idx] += 1; assert cp < V; off = 0 + assert len({s for s, w in pat}) == len(pat) + for s, w in pat: + assert s in win[idx][2] and off + w <= r + slots.append([idx, cp, off, w, s, pool[s, w].pop(0)]); off += w + rem[idx, cp] = r - off + assert all(n == V for n in used.values()) and len(used) == len(win) + return slots, rem + + +def idle_basis(q): + """PR #433 / #458: the parent's orthonormal idle basis U_q (+) I for port q (H = 9 local coordinates, M = 73)""" + z = next(i for i in range(H) if not (q >> i & 1)); a = q ^ (1 << z); order = list(range(H)); order[0], order[z] = order[z], order[0] + return [(1 << i) ^ (a if a >> i & 1 else 0) for i in order] + [1 << i for i in range(H, M)] + + +def spectators(q, pending, off, w): + """indices (into B_q) of the e = 9 - w spectator coordinates of a residual at pending[off:off+w]""" + B = idle_basis(q); occ = [B.index(x) for x in pending[off:off + w]] + assert len(set(occ)) == w + sp = [j for j in range(M) if j not in occ][:H - w] + assert len(sp) == H - w + return sp diff --git a/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py new file mode 100644 index 0000000000..629de3b6ce --- /dev/null +++ b/research/rank-sector-async/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py @@ -0,0 +1,280 @@ +# GK: modified copy of PR #433's complex_replay.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5 +# (Anthropic), via Claude Code. Every change is marked "GK:". On a word without start_extra / target_levels the behaviour +# and every written file equal PR #433's (regression anchor in verify.py). +import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__))) +# Adapted for heterogeneous centres by icekylinx with Codex assistance. +"""Independent read-back of the serialized local/global instruction stream.""" +import copy,gzip,hashlib,importlib.util,json,math +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +OUT=Path('split-centres');P=OUT/'GLOBAL-TEMPLATE.json.gz' +ir=json.load(gzip.open(P));c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz')) +integration=json.loads((OUT/'INTEGRATION.json').read_text()) +assert hashlib.sha256(gzip.decompress(P.read_bytes())).hexdigest()==integration['global_template_sha256'] +assert c['ports']==json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))['ports'] +v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames'] +from gk_common import tile # GK +widths=[h-len(frames[c['start'][2*v+i]]) for i in range(R)] +assign,nb,pads=tile([(rep,i,widths[i]) for rep in range(8) for i in range(R)]);W=7680+9*nb +levels={int(t):f for t,f in c.get('target_levels',{}).items()} +entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0];plain={r for r in range(n) if r not in set(entering)} # GK +def contains(a,b): + for x in a: + for y in b: + if x>>(y.bit_length()-1)&1:x^=y + if x:return False + return True +def local(events,back): + rows={('L',r):{r:Q(1)} for r in range(n)} + norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={} + hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256();chain={};wrappers=[] + allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done'] + for event in events: + tag=event[0] + if tag=='phase': + phases.append(event[1]);assert phases==allowed[:len(phases)] + if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==entering # GK + if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v)) # GK + if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final'])) + assert not private + elif tag=='residual_adapter': # GK: paid wrappers of entering helpers: R_E^-1 before the invocation, L_E^-1 after the full-frame cleanup + _,kind,r,f=event;assert r in entering and f==c['start'][r] and kind in ('pre','post') + assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup') + assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f)) + elif tag=='adapter': + assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]] + (entry if event[1]=='old_to_new' else exit).append((event[2],event[3])) + elif tag=='climb': + _,part,r,a,b,rank=event + assert not private and phases[-1]==part and cur[r]==a + assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0 + hist[rank]+=1;cur[r]=b + elif tag=='center': + _,k,a,b,rank=event + assert phases[-1]=='centers' and private=={('C',k):a} + cf=c['center_frames'][k];cr=len(frames[cf]) + # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child + assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a]) + assert rank==abs(len(frames[a])-len(frames[b]))>0 + chain.setdefault(k,[]).append((a,b)) + private['C',k]=b;hist[rank]+=1;centers.append(k) + elif tag=='scalar': + _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None + if target[0]=='C' and op=='clear': + assert private.get(target,f)==f + private.pop(target,None) + else: + for r in (target,source): + if r is None:continue + if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f) + else: + if r==target and r not in private:private[r]=f + assert private[r]==f + if op=='clear':rows[target]={};norm[target]=Q(0) + elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source] + elif op=='scale': + q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator + assert a&(a-1)==0 and b&(b-1)==0 + rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q) + else: + q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator + assert source!=target and b&(b-1)==0 + # Independent symbolic replay of the cleared coefficient work. + w=0 + for bit in bin(a)[2:]:w=2*w+int(bit) + assert Q(w,b)*(1 if q>0 else -1)==q + prefix=max(prefix,Q(a)*norm[source]) + norm[target]=norm.get(target,Q(0))+abs(q)*norm[source] + row=rows.setdefault(target,{}) + for j,x in list(rows[source].items()): + z=row.get(j,Q(0))+q*x + if z:row[j]=z + else:row.pop(j,None) + prefix=max(prefix,norm[target]) + else:raise AssertionError(tag) + assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private + assert sorted(r for k,r,_ in wrappers if k=='pre')==entering and sorted(r for k,r,_ in wrappers if k=='post')==entering # GK + for k,st in chain.items(): # GK: the steps of each centre chain link up and end at the centre frame + cf=c['center_frames'][k] + if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1)) + else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1)) + assert all(not row for reg,row in rows.items() if reg[0]=='C') + for r in range(n): + expected={r:Q(1)} + if back and r= W). sole=False skips only the + sole-owner assertion (used by a control to show that the footprints themselves are fine).""" + fam=Counter(f for f,_ in owners);foot={} + for i,(f,route) in enumerate(owners): + assert f=240 and route[0]==2,('bank class: helpers only',i,f);w=widths[i-240] + if w==9: assert len(route)==2,('width-9 helper in a pure bank',i) + else: + if sole: assert fam[f]==1,('entering helper shares its bank family in one invocation',i,f) + assert len(route)==4 and route[2]==w and len(set(route[3]))==9-w==len(route[3]),('entering helper without a spectator record',i) + assert route[3]==list(range(len(occ[f]),len(occ[f])+9-w)) and len(occ[f])+9-w<=73,('spectators are not the first cells beyond the residuals',i,f) + cells=residual_cells(route)|(set(route[3]) if len(route)==4 else set()) + assert len(cells)==9 and not cells&foot.setdefault(f,set()),('footprints overlap on a bank family',i,f);foot[f]|=cells +def global_check(t): + assert t['live']==W and t['physical']==W+R+len(c['centers'])+2 # GK + occ={} + for call in t['calls']: + for fam,route in call['owners'][240:]:occ.setdefault(fam,set()).update(residual_cells(route)) + assert all(cs==set(range(len(cs))) for cs in occ.values()),'bank residuals are packed from cell 0' + # Eight data-wire scalar columns, independently recomposed. + matrix=[[int(i==j) for j in range(8)] for i in range(8)] + for e in t['recipe']: + if e['kind']=='local': + a=2*e['pair'];b=a+1;dst,src,q=(a,b,-1) if e['reverse'] else (b,a,1) + matrix[dst]=[x+q*y for x,y in zip(matrix[dst],matrix[src])] + elif e['kind']=='bridge': + i,j,q=e['dst'],e['src'],e['coefficient'] + matrix[2*i]=[x+q*y for x,y in zip(matrix[2*i],matrix[2*j])] + matrix[2*j+1]=[x-q*y for x,y in zip(matrix[2*j+1],matrix[2*i+1])] + else: + assert e['kind']=='terminal';old=copy.deepcopy(matrix) + for i in range(4):matrix[2*i]=old[2*i+1];matrix[2*i+1]=[-x for x in old[2*i]] + assert matrix==[[int(i==j) for j in range(8)] for i in range(8)] + seen=set();hist=Counter();pairs={e['stage']:e for e in t['recipe'] if e['kind']=='local'} + for call in t['calls']: + stage,rep,pair=call['stage'],call['replica'],call['pair'] + assert (stage,rep) not in seen;seen.add((stage,rep)) + assert pair==pairs[stage]['pair'] + assert call['orientation']==('backward' if pairs[stage]['reverse'] else 'forward') + assert len(call['owners'])==800 + for r,(fam,route) in enumerate(call['owners']): + if r<240:assert fam==rep*960+(2*pair+r//120)*120+r%120 and route==[1,stage,r%120] + else: + bk,off_,w_,pure_,sp_=assign[rep,r-240];assert fam==7680+stage*nb+bk and route==([2,off_//9] if (w_==9 and pure_) else [2,off_,w_,list(sp_)]) # GK + assert len(set((f,json.dumps(r)) for f,r in call['owners']))==800 + bank_rule(call['owners'],occ) # GK: the rule on every register class, stated independently of tile() + for r,z in profiles[call['orientation']].items():hist[r]+=z + assert seen=={(s,r) for s in range(9) for r in range(8)} + for child in t['idle_children']:hist[child['rank']]+=child['replicas'] + assert t['bank_padding']=={'families':list(range(7680,W)),'axis':72,'child_rank':1} + for r_,z_ in pads.items():hist[r_]+=z_*9 # GK + assert t['cover_final_correction']['families']==[0,W] + assert t['cover_final_correction']['charged_calls_per_cover']==W + assert t['execution_schedule'][-1]=={'kind':'translate_every_live_family',**{k:v for k,v in t['cover_final_correction'].items() if k!='kind'}} + assert 73*W-sum(r*z for r,z in hist.items())==2496 + return hist +H=global_check(ir) +# Derivative repair: select two genuine width-9 owners; a fixed route may already match. +pure_alias=[r for r in range(240,800) if widths[r-240]==9 and len(ir['calls'][0]['owners'][r][1])==2] +assert len(pure_alias)>=2 +alias_src,alias_dst=pure_alias[:2] +assert ir['calls'][0]['owners'][alias_src]!=ir['calls'][0]['owners'][alias_dst] +def alias_owner(owners): + owners[alias_dst]=copy.deepcopy(owners[alias_src]) +for name,mut in [('missing_padding',lambda t:t['bank_padding']['families'].pop()), + ('aliased_owner',lambda t:alias_owner(t['calls'][0]['owners'])), + ('missing_cover_phase',lambda t:t['cover_final_correction'].__setitem__('charged_calls_per_cover',0))]: + t=copy.deepcopy(ir);mut(t) + assert t!=ir,('vacuous global mutation',name) + try:global_check(t) + except (AssertionError,KeyError):controls.append(name) + else:raise AssertionError('global mutation accepted: '+name) +# GK: controls of the rule itself, one per register class, run on bank_rule (not on the equality with tile()); only for words with entering +# helpers (the anchor's INDEPENDENT-REPLAY.json must stay byte-identical to PR #433's) +occ_all={} +for call in ir['calls']: + for fam_,route_ in call['owners'][240:]:occ_all.setdefault(fam_,set()).update(residual_cells(route_)) +def rule_control(name,mut,must): + o=copy.deepcopy(ir['calls'][0]['owners']);mut(o) + try:bank_rule(o,occ_all) + except AssertionError as e: + assert must in str(e),(name,str(e));controls.append(name) + else:raise AssertionError('rule mutation accepted: '+name) +bank_rule(ir['calls'][0]['owners'],occ_all) +rule_control('same_width_pure_helper_alias',alias_owner,'footprints overlap') +ent=[r for r in range(240,800) if widths[r-240]<9] +if entering: + a_,b_=ent[0],ent[1] + def to_one_bank(o): # bank class: b joins a's bank family at the next free cells, with a spectator of its own + fa=o[a_][0];free=len(occ_all[fa]);o[b_]=[fa,[2,free,widths[b_-240],[free+widths[b_-240]]]] + rule_control('two_entering_helpers_on_one_bank_family',to_one_bank,'shares its bank family') + rule_control('bank_spectator_is_a_residual_cell',lambda o:o[a_][1].__setitem__(3,[o[a_][1][1]]+o[a_][1][3][1:]),'first cells beyond') + rule_control('bank_spectator_shifted',lambda o:o[a_][1].__setitem__(3,[x+1 for x in o[a_][1][3]]),'first cells beyond') + rule_control('bank_spectator_record_dropped',lambda o:o[a_].__setitem__(1,o[a_][1][:3]),'without a spectator record') + rule_control('bank_spectator_count_wrong',lambda o:o[a_][1].__setitem__(3,o[a_][1][3]*2),'without a spectator record') + rule_control('second_owner_on_an_active_data_family',lambda o:o.__setitem__(241,[o[0][0],[1,0,0]]),'data class') + rule_control('helper_owner_on_an_active_data_family',lambda o:o.__setitem__(250,[o[3][0],[2,0]]),'data class') + rule_control('active_wire_on_a_bank_family',lambda o:o.__setitem__(5,[7680,[1,0,5]]),'bank class') + C_=len(c['centers']) + rule_control('owner_in_the_private_namespace_centres',lambda o:o.__setitem__(300,[W+3,[2,0]]),'private namespace') + rule_control('owner_in_the_private_namespace_reserved_tableau',lambda o:o.__setitem__(300,[W+C_+5,[2,0]]),'private namespace') + rule_control('owner_in_the_private_namespace_coefficient',lambda o:o.__setitem__(300,[W+C_+R+1,[2,0]]),'private namespace') + t=copy.deepcopy(ir);t['calls'][0]['owners'][0][0]+=960 # copies: an active owner of replica 0's invocation on a family of replica 1 + try:global_check(t) + except (AssertionError,KeyError):controls.append('active_owner_on_the_family_of_another_replica') + else:raise AssertionError('global mutation accepted: active_owner_on_the_family_of_another_replica') +assert dict(H)=={int(r):z for r,z in integration['global_profile'].items()} + +def load(name): + sp=importlib.util.spec_from_file_location('replay_hamming_'+name,Path('work/pr361/code/engines')/(name+'.py')) + m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m +M,B=load('moment'),load('base_two_moment');b=Q(integration['complex_b']);grid=Q(1,10**18) +assert M.moment(H,73,W,b,True)[1]<1>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<