diff --git a/research/rank-two-boundary-and-decoder-limits/FOLLOW-UP.md b/research/rank-two-boundary-and-decoder-limits/FOLLOW-UP.md new file mode 100644 index 0000000000..4e5eda0a9a --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/FOLLOW-UP.md @@ -0,0 +1,36 @@ +# Later decoder and connected-caller checks + +These follow-up results use different source interfaces from the frozen BIT +word. Their receipts are supplemental to the registered replay. + +- On [#7089](https://github.com/CrocSwap/integer-mult-bounds/pull/7089) head + `3a007633e5f96dcfba428eec4b4f3e32c5c2bd28`, the fixed schedule cannot produce + the fourth uncoded row from its 39 recorded banks with degree-zero left + operators. The dual reads just two coefficients of degree `D1 D3`. Only five + bank and translated-word pairs can meet the dual support, and their terms + cancel. The target pairs to one. A changed entrance did recover four rows in + the formal model, but used odd powers of Q with unpaid implementation. + Reassigning one query under even-Q controls is insufficient in the fixed + two-output late FULL layout. The quotient prefix has odd rank two, while + the two late axes require two additional independent directions. The + [dual receipt](follow-up/PR7089-UNBOUNDED-SUFFIX-DUAL.json) and + [quotient receipt](follow-up/PR7089-ONE-QUERY-ODD-DIMENSION-VERIFIED.json) + document the distinct scopes. +- On [#7002](https://github.com/CrocSwap/integer-mult-bounds/pull/7002) head + `ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b`, the connected sign header has + a sharp 39-transvection count on 38 roles for the given sign construction. + If 38 rank-one updates produced −I, their update directions would be a basis. + In that basis, the first updated row keeps diagonal entry +1 and is never + modified again. The pinned 39 updates attain −I. With two such updates per + HOST, the three thin units cannot simply be dropped. See the + [sign-header receipt](follow-up/PR7002-SIGN-HEADER-THIN-MINIMUM.json). +- We constructed noncoordinate idle projectors that commute through the + intervening role-level updates of that caller. All 181 incidences remain, + grouped into 76 jobs per port. The exact normalized controls matched all 38 + columns in both sign sectors. The raw complex budget, composed with the + retained F+H1 native invoice, still needs at least 821 rank-one cost + equivalents at κ = .005 before any physical or ordinary overhead. This + compares a constructed normalized schedule and a declared native tariff. + It leaves carried directions, different HOST words and BIT admission open. + See the [projectors](follow-up/PR7002-NONCOORDINATE-IDLE-WORD.json) and + [composed budget](follow-up/PR7002-ACTUAL-IDLE-COMPOSITION-BUDGET.json). diff --git a/research/rank-two-boundary-and-decoder-limits/LICENSE b/research/rank-two-boundary-and-decoder-limits/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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The frozen-boundary obstruction, the two +propagation screens and the 45-port caller cost check all held up in the +replay included here. The experiments also give an exact local source worth +retaining for a redesigned caller. + +## What the checks establish + +- **Frozen neighbors.** On the 27,818-event six-helper-handoff word, exact + rational nullspaces give zero initial extension and zero terminal shrink + dimension on all 111 ports. The calculation takes the same-chart ADD + components between MOVE and CLEAR events into account. It holds with the + adjacent frame subspaces fixed. +- **Propagating the frame changes.** The saved profiles contain 6,993 + single-seed cases and 8,040 selected paired or collective cases. Every + profile worsens the native helper-minus-paid moment at κ = .005, .006 + and .01, with no independent main-output credit. At .01 the best deltas + are about −51.4191 and −36.0921 respectively. The paired census used up + to twelve leading seeds per direction for pair tests and one simultaneous + seed set. The published replay rechecks every saved price with integer + interval arithmetic. It does not regenerate the propagation census. +- **A source that passes locally.** Fused boundary bridges protected 45 + planes simultaneously. The retained normalized source receipt covers + 775 arbitrary input and scratch columns. The separate audit covers the + rational frames, ownership and nested-query identities. Paid rank mass + stays 5,129, with a small increase in the concave moment. Physical BIT + phases, address semantics and arbitrary tensor width are still open. +- **Its existing caller tariff fails.** The old four-factor main path has + off-diagonal rank at most `2+6+6+6=20`. For block matrices, + `B(MN)=A(M)B(N)+B(M)D(N)`, so the bound follows by rank subadditivity. + The declared target tariff grants the other main outputs, pure centers and + helpers and charges no decoder. It still has signed margin below + −154.532 at κ = .005 and below −283.109 at κ = .01. This applies to the + declared target tariff and that factored path. A different allocation or + caller remains open. + +There is no new conditional κ claim here. In particular the historical +rank-two and free-shear screens were conditional budgets for unbuilt +constructions. The five inherited framework assumptions and the matching +complex/BIT, physical, precision and outer obligations remain. + +## Reproduce + +From this directory, run `python3 -B verify.py` using Python 3.10 or newer. +The checker verifies the public evidence hashes, regenerates the exact +111-port nullspaces from the normalized word and frame data, reprices all +15,033 saved profiles at the three specified thresholds, and recomputes +the 45-port tariff signs. It works without a network or solver. Historical +checks on the emitted 45-port word are preserved as receipts. The standalone +replay here covers its tariff and does not rerun that full word. + +[Evidence provenance](evidence/provenance.json) records original source +hashes, the exact retained frames and word, and the projection used to +package the saved price inputs. [Follow-up](FOLLOW-UP.md) records the later +connected-caller and decoder checks separately. + +## Open next questions + +1. Can a revised native path keep rank-seven diagonals while protecting a + second direction? Start by changing one ADD component and checking all + affected helper endpoints and the actual paid profile. +2. Can a different productive caller use the protected planes without the + rank-20 factored path? Start with exact forward and reverse endpoint + checks and price the whole proposed target bank before adding a decoder. +3. Can one paid transport carry the required repair over multiple cuts + without increasing its rank or changing another output? Keep all + arbitrary owners, and charge finite phase, scalar and cleanup work. + +## Credit + +Rohan Arun, with substantial OpenAI Codex assistance and Claude-assisted +earlier route exploration. The retained native and frame lineage includes +DreamingOfClouds' [#589](https://github.com/CrocSwap/integer-mult-bounds/pull/589) +and its retained predecessors. The later comparisons use unpaidmoon's +[#7089](https://github.com/CrocSwap/integer-mult-bounds/pull/7089) and CubeJerry's +[#6824](https://github.com/CrocSwap/integer-mult-bounds/pull/6824) and +[#7002](https://github.com/CrocSwap/integer-mult-bounds/pull/7002). +New material is Apache-2.0. diff --git a/research/rank-two-boundary-and-decoder-limits/SOURCES.json b/research/rank-two-boundary-and-decoder-limits/SOURCES.json new file mode 100644 index 0000000000..b06c2f774e --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "17469fff78c22941280f04d39dc5a1faee09c840", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + } + ] +} diff --git a/research/rank-two-boundary-and-decoder-limits/TASK.json b/research/rank-two-boundary-and-decoder-limits/TASK.json new file mode 100644 index 0000000000..25a777d67c --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/TASK.json @@ -0,0 +1,89 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 8, + "base_commit": "17469fff78c22941280f04d39dc5a1faee09c840", + "original_card": { + "id": "joint-query-controller", + "question": "Can a changed query demand or caller remove real work while satisfying native chronology and restoration?", + "starting_points": [ + "docs/research/current-priorities.md", + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md" + ], + "methods": [ + "Construct and independently check one source-bound instance of the stated first experiment.", + "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change." + ], + "acceptance_gate": "A source-bound arbitrary-input identity and legal producer/consumer boundary with the complete paid and productive target invoice, including restoration, ownership, native alignment and extra charges. Price under the actual current model; historical ceiling.py assumptions must be established before use. A favorable optimistic relaxation keeps a route open but is not a completed supplier. A scoped local result remains useful; expansion requires the family-level budget gate.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.", + "scope": "Source-bound orientation only, not a supplier replay or theorem proof." + }, + "first_experiment": "Choose an exact caller and a new demand/interface hypothesis. Read the scoped #5617/#5631/#5649/#5747 and #5720/#5745 objections before rebuilding an excluded schedule. Compare the complete matched source/consumer protocols including all retained helper outputs. For an active-mode injection, first check #5745: its canonical delivery claim repays the eight removed centre jobs. Audit that exact claim or change its channel/feedback hypothesis; do not repeat the same free-injection search. Stop if the full favorable budget fails or the required restored output is unobservable.", + "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.", + "allowed_variations": [ + "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes." + ], + "scope_change_triggers": [ + "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.", + "Treating an archived proposal or local numerical pass as complete supplier admission." + ], + "overlap_terms": [ + "query demand", + "active mode", + "5720", + "5745", + "5747", + "caller" + ], + "existing_checks": [ + { + "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.", + "evidence": "research/qq16-caller-install/README.md", + "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.", + "status": "author-checked", + "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.", + "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.", + "status": "reviewed", + "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137", + "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + } + ] + }, + "scope_status": "refined", + "actual_scope": "Check the frozen-word and coupled rank-two native entrance variants and the declared 45-port caller bill.", + "scope_change_reason": "These saved experiments isolate which fixed-word and caller interfaces block a second protected direction.", + "bottleneck_link": "A second protected direction has to preserve a funded independent output bank after charging all changed native jobs.", + "stop_rule": "Close only the stated finite families and retain source pins and price checks for changed-source follow-ups.", + "outcome": "negative-result", + "evidence": "README.md, verify.py, and evidence/provenance.json", + "author": "Rohan Arun", + "ai_assistance": "Substantial OpenAI Codex assistance and Claude-assisted earlier exploration.", + "open_questions": [ + { + "question": "Can a changed native path preserve rank-seven diagonals with rank-two protection?", + "why_it_matters": "The tested rank-two main path loses two off-diagonal ranks in the caller.", + "first_step": "Change one ADD component and recount paid jobs and all helper outputs.", + "blocked_by": "The isolated fixed-word extension space is zero on all 111 ports." + }, + { + "question": "Can a redesigned caller use the protected planes affordably?", + "why_it_matters": "A complete independent output bank and a nonnegative signed bill are needed.", + "first_step": "Replay the actual all-input word and price each retained output against all paid jobs.", + "blocked_by": "The declared 45-port tariff is already negative before adding a decoder." + } + ] +} diff --git a/research/rank-two-boundary-and-decoder-limits/VERIFY.json b/research/rank-two-boundary-and-decoder-limits/VERIFY.json new file mode 100644 index 0000000000..c41b249c31 --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/VERIFY.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 90, + "checks": "Verify evidence hashes, recompute 111 exact boundary nullspaces, reprice all 15033 saved rank profiles at three thresholds, and recheck the declared 45-port tariff." + } + ] +} diff --git a/research/rank-two-boundary-and-decoder-limits/boundary.py b/research/rank-two-boundary-and-decoder-limits/boundary.py new file mode 100644 index 0000000000..28a64c0bc8 --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/boundary.py @@ -0,0 +1,58 @@ +"""Exact same-word boundary-plane enlargement with ADD-component propagation. +No all-frames rank2 impossibility is claimed: neighbors remain frozen. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import defaultdict +import gzip +import json +P=Path(__file__).resolve().parent +def nullspace(rows,n=8): + a=[[Q(x) for x in row] for row in rows if any(row)];pivot=[];k=0 + for j in range(n): + p=next((i for i in range(k,len(a)) if a[i][j]),None) + if p is None:continue + a[k],a[p]=a[p],a[k];v=a[k][j];a[k]=[x/v for x in a[k]] + for i in range(len(a)): + if i!=k and a[i][j]:v=a[i][j];a[i]=[x-v*y for x,y in zip(a[i],a[k])] + pivot.append(j);k+=1 + if k==len(a):break + out=[] + for free in range(n): + if free in pivot:continue + v=[Q(i==free) for i in range(n)] + for i,j in enumerate(pivot):v[j]=-a[i][free] + out.append(v) + return out + +def boundary_rows(): + w=json.loads(gzip.decompress((P/'evidence/native-word.json.gz').read_bytes())) + frames=json.loads(gzip.decompress((P/'evidence/frames.json.gz').read_bytes()))['frames'] + parent=[];frame=[] + def new(f):parent.append(len(parent));frame.append(f);return len(parent)-1 + def root(x): + while parent[x]!=x:parent[x]=parent[parent[x]];x=parent[x] + return x + def union(a,b): + a,b=root(a),root(b) + if a!=b:assert frame[a]==frame[b];parent[b]=a + current=[new(f) for f in w['initial']]+[new(None) for _ in w['owned']];initial=current.copy();edges=[] + for e in w['program']: + if e[0]=='CLEAR':current[e[1]]=new(e[2]) + elif e[0]=='ADD':assert frame[root(current[e[1]])]==frame[root(current[e[2]])]==e[3];union(current[e[1]],current[e[2]]) + else: + _,d,a,b,q=e;assert frame[root(current[d])]==a;v=new(b);edges.append((current[d],v,q));current[d]=v + neighbors=defaultdict(set) + for a,b,q in edges: + a,b=root(a),root(b);neighbors[a].add(frame[b]);neighbors[b].add(frame[a]) + rows=[] + for i in range(111): + x=root(initial[i]);y=root(current[111+i]);fx,fy=frame[x],frame[y];assert frames[str(fx)]['dim']==1 and frames[str(fy)]['dim']==7 + q=frames[str(fx)]['B'][0];cx=[q];cy=[q] + for f in neighbors[x]: + if frames[str(f)]['dim']>1:cx+=frames[str(f)]['A'] + for f in neighbors[y]: + if frames[str(f)]['dim']<7:cy+=frames[str(f)]['B'] + nx,ny,both=nullspace(cx),nullspace(cy),nullspace(cx+cy) + rows.append({'port':i,'initial_control_ADD_component':x,'final_destination_ADD_component':y,'initial_frame':fx,'final_frame':fy,'initial_plane_extension_dimension':len(nx),'final_complement_shrink_dimension':len(ny),'paired_legal_second_direction_dimension':len(both),'basis':[[str(x) for x in v] for v in both],'initial_larger_neighbor_frames':sorted(f for f in neighbors[x] if frames[str(f)]['dim']>1),'final_smaller_neighbor_frames':sorted(f for f in neighbors[y] if frames[str(f)]['dim']<7)}) + return rows diff --git a/research/rank-two-boundary-and-decoder-limits/evidence/45-port-audit.json b/research/rank-two-boundary-and-decoder-limits/evidence/45-port-audit.json new file mode 100644 index 0000000000..1ac8928815 --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/evidence/45-port-audit.json @@ -0,0 +1,24 @@ +{ + "all_original_normalized_public_responses_preserved": true, + "all_owned_final_zero": true, + "all_rational_frame_projectors_symmetric_idempotent": true, + "arbitrary_owned_columns": 99, + "complete_decoder": false, + "every_emitted_MOVE_projector_pair_nested": true, + "negative_controls": { + "missing_bridge_MOVE_detected": true, + "missing_final_scratch_CLEAR_detected": true + }, + "new_kappa": false, + "pins": { + "two-pass-continuation-20261022/decoder-continuation-20261025/root/audit_45_port_rank2_fused_bridge_source.py": "35fb7f1676d1cdebe2014619f877ddd47528f21b54665443fdfe531e9b3d1836", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-helper-handoff-construction-2/FINAL-WORD.json.gz": "dd86be7f1618697bfa64e83fa84c9519e8f5c06b6dfb65b7c41ed8ed13dba56f", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-local-rank2-45-port-bridge-source/FRAMES.json": "676fea75952f1ef00c8d8d94bfe1df2ba24844fd06dcfcecdadd3930c3b44afc", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-local-rank2-45-port-bridge-source/RESULT.json": "2c85453a8ede7c144e6e1e7a00eccc03e68ca754dab6d674b3cb9e58d03b5790", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-local-rank2-45-port-bridge-source/WORD.json.gz": "7a7a694d3635fe9cceec32dda7e04d536fc79df0995aaa9164a90856315e6d8c" + }, + "public_columns": 676, + "scope": "Separate primary-agent checker; shares pinned frame data and Fraction arithmetic, not an external independent review. No actual Fourier phase/all-width implementation or productive caller.", + "status": "PASS_SEPARATE_PACKET_CHART_NESTING_BILL_AND_NORMALIZED_REPLAY", + "time_utc": "2026-10-26T02:42:53.384584+00:00" +} diff --git a/research/rank-two-boundary-and-decoder-limits/evidence/45-port-caller.json b/research/rank-two-boundary-and-decoder-limits/evidence/45-port-caller.json new file mode 100644 index 0000000000..95bfa6eb61 --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/evidence/45-port-caller.json @@ -0,0 +1,72 @@ +{ + "UNCONSTRUCTED_target_with90_rank20_main_rows": { + "1": 3, + "16": 9, + "20": 90, + "22": 132, + "4": 30, + "7": 3, + "8": 1299 + }, + "complete_decoder": false, + "factor_rank_bounds": { + "each_native_d": 6, + "main_factored_path_C_d3_d2_d1_rank_at_most": 20, + "original_unchanged_pair_bound": 22, + "protected_C": 2 + }, + "new_kappa": false, + "optimistic_margins_before_decoder": { + "1/100": { + "decimal_check": [ + "-283.10957974420802070593594751282890205211980372530288318126232789033255631791482142", + "-283.10957974420802070593594751282890205211980372530288318126232789033255631791475854" + ], + "rational": [ + "-14155478987210401035296797375641445102605990186265144159063116394516627815895741071/50000000000000000000000000000000000000000000000000000000000000000000000000000000", + "-14155478987210401035296797375641445102605990186265144159063116394516627815895737927/50000000000000000000000000000000000000000000000000000000000000000000000000000000" + ] + }, + "1/200": { + "decimal_check": [ + "-154.53200665887459930749042223216745160303090269480812639539420154852518929626382578", + "-154.5320066588745993074904222321674516030309026948081263953942015485251892962637629" + ], + "rational": [ + "-7726600332943729965374521111608372580151545134740406319769710077426259464813191289/50000000000000000000000000000000000000000000000000000000000000000000000000000000", + "-1545320066588745993074904222321674516030309026948081263953942015485251892962637629/10000000000000000000000000000000000000000000000000000000000000000000000000000000" + ] + }, + "3/500": { + "decimal_check": [ + "-180.4030189514891109822322716367344726030358098892356580126142410700044434286549032", + "-180.40301895148911098223227163673447260303580988923565801261424107000444342865484032" + ], + "rational": [ + "-225503773689361388727790339545918090753794762361544572515767801337505554285818629/1250000000000000000000000000000000000000000000000000000000000000000000000000000", + "-70469929277925433977434481108099403360560863237982678911177437917970485714318297/390625000000000000000000000000000000000000000000000000000000000000000000000000" + ] + } + }, + "pins": { + "two-pass-continuation-20261022/decoder-continuation-20261025/helper-pipeline/data-aligned-followup/audit_paid_center_completion.py": "09098d92f2e8eb924fdf5d9b288ebe1e3448b8c33334575ab4ffcce1d68fe2ac", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/BIT-FIXED-TARGET-AFFORDABLE-DECODER-BILLS.json": "daf59f000bdc1fe9bd2de5e645e9166ada3776a80d8c7ee9c085e8cc4c25c2fc", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-local-rank2-45-port-bridge-source/MOMENT-INCREMENT.json": "4d94445b3096df0c85cbdd7a74a7917b31894a928ab6c219c7c4cf99dfd8ea5f", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-local-rank2-45-port-bridge-source/RESULT.json": "2c85453a8ede7c144e6e1e7a00eccc03e68ca754dab6d674b3cb9e58d03b5790", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/screen_45_port_existing_caller_ceiling.py": "0d484cfa9297ce16b0a08032a53b5e62b9c3a2f5043e8f1601a7321056c3b65f" + }, + "proof": "For a symplectic block product M*N, B(MN)=A(M)B(N)+B(M)D(N), so rank(B(MN))<=rank(B(M))+rank(B(N)). Hence the fixed four-factor path C*d3*d2*d1 has B-rank<=2+6+6+6=20. This bounds only that product path; sums, extra queries and different caller layouts require new analysis.", + "scope": "Only the usual factored path and target tariff are screened. Pure rank16 centers, unaffected main outputs, helper credits and inherited early-query bill are granted as in the old hypothetical target, with no decoder cost added. This neither constructs an endpoint bank nor rules out arbitrary callers. In particular extra ambient directions or a different source word might retain rank7 diagonals with rank2 protection.", + "status": "COMPLETE_SCOPED_FACTORED_CALLER_TARGET_SCREEN", + "three_native_paid_plus_inherited_early_queries": { + "0": 105, + "1": 4155, + "2": 4056, + "3": 207, + "4": 231, + "5": 216, + "6": 51, + "7": 30 + }, + "time_utc": "2026-10-26T02:44:03.459163+00:00" +} diff --git a/research/rank-two-boundary-and-decoder-limits/evidence/45-port-cost.json b/research/rank-two-boundary-and-decoder-limits/evidence/45-port-cost.json new file mode 100644 index 0000000000..ac35fc1eed --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/evidence/45-port-cost.json @@ -0,0 +1,60 @@ +{ + "added_native_moment_not_a_kappa": { + "1/100": { + "decimal_check": [ + "1.34196392974544353810196294848848395293097751142759662017809315669200121516377899", + "1.34196392974544353810196294848848395293097751142759662017809315669200121516377997" + ], + "rational": [ + "134196392974544353810196294848848395293097751142759662017809315669200121516377899/100000000000000000000000000000000000000000000000000000000000000000000000000000000", + "134196392974544353810196294848848395293097751142759662017809315669200121516377997/100000000000000000000000000000000000000000000000000000000000000000000000000000000" + ] + }, + "1/200": { + "decimal_check": [ + "0.67450245610319901219358585722641345165970010701093708237080609268387610455759664", + "0.67450245610319901219358585722641345165970010701093708237080609268387610455759762" + ], + "rational": [ + "4215640350644993826209911607665084072873125668818356764817538079274225653484979/6250000000000000000000000000000000000000000000000000000000000000000000000000000", + "33725122805159950609679292861320672582985005350546854118540304634193805227879881/50000000000000000000000000000000000000000000000000000000000000000000000000000000" + ] + }, + "3/500": { + "decimal_check": [ + "0.80855579658458428768071905995132138790996948470971041445499942248251239725614796", + "0.80855579658458428768071905995132138790996948470971041445499942248251239725614894" + ], + "rational": [ + "20213894914614607192017976498783034697749237117742760361374985562062809931403699/25000000000000000000000000000000000000000000000000000000000000000000000000000000", + "40427789829229214384035952997566069395498474235485520722749971124125619862807447/50000000000000000000000000000000000000000000000000000000000000000000000000000000" + ] + } + }, + "complete_decoder": false, + "helper_endpoints_unchanged": 445, + "new_kappa": false, + "paid_profile_delta": { + "0": 35, + "1": 55, + "2": 10, + "3": -10, + "4": 33, + "5": -30, + "6": 6, + "7": -9 + }, + "paid_rank_mass_delta": 0, + "pins": { + "two-pass-continuation-20261022/decoder-continuation-20261025/helper-pipeline/data-aligned-followup/audit_paid_center_completion.py": "09098d92f2e8eb924fdf5d9b288ebe1e3448b8c33334575ab4ffcce1d68fe2ac", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-helper-handoff-construction-2/FINAL-WORD.json.gz": "dd86be7f1618697bfa64e83fa84c9519e8f5c06b6dfb65b7c41ed8ed13dba56f", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-helper-handoff-construction-2/RESULT.json": "6374a8fac2eeff21b942ddce35af7367c1d8665f0db6da21367646e93c4fbe9c", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-local-rank2-45-port-bridge-source/RESULT.json": "2c85453a8ede7c144e6e1e7a00eccc03e68ca754dab6d674b3cb9e58d03b5790", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-local-rank2-45-port-bridge-source/WORD.json.gz": "7a7a694d3635fe9cceec32dda7e04d536fc79df0995aaa9164a90856315e6d8c", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/price_45_port_rank2_fused_source.py": "5d035a773f8dccec76db67280040e7e5b639c208aa8a4d9256848fb9a7d3fa1a" + }, + "protected_rank2_pairs": 45, + "scope": "Price of emitted normalized source only. Rank2 protected input preparation, actual caller, terminal decoder, phases and all-width/address admission must be supplied; no output-bank credit is granted here.", + "status": "PASS_EXACT_45_PORT_EMITTED_SOURCE_PAID_MOMENT_INCREMENT", + "time_utc": "2026-10-26T02:43:08.454066+00:00" +} diff --git a/research/rank-two-boundary-and-decoder-limits/evidence/45-port-source.json b/research/rank-two-boundary-and-decoder-limits/evidence/45-port-source.json new file mode 100644 index 0000000000..a8897f67b0 --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/evidence/45-port-source.json @@ -0,0 +1,2232 @@ +{ + "additional_owned_scratch": 90, + "all_original_normalized_public_outputs_preserved": true, + "all_owned_scratch_final_zero": true, + "complete_decoder": false, + "full_native_physical_phase_replay": false, + "fused_groups": [ + { + "destination": 111, + "sources": [ + 243, + 9, + 246 + ] + }, + { + "destination": 112, + "sources": [ + 457, + 626, + 93 + ] + }, + { + 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"main_diagonal_cross_rank_counts": { + "(6, 6, 8)": 45, + "(7, 7, 8)": 66 + }, + "new_kappa": false, + "normalized_columns_checked": 775, + "old_paid_rank_mass": 5129, + "packet": "WORD.json.gz", + "packet_sha256": "7a7a694d3635fe9cceec32dda7e04d536fc79df0995aaa9164a90856315e6d8c", + "paid": { + "0": 35, + "1": 1378, + "2": 1352, + "3": 69, + "4": 77, + "5": 72, + "6": 17, + "7": 10 + }, + "paid_rank_mass": 5129, + "pins": { + "rank2-central-analysis-20261021/native-escape/bit-admission/source/research/kappa-rebuild/bit/sources/pr589-regenerated/records/frames.json": "d006b3bfe0c04afecfea7aecfa59dfe4298b99501c70da3938e40289bc2f5010", + "two-pass-continuation-20261022/decoder-continuation-20261025/center-reuse/data-aligned-followup/check_bit_raw_first_temporal_word.py": "f35ada1b0d2fe8ad54b89cc2595948bafbb23d7f2eb010ba04151572da7ddd0f", + "two-pass-continuation-20261022/decoder-continuation-20261025/center-reuse/data-aligned-followup/check_bit_three_stage_geometry.py": 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"two-pass-continuation-20261022/decoder-continuation-20261025/root/emit_45_port_rank2_fused_bridge_source.py": "ba0b5b71e88220017850cb9db57645938cad110d912c963e56c7a0c99099f7c8" + }, + "protected_rank2_pairs": 45, + "scope": "45 main pairs gain protected dimension2 while66 main pairs and all helper endpoints are unchanged. Exact nested-projector identities and normalized source replay pass, including arbitrary scratch inputs. 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Changing neighboring frames, scalar gate order, simultaneous larger component systems, nonnested Gaussian factorizations and extra paid queries remain open. No conditional kappa or universal rank2 obstruction follows.", + "status": "COMPLETE_SCOPED_RANK2_BOUNDARY_COMPONENT_DIRECTION_SCREEN", + "terminal_shrink_dimension_histogram": { + "0": 111 + }, + "time_utc": "2026-10-26T02:20:32.992934+00:00" +} diff --git a/research/rank-two-boundary-and-decoder-limits/evidence/frames.json.gz b/research/rank-two-boundary-and-decoder-limits/evidence/frames.json.gz new file mode 100644 index 0000000000..5590407cef Binary files /dev/null and b/research/rank-two-boundary-and-decoder-limits/evidence/frames.json.gz differ diff --git a/research/rank-two-boundary-and-decoder-limits/evidence/native-word.json.gz b/research/rank-two-boundary-and-decoder-limits/evidence/native-word.json.gz new file mode 100644 index 0000000000..994d688706 Binary files /dev/null and b/research/rank-two-boundary-and-decoder-limits/evidence/native-word.json.gz differ diff --git a/research/rank-two-boundary-and-decoder-limits/evidence/paired-invoice.json b/research/rank-two-boundary-and-decoder-limits/evidence/paired-invoice.json new file mode 100644 index 0000000000..b432d9538d --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/evidence/paired-invoice.json @@ -0,0 +1,289 @@ +{ + "complete_decoder": false, + "new_kappa": false, + "pins": { + "two-pass-continuation-20261022/decoder-continuation-20261025/helper-pipeline/data-aligned-followup/audit_paid_center_completion.py": "09098d92f2e8eb924fdf5d9b288ebe1e3448b8c33334575ab4ffcce1d68fe2ac", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/BIT-PAIRED-RANK2-PROPAGATION-SCREEN.json": "f81e42cafcb7940dffd9f4611146c8443cfcb8204caf6617777e7eef1f422e9e", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-helper-handoff-construction-2/RESULT.json": "6374a8fac2eeff21b942ddce35af7367c1d8665f0db6da21367646e93c4fbe9c" + }, + "scope": "Only native helper minus paid query costs; main caller target absent. 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input rank profiles reused, physical/native rank census not independently replayed.", + "status": "PASS_SEPARATE_INTEGER_BISECTION_ALL_CASE_SIGN_AUDIT" +} diff --git a/research/rank-two-boundary-and-decoder-limits/evidence/single-representative.json b/research/rank-two-boundary-and-decoder-limits/evidence/single-representative.json new file mode 100644 index 0000000000..7b49fd00f2 --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/evidence/single-representative.json @@ -0,0 +1,65 @@ +{ + "all_normalized_forward_backward_columns": 685, + "all_owned_final_zero": true, + "complete_decoder": false, + "direction": [ + 0, + 0, + 1, + -1, + -1, + -1, + 0, + 0 + ], + "full_native_physical_phase_replay": false, + "helpers_relative_rank_profile": { + "1": 1, + "4": 10, + "7": 1, + "8": 433 + }, + "main_diagonal_and_cross_rank_counts": { + "(6, 6, 8)": 1, + "(7, 7, 8)": 84, + "(8, 8, 8)": 26 + }, + "new_kappa": false, + "old_paid_rank_mass": 5129, + "old_protected_query_excess_metric": 111, + "packet": "WORD.json.gz", + "packet_sha256": "ed866e52b809eb2b2d10cbabf1b5972ff406f93b403b79021531b9e90f88c0a9", + "paid": { + "0": 197, + "1": 1116, + "2": 1187, + "3": 224, + "4": 57, + "5": 72, + "6": 42, + "7": 16, + "8": 9 + }, + "paid_rank_mass": 5186, + "pins": { + "rank2-central-analysis-20261021/native-escape/bit-admission/source/research/kappa-rebuild/bit/sources/pr589-regenerated/records/frames.json": "d006b3bfe0c04afecfea7aecfa59dfe4298b99501c70da3938e40289bc2f5010", + "two-pass-continuation-20261022/decoder-continuation-20261025/center-reuse/data-aligned-followup/check_bit_raw_first_temporal_word.py": "f35ada1b0d2fe8ad54b89cc2595948bafbb23d7f2eb010ba04151572da7ddd0f", + "two-pass-continuation-20261022/decoder-continuation-20261025/center-reuse/data-aligned-followup/check_bit_three_stage_geometry.py": "11d9c5e61ea8988b6997bca2c6e0227a16d5e5561ec767a754aa8a621bfbcba0", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/BIT-COUPLED-RANK2-BOUNDARY-PROPAGATION.json": "ad8ce7ced84b2cc6b8a24a7d077b586d696b422fbf0d9aaef79376df2e1011aa", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/audit_bit_helper_handoff_packet.py": "beca307cd55b52ed69373d7410439b448009d65e43f59d09424aa20b68e637ee", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-coupled-rank2-component-candidate/FRAMES.json": "e488fbe8998d550ee86a82178108e23a7abf120636ede552aaf53e9d4ef76684", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-helper-handoff-construction-2/FINAL-WORD.json.gz": "dd86be7f1618697bfa64e83fa84c9519e8f5c06b6dfb65b7c41ed8ed13dba56f", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/bit-helper-handoff-construction-2/RESULT.json": "6374a8fac2eeff21b942ddce35af7367c1d8665f0db6da21367646e93c4fbe9c", + "two-pass-continuation-20261022/decoder-continuation-20261025/root/emit_coupled_rank2_component_candidate.py": "97d76e36a1ecaf1ea2b51ea9a2a87bfc8094e80d5ef6ff9a051675558a4d79e2" + }, + "protected_query_excess_metric": 86, + "scope": "One rank2 protected plane is exactly realized in rational frame algebra, but26 other main pairs lose the old protected-query excess and the paid rank mass rises57. 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"per_port_saved_interval": [ + "8.69021065208131648934273669117805262146729220", + "8.69021065208131648934273669117805262147063589" + ], + "104_port_saving_over_coordinate_lower": "396.976217584871796346219095780246739493152900", + "scope": "Exact normalized role-level relocation by orthogonal projectors, with all-column rational controls. Requires physical whole-idle composition, ordinary map costs, and the native HOST construction." +} \ No newline at end of file diff --git a/research/rank-two-boundary-and-decoder-limits/follow-up/PR7002-SIGN-HEADER-THIN-MINIMUM.json b/research/rank-two-boundary-and-decoder-limits/follow-up/PR7002-SIGN-HEADER-THIN-MINIMUM.json new file mode 100644 index 0000000000..79ca6f4734 --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/follow-up/PR7002-SIGN-HEADER-THIN-MINIMUM.json @@ -0,0 +1,14 @@ +{ + "status": "PASS_CONNECTED_SIGN_HEADER_SHEAR_COUNT_SHARP", + "source_sha256": "be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34", + "dimension": 38, + "native_stage_count": 18, + "minimum_transvections": 39, + "minimum_thin_given_two_transvections_per_host": 3, + "proof": [ + "For M=prod(I+x_i y_i^T), image(M-I) is contained in span(x_i). M=-I implies rank(M-I)=n in characteristic not two. Hence at least n factors.", + "With exactly n factors their x_i form a basis. In that basis each chronological factor changes only its own coordinate row and adds a functional vanishing on that coordinate. The first changed row therefore has diagonal coefficient +1 and no later factor changes that row. It cannot be a row of -I.", + "The exact rational replay of the pinned n+1 factors produces -I and each factor satisfies y_i^T x_i=0, attaining the lower bound." + ], + "scope": "After normalizing ordinary basis changes, the sign specialization uses exactly a product of square-zero rank-one transvections and each HOST provides at most two. Changed native semantics, sign-dependent ordinary operators, other header targets, and extra independent roles are outside scope." +} \ No newline at end of file diff --git a/research/rank-two-boundary-and-decoder-limits/follow-up/PR7089-ONE-QUERY-ODD-DIMENSION-VERIFIED.json b/research/rank-two-boundary-and-decoder-limits/follow-up/PR7089-ONE-QUERY-ODD-DIMENSION-VERIFIED.json new file mode 100644 index 0000000000..ed84502c41 --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/follow-up/PR7089-ONE-QUERY-ODD-DIMENSION-VERIFIED.json @@ -0,0 +1,142 @@ +{ + "source_head": "3a007633e5f96dcfba428eec4b4f3e32c5c2bd28", + "source_sha256": "f54ad772394fbb6ae735555738c7fe7e2102a10829419f27a7ba5267eeb89ef7", + "prefix_banks": [ + "right:0", + "right:1", + "right:2", + "right:3", + "response0", + "query0:0", + "query0:1", + "query0:2", + "query0:3", + "FULL1:0", + "FULL1:1", + "FULL1:2", + "FULL1:3", + "IDLE:0", + "IDLE:1", + "IDLE:2", + "IDLE:3" + ], + "odd_prefix_rows": [ + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "0" + ], + [ + "1", + "0", + "-1", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "0" + ], + [ + "1", + "0", + "-1", + "0" + ], + [ + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0" + ] + ], + "odd_prefix_span_generators": [ + "e_y0", + "e_x0-e_x1" + ], + "odd_prefix_rank": 2, + "rank_with_both_late_axes": 4, + "postquery_odd_dimension_increment_at_most": 1, + "status": "PASS_FIXED_PREFIX_ONE_QUERY_ODD_DIMENSION_OBSTRUCTION", + "argument": [ + "At grade D1, one query response adds at most one odd coefficient vector. Arbitrarily many even-Q controls cannot enlarge that increment in this quotient.", + "At grade D1D3, the only source rows are FULL3 outputs X' = D3(X-QY), Y' = D3Y. Degree-zero even-Q decoding is scalar in the quotient.", + "The two independent pure odd late targets force these two source rows to have zero even part. Consequently Y_even=0, Y'_odd=Y_odd and X'_odd=X_odd, up to the common D3 shift.", + "Thus both late odd axes must lie in the odd prefix span enlarged by the single response. They are independent modulo that span, so the enlargement is too small." + ], + "scope": "Fixed PR7089 prefix through the first FULL and IDLE; any single query2 argument in the fixed formal source model; one two-output FULL3 as the only D1D3 producer; arbitrary even-Q, degree-zero postprocessing; no additional physical relations or extra paid transforms." +} \ No newline at end of file diff --git a/research/rank-two-boundary-and-decoder-limits/follow-up/PR7089-UNBOUNDED-SUFFIX-DUAL.json b/research/rank-two-boundary-and-decoder-limits/follow-up/PR7089-UNBOUNDED-SUFFIX-DUAL.json new file mode 100644 index 0000000000..3cd30e92eb --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/follow-up/PR7089-UNBOUNDED-SUFFIX-DUAL.json @@ -0,0 +1,73 @@ +{ + "upstream_head": "3a007633e5f96dcfba428eec4b4f3e32c5c2bd28", + "fixed_schedule": true, + "banks": 39, + "possibly_nonzero_pairings": { + "right:0": 0, + "right:1": 0, + "right:2": 0, + "right:3": 0, + "response0": 0, + "query0:0": 0, + "query0:1": 0, + "query0:2": 0, + "query0:3": 0, + "FULL1:0": 0, + "FULL1:1": 0, + "FULL1:2": 0, + "FULL1:3": 0, + "IDLE:0": 0, + "IDLE:1": 0, + "IDLE:2": 0, + "IDLE:3": 0, + "response2": 0, + "bridge_query2:0": 0, + "bridge_query2:1": 0, + "bridge_query2:2": 0, + "bridge_query2:3": 0, + "bridge_minus:0": 0, + "bridge_minus:1": 0, + "bridge_minus:2": 0, + "bridge_minus:3": 0, + "FULL3:0": 0, + "FULL3:1": 0, + "FULL3:2": 1, + "FULL3:3": 1, + "response4": 1, + "query4:0": 0, + "query4:1": 0, + "query4:2": 1, + "query4:3": 0, + "left:0": 0, + "left:1": 0, + "left:2": 0, + "left:3": 1 + }, + "target_pairing": "1", + "dual": [ + [ + 0, + [ + -1, + 2 + ], + [ + 1, + 1 + ], + "-1" + ], + [ + 3, + [ + 1 + ], + [ + 1, + 1 + ], + "1" + ] + ], + "scope": "All degree-zero left group-algebra combinations of the recorded banks. A translate can hit either dual monomial only at the unique group word solving w*existing=desired, and D powers are preserved. Changed schedule, extra positive-degree operators, and additional physical quotient relations are outside the proof." +} diff --git a/research/rank-two-boundary-and-decoder-limits/verify.py b/research/rank-two-boundary-and-decoder-limits/verify.py new file mode 100644 index 0000000000..18f51087fa --- /dev/null +++ b/research/rank-two-boundary-and-decoder-limits/verify.py @@ -0,0 +1,114 @@ +"""Replay the frozen-boundary calculation and reprice the saved rank profiles.""" +from fractions import Fraction +import gzip +from hashlib import sha256 +import json +from pathlib import Path + +from boundary import boundary_rows + +EVIDENCE = Path(__file__).resolve().parent / "evidence" +SCALE = 10**30 + +def load(name): + data = (EVIDENCE / name).read_bytes() + return json.loads(gzip.decompress(data) if name.endswith(".gz") else data) + +def enclosure(rank, saving): + exponent = 1 - saving + target = rank**exponent.numerator * SCALE**exponent.denominator + lower, upper = 0, (rank + 1) * SCALE + while upper - lower > 1: + mid = (lower + upper) // 2 + if mid**exponent.denominator <= target: + lower = mid + else: + upper = mid + return lower, upper + +def signed_histograms(*terms): + result = [0] * 23 + for sign, histogram in terms: + for rank, count in histogram.items(): + result[int(rank)] += sign * count + return result + +def moment_bounds(coefficients, powers): + lower = upper = 0 + for rank, coefficient in enumerate(coefficients): + if rank == 0 or coefficient == 0: + continue + lo, hi = powers[rank] + if coefficient < 0: + lo, hi = hi, lo + lower += coefficient * lo + upper += coefficient * hi + return Fraction(lower, SCALE), Fraction(upper, SCALE) + +def overlap(first, second): + return max(first[0], second[0]) <= min(first[1], second[1]) + +def published_interval(entry): + return tuple(map(Fraction, entry["rational"])) + +def best_bound(rows): + return max(lo for lo, _ in rows), max(hi for _, hi in rows) + +def main(): + assert __debug__, "Run without optimization" + provenance = load("provenance.json") + for name, expected in provenance["published_evidence_sha256"].items(): + assert sha256((EVIDENCE / name).read_bytes()).hexdigest() == expected, name + + rows = boundary_rows() + assert rows == load("boundary.json")["cases"] + assert len(rows) == 111 + for row in rows: + assert row["initial_plane_extension_dimension"] == 0 + assert row["final_complement_shrink_dimension"] == 0 + print("PASS: zero frozen-neighbor endpoint extensions on 111 ports") + + data = load("profiles.json.gz") + single_audit = load("single-invoice-audit.json")["rows"] + paired_audit = load("paired-invoice.json")["summaries"] + caller = load("45-port-caller.json") + baseline = data["baseline"] + + for historical in single_audit: + saving = Fraction(historical["kappa"]) + powers = {rank: enclosure(rank, saving) for rank in range(1, 23)} + for name, expected in (("single", 6993), ("paired", 8040)): + bounds = [] + retained = [] + for row in data[name]: + coeff = signed_histograms((1, row["helper"]), (-1, row["paid"]), + (-1, baseline["helper_targets"]), (1, baseline["paid"])) + interval = moment_bounds(coeff, powers) + assert interval[1] < 0 + bounds.append(interval) + if row.get("retained_rank2_seeds"): + retained.append(interval) + assert len(bounds) == expected + best = best_bound(bounds) + if name == "paired": + published = paired_audit[str(saving)] + assert overlap(best, published_interval(published["best_delta"])) + assert overlap(best_bound(retained), published_interval(published["best_retaining_any_rank2_plane_delta"])) + else: + assert historical["negative_cases"] == expected + assert abs(best[1] - Fraction(historical["best_upper_bound"])) < Fraction(1, 10**22) + print(f"PASS: {name}, kappa={saving}, {expected} negative profiles, best upper bound {float(best[1]):.9f}") + + factors = caller["factor_rank_bounds"] + assert factors["protected_C"] + 3 * factors["each_native_d"] == factors["main_factored_path_C_d3_d2_d1_rank_at_most"] == 20 + coefficient = signed_histograms((1, caller["UNCONSTRUCTED_target_with90_rank20_main_rows"]), + (-1, caller["three_native_paid_plus_inherited_early_queries"])) + margin = moment_bounds(coefficient, powers) + assert margin[1] < 0 + assert overlap(margin, published_interval(caller["optimistic_margins_before_decoder"][str(saving)])) + print(f"PASS: fixed 45-port caller tariff at kappa={saving}, upper margin {float(margin[1]):.9f}") + +if __name__ == "__main__": + if not __debug__: + raise SystemExit("Run without Python optimization") + main()