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legal scalar corridor; fixed interfaces.", + "total_second_prices": 18299554 +} diff --git a/research/staged544-losing-first-d2/LEDGER.json b/research/staged544-losing-first-d2/LEDGER.json new file mode 100644 index 0000000000..2f9c00d9d9 --- /dev/null +++ b/research/staged544-losing-first-d2/LEDGER.json @@ -0,0 +1,234 @@ +{ + "acceptance": "Scoped raw-moment obstruction; no new supplier, kappa or physical admission.", + "providers": { + "base": { + "added_gates_helpers_buffers": 0, + "all_combined_histograms_recorded": "pair_census.variable_frame.profiles", + "all_first_profiles_recorded": "pair_census.variable_frame.states", + "all_second_price_rank_masses": 5134, + "all_two_edit_scalar_height": { + "all_two_edit_denominator_bits_at_most": 11, + "all_two_edit_numerator_bits_at_most": 11, + "argument": "Each ADD conjugates only through existing corridor scales once; two selections of the same ADD telescope. 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All other coefficients and all native maps are unchanged.", + "corridors": 39, + "maximum_absolute_scale_exponent": 2, + "maximum_sum_absolute_scale_exponents_per_ADD_corridor": 7, + "status": "constructive finite upper bound, not a measured maximum or uniform all-size precision tariff" + }, + "baseline_local_profile": { + "1": 2440, + "2": 725, + "3": 224, + "4": 102, + "5": 20, + "8": 8 + }, + "dirty_buffers": 91, + "entrance_frames_sha256": "e82d4f3c4e35e6aaf384c90fc7cc3ed89ad939a7760ad5f06aff80a519c7353c", + "exit_frames_sha256": "ebd6650741d3b91cd4c0c7f4c5d5aa680094654768f3c0a0342864ab79c4e5dc", + "first_recursive_children_range": [ + 3519, + 3521 + ], + "first_scalar_coefficient_bound": { + "maximum_denominator_bits": 4, + "maximum_numerator_bits": 4 + }, + "helper_roles": 408, + "helper_width_inventory": { + "4": 26, + "5": 2, + "6": 18, + "7": 53, + "8": 96, + "9": 213 + }, + "inherited_outer_profile": { + "1": 7990332, + "2": 2349000, + "3": 748971, + "32": 1, + "4": 330480, + "48": 137911, + "5": 69479, + "8": 25920 + }, + "inherited_outer_profile_status": "Authenticated predecessor source only; no fresh outer reconstruction or admission.", + "initial_operator_corrections": 36, + "live_inputs": 632, + "local_status": "Proved finite chronological invoice and compositional dirty algebra under fixed word/frame contract.", + "native_warps": 72, + "new_supplier_or_kappa": false, + "physical_status": "Unknown/inherited obligations are explicitly listed; no physically admitted implementation is claimed.", + "primitive_inventory": { + "A": { + "add": 3557, + "scale": 498, + "warp": 24 + }, + "B": { + "add": 1796, + "scale": 73 + }, + "cleanup": { + "add": 4633, + "scale": 519, + "warp": 72 + }, + "compensation": { + "add": 5736 + }, + "cut": { + "add": 176 + }, + "precondition": { + "add": 136, + "scale": 56 + }, + "restore": { + "add": 196, + "scale": 16 + } + }, + "proved": [ + "Local chronological recursive invoices, fixed native maps/cuts and helper widths", + "Exact rational first-block equality for every admitted first move on arbitrary dirty inputs", + "Complete baseline free-operator replay and deterministic first/final replay controls", + "Recomputed inverse cleanup and full first-word resource inventories in sampled whole-word controls" + ], + "rank_mass": 5134, + "recursive_children": 3519, + "second_relaxed_recursive_children_range": [ + 3519, + 3523 + ], + "source_scalar_coefficient_bound": { + "maximum_denominator_bits": 4, + "maximum_numerator_bits": 4 + }, + "unknown": [ + "Fresh native Gaussian/Clifford realization and phase", + "Physical hosting/allocation and complete owner chronology", + "Uniform coefficient/precision/stock/tape costs", + "All-size compiler, outer/supplier admission", + "Analytic transfer and BIT H1-H5" + ], + "unknown_costs_are_zero": false + } + }, + "schema_version": 1 +} diff --git a/research/staged544-losing-first-d2/PROOF.md b/research/staged544-losing-first-d2/PROOF.md new file mode 100644 index 0000000000..e90838527e --- /dev/null +++ b/research/staged544-losing-first-d2/PROOF.md @@ -0,0 +1,169 @@ +# Losing-first displacement-two retiming: contract and exact reduction + +This is a source-bound finite certificate with a written argument. It is not a +formal-kernel proof or full multiplication/supplier admission. The scalar move +rules, frame lattice and sign argument are credited reuse from PR3886/3942. +The new domain fixes first final displacement exactly two and excludes neutral +first profiles. Both literal PR3734 providers are checked separately. + +## Fixed contract + +Move one existing ADD across exactly two consecutive scalar instructions inside +one original A-after-prelude, B-between-native-warps, or restore corridor. The +crossed instructions are ADDs satisfying the sufficient commutation condition, +or nonzero SCALEs with exact coefficient conjugation. Choose every legal binary +common first frame. The intermediate word must satisfy the unchanged boundaries +and have a nonzero, exactly sign-certified losing raw recursive profile. + +Then retime any existing ADD to any cut in its allowed scalar corridor, with +any legal common binary frame. There is no second distance bound. The first +moved ADD may be selected again. All other instructions/frames, entrances, +target and centre cuts, native maps/cuts, helper identities and exits, wrappers +and caller contracts remain fixed. No gates or buffers are added or removed. +Cleanup is rederived as the inverse of the edited programme with the inherited +buffer substitution. A final word must satisfy the same boundary contract. + +The raw objective is sum n_r r^(1-a), for real 0i), so the absolute displacement is +exactly two. Every cut must lie in the scalar corridor found by the unchanged +PR3886 sufficient crossing predicate. Native warps and phase/prelude boundaries +are never crossed. + +For either touched register, remove the original event and read its predecessor +frame P and next constraint Q. A common new frame F must satisfy +L=P1+P2 <= F <= H=Q1 intersect Q2. Every admissible dimension is priced, with +removal and insertion costs reconstructed from these frames. First price cells +with a zero signed histogram are excluded explicitly: they are not losing +starts. PR3886's independently regenerated single-move census proves the +remaining first profiles are non-improving; the exact prefix certificate makes +each nonzero one strictly losing throughout 0 1+4`; it is not a new improvement on the pinned word. + +LEDGER.json records the baseline recursive profile, children and rank mass, +all changed intermediate profiles, combined histograms, helper widths, +primitive/native inventory, entrance/exit fingerprints and coefficient bit +bounds. First-move losses are charged before concluding anything about the +second move. Unknown fresh native/phase, physical allocation/hosting, +precision/stock/tape, all-size/compiler, outer/supplier, analytic and BIT costs +remain unknown or explicitly inherited; they are not priced at zero. There is +no new kappa, selected-frontier change or unconditional multiplication theorem. + +## Scope, overlap and credit + +Explicit user-assigned `scalar-to-moment` continuation, canonical main +20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6 at entry. +TASK.json retains the actual scope, expansion decision, overlap coverage, +claim, checkpoints and stopping rule. PR3945 changes terminal/native interfaces +and therefore lies outside this fixed-input search; no claim about its new +supplier follows from these frozen-baseline results. + +Credit dataisfire/PR3734, PR3886, PR3941, PR3942, Jeremy Kothe/PR2957, PR2979 and +the staged-entry/retiming chain, Dugongue/PR3863 and the ranked-pair/MathProof +predecessors. PR3942 supplies the exact all-subspace enumeration and the +same-gate/disjoint second-move reduction; search.py is an explicitly adapted +derivative. PR3941 supplies the dirty-block checking method. Their original +source/proof is retained for comparison where applicable. + +Sagar Thakrar's auditor and roger-sato's semantic adapter are reused unchanged, +including Arham Tahir's frame-contract attribution. They are not newly +independent interpreters. New displacement-two census, dirty checks, controls +and packaging by Chris R / Clear1nsight with substantial OpenAI Codex assistance. +Apache-2.0 and retained source notices apply. No independent human review or +formal-kernel acceptance is claimed. + +## Open next questions + +* Neutral frame-preserving first moves across exactly two neighbours remain a + nearby gap. This package excludes every neutral first move; PR3941 covers + neutral changed-frame starts through two and adjacent frame-preserving ADD + swaps, and PR3942 stops at displacement one. Their union is not the complete + radius-two two-edit class. Enumerate those fixed-frame starts and derive the + new insertion-gap prices before a separate census; the frozen-baseline + adjacent certificate cannot simply be iterated. + +* A first move of displacement three or farther remains outside this bounded + domain. Before expanding, pin one concrete candidate and explain which + projected-frame interaction is newly available, then derive its second-move + and physical invoice. This requires a separate expansion decision, rather + than automatically adding another radius or seed. +* A simultaneous two-frame rewrite without a legal intermediate has a different + contract. Supply one exact before/after word and arbitrary-dirty restoration + identity before attempting the proposed rank exchange or an aggregate price. +* The changed-terminal supplier in PR3945 needs its own source-bound review. + These fixed-interface exclusions do not certify or refute that construction. diff --git a/research/staged544-losing-first-d2/RESULT-base.json b/research/staged544-losing-first-d2/RESULT-base.json new file mode 100644 index 0000000000..1daffe97ae --- /dev/null +++ b/research/staged544-losing-first-d2/RESULT-base.json @@ -0,0 +1 @@ +{"pair_census":{"dirty_validation":{"all_first_dirty_blocks":797,"coefficient_bound":{"maximum_denominator_bits":4,"maximum_numerator_bits":4},"proof":"Every first scalar block equals its source on independent rational symbols; unchanged surrounding free operators compose with that equality. Inverse cleanup is rederived; baseline and sampled complete words additionally replay all 723 symbolic 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diff --git a/research/staged544-losing-first-d2/RESULT-extra.json b/research/staged544-losing-first-d2/RESULT-extra.json new file mode 100644 index 0000000000..899d8fd790 --- /dev/null +++ b/research/staged544-losing-first-d2/RESULT-extra.json @@ -0,0 +1 @@ +{"pair_census":{"dirty_validation":{"all_first_dirty_blocks":797,"coefficient_bound":{"maximum_denominator_bits":4,"maximum_numerator_bits":4},"proof":"Every first scalar block equals its source on independent rational symbols; unchanged surrounding free operators compose with that equality. 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"d1000454afc30925dc4b447a6f007e4b7dcbbab3" + } + } + ], + "method_predecessors": [ + { + "pr": 3886, + "author": "Chris R / Clear1nsight", + "source_commit": "359fe0fe77d29544972fd22ee674085ed5a3b4d0", + "scope": "Single-move theorem, chronological trace, retiming applier, and all-power certificate are reused explicitly." + }, + { + "pr": 3863, + "author": "Dugongue", + "head": "635fe84596c19016f3d0316a5cf7abbe48285490", + "scope": "Uniform rational paid-profile credit and proposed 2+2 to 1+3 target; read, not reimplemented as new mathematics." + }, + { + "pr": 2957, + "author": "Jeremy Kothe", + "retained_record": "research/rank7-joint-endframes/data/REWRITES-2957.json", + "retained_record_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "scope": "Already-retained commuting swap used as a counterfactual rollback/recovery positive control." + }, + { + "pr": 3942, + "source_commit": "1416f8cd6bfb2f2eb9aa5cc22f0388a85fdbac91", + "scope": "Exact all-subspace first-frame enumeration, unrestricted interacting-second pricing, and same-gate/disjoint reduction reused. New first displacement exactly two with losing intermediates." + }, + { + "pr": 3941, + "source_commit": "001ebcdb3f86a7f9d5f5897f9cf5a84e74dd1822", + "scope": "Neutral frame-changing displacement-two domain already covered; excluded from this losing-only census. Exact dirty-block checker method reused." + } + ], + "external_snapshot_contract": "Package-local exact source snapshots are authenticated by byte count, SHA256, and Git blob. Their source heads are attribution pins, not runtime Git ancestry requirements. The standalone verifier is Git-free." +} diff --git a/research/staged544-losing-first-d2/TASK.json b/research/staged544-losing-first-d2/TASK.json new file mode 100644 index 0000000000..3f8fe2ee5b --- /dev/null +++ b/research/staged544-losing-first-d2/TASK.json @@ -0,0 +1,123 @@ +{ + "schema_version": 1, + "task_id": "scalar-to-moment", + "priority_revision": 6, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "original_card": { + "id": "scalar-to-moment", + "question": "Can one known scalar simplification be converted into an actual paid-profile improvement?", + "starting_points": [ + "research/r439-bsection-stars-seed01/README.md", + "certificates/selected-result.json" + ], + "methods": [ + "Derive the changed legal frame itinerary and exact child histogram.", + "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract." + ], + "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Observe that the positive control improves scalar counts while retaining the paid histogram.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Choose one simplification and derive the complete changed frame itinerary, or prove why it cannot change the histogram.", + "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.", + "allowed_variations": [ + "One existing scalar simplification and one proposed frame-path change." + ], + "scope_change_triggers": [ + "Submitting only another scalar count as completion of a paid-profile task." + ], + "overlap_terms": [ + "scalar simplification", + "paid profile", + "R439" + ] + }, + "author": "Chris R / Clear1nsight", + "scope_status": "changed", + "scope_change_reason": "Explicit user-assigned losing-first displacement-exactly-two continuation of PR3941/3942. PR3942 covers first displacement at most one; PR3941 covers neutral frame-changing first moves through two. No task reroll.", + "actual_scope": "Both frozen PR3734 words; a strictly losing first ADD retiming at final displacement exactly two across scalar instructions, every first subspace; then any legal second ADD retiming in its original scalar corridor, with interfaces fixed. Same-gate and disjoint second cases use the credited PR3942 reduction.", + "budget_minutes": 60, + "session_start_utc": "2026-10-19T05:54:18Z", + "verification_reserve_start_utc": "2026-10-19T06:39:18Z", + "stop_utc": "2026-10-19T06:54:18Z", + "outcome": "negative-result", + "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19032051", + "entry_checkpoint": { + "utc": "2026-10-19T05:54:18Z", + "canonical_main": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "priority_revision": 6, + "selected_frontier_changed": false + }, + "overlap_coverage": { + "open_pr_bodies": 649, + "complete_rest_pages": 7, + "fetched_utc": "2026-10-19T05:57:16Z", + "helper": "Current-main find_overlap.py --task scalar-to-moment over connector-populated cache", + "discussions": "Current retiming handoff and visible neighbouring handoffs read in signed-in Chrome. No complete Discussion pagination or exhaustive novelty claim.", + "nearest": [ + "PR3886 single-move premise", + "PR3941 neutral-first two-edit domain", + "PR3942 losing radius-one first domain", + "PR3945 changed terminal/native supplier; outside fixed-interface domain" + ] + }, + "family_expansion_decision": { + "decision": "One explicitly assigned finite extension, then stop; no automatic larger search", + "boundary": "Fixed entrances, target/centre/native cuts, exits, helper identities, buffers and caller contract. Two existing ADDs; no added instructions or helpers.", + "proved_costs": [ + "Exact local recursive child histogram and rank mass", + "Primitive/native inventory and helper/dirty-buffer roles", + "Exact arbitrary-dirty local block identities and baseline free operator" + ], + "unknown_costs": [ + "Fresh native Gaussian/Clifford phase", + "Physical hosting/allocation", + "Uniform coefficient/precision/stock/tape", + "All-size compiler and outer/supplier admission", + "Analytic/BIT" + ], + "decision_test": "One legal strictly improving literal witness with complete changed invoice, or exact obstruction on the finite losing-first displacement-two domain. Stop with precise partial coverage if not completed." + }, + "open_questions": [ + { + "question": "Can a neutral frame-preserving first move across exactly two neighbours unlock a second gain?", + "why_it_matters": "This package excludes all neutral first moves; PR3941 covers neutral changed-frame starts through two and adjacent frame-preserving ADD swaps, while PR3942 stops at displacement one. Their union is not the complete radius-two class.", + "first_step": "Enumerate the fixed-frame displacement-two first words and derive the genuinely new insertion-gap prices; do not iterate a baseline-specific adjacent certificate.", + "blocked_by": "A fresh exact reduction or bounded complete census with the full dirty and cost contract." + }, + { + "question": "Can a losing first move at displacement three or farther unlock a gain?", + "why_it_matters": "The present bounded domain does not imply a global barrier.", + "first_step": "Pin one literal outside-domain word and price every interacting second move.", + "blocked_by": "Separate expansion decision and complete dirty/physical ledger." + }, + { + "question": "Can a simultaneous two-frame rewrite with no legal sequential intermediate implement a gain?", + "why_it_matters": "Sequential legal retimings need not cover direct equivalent rewrites.", + "first_step": "Supply an exact before/after identity and restoration contract.", + "blocked_by": "Explicit legal word and complete paid invoice." + } + ], + "ai_assistance": "Substantial OpenAI Codex assistance. PR3886/3942 routines and retained auditors are credited reuse; no human or kernel review claimed.", + "stop_rule": "Finish only declared finite class, verify and publish focused finding or precise partial handoff; do not merge, close PRs or change frontier.", + "bottleneck_link": "A local scalar rewrite matters only if its complete changed frame itinerary and child histogram improve the paid moment; this checks whether a losing displacement-two intermediate creates that opportunity.", + "evidence": "Both literal providers complete: 797 legal losing first subspace states and 9,149,777 second cut/dimension prices per provider; 48 combined signed types, all exactly non-improving for every real 0>x&1};high_points={x for x in range(512) if high>>x&1} + representatives=[];covered=set(low_points) + for v in sorted(high_points-low_points): + if v not in covered:representatives.append(v);covered.update({v^x for x in low_points}) + answer=set() + for combo in combinations(representatives,dimension-R.rank(low)): + points={x^y for x in low_points for y in xor_span(combo)} + if len(points)==1<=0 for x in prefixes),caps,prefixes + +sources=json.loads((P/'SOURCES.json').read_text()) +row=sources['snapshots'][0] +rejects(lambda:V.authenticate((P/row['local']).read_bytes()+b'x',row),'source_corruption') +rejects(lambda:S.frames(1,R.span((1,2,4,8,16)),1),'quotient_resource_guard') +need([len(independent_frames(1,R.span((1,2,4)),d)) for d in range(4)]==[1,7,7,1],'known subspace lattice') +checks['known_lattice']+=1 +for tag in ('base','extra'): + word=V.load(tag);variable,counts,intervals=S.first_moves(word) + need(variable and all(any(v[4]) and abs(v[2]-(v[2]>v[1])-v[1])==2 for v in variable),'scope includes neutral or wrong displacement') + for low,high,d in intervals: + need(set(S.frames(low,high,d))==independent_frames(low,high,d),'all first-frame subspaces') + checks['independent_frame_intervals']+=1 + # Independent cut enumeration and direct scans of each register's events. + # No primary candidates/geometry/first_moves routine supplies these prices. + nodes,where,_=R.tracing(word);expected=set();price_cells=0;neutral_cells=0 + rank=lambda mask:mask.bit_count().bit_length()-1 + for sec in S.PHASES: + gates=word[sec] + for lo,hi in R.segments(word,sec): + occ={} + for j in range(lo,hi): + for r in (gates[j][1:3] if gates[j][0]=='add' else gates[j][1:2]):occ.setdefault(r,[]).append(j) + for i in range(lo,hi): + g=gates[i] + if g[0]!='add':continue + for cut in (i-2,i+3): + if not lo<=cut<=hi:continue + crossed=gates[i+1:cut] if cut>i else gates[cut:i] + legal=all((g[1]!=h[2] and h[1]!=g[2]) if h[0]=='add' else (h[0]=='scale' and h[2]!=0) for h in crossed) + if not legal:continue + removal=[0]*10;bounds=[] + for r in g[1:3]: + seq=nodes[r];pos=where[((sec,i),r)];a,u=seq[pos][2:4];b=seq[pos+1][3] + removal[rank(u)-rank(a)]-=1;removal[rank(b)-rank(u)]-=1;removal[rank(b)-rank(a)]+=1 + before=[j for j in occ[r] if j!=i and j=cut] + a=R.span(tuple(gates[before[-1]][-1])) if before else seq[where[((sec,occ[r][0]),r)]][2] + b=R.span(tuple(gates[after[0]][-1])) if after else seq[where[((sec,occ[r][-1]),r)]+1][3] + bounds.append((a,b)) + low=R.join(bounds[0][0],bounds[1][0]);high=bounds[0][1]&bounds[1][1] + if low&~high:continue + for d in range(rank(low),rank(high)+1): + price_cells+=1;delta=removal.copy() + for a,b in bounds: + delta[rank(b)-rank(a)]-=1;delta[d-rank(a)]+=1;delta[rank(b)-d]+=1 + delta[0]=0;delta=tuple(delta) + if not any(delta):neutral_cells+=1;continue + for frame in independent_frames(low,high,d):expected.add((sec,i,cut,frame,delta)) + actual={(sec,i,cut,frame,delta) for sec,i,cut,frame,delta,_ in variable} + need(actual==expected and len(actual)==len(variable),'independent first-domain inventory') + need(price_cells==counts['first_price_cells'] and neutral_cells==counts['neutral_price_cells_excluded'],'independent first price cells') + checks['independent_first_records']+=len(expected) + # Direct corridor checks for every generated first: no hidden radius-one start. + for sec,i,cut,frame,delta,kind in variable: + crossed=word[sec][i+1:cut] if cut>i else word[sec][cut:i] + need(len(crossed)==2 and all(R.crosses(word[sec][i],g) for g in crossed),'first corridor') + ok,caps,prefixes=independent_sign(delta) + need(ok and any(prefixes),'first is not strictly losing') + checks['first_scope_and_sign']+=1 + # First-state ordering is deterministic; use one left and one right move. + for right in (False,True): + sec,i,cut,frame,delta,_=next(v for v in variable if (v[2]>v[1])==right) + middle=R.apply_move(word,sec,i,cut,R.basis(frame));lo,hi=min(i,cut),max(i+1,cut) + D.block_equal(word[sec][lo:hi],middle[sec][lo:hi]);checks['exact_dirty_three_gate_blocks']+=1 + middle['cleanup']=C.derive_cleanup(middle);bill,widths,*_=C.frame_bill(middle) + middle['report']['local_profile']={str(r):n for r,n in bill.items()} + A.semantics(C,middle);checks['full_dirty_intermediate_words']+=1 + moved=cut-(cut>i);restored=R.apply_move(middle,sec,moved,i+(moved lo and R.crosses(gate, gates[lower - 1]): + lower -= 1 + while upper < hi and R.crosses(gate, gates[upper]): + upper += 1 + if window is not None: + lower, upper = max(lower, window[0]), min(upper, window[1]) + cuts = [c for c in (i - 2, i + 3) if lower <= c <= upper] if first else range(lower, upper + 1) + reduced = {r: [x for x in occurrences[r] if x != i] for r in R.touched(gate)} + for cut in cuts: + if cut == i + 1: + continue + bounds = [] + for r in R.touched(gate): + indices = reduced[r] + j = bisect_left(indices, cut) + before = R.span(tuple(gates[indices[j - 1]][-1])) if j else entries[r] + after = R.span(tuple(gates[indices[j]][-1])) if j < len(indices) else exits[r] + bounds.append((before, after)) + low = R.join(bounds[0][0], bounds[1][0]) + high = bounds[0][1] & bounds[1][1] + if not R.contained(low, high): + continue + for dimension in range(R.rank(low), R.rank(high) + 1): + delta = removal[i].copy() + for before, after in bounds: + p, q = R.rank(before), R.rank(after) + delta[q - p] -= 1 + delta[dimension - p] += 1 + delta[q - dimension] += 1 + delta[0] = 0 + require(sum(r * n for r, n in enumerate(delta)) == 0, 'rank mass drift') + yield i, cut, dimension, low, high, tuple(delta) + +@lru_cache(maxsize=None) +def frames(low, high, dimension): + """All intermediate subspaces, not one representative per dimension.""" + require(R.contained(low, high), 'empty frame interval') + require(R.rank(low) <= dimension <= R.rank(high), 'invalid frame dimension') + require(R.rank(high) - R.rank(low) <= 4, 'first-frame resource bound exceeded') + current = {low} + for _ in range(dimension - R.rank(low)): + expanded = set() + for frame in current: + for v in range(1, 512): + if high >> v & 1 and not frame >> v & 1: + expanded.add(R.join(frame, R.span((v,)))) + current = expanded + return tuple(sorted(current)) + +def first_moves(word, auditor=None): + variable, counts, intervals = [], Counter(), set() + for section in PHASES: + gates = word[section] + for i, cut, dimension, low, high, delta in candidates(word, section, range(len(gates)), first=True): + require(abs(cut - (cut > i) - i) == 2, 'first displacement is not exactly two') + intervals.add((low, high, dimension)) + counts['first_price_cells'] += 1 + require(R.all_power_nonnegative(delta), 'unclassified first profile') + if delta == ZERO: + counts['neutral_price_cells_excluded'] += 1 + continue + for frame in frames(low, high, dimension): + counts['losing_subspace_records'] += 1 + variable.append((section, i, cut, frame, delta, 'displacement_two_losing')) + return variable, counts, intervals + +def variable_census(word, variable, auditor=None, progress=False): + D = module('dirty_blocks', P/'dirty_blocks.py') + baseline = R.tracing(word)[2] + histogram, first_histogram, counts = Counter(), Counter(), Counter() + states, block_checks, rejected, uncertified_witnesses = [], [], [], {} + for number, (section, i, cut, frame, first_delta, kind) in enumerate(variable): + middle = R.apply_move(word, section, i, cut, R.basis(frame)) + try: + intermediate = R.tracing(middle)[2] + except ValueError as error: + require(str(error) in ('source fixed boundary','source frame containment'), 'unexpected first rejection: '+str(error)) + rejected.append([section,i,cut,list(R.basis(frame)),str(error)]) + continue + require(tuple(intermediate.get(r, 0) - baseline.get(r, 0) if r else 0 for r in range(10)) == first_delta, + 'first actual invoice differs from relaxation') + if auditor is not None: + require(auditor.frame_bill(middle)[0] == intermediate, 'retained first-word invoice disagrees') + require(sum(r*n for r,n in intermediate.items())==sum(r*n for r,n in baseline.items()),'first rank mass differs') + lo,hi=min(i,cut),max(i+1,cut) + block_checks.append(D.block_equal(word[section][lo:hi],middle[section][lo:hi])) + first_histogram[first_delta]+=1 + moved = cut - (cut > i) + registers = set(R.touched(word[section][i])) + local=Counter() + for second_section in PHASES: + selected = [j for j, g in enumerate(middle[second_section]) + if g[0] == 'add' and registers.intersection(R.touched(g)) + and (second_section, j) != (section, moved)] + for j, target, dimension, low, high, second_delta in candidates(middle, second_section, selected): + delta = tuple(a + b for a, b in zip(first_delta, second_delta)) + histogram[delta] += 1 + local[delta] += 1 + if delta not in uncertified_witnesses and not R.all_power_nonnegative(delta): + # An insufficient sign certificate is retained, never treated as a gain. + uncertified_witnesses[delta]={'first':[section,i,cut,list(R.basis(frame)),list(first_delta)], + 'second':[second_section,j,target,dimension,low,high,list(second_delta)]} + n=sum(local.values());counts['first_words']+=1;counts['second_cut_dimensions']+=n + states.append({'first':[section,i,cut,list(R.basis(frame)),list(first_delta)],'profile':intermediate, + 'second_cut_dimensions':n,'second_histogram_sha256':digest(sorted((list(d),n) for d,n in local.items()))}) + if progress and (number%50==0 or number+1==len(variable)): + print('FIRST_AND_SECOND',number+1,'of',len(variable),'prices',counts['second_cut_dimensions'],flush=True) + return {'counts':dict(counts),'first_profiles':rows(first_histogram),'profiles':rows(histogram), + 'states':states,'dirty_block_checks':len(block_checks),'dirty_block_stream_sha256':digest(block_checks), + 'boundary_rejected':rejected,'uncertified_witnesses':list(uncertified_witnesses.values())} + +def compute(word, auditor=None, progress=False): + variable, counts, intervals = first_moves(word, auditor) + if progress:print('FIRST_DOMAIN',dict(counts),'intervals',len(intervals),flush=True) + serial = [[s, i, c, list(R.basis(f)), list(d), k] for s, i, c, f, d, k in variable] + return {'first_counts': dict(sorted(counts.items())), 'first_digest': digest(serial), + 'first_intervals':[[l,h,d] for l,h,d in sorted(intervals)], + 'max_first_quotient_dimension': max(R.rank(h)-R.rank(l) for l,h,_ in intervals), + 'variable_frame': variable_census(word, variable, auditor, progress)} diff --git a/research/staged544-losing-first-d2/vendor/SOURCE-CREDITS.md b/research/staged544-losing-first-d2/vendor/SOURCE-CREDITS.md new file mode 100644 index 0000000000..c054fad87e --- /dev/null +++ b/research/staged544-losing-first-d2/vendor/SOURCE-CREDITS.md @@ -0,0 +1,14 @@ +# Source credit and independence + +New work: dataisfire with substantial OpenAI Codex assistance, Apache-2.0. No independent human review, fresh third-party AI review or proof-kernel verification is claimed. + +The construction extends [PR3682](https://github.com/CrocSwap/integer-mult-bounds/pull/3682), head431e6c6023ef352c41696469de7fb614cd4ded8c. Its retimed word, actual T360 source clock and immutable native/parent framework are retained. The complete new source/receipt snapshot is bound by REPLAY-INPUTS.json. The new ordinary source stage is an explicit pinned record applied after the unchanged predecessor reconstruction. + +- [PR3605](https://github.com/CrocSwap/integer-mult-bounds/pull/3605), Ross Richardson, supplies the staged-entrance mechanism, literal cleanup and exact Gaussian residual-check pattern. staged_pair.py is retained; the new544 shear and its proof are separate. +- [PR3638](https://github.com/CrocSwap/integer-mult-bounds/pull/3638), head d62e1acd7518a231440383f0d0dddf54d6edf8c1, supplies the T360 source-window clock, chronological aggregate model and integral-network/literal construction, with its retained PR3605 and earlier credits. The new inventory, integer incumbent and literal fill are recomputed. No predecessor owner receipt is used as proof of the new fill. +- [PR3687](https://github.com/CrocSwap/integer-mult-bounds/pull/3687) and [PR3693](https://github.com/CrocSwap/integer-mult-bounds/pull/3693), Sagar Thakrar and roger-sato with their credited AI assistance, supply audit_core.py and the whole-word semantics adapter audit_verify.py. These bytes are retained and reused. They are independent of the current constructor in the stated interpreter scope, not a newly written independent audit or new reviewer approval. +- The coupled-word source lineage includes PR3133, PR2979, Marius-Paul Dumitrean, dcharb78, Jeremy Kothe and the retained native/owner/block-norm/outer authors. All notices and scientific engines inside the source snapshot remain intact. + +owner_audit.py is a standalone standard-library adaptation of the source-window/family/prefix/invoice predicates in PR3638's independent_literal.py. It imports no producer, optimizer or retained owner checker. Its source template, plan and actual native canonical words are authenticated inputs. Three controls mutate actual literal roles and must fail for the intended reason. It shares the credited contract interpretation; it is not evidence of independent human agreement. + +The rational finite-price enclosure is retained from the PR3682 sources. New script adapters bind it to the actual finite histogram. Native forward/backward scalar replay, wrapper/phase lowering and all-column warp recipes were freshly run for both new words; unchanged native and parent ancestry is explicitly reused. The separate new544 span(414,51) residual check includes global Gaussian phase. diff --git a/research/staged544-losing-first-d2/vendor/audit_core.py b/research/staged544-losing-first-d2/vendor/audit_core.py new file mode 100644 index 0000000000..8b5e1d5f2a --- /dev/null +++ b/research/staged544-losing-first-d2/vendor/audit_core.py @@ -0,0 +1,480 @@ +"""Independent exact semantics and binary-frame bill for the BORROW-WORD format. + +Standard library only. Nothing is imported from the audited authors' code +(PR3133/PR3605 producers, cleanup generator, evaluator or frame solver); the word +format and its semantic contract were read from those pinned sources and are +credited there. The frame-bill and free-word structure (point-set spans, warp +frame and lifted-frame checks, target levels keyed by register, dual symbol +naming) re-implements, without importing, Arham Tahir's +research/coupled-carrier-independent-audit/verify.py (Apache-2.0) and shares its +reading of the contract, so this module is not independent of that audit. + +Sagar Thakrar (thakrarsagar), with substantial AI assistance from Claude +(Anthropic, Claude Opus 5.5). Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q + +V, N, H = 112, 704, 9 # sources 0..111, targets 112..223, helpers 224..703 +DUAL = 10 ** 6 # offset naming the independent dual symbols D_k = K_k^(-T) + + +class AuditFailure(Exception): + """Explicit failure; never disabled by python -O.""" + + +def need(ok, *why): + if not ok: + raise AuditFailure(' '.join(map(str, why))) + + +def is_target(r): + return V <= r < 2 * V + + +def touched(g): + return g[1:3] if g[0] == 'add' else g[1:2] + + +# ---------------------------------------------------------------------------- +# Binary frames: a subspace of F_2^9 is stored as a 512-bit point-set mask +# (bit x set iff x lies in the subspace). Containment is mask inclusion. +# ---------------------------------------------------------------------------- +_SPAN = {} + + +def span(vectors): + key = tuple(vectors) + mask = _SPAN.get(key) + if mask is None: + points = {0} + for u in key: + need(type(u) is int and 0 <= u < 512, 'frame vector out of range', u) + if u not in points: + points |= {p ^ u for p in points} + mask = sum(1 << p for p in points) + _SPAN[key] = mask + return mask + + +def points(mask): + return [x for x in range(512) if mask >> x & 1] + + +def dim(mask): + size = bin(mask).count('1') + need(size and size & (size - 1) == 0, 'not a subspace point set') + return size.bit_length() - 1 + + +FULL = (1 << 512) - 1 +ZERO = 1 + + +def hyperplane(port): + return sum(1 << x for x in range(512) if bin(x & port).count('1') % 2 == 0) + + +def warp_images(columns): + """Images of all 512 vectors under the F_2-linear map with columns G e_i.""" + need(len(columns) == H and all(type(c) is int and 0 <= c < 512 for c in columns), 'warp columns') + images = [0] * 512 + for x in range(1, 512): + low = x & -x + images[x] = images[x ^ low] ^ columns[low.bit_length() - 1] + need(len(set(images)) == 512, 'singular warp') + return images + + +def image_mask(images, mask): + return sum(1 << images[x] for x in points(mask)) + + +def lagrangian_action_ok(images, U, E): + """K_G(x,z)=(Gx, Gx+G^{-T}(x+z)) is symplectic and maps L_U to L_E, L_0 and L_FULL to themselves. + + L_U={(x,x+p): x in U, p in U^perp}. This is the binary frame action only; it + is not a Clifford phase or Gaussian-product certificate. For invertible G with + G(U)=E it is implied by the frame-map check ( = ), so it is a + consistency check of the implementation, not extra evidence. + """ + inverse = [0] * 512 + for x, y in enumerate(images): + inverse[y] = x + # G^{-T} z: bit j of the result is . + git = lambda z: sum((bin(inverse[1 << j] & z).count('1') & 1) << j for j in range(H)) + lift = lambda x, z: (images[x], images[x] ^ git(x ^ z)) + pair = lambda a, b: (bin(a[0] & b[1]).count('1') + bin(a[1] & b[0]).count('1')) & 1 + basis = [(1 << i, 0) for i in range(H)] + [(0, 1 << i) for i in range(H)] + lifted = [lift(*b) for b in basis] + if any(pair(lifted[i], lifted[j]) != pair(basis[i], basis[j]) for i in range(18) for j in range(i + 1, 18)): + return False + + def frame(mask): + us = points(mask) + perp = [p for p in range(512) if all(bin(p & u).count('1') % 2 == 0 for u in us)] + return {(u, u ^ p) for u in us for p in perp} + return all({lift(*pt) for pt in frame(a)} == frame(b) for a, b in ((ZERO, ZERO), (FULL, FULL), (U, E))) + + +# ---------------------------------------------------------------------------- +# Chronological binary-frame bill (BORROW-WORD contract) +# ---------------------------------------------------------------------------- +def frame_bill(w, lagrangian=False): + rep = w['report'] + need((rep['v'], 2 * rep['v'] + rep['R'], rep['h']) == (V, N, H), 'word geometry') + removed = set(w['removed']) + need(len(removed) == len(w['removed']) and all(2 * V <= r < N for r in removed), 'removed helpers') + live = [r for r in range(N) if r not in removed] + liveset = set(live) + B, warps = w['B'], w['warps'] + for k, (pos, lender, cols, U, E) in enumerate(warps, 1): + need(0 <= pos <= len(B), 'warp position', k) + need(lender in liveset and not is_target(lender), 'warp lender', k) + images = warp_images(cols) + su, se = span(U), span(E) + need(dim(su) == len(U) == len(E) == dim(se), 'warp frame bases', k) + need(image_mask(images, su) == se, 'warp does not map its frame', k) + if lagrangian: + need(lagrangian_action_ok(images, su, se), 'lifted frame action', k) + for name in ('A', 'B', 'restore'): + for g in w[name]: + if g[0] != 'warp': + need(all(r in liveset for r in touched(g)), 'removed/out-of-range register', name, g) + if g[0] == 'add' and not is_target(g[1]): + need(not is_target(g[2]), 'non-target reads a target', name, g) + need(all(g[-1] is None and is_target(g[1]) and g[0] == 'add' for g in w['cut']), 'cut gates') + need(all(g[-1] == [] and is_target(g[1]) for g in w['precondition'] + w['compensation']), 'zero-frame wrapper writes') + need(all(not is_target(g[1]) for g in w['restore']), 'restore writes a target') + + ports = w['ports'] + start, end = {}, {} + for r in live: + if r < V: + start[r], end[r] = span((ports[r],)), FULL + elif r < 2 * V: + start[r], end[r] = ZERO, hyperplane(ports[r - V]) + else: + start[r], end[r] = ZERO, FULL + for q, U in w['start_extra'].items(): + need(int(q) in liveset and int(q) >= 2 * V, 'entrance names a live helper', q) + start[int(q)] = span(U) + for q, U in w['helper_final'].items(): + need(int(q) in liveset and int(q) >= 2 * V, 'terminal names a live helper', q) + end[int(q)] = span(U) + + current, bill, chain = dict(start), Counter(), {} + + def climb(r, mask, where): + need(current[r] & ~mask == 0, 'frame containment fails', where, r) + d = dim(mask) - dim(current[r]) + if d: + bill[d] += 1 + chain.setdefault(r, []).append((where, d, mask)) + current[r] = mask + + npre = w['prelude_events'] + for i, g in enumerate(w['A']): + if g[0] == 'warp': + need(i < npre and len(g) == 5, 'warp outside the prelude', i) + _, r, op, fr, to = g + need(op != 0 and abs(op) <= len(warps) and warps[abs(op) - 1][1] == r, 'prelude warp lender', i) + images = warp_images(warps[abs(op) - 1][2]) + if op < 0: + inverse = [0] * 512 + for x, y in enumerate(images): + inverse[y] = x + images = inverse + need(image_mask(images, span(fr)) == span(to), 'prelude warp frame action', i) + need(current[r] == span(fr), 'prelude warp entry frame', i, r) + current[r] = span(to) + chain.setdefault(r, []).append((('A', i), 'warp', span(to))) + else: + if i < npre: + need(is_target(g[1]), 'prelude scalar writes a non-target', i) + for r in touched(g): + climb(r, span(g[-1]), ('A', i)) + levels = {V + int(t): span(U) for t, U in w['target_levels'].items()} + need(all(current[t] == levels.get(t, ZERO) for t in range(V, 2 * V)), 'target cut levels') + for q, U in zip(w['centers'], w['center_frames']): + U = span(U) + need(current[q] == U, 'centre entry frame', q) + served = {levels.get(g[1], ZERO) for g in w['cut'] if g[2] == q} + for T in sorted(served, key=lambda m: -dim(m)): + need(T & ~U == 0, 'centre descent not nested', q) + d = dim(U) - dim(T) + if d: + bill[d] += 1 + chain.setdefault(q, []).append((('centre',), d, T)) + U = T + at = {} + for k, rec in enumerate(warps, 1): + at.setdefault(rec[0], []).append(k) + for p in range(len(B) + 1): + for k in at.get(p, ()): + _, lender, _, U, E = warps[k - 1] + need(current[lender] == span(U), 'native warp entry frame', k, lender) + current[lender] = span(E) + chain.setdefault(lender, []).append((('warp', k), 'warp', span(E))) + if p < len(B): + for r in touched(B[p]): + climb(r, span(B[p][-1]), ('B', p)) + for i, g in enumerate(w['restore']): + for r in touched(g): + climb(r, span(g[-1]), ('restore', i)) + for r in live: + climb(r, end[r], ('end',)) + restored = set(map(int, w['helper_final'])) + need(all(end[r] == FULL for r in live if r not in restored and not is_target(r)), 'a FULL-cleanup register ends low') + widths = Counter(dim(end[r]) - dim(start[r]) for r in live if r >= 2 * V) + return dict(sorted(bill.items())), dict(sorted(widths.items())), chain, start, end + + +def hygiene(w): + """Inherited structural contract: dyadic scalars, power-of-two scales, wrapper and correction access.""" + entering = set(map(int, w['start_extra'])) + restored = set(map(int, w['helper_final'])) + live = set(range(N)) - set(w['removed']) + for name in ('precondition', 'compensation', 'A', 'cut', 'B', 'restore', 'cleanup'): + for g in w[name]: + if g[0] == 'warp': + continue + q = Q(g[3], g[4]) if g[0] == 'add' else Q(g[2], g[3]) + need(q != 0 and q.denominator & (q.denominator - 1) == 0, 'non-dyadic scalar', name, g) + if g[0] == 'scale': + need(abs(q.numerator) & (abs(q.numerator) - 1) == 0, 'non power-of-two scale', name, g) + for g in w['precondition'] + w['compensation']: + need(not any(r in entering | restored for r in touched(g)), 'wrapper touches an entering or restored helper', g) + for c in w['initial_corrections']: + word = c['operator_word'] + need(is_target(c['target']) and c['source'] in live and c['source'] >= 2 * V + and c['source'] not in entering, 'correction access', c) + need(word and all(w['warps'][abs(o) - 1][1] == c['source'] for o in word), 'correction operator lender', c) + q = Q(c['coefficient']) + need(q != 0 and q.denominator & (q.denominator - 1) == 0, 'correction coefficient', c) + return True + + +# ---------------------------------------------------------------------------- +# Literal inverse cleanup, derived from the contract +# ---------------------------------------------------------------------------- +def ordinary_forward(w): + """Chronological non-wrapper actions whose inverse forms cleanup.""" + out = [g for g in w['A'][w['prelude_events']:]] + at = {} + for k, rec in enumerate(w['warps'], 1): + at.setdefault(rec[0], []).append(['warp', rec[1], k]) + for p in range(len(w['B']) + 1): + out += at.get(p, []) + if p < len(w['B']): + out.append(w['B'][p]) + return out + list(w['restore']) + + +def derive_cleanup(w): + restored = set(map(int, w['helper_final'])) + buf = lambda r: r + N if r in restored else r + full = [256, 128, 64, 32, 16, 8, 4, 2, 1] + out = [] + for g in reversed(ordinary_forward(w)): + if g[0] == 'warp': + out.append(['warp', buf(g[1]), -g[2], full]) + elif is_target(g[1]): + continue + elif g[0] == 'add': + out.append(['add', buf(g[1]), buf(g[2]), -g[3], g[4], full]) + else: + need(g[0] == 'scale', 'unknown primitive', g) + out.append(['scale', buf(g[1]), g[3], g[2], full]) + return out + + +def same_cleanup(a, b): + norm = lambda c: [(g[:-1], span(g[-1])) for g in c] + return len(a) == len(b) and norm(a) == norm(b) + + +# ---------------------------------------------------------------------------- +# Exact free-operator semantics. A value is a dict {(input, word): Fraction}; +# word is a reduced tuple of signed operator ids (leftmost = applied last). +# ---------------------------------------------------------------------------- +def program(w, cleanup=None): + """Literal executed sequence: corrections, wrapper, A, cut, B+warps, restore | cleanup.""" + items = [('corr', c['target'], c['source'], tuple(c['operator_word']), Q(c['coefficient'])) + for c in w['initial_corrections']] + items += w['precondition'] + w['compensation'] + w['A'] + w['cut'] + at = {} + for k, rec in enumerate(w['warps'], 1): + at.setdefault(rec[0], []).append(['warp', rec[1], k]) + for p in range(len(w['B']) + 1): + items += at.get(p, []) + if p < len(w['B']): + items.append(w['B'][p]) + items += w['restore'] + return items, list(w['cleanup'] if cleanup is None else cleanup) + + +def dual_op(op): + return (1 if op > 0 else -1) * (abs(op) + DUAL) + + +def _left(op, word): + return word[1:] if word and word[0] == -op else (op,) + word + + +def _right(word, op): + return word[:-1] if word and word[-1] == -op else word + (op,) + + +def _axpy(dst, src, q): + for key, x in src.items(): + y = dst.get(key, 0) + q * x + if y: + dst[key] = y + else: + dst.pop(key, None) + + +def forward_rows(w, cleanup=None, dual=False, symbolic_buffers=True, snapshot=None): + """Schrodinger pass: every register's value as a combination of initial inputs. + + Live inputs are independent symbols. Private buffers are independent symbols + when symbolic_buffers is set (dirty), otherwise zero. The optional snapshot + callback sees the rows at the cleanup boundary. + """ + removed = set(w['removed']) + live = [r for r in range(N) if r not in removed] + restored = sorted(map(int, w['helper_final'])) + rows = {r: {(r, ()): Q(1)} for r in live} + for c in restored: + rows[c + N] = {(c + N, ()): Q(1)} if symbolic_buffers else {} + prefix, tail = program(w, cleanup) + + def apply(g): + kind = g[0] + if kind == 'add': + t, s, q = g[1], g[2], Q(g[3], g[4]) + need(t != s and q, 'add gate', g) + if dual: + t, s, q = s, t, -q + _axpy(rows[t], rows[s], q) + elif kind == 'scale': + q = Q(g[2], g[3]) + need(q != 0, 'zero scale', g) + if dual: + q = 1 / q + rows[g[1]] = {k: q * x for k, x in rows[g[1]].items()} + elif kind == 'warp': + op = dual_op(g[2]) if dual else g[2] + rows[g[1]] = {(var, _left(op, word)): x for (var, word), x in rows[g[1]].items()} + elif kind == 'corr': + _, t, s, word, c = g + if dual: + src, ops, dst, c = rows[t], [-dual_op(o) for o in word], s, -c + else: + src, ops, dst = rows[s], list(reversed(word)), t + moved = {} + for (var, wd), x in src.items(): + for o in ops: + wd = _left(o, wd) + moved[var, wd] = x + _axpy(rows[dst], moved, c) + else: + raise AuditFailure('unknown primitive ' + repr(g)) + + for g in prefix: + apply(g) + if snapshot is not None: + snapshot(rows) + for g in tail: + apply(g) + return rows + + +def reverse_columns(w, cleanup=None, upto_cleanup=False): + """Heisenberg pull-back: process the forward program backwards. + + cols[s] = {(output, word): coefficient}: the final output register 'output' + contains coefficient*word*x_s. Words grow on the right. Every live input and + every private buffer is an independent symbol. + """ + removed = set(w['removed']) + live = [r for r in range(N) if r not in removed] + restored = sorted(map(int, w['helper_final'])) + regs = live + [c + N for c in restored] + cols = {r: {(r, ()): Q(1)} for r in regs} + prefix, tail = program(w, cleanup) + seq = prefix if upto_cleanup else prefix + tail + for g in reversed(seq): + kind = g[0] + if kind == 'add': + t, s, q = g[1], g[2], Q(g[3], g[4]) + need(t != s and q, 'add gate', g) + _axpy(cols[s], cols[t], q) + elif kind == 'scale': + q = Q(g[2], g[3]) + need(q != 0, 'zero scale', g) + cols[g[1]] = {k: q * x for k, x in cols[g[1]].items()} + elif kind == 'warp': + op = g[2] + cols[g[1]] = {(out, _right(word, op)): x for (out, word), x in cols[g[1]].items()} + elif kind == 'corr': + _, t, s, word, c = g + moved = {} + for (out, wd), x in cols[t].items(): + for o in word: + wd = _right(wd, o) + moved[out, wd] = x + _axpy(cols[s], moved, c) + else: + raise AuditFailure('unknown primitive ' + repr(g)) + return cols + + +def transpose(cols): + rows = {} + for s, col in cols.items(): + for (r, word), x in col.items(): + rows.setdefault(r, {})[s, word] = x + return rows + + +def endpoint_defects(w, rows, dual=False): + """Compare final rows with the contract on the zero-buffer (live-input) domain. + + Returns (bad live registers, dirty buffers, buffer->live leaks, buffer self-map identity). + """ + removed = set(w['removed']) + live = [r for r in range(N) if r not in removed] + restored = sorted(map(int, w['helper_final'])) + bad = [] + for r in live: + expect = {(r, ()): Q(1)} + if dual and r < V: + expect[r + V, ()] = Q(-1) + if not dual and is_target(r): + expect[r - V, ()] = Q(1) + got = {k: x for k, x in rows.get(r, {}).items() if k[0] < N} + if got != expect: + bad.append(r) + dirty = [c for c in restored if any(k[0] < N for k in rows.get(c + N, {}))] + leaks = sorted({r for r in live for k in rows.get(r, {}) if k[0] >= N}) + buffer_identity = all({k: x for k, x in rows.get(c + N, {}).items() if k[0] >= N} == {(c + N, ()): Q(1)} + for c in restored) + return bad, dirty, leaks, buffer_identity + + +def boundary_defects(w, rows): + """Contract at the cleanup boundary (forward): targets sheared, restored helpers clean and isolated.""" + restored = set(map(int, w['helper_final'])) + out = [] + for t in range(V, 2 * V): + if {k: x for k, x in rows[t].items() if k[0] < N} != {(t, ()): Q(1), (t - V, ()): Q(1)}: + out.append(('target', t)) + for c in restored: + if rows[c] != {(c, ()): Q(1)}: + out.append(('restored', c)) + for r, row in rows.items(): + if r < N and r not in restored and any(k[0] in restored for k in row): + out.append(('restored input read', r)) + return out diff --git a/research/staged544-losing-first-d2/vendor/audit_verify.py b/research/staged544-losing-first-d2/vendor/audit_verify.py new file mode 100644 index 0000000000..7f9fc1df42 --- /dev/null +++ b/research/staged544-losing-first-d2/vendor/audit_verify.py @@ -0,0 +1,254 @@ +#!/usr/bin/env python3 +"""Whole-word cross-check of published RETIMED and DELAYED supplier words. + +Reuses Sagar Thakrar's exact PR3687 audit_core, unchanged and authenticated +before execution. This is not a new interpreter. No construction/native checker +is imported. roger-sato with substantial OpenAI Codex assistance; Apache-2.0. +""" +from collections import Counter +from copy import deepcopy +import gzip +import hashlib +import json +from pathlib import Path +import sys +import types + +HERE = Path(__file__).resolve().parent +STAGED = {1: 2439, 2: 726, 3: 224, 4: 102, 5: 20, 8: 8} +RETIMED = {1: 2437, 2: 724, 3: 226, 4: 102, 5: 20, 8: 8} +WIDTHS = {4: 26, 5: 2, 6: 18, 7: 52, 8: 97, 9: 213} +MOVES = ((591, 1045, 640, 644, 2, [423, 65, 20, 10]), + (641, 1085, 656, 660, -1, [427, 96, 24, 6])) +SOURCE_COMMITS = { + 3605: '3efbb5de06a49ffeea6684482f2d3fe48cdca3fb', + 3642: '044d24f12e74f228dd462c07ae2d7f3ea35e2be9', + 3653: '607a09ff441c79b215a8127a81f4cc70021d0d9b', + 3682: '431e6c6023ef352c41696469de7fb614cd4ded8c', + 3687: 'f798838eb8ede4178e94f240e7b7e54b3f80c82d', +} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def authenticate(): + rows = json.loads((HERE / 'SOURCES.json').read_text())['snapshots'] + expected = {(3687, 'vendor/audit_core.py')} + for provider in ('base', 'extra'): + expected.update((number, f'inputs/{kind}-{provider}.json.gz') for number, kind in + ((3605, 'STAGED'), (3642, 'RETIMED'), (3653, 'RETIMED'), (3682, 'DELAYED'))) + keys = [(row['source_pr'], row['local']) for row in rows] + need(len(keys) == len(expected) and set(keys) == expected, 'source mapping inventory differs') + for row in rows: + need(row['source_commit'] == SOURCE_COMMITS[row['source_pr']], 'source commit differs') + raw = (HERE / row['local']).read_bytes() + need(len(raw) == row['bytes'], 'source byte length: ' + row['local']) + need(hashlib.sha256(raw).hexdigest() == row['sha256'], 'source SHA256: ' + row['local']) + blob = hashlib.sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest() + need(blob == row['git_blob'], 'source Git blob: ' + row['local']) + core = types.ModuleType('retained_audit_core') + path = HERE / 'vendor/audit_core.py' + # Execute the authenticated source bytes, without accepting a .pyc cache. + exec(compile(path.read_bytes(), str(path), 'exec'), core.__dict__) + return core + + +def load(kind, provider): + return json.loads(gzip.decompress((HERE / 'inputs' / f'{kind}-{provider}.json.gz').read_bytes())) + + +def events(w): + result = [] + for pos in range(len(w['B']) + 1): + result += [('warp', k, deepcopy(rec)) for k, rec in enumerate(w['warps']) if rec[0] == pos] + if pos < len(w['B']): + result.append(('gate', pos, deepcopy(w['B'][pos]))) + return result + + +def replace_events(w, seq): + result = deepcopy(w) + body, warps = [], [None] * len(w['warps']) + for kind, label, gate in seq: + gate = deepcopy(gate) + if kind == 'gate': + body.append(gate) + else: + gate[0] = len(body) + warps[label] = gate + need(all(rec is not None for rec in warps), 'lost warp in reconstruction') + result['B'], result['warps'] = body, warps + return result + + +def reconstruct(C, staged, kind): + """Literal prose recipes: adjacent shear swap, or move before first producer. + + This repeats the credited local structural arguments as an input control; + the new evidence is the full word calculation below. + """ + seq = events(staged) + for start, stop, donor, pivot, coefficient, frame in MOVES: + source = next(x for x in seq if x[:2] == ('gate', start)) + need(source[2] == ['add', donor, pivot, coefficient, 1, [429, 30]], 'source release') + if kind == 'RETIMED': + target = next(x for x in seq if x[:2] == ('gate', start + 1)) + need(target[2][0] == 'add' and target[2][2] == pivot, 'adjacent same-pivot shear') + need(not any(rec[0] == start + 1 for rec in staged['warps']), 'unexpected crossed warp') + where = seq.index(target) + 1 + else: + target = next(x for x in seq if x[:2] == ('gate', stop)) + writes = [i for i, g in enumerate(staged['B']) if i > start and g[1] == pivot] + need(writes[0] == stop, 'first producer cut') + where = seq.index(target) + changed = deepcopy(source[2]) + changed[-1] = frame + seq.insert(where, ('gate', -pivot, changed)) + seq.remove(source) + result = replace_events(staged, seq) + result['cleanup'] = C.derive_cleanup(result) + result['report']['local_profile'] = {str(k): v for k, v in RETIMED.items()} + return result + + +def semantics(C, w): + """All live and buffer inputs are symbols, with no zero-buffer assumption.""" + def endpoint(name, result): + bad_live, dirty_buffers, leaks, buffer_identity = result + need(not bad_live and not dirty_buffers and not leaks and buffer_identity, + name + ' endpoint: ' + repr(result)) + boundary = {} + rows = C.forward_rows(w, symbolic_buffers=True, + snapshot=lambda values: boundary.setdefault('defects', C.boundary_defects(w, values))) + endpoint('forward', C.endpoint_defects(w, rows)) + dual_rows = C.forward_rows(w, dual=True, symbolic_buffers=True) + endpoint('dual', C.endpoint_defects(w, dual_rows, dual=True)) + need(not boundary['defects'], 'cleanup boundary: ' + repr(boundary['defects'])) + pulled = C.transpose(C.reverse_columns(w)) + need(pulled == {r: row for r, row in rows.items() if row}, 'reverse pull-back differs from forward') + pre = C.transpose(C.reverse_columns(w, upto_cleanup=True)) + pre = {r: pre.get(r, {}) for r in set(pre) | set(range(C.N))} + need(not C.boundary_defects(w, pre), 'reverse cleanup-boundary contract') + live = C.N - len(w['removed']) + buffers = len(w['helper_final']) + need((live, buffers, len(rows)) == (632, 91, 723), 'complete symbolic domain') + # Endpoint expectations are derived by the retained checker: live x,y,h + # map to x,y+x,h; all private buffer symbols return unchanged. + return {'live_inputs': live, 'dirty_buffers': buffers, 'matrix_dimension': len(rows), + 'forward': 'PASS', 'dual': 'PASS', 'reverse_pullback_equals_forward': True, + 'cleanup_boundary_forward_and_reverse': 'PASS', + 'buffer_to_live_leaks': 0, 'buffer_self_map': 'identity', + 'nonzero_endpoint_terms': sum(len(row) for row in rows.values())} + + +def inspect(C, w, profile): + C.hygiene(w) + bill, widths, chain, _, _ = C.frame_bill(w) + need(bill == profile, 'computed profile differs') + need(w['report']['local_profile'] == {str(k): v for k, v in bill.items()}, 'declared profile differs') + need(widths == WIDTHS, 'helper widths differ') + need(w['cleanup'] == C.derive_cleanup(w), 'literal cleanup differs') + return {'semantics': semantics(C, w), 'profile': bill, 'widths': widths, + 'rank_mass': sum(r * n for r, n in bill.items())}, chain + + +def expect_rejection(C, fn, phrase): + try: + fn() + except (ValueError, C.AuditFailure) as exc: + need(phrase in str(exc), 'wrong rejection: ' + str(exc)) + return phrase + raise ValueError('mutant unexpectedly passed: ' + phrase) + + +def negative_controls(C, staged, w, kind): + controls = [] + for _, _, donor, pivot, _, _ in MOVES: + seq = events(w) + release = next(x for x in seq if x[0] == 'gate' and x[2][0] == 'add' and x[2][1:3] == [donor, pivot]) + for defect in ('omit', 'flip', 'cross_first_producer'): + changed = deepcopy(seq) + index = seq.index(release) + if defect == 'omit': + changed.pop(index) + elif defect == 'flip': + changed[index][2][3] *= -1 + else: + producer = next(x for x in changed[index + 1:] if x[0] == 'gate' and x[2][1] == pivot) + moved = changed.pop(index) + changed.insert(changed.index(producer) + 1, moved) + bad = replace_events(w, changed) + bad['cleanup'] = C.derive_cleanup(bad) + # Repair the literal inverse so stale cleanup is not the rejection. + reason = expect_rejection(C, lambda: semantics(C, bad), 'forward endpoint') + controls.append({'defect': defect, 'pivot': pivot, 'rejected_by': reason}) + old_cleanup = deepcopy(w) + old_cleanup['cleanup'] = staged['cleanup'] + # The inverse shears commute: this is a format failure, not a wrong operator. + semantic_control = semantics(C, old_cleanup) + need(old_cleanup['cleanup'] != C.derive_cleanup(old_cleanup), 'old cleanup unexpectedly literal') + controls.append({'defect': 'old_cleanup_order', 'semantics': semantic_control, + 'rejected_by': expect_rejection(C, lambda: inspect(C, old_cleanup, RETIMED), 'literal cleanup differs')}) + old_frames = deepcopy(w) + for gate in old_frames['B']: + if gate[0] == 'add' and gate[1:3] in ([640, 644], [656, 660]): + gate[-1] = [429, 30] + need(semantics(C, old_frames) == semantic_control, 'frame-only mutation changed operator') + if kind == 'RETIMED': + need(C.frame_bill(old_frames)[0] == STAGED, 'old frame control does not restore staged bill') + controls.append({'defect': 'old_release_frames', 'semantic_operator': 'PASS', + 'profile': STAGED, 'rejected_by': expect_rejection(C, lambda: inspect(C, old_frames, RETIMED), 'computed profile differs')}) + else: + # The later release encounters a donor that has already climbed, so + # the original rank-2 frame is now illegal, despite the same operator. + controls.append({'defect': 'old_release_frames', 'semantic_operator': 'PASS', + 'rejected_by': expect_rejection(C, lambda: inspect(C, old_frames, RETIMED), 'frame containment fails')}) + fake_report = deepcopy(w) + fake_report['report']['local_profile']['1'] += 1 + controls.append({'defect': 'wrong_declared_profile', 'rejected_by': + expect_rejection(C, lambda: inspect(C, fake_report, RETIMED), 'declared profile differs')}) + return controls + + +def run(C): + results = {} + for provider in ('base', 'extra'): + staged = load('STAGED', provider) + control, old_chain = inspect(C, staged, STAGED) + records = {'STAGED': control} + for kind in ('RETIMED', 'DELAYED'): + w = load(kind, provider) + need(reconstruct(C, staged, kind) == w, 'prose reconstruction differs: ' + kind) + record, chain = inspect(C, w, RETIMED) + deltas = {} + for register in set(chain) | set(old_chain): + before = Counter(d for _, d, _ in old_chain.get(register, []) if type(d) is int and d > 0) + after = Counter(d for _, d, _ in chain.get(register, []) if type(d) is int and d > 0) + delta = {r: after[r] - before[r] for r in set(after) | set(before) if after[r] != before[r]} + if delta: + deltas[register] = delta + need(deltas == {640: {1: -1, 2: -1, 3: 1}, 656: {1: -1, 2: -1, 3: 1}}, 'per-register invoice differs') + record['prose_reconstruction'] = 'exact complete JSON equality' + record['changed_register_bills'] = deltas + record['controls'] = negative_controls(C, staged, w, kind) + records[kind] = record + print('CHECKED', provider, kind, '723-register forward/dual/pull-back and 9 controls', flush=True) + results[provider] = records + return {'status': 'PASS_RETIMED_AND_DELAYED_WHOLE_WORD_AUDIT', + 'scope': 'Reused PR3687 interpreter; finite exact operator/frame audit only. No native Gaussian, owner, root, or complete supplier claim.', + 'providers': results} + + +if __name__ == '__main__': + need(sys.argv[1:] in ([], ['--write']), 'usage: verify.py [--write]') + C = authenticate() + result = run(C) + output = json.dumps(result, sort_keys=True, indent=2) + '\n' + if sys.argv[1:] == ['--write']: + (HERE / 'RESULT.json').write_text(output) + else: + need((HERE / 'RESULT.json').read_text() == output, 'committed result differs') + print(result['status']) diff --git a/research/staged544-losing-first-d2/vendor/pr3942_PROOF.md b/research/staged544-losing-first-d2/vendor/pr3942_PROOF.md new file mode 100644 index 0000000000..9c44765e69 --- /dev/null +++ b/research/staged544-losing-first-d2/vendor/pr3942_PROOF.md @@ -0,0 +1,162 @@ +# Local-first two-ADD retiming obstruction + +## Statement and fixed contract + +Fix either literal PR3734 provider retained in `inputs/`. A first existing ADD +may change its common binary frame in place, or move across exactly one adjacent +ADD or nonzero SCALE and change that frame. A second existing ADD may then move +any distance inside its allowed scalar corridor and choose any common binary +frame. Both the intermediate and final words must satisfy the fixed boundaries. +Every other gate, gate frame, entrance, target/centre cut, native warp, and exit +is unchanged. Each move stays within A after its prelude, B between native warp +cuts, or restore. ADD crossings use the sufficient condition +`destination(g) != source(h)` and `destination(h) != source(g)`; SCALE crossings +use exact conjugation. These are the PR3886 move rules, not every possible +semantics-preserving rewrite. The same ADD may be chosen twice. + +**Theorem.** Every word in this class has new-minus-old raw rank moment at least +zero for every real `0 < a < 1`. The raw moment is `sum n_r r^(1-a)`. This is a +finite source-bound theorem conditional on the explicitly stated word/frame +contract, supported by the exact census below. It is not a universal two-gate +barrier or supplier admission. + +The first move need not be neutral. The census also includes every locally +losing first move in this radius-one class. The second move has no radius bound. +A simultaneous edit which needs an illegal intermediate, a longer first move, +a moved SCALE, extra/deleted gates, warp/phase crossings, or another changed +boundary is outside the statement. + +## 1. Reused scalar and single-move facts + +The elementary matrix `I+cE_ds` commutes with `I+bE_uv` under the displayed +sufficient condition. Moving it right across a scale q at d multiplies c by q; +a scale at s divides c by q. Moving left reverses these factors. The source +scales are nonzero powers of two, so coefficients remain dyadic. These are +identities on arbitrary inputs, including dirty helpers. Cleanup is defined as +the literal inverse of the edited forward programme, with the inherited buffer +substitution; it does not require zero dirty state. + +The PR3886 trace, move applier, complete single-move census, and sign criterion +are reused verbatim. The primary replay regenerates all 1,776,295 single-move +cut/dimension cases separately for each provider and compares the entire frozen +receipt, rather than trusting its old PASS flag. That census proves every +single-move delta is nonnegative for all real `0 lo and R.crosses(gate, gates[lower - 1]): + lower -= 1 + while upper < hi and R.crosses(gate, gates[upper]): + upper += 1 + if window is not None: + lower, upper = max(lower, window[0]), min(upper, window[1]) + cuts = [c for c in (i - 1, i, i + 2) if lower <= c <= upper] if first else range(lower, upper + 1) + reduced = {r: [x for x in occurrences[r] if x != i] for r in R.touched(gate)} + for cut in cuts: + if cut == i + 1: + continue + bounds = [] + for r in R.touched(gate): + indices = reduced[r] + j = bisect_left(indices, cut) + before = R.span(tuple(gates[indices[j - 1]][-1])) if j else entries[r] + after = R.span(tuple(gates[indices[j]][-1])) if j < len(indices) else exits[r] + bounds.append((before, after)) + low = R.join(bounds[0][0], bounds[1][0]) + high = bounds[0][1] & bounds[1][1] + if not R.contained(low, high): + continue + for dimension in range(R.rank(low), R.rank(high) + 1): + delta = removal[i].copy() + for before, after in bounds: + p, q = R.rank(before), R.rank(after) + delta[q - p] -= 1 + delta[dimension - p] += 1 + delta[q - dimension] += 1 + delta[0] = 0 + require(sum(r * n for r, n in enumerate(delta)) == 0, 'rank mass drift') + yield i, cut, dimension, low, high, tuple(delta) + +@lru_cache(maxsize=None) +def frames(low, high, dimension): + """All intermediate subspaces, not one representative per dimension.""" + require(R.contained(low, high), 'empty frame interval') + require(R.rank(low) <= dimension <= R.rank(high), 'invalid frame dimension') + require(R.rank(high) - R.rank(low) <= 4, 'first-frame resource bound exceeded') + current = {low} + for _ in range(dimension - R.rank(low)): + expanded = set() + for frame in current: + for v in range(1, 512): + if high >> v & 1 and not frame >> v & 1: + expanded.add(R.join(frame, R.span((v,)))) + current = expanded + return tuple(sorted(current)) + +def first_moves(word): + fixed, variable, seen = {}, [], set() + counts = Counter() + interval_checks = set() + for section in PHASES: + gates = word[section] + for i, cut, dimension, low, high, delta in candidates(word, section, range(len(gates)), first=True): + interval_checks.add((low, high, dimension)) + for frame in frames(low, high, dimension): + if frame == R.span(tuple(gates[i][-1])): + if cut == i: + continue + pair = (section, min(i, cut)) + if pair in seen: + continue + seen.add(pair) + require(delta == ZERO, 'fixed-frame swap was not neutral') + fixed[pair] = (i, cut, frame) + counts['fixed_adjacent'] += 1 + else: + kind = ('frame_only' if cut == i else 'adjacent') + ('_neutral' if delta == ZERO else '_losing') + require(R.all_power_nonnegative(delta), 'first move unexpectedly improves') + variable.append((section, i, cut, frame, delta, kind)) + counts[kind] += 1 + # A separate structural enumeration checks completeness of fixed-frame swaps. + direct = set() + for section in PHASES: + gates = word[section] + for lo, hi in R.segments(word, section): + for p in range(lo, hi - 1): + g, h = gates[p:p + 2] + if g[0] != 'add' and h[0] != 'add': + continue + a, b = (g, h) if g[0] == 'add' else (h, g) + if not R.crosses(a, b): + continue + if set(R.touched(g)) & set(R.touched(h)) and R.span(tuple(g[-1])) != R.span(tuple(h[-1])): + continue + direct.add((section, p)) + require(set(fixed) == direct, 'fixed-swap enumerators disagree') + return fixed, variable, counts, interval_checks + +def bridge_census(word, fixed): + """Only the newly opened gap can have a new price after a fixed-frame swap.""" + histogram, counts = Counter(), Counter() + nonzero = [] + for section in PHASES: + gates = word[section] + touched = [set(R.touched(g)) for g in gates] + for lo, hi, occurrences, entries, exits, removal in geometry(word, section): + for p in range(lo, hi - 1): + if (section, p) not in fixed: + continue + counts['first_pairs'] += 1 + g, h = gates[p:p + 2] + selected = sorted({j for r in touched[p] for j in occurrences[r] + if gates[j][0] == 'add' and j not in (p, p + 1) + and touched[j] & touched[p + 1]}) + for j in selected: + counts['bridge_gates'] += 1 + crossed = gates[j + 1:p] + [h] if j < p else [g] + gates[p + 2:j] + if not all(R.crosses(gates[j], e) for e in crossed): + continue + counts['scalar_legal'] += 1 + bounds = [] + for r in R.touched(gates[j]): + indices = occurrences[r] + left = bisect_left(indices, p) - 1 + if left >= 0 and indices[left] == j: + left -= 1 + before = R.span(tuple(gates[indices[left]][-1])) if left >= 0 else entries[r] + right = bisect_left(indices, p + 2) + if right < len(indices) and indices[right] == j: + right += 1 + after = R.span(tuple(gates[indices[right]][-1])) if right < len(indices) else exits[r] + if r in touched[p + 1]: + before = R.span(tuple(h[-1])) + if r in touched[p]: + after = R.span(tuple(g[-1])) + bounds.append((before, after)) + low = R.join(bounds[0][0], bounds[1][0]) + high = bounds[0][1] & bounds[1][1] + if not R.contained(low, high): + continue + for dimension in range(R.rank(low), R.rank(high) + 1): + delta = removal[j].copy() + for before, after in bounds: + a, b = R.rank(before), R.rank(after) + delta[b - a] -= 1 + delta[dimension - a] += 1 + delta[b - dimension] += 1 + delta[0] = 0 + histogram[tuple(delta)] += 1 + if any(delta): + nonzero.append([section, p, j, dimension, delta]) + counts['candidate_dimensions'] += 1 + return {'counts': dict(counts), 'profiles': rows(histogram), 'nonzero_cases': nonzero} + +def variable_census(word, variable, auditor=None, progress=False): + baseline = R.tracing(word)[2] + histogram, by_kind = Counter(), {} + for number, (section, i, cut, frame, first_delta, kind) in enumerate(variable): + middle = R.apply_move(word, section, i, cut, R.basis(frame)) + intermediate = R.tracing(middle)[2] + require(tuple(intermediate.get(r, 0) - baseline.get(r, 0) if r else 0 for r in range(10)) == first_delta, + 'first actual invoice differs from relaxation') + if auditor is not None: + require(auditor.frame_bill(middle)[0] == intermediate, 'retained first-word invoice disagrees') + moved = cut - (cut > i) + registers = set(R.touched(word[section][i])) + counts = by_kind.setdefault(kind, Counter()) + counts['first_words'] += 1 + for second_section in PHASES: + selected = [j for j, g in enumerate(middle[second_section]) + if g[0] == 'add' and registers.intersection(R.touched(g)) + and (second_section, j) != (section, moved)] + for _, _, _, _, _, second_delta in candidates(middle, second_section, selected): + delta = tuple(a + b for a, b in zip(first_delta, second_delta)) + histogram[delta] += 1 + counts['second_cut_dimensions'] += 1 + if progress and number % 100 == 0: + print('Checked first word', number, 'of', len(variable), flush=True) + return {'by_kind': {k: dict(v) for k, v in sorted(by_kind.items())}, 'profiles': rows(histogram)} + +def compute(word, auditor=None, progress=False): + fixed, variable, counts, intervals = first_moves(word) + serial = [[s, p, i, c, list(R.basis(f))] for (s, p), (i, c, f) in sorted(fixed.items())] + serial += [[s, i, c, list(R.basis(f)), list(d), k] for s, i, c, f, d, k in variable] + return {'first_counts': dict(sorted(counts.items())), 'first_digest': digest(serial), + 'max_first_quotient_dimension': max(R.rank(h) - R.rank(l) for l, h, _ in intervals), + 'fixed_frame': bridge_census(word, fixed), + 'variable_frame': variable_census(word, variable, auditor, progress)} diff --git a/research/staged544-losing-first-d2/vendor/retiming.py b/research/staged544-losing-first-d2/vendor/retiming.py new file mode 100644 index 0000000000..c33d7bbcdf --- /dev/null +++ b/research/staged544-losing-first-d2/vendor/retiming.py @@ -0,0 +1,269 @@ +# SPDX-License-Identifier: Apache-2.0 +"""Exact, fixed-neighbour single-ADD retiming relaxation. + +Chris R / Clear1nsight, with substantial OpenAI assistance. The BORROW-WORD +frame contract and scalar-retiming mechanism are credited in README.md. +This module does not import the retained auditor or a numerical optimiser. +""" +from bisect import bisect_left +from collections import Counter +from copy import deepcopy +from fractions import Fraction +from functools import lru_cache + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +@lru_cache(maxsize=None) +def span(vectors): + points = {0} + for v in vectors: + need(type(v) is int and 0 <= v < 512, 'invalid frame vector') + points |= {x ^ v for x in tuple(points)} + return sum(1 << x for x in points) + + +@lru_cache(maxsize=None) +def basis(mask): + answer = [] + have = 1 + for v in range(1, 512): + if (mask >> v) & 1 and not (have >> v) & 1: + answer.append(v) + have = span(tuple(answer)) + need(have == mask, 'not a binary subspace') + return tuple(answer) + + +@lru_cache(maxsize=None) +def join(a, b): + return span(basis(a) + basis(b)) + + +@lru_cache(maxsize=None) +def rank(mask): + n = mask.bit_count() + need(n > 0 and n & (n - 1) == 0, 'invalid subspace cardinality') + return n.bit_length() - 1 + + +def contained(a, b): + return not a & ~b + + +def touched(gate): + return gate[1:3] if gate[0] == 'add' else gate[1:2] + + +def tracing(word): + """Own chronological trace; centre descent is NOT persistent state. + + A check node is a fixed boundary, not a charged instruction. The census + relaxes it to a virtual climb. Every legal witness has zero such charge. + """ + full = (1 << 512) - 1 + live = set(range(704)) - set(word['removed']) + start, end = {}, {} + for r in live: + if r < 112: + start[r], end[r] = span((word['ports'][r],)), full + elif r < 224: + p = word['ports'][r - 112] + start[r] = 1 + end[r] = sum(1 << x for x in range(512) if (x & p).bit_count() % 2 == 0) + else: + start[r], end[r] = 1, full + for r, fr in word['start_extra'].items(): + start[int(r)] = span(tuple(fr)) + for r, fr in word['helper_final'].items(): + end[int(r)] = span(tuple(fr)) + current = dict(start) + nodes = {r: [] for r in live} + where = {} + bill = Counter() + + def event(r, frame, address, kind='climb'): + before = current[r] + if kind != 'map': + need(contained(before, frame), 'source frame containment') + d = rank(frame) - rank(before) + if kind == 'check': + need(d == 0, 'source fixed boundary') + elif d: + bill[d] += 1 + if kind == 'climb': + where[(address, r)] = len(nodes[r]) + nodes[r].append((address, kind, before, frame)) + current[r] = frame + + for i, gate in enumerate(word['A']): + if gate[0] == 'warp': + event(gate[1], span(tuple(gate[3])), ('check-A', i), 'check') + event(gate[1], span(tuple(gate[4])), ('map-A', i), 'map') + else: + for r in touched(gate): + event(r, span(tuple(gate[-1])), ('A', i)) + levels = {112 + int(r): span(tuple(fr)) for r, fr in word['target_levels'].items()} + for r in range(112, 224): + event(r, levels.get(r, 1), ('target-cut', r), 'check') + for r, fr in zip(word['centers'], word['center_frames']): + u = span(tuple(fr)) + event(r, u, ('centre-cut', r), 'check') + served = {levels.get(g[1], 1) for g in word['cut'] if g[2] == r} + for v in sorted(served, key=lambda x: -rank(x)): + need(contained(v, u), 'centre nesting') + if rank(u) > rank(v): + bill[rank(u) - rank(v)] += 1 + u = v + # The main forward register remains at its declared centre entry. + warps = {} + for j, rec in enumerate(word['warps']): + warps.setdefault(rec[0], []).append((j, rec)) + for i in range(len(word['B']) + 1): + for j, rec in warps.get(i, []): + event(rec[1], span(tuple(rec[3])), ('check-B', j), 'check') + event(rec[1], span(tuple(rec[4])), ('map-B', j), 'map') + if i < len(word['B']): + gate = word['B'][i] + for r in touched(gate): + event(r, span(tuple(gate[-1])), ('B', i)) + for i, gate in enumerate(word['restore']): + for r in touched(gate): + event(r, span(tuple(gate[-1])), ('restore', i)) + for r in live: + event(r, end[r], ('end',)) + return nodes, where, dict(sorted(bill.items())) + + +def crosses(g, h): + """Sufficient exact scalar normal form, not all algebraic commutations.""" + if h[0] == 'add': + return g[1] != h[2] and h[1] != g[2] + return h[0] == 'scale' and h[2] != 0 + + +def segments(word, section): + if section == 'A': + cuts = [word['prelude_events'], len(word['A'])] + elif section == 'B': + cuts = sorted({0, len(word['B'])} | {rec[0] for rec in word['warps']}) + else: + cuts = [0, len(word[section])] + return list(zip(cuts, cuts[1:])) + + +def caps(delta): + return [sum(n * min(r, k) for r, n in enumerate(delta)) for k in range(1, 10)] + + +def all_power_nonnegative(delta): + """Sufficient exact certificate using decreasing positive curvatures.""" + values = caps(delta) + prefix = 0 + for value in values[:-1]: + prefix += value + if prefix < 0: + return False + return values[-1] == 0 + + +def census(word): + nodes, where, bill = tracing(word) + deltas = Counter() + counts = {} + for section in ('A', 'B', 'restore'): + gates = word[section] + count = 0 + for lo, hi in segments(word, section): + occurrences = {} + for i in range(lo, hi): + need(gates[i][0] in ('add', 'scale'), 'unexpected scalar segment') + for r in touched(gates[i]): + occurrences.setdefault(r, []).append(i) + for i in range(lo, hi): + g = gates[i] + if g[0] != 'add': + continue + lower = i + while lower > lo and crosses(g, gates[lower - 1]): + lower -= 1 + upper = i + 1 + while upper < hi and crosses(g, gates[upper]): + upper += 1 + removal = [0] * 10 + reduced, entries, exits = {}, {}, {} + for r in touched(g): + seq = nodes[r] + pos = where[((section, i), r)] + _, _, p, u = seq[pos] + need(pos + 1 < len(seq) and seq[pos + 1][1] != 'map', 'missing successor') + q = seq[pos + 1][3] + removal[rank(u) - rank(p)] -= 1 + removal[rank(q) - rank(u)] -= 1 + removal[rank(q) - rank(p)] += 1 + indices = occurrences[r] + reduced[r] = [x for x in indices if x != i] + entries[r] = seq[where[((section, indices[0]), r)]][2] + last = where[((section, indices[-1]), r)] + need(seq[last + 1][1] != 'map', 'missing exit check') + exits[r] = seq[last + 1][3] + for cut in range(lower, upper + 1): + if cut == i + 1: # Same placement as cut i, counted once. + continue + boundaries = [] + for r in touched(g): + indices = reduced[r] + j = bisect_left(indices, cut) + p = span(tuple(gates[indices[j - 1]][-1])) if j else entries[r] + q = span(tuple(gates[indices[j]][-1])) if j < len(indices) else exits[r] + boundaries.append((p, q)) + lower_frame = join(boundaries[0][0], boundaries[1][0]) + upper_frame = boundaries[0][1] & boundaries[1][1] + if not contained(lower_frame, upper_frame): + continue + dims = [(rank(p), rank(q)) for p, q in boundaries] + for d in range(rank(lower_frame), rank(upper_frame) + 1): + delta = removal.copy() + for p, q in dims: + delta[q - p] -= 1 + delta[d - p] += 1 + delta[q - d] += 1 + delta[0] = 0 + need(sum(r * n for r, n in enumerate(delta)) == 0, 'rank mass drift') + deltas[tuple(delta)] += 1 + count += 1 + counts[section] = count + return {'per_section': counts, 'candidates': sum(counts.values()), + 'source_profile': bill, + 'deltas': [{'delta': {r: n for r, n in enumerate(d) if n}, 'count': n, + 'caps': caps(d), 'certificate': all_power_nonnegative(d)} + for d, n in sorted(deltas.items())]} + + +def apply_move(word, section, index, cut, frame): + """Apply one exact scalar retiming. Caller must rederive cleanup and audit.""" + need(section in ('A', 'B', 'restore'), 'unknown section') + gates = word[section] + need(type(index) is int and 0 <= index < len(gates), 'bad source index') + need(type(cut) is int and 0 <= cut <= len(gates), 'bad insertion cut') + need(any(lo <= index < hi and lo <= cut <= hi for lo, hi in segments(word, section)), + 'crosses prelude or native warp boundary') + g = deepcopy(gates[index]) + need(g[0] == 'add', 'only ADD moves are covered') + crossed = gates[index + 1:cut] if cut > index else gates[cut:index] + need(all(crosses(g, h) for h in crossed), 'noncommuting scalar barrier') + coefficient = Fraction(g[3], g[4]) + for h in crossed: + if h[0] == 'scale' and h[1] in touched(g): + power = (1 if h[1] == g[1] else -1) * (1 if cut > index else -1) + coefficient *= Fraction(h[2], h[3]) ** power + g[3:5] = [coefficient.numerator, coefficient.denominator] + g[-1] = list(basis(span(tuple(frame)))) + result = deepcopy(word) + result[section].pop(index) + result[section].insert(cut - (cut > index), g) + # Segment length and all warp cuts are unchanged. No warp is crossed. + return result diff --git a/research/staged544-losing-first-d2/verify.py b/research/staged544-losing-first-d2/verify.py new file mode 100644 index 0000000000..09a89c879b --- /dev/null +++ b/research/staged544-losing-first-d2/verify.py @@ -0,0 +1,191 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Read-only exact replay; --emit explicitly regenerates an external receipt.""" +import argparse +import gzip +import hashlib +import json +from pathlib import Path +import types +from collections import Counter +from copy import deepcopy +import time + +P = Path(__file__).resolve().parent + +def require(ok, message): + if not ok: + raise ValueError(message) + +def module(name, path): + value = types.ModuleType(name) + value.__file__ = str(path) + exec(compile(path.read_bytes(), str(path), 'exec'), value.__dict__) + return value + +def authenticate(raw, row): + require(len(raw) == row['bytes'], 'source length: ' + row['local']) + require(hashlib.sha256(raw).hexdigest() == row['sha256'], 'source SHA256: ' + row['local']) + blob = hashlib.sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest() + require(blob == row['git_blob'], 'source Git blob: ' + row['local']) + +def setup(): + sources = json.loads((P / 'SOURCES.json').read_text()) + for row in sources['snapshots']: + authenticate((P / row['local']).read_bytes(), row) + return (module('owned_search', P / 'search.py'), + module('retained_auditor', P / 'vendor/audit_core.py'), + module('retained_semantics', P / 'vendor/audit_verify.py')) + +def load(tag): + return json.loads(gzip.decompress((P / 'inputs' / f'BORROW-WORD-43{tag}.json.gz').read_bytes())) + +def calculate(tag, progress=False): + S, C, A = setup() + word = load(tag) + C.hygiene(word) + bill, inventory, *_ = C.frame_bill(word) + require(bill == {int(r): n for r, n in word['report']['local_profile'].items()}, 'source declared invoice') + require(S.R.tracing(word)[2] == bill, 'source trace disagreement') + require(C.derive_cleanup(word) == word['cleanup'], 'source inverse cleanup') + baseline = S.R.census(word) + expected = json.loads((P / 'inputs/SINGLE-CENSUS.json').read_text())[tag] + require(json.loads(json.dumps(baseline)) == expected, 'predecessor single-move census differs') + require(all(row['certificate'] for row in baseline['deltas']), 'single-move premise failed') + result = S.compute(word, C, progress) + proof_rows=result['variable_frame']['profiles'] + if not all(row['certificate'] for row in proof_rows): + raise ValueError('unresolved combined signs; no obstruction claimed: '+repr(result['variable_frame']['uncertified_witnesses'])) + result['dirty_validation']=dirty_validation(S,C,A,word,result['variable_frame']['states']) + result['ledger']=ledger(S,C,word,result) + + return {'schema_version': 1, 'provider': tag, 'source_canonical': S.digest(word), + 'source_profile': bill, 'width_inventory': inventory, + 'single_move_candidates': baseline['candidates'], + 'single_census_digest': S.digest(baseline), + 'source_semantics': A.semantics(C, word), 'pair_census': result} + +def normal(value):return json.loads(json.dumps(value,sort_keys=True)) + +def ledger(S,C,word,result): + bill,widths,_,start,end=C.frame_bill(word) + primitives={sec:dict(sorted(Counter(g[0] for g in word[sec]).items())) for sec in + ('precondition','compensation','A','cut','B','restore','cleanup')} + first=result['variable_frame']['states'] + masses={sum(int(r)*n for r,n in x['profile'].items()) for x in first} + require(masses=={sum(r*n for r,n in bill.items())},'first rank masses') + return {'baseline_local_profile':bill,'recursive_children':sum(bill.values()), + 'rank_mass':sum(r*n for r,n in bill.items()),'helper_width_inventory':widths, + 'helper_roles':sum(widths.values()),'dirty_buffers':len(word['helper_final']), + 'live_inputs':C.N-len(word['removed']),'primitive_inventory':primitives, + 'native_warps':len(word['warps']),'initial_operator_corrections':len(word['initial_corrections']), + 'first_recursive_children_range':[min(sum(x['profile'].values()) for x in first),max(sum(x['profile'].values()) for x in first)], + 'all_first_profiles_recorded':'pair_census.variable_frame.states', + 'all_combined_histograms_recorded':'pair_census.variable_frame.profiles', + 'entrance_frames_sha256':S.digest({str(k):str(v) for k,v in start.items()}), + 'exit_frames_sha256':S.digest({str(k):str(v) for k,v in end.items()}), + 'added_gates_helpers_buffers':0,'source_scalar_coefficient_bound':coefficient_bound(word), + 'first_scalar_coefficient_bound':result['dirty_validation']['coefficient_bound'], + 'proved':['Local chronological recursive invoices, fixed native maps/cuts and helper widths', + 'Exact rational first-block equality for every admitted first move on arbitrary dirty inputs', + 'Complete baseline free-operator replay and deterministic first/final replay controls', + 'Recomputed inverse cleanup and full first-word resource inventories in sampled whole-word controls'], + 'unknown':['Fresh native Gaussian/Clifford realization and phase','Physical hosting/allocation and complete owner chronology', + 'Uniform coefficient/precision/stock/tape costs','All-size compiler, outer/supplier admission','Analytic transfer and BIT H1-H5'], + 'unknown_costs_are_zero':False,'new_supplier_or_kappa':False} + +def coefficient_bound(word): + a=[g for sec in ('A','B','restore') for g in word[sec] if g[0]=='add'] + return {'maximum_numerator_bits':max(abs(g[3]).bit_length() for g in a), + 'maximum_denominator_bits':max(g[4].bit_length() for g in a)} + +def dirty_validation(S,C,A,word,states): + # Local block equality was checked for every first word during the census. + # Whole-word samples additionally exercise the retained production interpreter. + samples={0,len(states)-1} + for sec in S.PHASES: + group=[i for i,x in enumerate(states) if x['first'][0]==sec] + if group: + samples.update((group[0],group[len(group)//2],group[-1])) + rows=[];bound=coefficient_bound(word);second_blocks=[] + D=module('dirty_oracle',P/'dirty_blocks.py') + for ordinal in sorted(samples): + sec,i,cut,fr,delta=states[ordinal]['first'] + middle=S.R.apply_move(word,sec,i,cut,fr) + middle['cleanup']=C.derive_cleanup(middle) + bill,widths,*_=C.frame_bill(middle) + middle['report']['local_profile']={str(r):n for r,n in bill.items()} + C.hygiene(middle) + semantic=A.semantics(C,middle) + b=coefficient_bound(middle) + bound={k:max(bound[k],b[k]) for k in bound} + moved=cut-(cut>i) + restored=S.R.apply_move(middle,sec,moved,i+(moved=d:break + if not mask>>v&1:frame.append(v);mask=S.R.span(tuple(frame)) + require(len(frame)==d,'second frame realization') + final=S.R.apply_move(middle,section,j,target,frame) + try:fb,fw,*_=C.frame_bill(final) + except C.AuditFailure:continue + require(fw==widths,'second helper width drift') + actual=tuple(fb.get(r,0)-bill.get(r,0) if r else 0 for r in range(10)) + require(actual==sd,'second real invoice differs') + lo,hi=min(j,target),max(j+1,target) + check=D.block_equal(middle[section][lo:hi],final[section][lo:hi]) + final['cleanup']=C.derive_cleanup(final);final['report']['local_profile']={str(r):n for r,n in fb.items()} + C.hygiene(final) + second={'section':section,'index':j,'cut':target,'frame':frame,'profile':fb, + 'block':check,'semantics':A.semantics(C,final)} + break + if second:break + require(second is not None,'no legal second control') + rows.append({'first_state':ordinal,'semantics':semantic,'literal_undo':'PASS','second':second}) + # Meter all first scalar conjugations without replaying complete words. + for state in states: + sec,i,cut,fr,_=state['first'];g=word[sec][i] + from fractions import Fraction + coefficient=Fraction(g[3],g[4]) + crossed=word[sec][i+1:cut] if cut>i else word[sec][cut:i] + for h in crossed: + if h[0]=='scale' and h[1] in S.R.touched(g): + power=(1 if h[1]==g[1] else -1)*(1 if cut>i else -1) + coefficient*=Fraction(h[2],h[3])**power + bound['maximum_numerator_bits']=max(bound['maximum_numerator_bits'],abs(coefficient.numerator).bit_length()) + bound['maximum_denominator_bits']=max(bound['maximum_denominator_bits'],coefficient.denominator.bit_length()) + return {'all_first_dirty_blocks':len(states),'whole_word_samples':rows,'coefficient_bound':bound, + 'proof':'Every first scalar block equals its source on independent rational symbols; unchanged surrounding free operators compose with that equality. Inverse cleanup is rederived; baseline and sampled complete words additionally replay all 723 symbolic inputs.'} + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--provider', choices=('base', 'extra'), required=True) + parser.add_argument('--emit', type=Path) + parser.add_argument('--progress', action='store_true') + args = parser.parse_args() + result = calculate(args.provider, args.progress) + if args.emit: + require(not args.emit.resolve().is_relative_to(P), 'write regenerated receipt outside the package') + args.emit.write_text(json.dumps(result, sort_keys=True, separators=(',', ':')) + '\n') + else: + expected = json.loads((P / f'RESULT-{args.provider}.json').read_text()) + require(json.loads(json.dumps(result)) == expected, 'complete pair receipt differs') + print(json.dumps({'status': 'PASS_STAGED544_LOSING_FIRST_D2', 'provider': args.provider, + 'first_counts': result['pair_census']['first_counts'], + 'result_sha256': hashlib.sha256(json.dumps(result, sort_keys=True, separators=(',', ':')).encode()).hexdigest(), + 'new_supplier': False}, sort_keys=True)) + +if __name__ == '__main__': + main()