From 1d49e6c75e608dd29c4fb2794463c8dc36df037f Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 1 Nov 2026 22:40:21 -0600 Subject: [PATCH 01/32] Research mixed projector root at conditional kappa 0.00327980 --- .../CONTROLLER.json | 4019 +++++++++++++++++ research/mixed-projector-query-root/NOTICE | 287 ++ research/mixed-projector-query-root/PROOF.md | 172 + research/mixed-projector-query-root/README.md | 52 + .../mixed-projector-query-root/RESULT.json | 427 ++ research/mixed-projector-query-root/ROOT.json | 1319 ++++++ .../mixed-projector-query-root/SOURCES.json | 132 + research/mixed-projector-query-root/TASK.json | 91 + .../mixed-projector-query-root/VALIDATION.md | 28 + .../mixed-projector-query-root/VERIFY.json | 48 + .../mixed-projector-query-root/algebra.py | 74 + .../mixed-projector-query-root/controller.py | 220 + .../module_check.py | 149 + .../mixed-projector-query-root/physical.py | 88 + .../mixed-projector-query-root/pricing.py | 167 + research/mixed-projector-query-root/verify.py | 100 + 16 files changed, 7373 insertions(+) create mode 100644 research/mixed-projector-query-root/CONTROLLER.json create mode 100644 research/mixed-projector-query-root/NOTICE create mode 100644 research/mixed-projector-query-root/PROOF.md create mode 100644 research/mixed-projector-query-root/README.md create mode 100644 research/mixed-projector-query-root/RESULT.json create mode 100644 research/mixed-projector-query-root/ROOT.json create mode 100644 research/mixed-projector-query-root/SOURCES.json create mode 100644 research/mixed-projector-query-root/TASK.json create mode 100644 research/mixed-projector-query-root/VALIDATION.md create mode 100644 research/mixed-projector-query-root/VERIFY.json create mode 100644 research/mixed-projector-query-root/algebra.py create mode 100644 research/mixed-projector-query-root/controller.py create mode 100644 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Apache-2.0. No subagents. + +The new contribution is the normalized six-field root, its weighted binary +children, exact complete caller, full invoice and conditional bound. +The shortest central-involution query tuple is from the credited +five-call-projector-rigidity package by Ali Romman with OpenAI Codex. +The binary query extension is PR6348. The unchanged native source is PR6349. +The simple normalization identity is not claimed as a new general algebra theorem. +The native construction, scalar compression and inherited proof engines are +predecessor work. Their exact source notices follow. + +Source: research/balanced-query-tree/NOTICE + +Binary query-tree caller + +New construction, proof and code: Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. No subagents. + +Cinna Davis supplies the productive path caller, query thinning and exact Laurent factorization. Ali Romman supplies the all-forward P104 binding in PR5544 and the retained-operand word in PR6167. The native word and interval/compiler lineage remain predecessor work. The new contribution is the four-field query extension, its tree composition, complete invoice and conditional price. + +The authenticated PR6167 notice follows. + +Retained-operand descent: Ali Romman, with substantial OpenAI Codex assistance. +Apache-2.0. + +The exact source word and price are from DreamingOfClouds, PR6144 and PR6143, +with Claude Opus 5.5 (Anthropic), via Claude Code. They extend PR6030 and PR5907. +The source reader is adapted from that work. The gzip portability controls +retain Douglas Colkitt and Maxime Fleury credit. + +The pinned PR5827 checker and all earlier source notices are retained below. + +Unread-register path resynthesis +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author-side. + +Mason Hale supplied PR5811, the complete two-block composition and the exact +role92 remapping and fourth accumulation. The earlier elementary accumulation, +retained-copy and second-block work is by Ali Romman. Joel Pulikkan supplied +R22. Dugongue supplied the concurrent baseline composition proof. Their source +notice and proof are retained byte for byte under inputs/pr5811-*. + +The source closure retains flyingviper, Cinna Davis, David Arias, Gareth +Davidson, Jacob Alan Sussman, zxv, Cao Yifan, Pierre-Loic Doulcet, thu-nmrc, +Scratch-net and all native/helper/controller/compiler/geometry/analytic +predecessors. The exact PR5786 source archive and its nested notices remain. +This package does not claim any predecessor construction as new. + +Exact PR5811 vendor/accumulated/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +Accumulated native updates +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. The same assistant made the construction and the author checks. + +Concurrent scope: Discussion5125 now tests retained copies in the transposed +supplier. That route uses the same source/destination duality. This package +claims the three fixed forward-supplier groups and their complete result, +not the elementary accumulation identity or the broader transposed search. + +Exact source: PR5786 at 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. +The complete predecessor notice follows unchanged. + +Asynchronous helper hubs +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. + +Retained native copies from PR5774 at 7d6ec0cdef31d0c37b7d2563e709979caa0d5eae. +All prior credit follows unchanged. + +Paid intermediate meetings and collective helper splits. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. All checks are author-side calculations. + +The complete PR5718 notice follows unchanged. + +Four paid interior public-basis changes. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. + +The following exact notice is retained from PR5660. + +New helper-subspace construction, proof and replay: +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The same assistant performed the construction and author-side checks. + +Retained contributions: +flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613 +relay/split compositions. +Scratch-net: PR5606 prepared-helper identities and target debit. +Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source. +Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame +change, PR5580 contact step, +and PR5544/5545 complete P104 caller. +Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. +DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. +thu-nmrc: PR5551 contact improvements. +Gareth Davidson (bitplane): PR2305 source composition. +David Arias: PR2152 coalesced P104 word. +Cinna Davis: PR2219 private reuse and the controller lineage. +Jacob Alan Sussman: productive mixed-target recursion. +zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage. +GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept. +The retained source notices preserve earlier geometry, BIT and analytic credit. + +The elementary rank-one basis identity is not claimed as a new general +linear-algebra theorem. The contribution is its explicit independent-target +use on this P104 word and the complete conditional kappa improvement. + +New contribution: Ali Romman, with substantial OpenAI Codex assistance. +The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644. +The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit. +The compensated triangle method retains Cinna Davis PR4692 credit. +No subagents were used for this contribution. Apache-2.0. + +Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by +Ali Romman corroborates it. This package credits that released composition +and contributes the further four-gate placement. + +New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices. + +Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial +OpenAI Codex assistance, including independent AI review agents. Apache-2.0. + +Retained native-copy construction +Prepared by Ali Romman with substantial OpenAI Codex assistance. No subagents. +The paid-meeting source is PR5751 by Ali Romman with OpenAI Codex assistance. +The dimension-four span [265,194,164,75] is from Joel Pulikkan / GamingPuzzled +PR5739, with Claude Opus 5.5 assistance. The R22 block edits are not included. +The retained-copy mechanism, exact constructor, source-specific verification, +new price and proof are the contribution of this package. Apache-2.0. + +Exact PR5811 vendor/blocks/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +The second block is PR5796 at4b30391e633ba0c7c674f03586ae97d443e9bc9c, by Ali Romman with substantial OpenAI Codex assistance, following Joel Pulikkan/GamingPuzzled R22. Exact notice, plan, proof and source words are retained in source/SECOND-* unchanged. + +The final immediate source is PR5786 asynchronous helper hubs by Ali Romman with substantial OpenAI Codex assistance. Its three temporal helper splits and complete completion parameters are retained and credited. The earlier PR5774-only composition is a superseded checkpoint, not a separate contribution. + +New complete retained-copy and R22 composition: Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. + +The thirteen retained native conversions and changed helper targets are by Ali Romman with OpenAI Codex assistance in PR5774. The R22 block and rank-four basis are by Joel Pulikkan (GamingPuzzled), with Claude Opus5.5 assistance, in PR5739/5756. The complete source archive and R22 notice remain unchanged. + +The construction retains Ali Romman PR5751 paid intermediate meetings, flyingviper PR5718 boundary splits, Cinna Davis's productive controller, Jacob Alan Sussman's productive recursion, zxv and Cao Yifan's interval/compiler line, and every P104/native/BIT predecessor in the source notices. The source engines are reused under exact byte bindings, not claimed as new implementations. + +Source: research/p104-native-input-lifting/NOTICE + +Native helper input lifting +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author checks. + +The direct source is PR6314 at 36533d4d1b4e2dd8672427461b12de3001b85810, +by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +It compresses the scalar word of PR6167 without a kappa change. +The four native input lifts and their complete conditional price are new here. +The basis identity is elementary linear algebra; no new general theorem +for that identity is claimed. + +The PR6167 source notice follows unchanged. Its nested source archive also +retains the earlier notices. + +Retained-operand descent: Ali Romman, with substantial OpenAI Codex assistance. +Apache-2.0. + +The exact source word and price are from DreamingOfClouds, PR6144 and PR6143, +with Claude Opus 5.5 (Anthropic), via Claude Code. They extend PR6030 and PR5907. +The source reader is adapted from that work. The gzip portability controls +retain Douglas Colkitt and Maxime Fleury credit. + +The pinned PR5827 checker and all earlier source notices are retained below. + +Unread-register path resynthesis +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author-side. + +Mason Hale supplied PR5811, the complete two-block composition and the exact +role92 remapping and fourth accumulation. The earlier elementary accumulation, +retained-copy and second-block work is by Ali Romman. Joel Pulikkan supplied +R22. Dugongue supplied the concurrent baseline composition proof. Their source +notice and proof are retained byte for byte under inputs/pr5811-*. + +The source closure retains flyingviper, Cinna Davis, David Arias, Gareth +Davidson, Jacob Alan Sussman, zxv, Cao Yifan, Pierre-Loic Doulcet, thu-nmrc, +Scratch-net and all native/helper/controller/compiler/geometry/analytic +predecessors. The exact PR5786 source archive and its nested notices remain. +This package does not claim any predecessor construction as new. + +Exact PR5811 vendor/accumulated/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +Accumulated native updates +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. The same assistant made the construction and the author checks. + +Concurrent scope: Discussion5125 now tests retained copies in the transposed +supplier. That route uses the same source/destination duality. This package +claims the three fixed forward-supplier groups and their complete result, +not the elementary accumulation identity or the broader transposed search. + +Exact source: PR5786 at 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. +The complete predecessor notice follows unchanged. + +Asynchronous helper hubs +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. + +Retained native copies from PR5774 at 7d6ec0cdef31d0c37b7d2563e709979caa0d5eae. +All prior credit follows unchanged. + +Paid intermediate meetings and collective helper splits. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. All checks are author-side calculations. + +The complete PR5718 notice follows unchanged. + +Four paid interior public-basis changes. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. + +The following exact notice is retained from PR5660. + +New helper-subspace construction, proof and replay: +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The same assistant performed the construction and author-side checks. + +Retained contributions: +flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613 +relay/split compositions. +Scratch-net: PR5606 prepared-helper identities and target debit. +Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source. +Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame +change, PR5580 contact step, +and PR5544/5545 complete P104 caller. +Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. +DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. +thu-nmrc: PR5551 contact improvements. +Gareth Davidson (bitplane): PR2305 source composition. +David Arias: PR2152 coalesced P104 word. +Cinna Davis: PR2219 private reuse and the controller lineage. +Jacob Alan Sussman: productive mixed-target recursion. +zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage. +GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept. +The retained source notices preserve earlier geometry, BIT and analytic credit. + +The elementary rank-one basis identity is not claimed as a new general +linear-algebra theorem. The contribution is its explicit independent-target +use on this P104 word and the complete conditional kappa improvement. + +New contribution: Ali Romman, with substantial OpenAI Codex assistance. +The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644. +The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit. +The compensated triangle method retains Cinna Davis PR4692 credit. +No subagents were used for this contribution. Apache-2.0. + +Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by +Ali Romman corroborates it. This package credits that released composition +and contributes the further four-gate placement. + +New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices. + +Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial +OpenAI Codex assistance, including independent AI review agents. Apache-2.0. + +Retained native-copy construction +Prepared by Ali Romman with substantial OpenAI Codex assistance. No subagents. +The paid-meeting source is PR5751 by Ali Romman with OpenAI Codex assistance. +The dimension-four span [265,194,164,75] is from Joel Pulikkan / GamingPuzzled +PR5739, with Claude Opus 5.5 assistance. The R22 block edits are not included. +The retained-copy mechanism, exact constructor, source-specific verification, +new price and proof are the contribution of this package. Apache-2.0. + +Exact PR5811 vendor/blocks/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +The second block is PR5796 at4b30391e633ba0c7c674f03586ae97d443e9bc9c, by Ali Romman with substantial OpenAI Codex assistance, following Joel Pulikkan/GamingPuzzled R22. Exact notice, plan, proof and source words are retained in source/SECOND-* unchanged. + +The final immediate source is PR5786 asynchronous helper hubs by Ali Romman with substantial OpenAI Codex assistance. Its three temporal helper splits and complete completion parameters are retained and credited. The earlier PR5774-only composition is a superseded checkpoint, not a separate contribution. + +New complete retained-copy and R22 composition: Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. + +The thirteen retained native conversions and changed helper targets are by Ali Romman with OpenAI Codex assistance in PR5774. The R22 block and rank-four basis are by Joel Pulikkan (GamingPuzzled), with Claude Opus5.5 assistance, in PR5739/5756. The complete source archive and R22 notice remain unchanged. + +The construction retains Ali Romman PR5751 paid intermediate meetings, flyingviper PR5718 boundary splits, Cinna Davis's productive controller, Jacob Alan Sussman's productive recursion, zxv and Cao Yifan's interval/compiler line, and every P104/native/BIT predecessor in the source notices. The source engines are reused under exact byte bindings, not claimed as new implementations. diff --git a/research/mixed-projector-query-root/PROOF.md b/research/mixed-projector-query-root/PROOF.md new file mode 100644 index 0000000000..27bdfe3e10 --- /dev/null +++ b/research/mixed-projector-query-root/PROOF.md @@ -0,0 +1,172 @@ +# A mixed projector root for independent Gaussian outputs + +This construction changes the caller. It keeps the complete PR6349 native +source. Four binary query suppliers, with 7, 2, 1 and 8 native leaves, enter +a six-field root. The root has three thin queries and three individual +whole idle jobs. It gives six independent Gaussian outputs. The child +suppliers give another 28 independent main outputs. + +The conditional claim is kappa 0.00327980. The five inherited framework +assumptions remain. This is not an unconditional multiplication theorem, +a materialized uniform word or an independent scientific review. + +## 1. An ordinary normalization of the native query + +Write q = Q^-1 for the actual common central Gaussian. The native checker +verifies Q^2 = Q^-2 = X with absolute phase +1. X is an ordinary translation +and X^2 = I. These identities hold under the retained tensor implementation. +Define + +```text +lambda = (1+i)I/2 + (1-i)X/2, +lambda^-1 = (1-i)I/2 + (1+i)X/2, +S = lambda q. +``` + +Then lambda^2 = X, S^2 = I, and lambda^-1 S = q. All these operators commute +with the fresh stage products D. The normalization is applied to the complete +field, using its global translation X. Its scalar coefficients stay outside +tensor powers. In general S is not the tensor power of the one-column S. + +The translation has disjoint two-address orbits. On one orbit lambda has +matrix [[a,b],[b,a]], where a=(1+i)/2 and b=(1-i)/2. Four ordinary complex +scalar operations implement it in place: + +```text +x <- x - i*y +x <- a*x +y <- (1+i)*y +y <- y - i*x. +``` + +Conjugate each coefficient to implement the inverse. No owned field, paid +Gaussian job or productive input is added. The pair map is unitary; each +displayed operation has growth at most two in the maximum norm. There are +four operations per address pair. A loop over the existing translation +pairs has linear data work. The ordinary-work bill below includes these +operations and translations. + +A child supplies D U(q), where U(q)=I+q E01, on two arbitrary fields. +Conjugation by diag(lambda,1), followed by U(-1), gives +D U(S-1). A thin query has the same conversion and retains its paid H1 +charge. Thus the central-involution root below has an actual native +implementation. Its output S is converted back to q by lambda^-1. + +## 2. The six-field root + +Use the shortest-query normal form from +`research/five-call-projector-rigidity/PROOF.md`. For i=0,...,5 set u_i=e_i. +Set u_6=(-1,1,-1,1,-1,1), and (v_i)_j=sign(i-j). Let R_i=u_i v_i. +Each R_i is square-zero and has rank one. Direct exact multiplication gives + +```text +(I-2R_6) ... (I-2R_0) = -I_6. +``` + +`ROOT.json` specifies an invertible rational basis F, four stage projectors +P_i, and their native two-field bases C_i. Full sites are 0, 1, 4 and 6. +Sites 2, 3 and 5 are thin. In F coordinates the four projector masks are + +| Site | Output coordinates in the stage | Rank | Native leaves | Extra whole idles | +| --- | --- | ---: | ---: | --- | +| 0 | 0,2 | 2 | 7 | none | +| 1 | 0,1,2 | 3 | 2 | one H16 | +| 4 | 0,3,4,5 | 4 | 1 | two H8 | +| 6 | 0,3 | 2 | 8 | none | + +The exact checker verifies P_i^2=P_i, P_i R_i=R_i P_i=R_i and pairwise +commutation of the four P_i. It also verifies that P_i commutes with the +query prefix (I-2R_i)...(I-2R_0). These conditions permit each independent +stage factor to move past its own query prefix. The two central characters +then give the same diagonal stage product, with scalar factor +1 or -1. +The checker also multiplies every independent stage coefficient directly. + +At a full site, C_i takes R_i to E01 and P_i to diag(I_r,0). Apply the child +supplier to the first two coordinates. Apply D_i separately to each of the +remaining r-2 coordinates. These are exactly the charged whole idle jobs. +All basis changes are emitted as rational ADD, SCALE and SWAP operations. +At a thin site, the corresponding C_i converts one paid query to R_i. + +Apply F at entry and F^-1 at exit. Apply lambda^-1 to all six root outputs. +Their independent stage supports are + +```text +ABCD, B, AB, CD, C, C. +``` + +For child sizes 7,2,1,8, the six Gaussian ranks are 145,17,73,73,9,9. +No root input is owned or initialized. The scalar basis maps are invertible. + +## 3. Binary children and full endpoint + +PR6348 supplies the unchanged four-field binary query extension. Each node +combines two query suppliers, one paid thin query and two whole idle jobs. +It returns another query supplier and two independent Gaussian outputs. +Its separate Laurent checker is replayed here under its source hash. + +The four child trees have 18 native leaves and 14 binary nodes. Their node +size counts are {2:8,3:1,4:3,7:1,8:1}. The root adds three thin queries. +The complete caller has 34 main fields per port, 18 distinct native stages, +17 thin queries, 14 paired whole idles and three individual whole idles. +Its 543 literal instructions include all basis maps and 20 normalizations. + +The full replay uses exact coefficients in Q(i)[Q,D_1,...,D_18]/(Q^4-1). +It checks all 1,156 input/output entries. Stage variables remain distinct. +It checks the complete Gaussian endpoint, not only the S=+1 and S=-1 cases. +Missing native calls, thin queries, paired idles, individual idles, +normalizations and central translations are rejected. + +Each native call receives 562 independent helper inputs. These are separate +from all main fields and from every other call's helpers. There are +18*562+34*104=13,652 productive fields. Calls execute in sequence. The 29 +owned labels, 32 native lifetimes and peak 13 fields remain as in PR6349. +Thin-query storage is reused between calls. Normalization adds no storage. + +The physical checker verifies all 7,488 native contacts, their absolute +phases, every output Gaussian and every paired or individual idle. The +fresh stage axes are orthonormal and fix the central port. The source word +receives its complete arbitrary-input, dense-transpose and native replay. + +## 4. Complete price and outer transfer + +The complete invoice has 67,092 paid jobs and 13,652 productive jobs. +Paid rank mass is 188,668; productive rank mass is 189,428. The surplus is +760. The maximum target rank is 145 and maximum paid rank is 64. The +emitted-event count agrees with a separate fixed-tree and root count. + +The strict raw crossing is in (0.00327981076011,0.00327981076012), between +adjacent points on the 10^-14 grid. `RESULT.json` records both rational +moment engines, completion, compiler and outer ledger. The claim is +0.00327980; the tested +saving is 0.003279805. The completion uses power 1024, cutoff 12, floor 13, +offset 1/7, reserve 10^-12 and decay 31/32. The logarithm power is 1100. +All local native, route and scalar costs remain charged. The new caller +uses a conservative 32 real scalar units per field per instruction, +including the normalization. Its complete ordinary bound is below 10^9. +The retained admitted BIT saving is .0034. All 54 strict and four functional +outer predicates must pass. + +The comparison is PR6353's published conditional .00315057. The present +source is PR6349; it does not consume PR6353's output-contracted word. +The source-relative gain is from the new caller, not new digits of an old +crossing. PR6353 and PR6350 retain their separate construction credit. + +The child-size discovery checked every tuple from 1 through 40 for this +fixed four-site root, at two floating trial savings. It selected 7,2,1,8. +That bounded search is not an exact optimality certificate or a search of +all root bases. The published bound depends only on the exact chosen word +and its complete rational replay. + +## Scope and open next questions + +The inherited assumptions are native_all_columns, owned_erasure, compiler, +precision_tape and analytic_recovery. Finite operator and compiler checks +do not discharge their full quantified statements. The large uniform word +and rounded multiplier are not materialized. No global optimality or +practical speedup is claimed. The selected frontier stays unchanged. + +An independent reviewer should first check the global-field normalization, +the charged rank-three and rank-four projectors, and input independence. +Then replay the exact source and complete invoice. A later improvement can +change this root or combine it with a verified source, but must include +every changed productive debit, ordinary operation and compiler cost. diff --git a/research/mixed-projector-query-root/README.md b/research/mixed-projector-query-root/README.md new file mode 100644 index 0000000000..92cb8835dd --- /dev/null +++ b/research/mixed-projector-query-root/README.md @@ -0,0 +1,52 @@ +# Conditional kappa 0.00327980 from a mixed projector root + +This caller gives conditional **kappa 0.00327980**, an increase of +**0.00012923 (about 4.10 percent)** over PR6353's .00315057. It keeps the +PR6349 native source and combines four PR6348 binary query suppliers in a +new six-field root. The selected frontier stays unchanged. + +The root permits paid stage projectors of ranks two, three and four. An +ordinary translation-based normalization supplies its central involution +and restores Gaussian outputs. The literal caller includes every +normalization, basis change, native call, thin query and complementary idle. +It has 18 native calls, 34 main fields per port and 67,092 paid jobs. + +Start with [PROOF.md](PROOF.md), [ROOT.json](ROOT.json), the literal +[CONTROLLER.json](CONTROLLER.json) and [RESULT.json](RESULT.json). +[VALIDATION.md](VALIDATION.md) states which checks actually ran. + +```sh +python3.12 -B scripts/research_package.py --package research/mixed-projector-query-root +python3.12 -I -B research/mixed-projector-query-root/verify.py +python3.12 -I -O -B research/mixed-projector-query-root/verify.py +``` + +Expected marker: `PASS_MIXED_PROJECTOR_QUERY_ROOT_KAPPA_00327980`. +The registered verifier uses only the Python standard library. + +Five inherited framework assumptions remain. The uniform word and rounded +multiplier are not materialized. Author replay and hosted CI do not replace +independent scientific review or formal-kernel acceptance. No global +optimum or practical runtime improvement is claimed. + +## Open next questions + +- Independently check the normalization on the complete field, the four + projectors, all arbitrary inputs and the complete paid bill. +- Test a different root or a verified improved source only with a new full + invoice, native binding, compiler and outer replay. + +[TASK.json](TASK.json) gives concrete first checks and remaining obligations. + +## Attribution and coordination + +New root, normalization, complete caller and verification: Ali Romman with +substantial OpenAI Codex assistance; no subagents. The query normal form, +PR6348 binary module and PR6349 source retain their separate credit. +Cinna Davis supplies the native query and thin-query interface. +DreamingOfClouds supplies PR6314's source compression with Claude Opus 5.5 +assistance. [NOTICE](NOTICE) retains the full native, helper, compiler, BIT +and outer lineage. Apache-2.0. + +[Canonical investigation](https://github.com/CrocSwap/integer-mult-bounds/discussions/5600#discussioncomment-19209322). +The source and owned-word searches in adjacent Discussions were excluded. diff --git a/research/mixed-projector-query-root/RESULT.json b/research/mixed-projector-query-root/RESULT.json new file mode 100644 index 0000000000..928f344f71 --- /dev/null +++ b/research/mixed-projector-query-root/RESULT.json @@ -0,0 +1,427 @@ +{ + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "binary_module": { + "coefficients": 16, + "identity": "L S A B Idle S^-1 C R = D_A D_B (U(q) direct-sum q direct-sum q^-1)", + "missing_idle_rejected": true, + "variables": [ + "q", + "D_A", + "D_B" + ] + }, + "caller": { + "coefficients": 1156, + "event_sha256": "27cb309b1013bc459ec7f93983dba26627255c35bbb4d38299ed4fd8f28c486b", + "events": 543, + "inputs": 34, + "native_stages": 18 + }, + "columns": { + "arithmetic": "Dense integer rows with binary denominators; reverse chronology", + "coefficients": 638401, + "columns": 799 + }, + "lifted_directions": [ + { + "basis": [ + 52 + ], + "departure_response": { + "496": "1", + "639": "-1", + "643": "-1/2" + }, + "frame": 595, + "input_direction": { + "496": "1", + "639": "-1", + "643": "-1/2" + }, + "primary": 496 + }, + { + "basis": [ + 82 + ], + "departure_response": { + "198": "1", + "648": "-1", + "649": "1" + }, + "frame": 597, + "input_direction": { + "648": "-1", + "649": "1" + }, + "primary": 649 + }, + { + "basis": [ + 51 + ], + "departure_response": { + "179": "1/2", + "663": "1", + "665": "-1" + }, + "frame": 105, + "input_direction": { + "663": "1", + "665": "-1" + }, + "primary": 663 + }, + { + "basis": [ + 30, + 42, + 384 + ], + "departure_response": { + "508": "1", + "631": "-1", + "635": "-1/2" + }, + "frame": 1093, + "input_direction": { + "508": "1", + "631": "-1", + "635": "-1/2" + }, + "primary": 508 + } + ], + "local": { + "endpoint_coefficients": 638401, + "helpers": { + "1": 14, + "2": 8, + "3": 4, + "4": 107, + "5": 14, + "6": 3, + "7": 9, + "8": 22, + "9": 381 + }, + "owned_fields": 29, + "owned_lifetimes": 32, + "paid": { + "1": 2217, + "2": 457, + "3": 497, + "4": 100, + "5": 161, + "6": 8, + "7": 9, + "8": 1 + }, + "paid_rank_mass": 5946, + "peak_owned_fields": 13, + "public_inputs": 770, + "real_scalar_allowance": 127088 + }, + "native": { + "distinct_maps": 2930, + "helper_normalizers": 1124, + "helpers": { + "1": 14, + "2": 8, + "3": 4, + "4": 107, + "5": 14, + "6": 3, + "7": 9, + "8": 22, + "9": 381 + }, + "main_adapters": 208, + "proof": "Every signed Pauli image and exact global phase; frame induction at every positive tensor width", + "recipe_payload_sha256": "18631697cf96cfcd625fd0210939bc40f095657324730955d15719b9c7385513", + "wrong_phase_rejected": true + }, + "negative_controls": { + "missing_carrier_move": "Scalar destination and coefficient", + "missing_first_carrier_subtraction": "All public and owned rows", + "missing_idle": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_idle_one": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_lambda": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_local": "Every native stage exactly once", + "missing_output_basis": "All public and owned rows", + "missing_q_power": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_query": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_second_carrier_subtraction": "All public and owned rows", + "old_input_chart": "Common scalar chart", + "wrong_649_injection": "All public and owned rows", + "wrong_663_injection": "All public and owned rows", + "wrong_intersection": "Nested chronological transport" + }, + "physical": { + "central_square_columns": 53248, + "central_translations": 16, + "full_calls": 18, + "main_targets": { + "145": 104, + "17": 1768, + "25": 208, + "33": 624, + "57": 208, + "65": 208, + "73": 208, + "9": 208 + }, + "new_paid_jobs": 0, + "ordinary_normalizations": 20, + "physical_contacts": 7488, + "ports": 104, + "route_payload_sha256": "79930ec6c09a8e4930556c925c354bb5431203eaf069d9373f056049c061289b", + "tensor_rule": "Factorwise native maps; scalar signs stay outside the tensor power.", + "whole_idle_jobs": { + "16": 1768, + "24": 208, + "32": 624, + "56": 208, + "64": 208, + "8": 208 + } + }, + "price": { + "compiler": { + "H": 70855400000000, + "N": "2^70855400000000", + "eta": { + "lower": "0.000000054900323468016292837875", + "upper": "0.000000054900323468016292837876" + }, + "gap": "1/1400000000", + "integer_test_exponent": 50611, + "logarithm_power": 1100, + "theta": "63/64", + "uniform_saving": "2295863/700000000", + "word_materialized": false + }, + "derivative_upper": "-177870484769676531090751061240712034497904012779690454216995569/784637716923335095479473677900958302012794430558004314112", + "full_forward_calls": 18, + "gain": "12923/100000000", + "kappa": "16399/5000000", + 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"a62fefda1709614157ba440d38c164c366a8b3322ab8f866b6b4bd47b9d83dbc" + }, + { + "path": "research/five-call-projector-rigidity/PROOF.md", + "usage": "provenance", + "git_blob": "04db617a97bf941fe277e834d2b2e18d6b735a22", + "sha256": "f917d2a88433e2c8a3ba48f76453a77af4cfed9cabff32ea8b60ce5abbab869c" + }, + { + "path": "research/five-call-projector-rigidity/README.md", + "usage": "provenance", + "git_blob": "e1784eb4cd40e4c6b0bdc2d916ce2fe364496bba", + "sha256": "807974f124ac0e1efc17af00dabff456f0b33c8186ae7246b4c96a8aca540a9b" + } + ] +} diff --git a/research/mixed-projector-query-root/TASK.json b/research/mixed-projector-query-root/TASK.json new file mode 100644 index 0000000000..4527fb934b --- /dev/null +++ b/research/mixed-projector-query-root/TASK.json @@ -0,0 +1,91 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 8, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "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", + "scope_change_reason": "Use a paid rank-three/rank-four mixed root with unequal binary children and a whole-field central-involution normalization. The source word remains fixed.", + "actual_scope": "Complete source-bound caller at conditional kappa 0.00327980, including all main fields, independent helpers, native phases, idle jobs, ordinary normalization, compiler and outer costs.", + "bottleneck_link": "Complex supplier; changes the full signed target and paid moment while retaining admitted BIT .0034.", + "outcome": "completed", + "evidence": "PROOF.md, ROOT.json, CONTROLLER.json, RESULT.json and VALIDATION.md.", + "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5600#discussioncomment-19209322", + "stop_rule": "Require exact arbitrary-input and native identities, global normalization, a complete invoice, both rational engines, compiler and outer checks before a kappa claim.", + "author": "Ali Romman", + "ai_assistance": "Substantial OpenAI Codex assistance; no subagents. All checks are author checks.", + "budget_minutes": null, + "open_questions": [ + { + "question": "Does independent review confirm the complete global-field normalization and mixed root?", + "why_it_matters": "The new mechanism uses a non-tensor normalization outside the native tensor word.", + "first_step": "Check PROOF.md section 1, module_check.py and the exact Q(i)[Q,D]/(Q^4-1) full caller replay.", + "blocked_by": "Independent review has not occurred." + }, + { + "question": "Can a verified improved source or changed root improve the complete price?", + "why_it_matters": "This construction is not a global optimum.", + "first_step": "Bind an exact source and all changed target debits; compare the complete invoice before native and compiler replay.", + "blocked_by": "Exact arbitrary-input and native source checks for any changed source." + } + ] +} diff --git a/research/mixed-projector-query-root/VALIDATION.md b/research/mixed-projector-query-root/VALIDATION.md new file mode 100644 index 0000000000..8cca54fb24 --- /dev/null +++ b/research/mixed-projector-query-root/VALIDATION.md @@ -0,0 +1,28 @@ +# Validation record + +This file records author checks. Independent scientific review and hosted CI +are separate checks. Do not infer their completion from a local pass. + +The exact root and ordinary normalization, all four Gaussian characters, +the 543-event complete caller and its six deletion controls passed locally. +The final normal author build passed the complete unchanged source, native +phases, 7,488 physical contacts, both rational price engines, compiler and +all 58 outer predicates at kappa 0.00327980. The actual one-, two- and +three-column Gaussian checks also passed. A two-column counterexample +rejects tensoring the one-column normalization in place of the required +global normalization. + +Environment: macOS 26.6.1 arm64, CPython 3.12.13. Published replay uses the +standard library. Discovery used NumPy, SciPy and SymPy; those searches are +not proof dependencies and are not part of the registered replay. + +The registered normal and optimized commands both passed, including the +exact retained receipt and all rejection controls. Metadata and source-pin +checks passed. The selected record retains SHA256 +`9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa`. + +The user instructed that this result stay local until they authorize a PR. +No branch push, PR or hosted CI is planned under that instruction. Local +committed-input checks and a sealed export will be recorded after they run. +Full source-history preflight needs the missing ancestry in this shallow +checkout. Independent scientific review remains open. diff --git a/research/mixed-projector-query-root/VERIFY.json b/research/mixed-projector-query-root/VERIFY.json new file mode 100644 index 0000000000..e0481dae44 --- /dev/null +++ b/research/mixed-projector-query-root/VERIFY.json @@ -0,0 +1,48 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/balanced-query-tree/CONTROLLER.json", + "research/balanced-query-tree/RESULT.json", + "research/balanced-query-tree/controller.py", + "research/balanced-query-tree/module_check.py", + "research/balanced-query-tree/physical.py", + "research/balanced-query-tree/pricing.py", + "research/p104-frontier-compression-2/WORD.json.gz", + "research/p104-native-input-lifting/RESULT.json", + "research/p104-native-input-lifting/SOURCES.json", + "research/p104-native-input-lifting/WORD.json.gz", + "research/p104-native-input-lifting/construct.py", + "research/p104-native-input-lifting/support.py", + "research/p104-native-input-lifting/verify.py", + "research/p104-retained-operand-descent/SOURCES.json", + "research/p104-retained-operand-descent/inputs/pr5827-source.tar", + "research/p104-retained-operand-descent/pricing.py", + "research/p104-retained-operand-descent/sources.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 590, + "checks": "Authenticate the unchanged native source; check exact root, global normalization, all native input columns, full physical caller, complete invoice, both interval engines, compiler and outer ledger." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 590, + "checks": "Repeat the complete source-bound scientific receipt and semantic rejection controls with assertions disabled." + } + ] +} diff --git a/research/mixed-projector-query-root/algebra.py b/research/mixed-projector-query-root/algebra.py new file mode 100644 index 0000000000..a06d6f6416 --- /dev/null +++ b/research/mixed-projector-query-root/algebra.py @@ -0,0 +1,74 @@ +"""Exact rational matrices and coefficients in Q(i). + +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +""" +from fractions import Fraction as Q + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def matrix(rows): + return [[Q(x) for x in row] for row in rows] + + +def eye(n): + return matrix([[int(i == j) for j in range(n)] for i in range(n)]) + + +def multiply(a, b): + return [[sum(x*y for x, y in zip(row, column)) for column in zip(*b)] for row in a] + + +def add(a, b, scale=1): + return [[x+scale*y for x, y in zip(row, other)] for row, other in zip(a, b)] + + +def inverse(a): + n = len(a) + rows = [row[:] + identity for row, identity in zip(a, eye(n))] + for j in range(n): + k = next((k for k in range(j, n) if rows[k][j]), None) + need(k is not None, 'Nonsingular rational matrix') + rows[j], rows[k] = rows[k], rows[j] + v = rows[j][j] + rows[j] = [x/v for x in rows[j]] + for k in range(n): + if k != j: + v = rows[k][j] + rows[k] = [x-v*y for x, y in zip(rows[k], rows[j])] + return [row[n:] for row in rows] + + +def coefficient(x): + return (Q(x), Q(0)) + + +def zadd(a, b): + return a[0]+b[0], a[1]+b[1] + + +def zmul(a, b): + return a[0]*b[0]-a[1]*b[1], a[0]*b[1]+a[1]*b[0] + + +def accumulate(dst, src, c=(Q(1), Q(0))): + for key, value in src.items(): + value = zadd(dst.get(key, (Q(0), Q(0))), zmul(c, value)) + if value != (0, 0): + dst[key] = value + else: + dst.pop(key, None) + + +def shifted(row, term): + result = [] + for cell in row: + target = {} + for key, value in cell.items(): + new = ((key[0]+term[0]) % 4,) + tuple(a+b for a, b in zip(key[1:], term[1:])) + accumulate(target, {new: value}) + result.append(target) + return result diff --git a/research/mixed-projector-query-root/controller.py b/research/mixed-projector-query-root/controller.py new file mode 100644 index 0000000000..d9c3330791 --- /dev/null +++ b/research/mixed-projector-query-root/controller.py @@ -0,0 +1,220 @@ +"""Emit the mixed projector root and its paid binary query suppliers. + +The binary child emitter is adapted from PR6348. Cinna Davis supplies the +native and thin-query interface. Ali Romman with OpenAI Codex assistance. +Apache-2.0. All ordinary normalization occurs outside tensor powers. +""" +from collections import Counter +from copy import deepcopy +from hashlib import sha256 +from pathlib import Path +import json + +from algebra import Q, accumulate, coefficient, eye, matrix, need, shifted, zmul + +HERE = Path(__file__).resolve().parent + + +def construct(): + data = json.loads((HERE/'ROOT.json').read_text()) + events, targets, nodes = [], {}, [] + stage, next_role = 0, 6 + + def emit(op, *args): + events.append([op, *args]) + + def mix(rows): + a = matrix(rows) + ops = [] + for j in range(6): + k = next(k for k in range(j, 6) if a[k][j]) + if k != j: + a[j], a[k] = a[k], a[j] + ops.append(['SWAP', j, k]) + c = 1/a[j][j] + if c != 1: + a[j] = [x*c for x in a[j]] + ops.append(['SCALE', j, str(c)]) + for k in range(6): + if k != j and a[k][j]: + c = -a[k][j] + a[k] = [x+c*y for x, y in zip(a[k], a[j])] + ops.append(['ADD', k, j, str(c)]) + need(a == eye(6), 'Complete scalar basis elimination') + for e in reversed(ops): + if e[0] == 'SCALE': + e[-1] = str(1/Q(e[-1])) + elif e[0] == 'ADD': + e[-1] = str(-Q(e[-1])) + emit(*e) + + def label(tree): + nonlocal stage + if tree == 1: + stage += 1 + return {'stage': stage, 'stages': [stage]} + left, right = map(label, tree) + return {'left': left, 'right': right, 'stages': left['stages']+right['stages']} + + roots = [label(t) for t in data['children']] + + def supplier(tree, x, y, exponent): + nonlocal next_role + if 'stage' in tree: + if exponent == -1: + emit('Q_POWER', x, -2) + emit('SWAP', x, y) + emit('LOCAL', tree['stage'], x, y) + emit('SWAP', x, y) + if exponent == -1: + emit('Q_POWER', x, 2) + return + a, b = next_role, next_role+1 + next_role += 2 + stages = tree['stages'] + nodes.append({'roles': [a, b], 'stages': stages, 'exponent': exponent}) + emit('SWAP', x, b) + emit('SWAP', y, a) + emit('SWAP', a, b) + emit('ADD', x, a, 1) + emit('ADD', b, y, -1) + emit('QUERY', a, b, -exponent) + emit('ADD', b, y, 1) + emit('ADD', x, a, -1) + emit('IDLE', a, b, stages) + emit('SCALE', y, -1) + supplier(tree['left'], y, x, -exponent) + emit('SCALE', y, -1) + supplier(tree['right'], x, y, exponent) + emit('ADD', x, a, 1) + emit('SCALE', a, -1) + emit('ADD', a, x, 1) + emit('SWAP', y, b) + emit('SCALE', b, -1) + emit('ADD', b, y, 1) + targets[a], targets[b] = (-exponent, stages), (exponent, stages) + + mix(data['input_basis']) + full_index = 0 + for site in data['sites']: + mix(site['inverse']) + # lambda=(1+i)/2+(1-i)*q^2/2, q=Q^-1. Its square is q^2. + emit('LAMBDA', 0, -1) + if site['full']: + tree = roots[full_index] + full_index += 1 + supplier(tree, 0, 1, 1) + for r in range(2, site['stage_rank']): + emit('IDLE_ONE', r, tree['stages']) + else: + emit('QUERY', 0, 1, -1) + emit('LAMBDA', 0, 1) + emit('ADD', 0, 1, -1) + mix(site['basis']) + mix(data['output_basis']) + for r, mask in enumerate(data['masks']): + emit('LAMBDA', r, -1) + selected = [s for bit, tree in zip(mask, roots) if bit for s in tree['stages']] + targets[r] = (-1, selected) + need(stage == 18 and next_role == 34, 'Complete mixed-root dimensions') + diagonal = [[targets[r][0], 0]+[int(s in targets[r][1]) for s in range(1, stage+1)] + for r in range(next_role)] + return {'schema': 'mixed-projector-query-root/1', 'roles': next_role, + 'stages': stage, 'ambient_rank': 9+8*stage, 'nodes': nodes, + 'events': events, 'diagonal': diagonal} + + +def replay(word): + n, width = word['roles'], word['stages']+2 + zero = (0,)*width + rows = [[{zero: coefficient(1)} if i == j else {} for j in range(n)] for i in range(n)] + seen = [] + for event in word['events']: + op = event[0] + if op == 'ADD': + _, dst, src, c = event + for a, b in zip(rows[dst], rows[src]): + accumulate(a, b, coefficient(c)) + elif op == 'SCALE': + _, dst, c = event + rows[dst] = [{key: zmul(coefficient(c), value) for key, value in cell.items()} + for cell in rows[dst]] + elif op == 'SWAP': + _, a, b = event + rows[a], rows[b] = rows[b], rows[a] + elif op in ('LOCAL', 'QUERY'): + if op == 'LOCAL': + _, stage, src, dst = event + exponent = -1 + seen.append(stage) + else: + _, dst, src, exponent = event + term = (exponent,)+(0,)*(width-1) + for a, b in zip(rows[dst], shifted(rows[src], term)): + accumulate(a, b) + if op == 'LOCAL': + term = (0,)+tuple(int(s == stage) for s in range(width-1)) + for r in (src, dst): + rows[r] = shifted(rows[r], term) + elif op == 'Q_POWER': + _, r, exponent = event + need(exponent in (-2, 2), 'Only even powers are ordinary translations') + rows[r] = shifted(rows[r], (exponent,)+(0,)*(width-1)) + elif op == 'LAMBDA': + _, r, sign = event + need(sign in (-1, 1), 'Unitary normalization or its inverse') + old = rows[r] + other = shifted(old, (2,)+(0,)*(width-1)) + rows[r] = [{} for _ in range(n)] + for dst, a, b in zip(rows[r], old, other): + accumulate(dst, a, (Q(1,2), Q(sign,2))) + accumulate(dst, b, (Q(1,2), Q(-sign,2))) + elif op in ('IDLE', 'IDLE_ONE'): + roles, stages = (event[1:3], event[3]) if op == 'IDLE' else ([event[1]], event[2]) + need(len(stages) == len(set(stages)), 'Distinct whole-idle stages') + term = (0,)+tuple(int(s in stages) for s in range(width-1)) + for r in roles: + rows[r] = shifted(rows[r], term) + else: + raise ValueError('Unknown caller opcode: '+op) + expected = [[{(word['diagonal'][i][0] % 4,)+tuple(word['diagonal'][i][1:]): coefficient(1)} + if i == j else {} for j in range(n)] for i in range(n)] + need(sorted(seen) == list(range(1, word['stages']+1)), 'Every native stage exactly once') + need(rows == expected, 'Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient') + return {'inputs': n, 'coefficients': n*n, 'native_stages': len(seen), + 'events': len(word['events']), 'event_sha256': sha256(json.dumps(word['events'],separators=(',',':')).encode()).hexdigest()} + + +def controls(word): + result = {} + for op in ['LOCAL', 'QUERY', 'IDLE', 'IDLE_ONE', 'LAMBDA', 'Q_POWER']: + bad = deepcopy(word) + del bad['events'][next(i for i,e in enumerate(bad['events']) if e[0] == op)] + try: + replay(bad) + except ValueError as error: + result['missing_'+op.lower()] = str(error) + else: + raise ValueError('Mutation accepted: '+op) + return result + + +def formula_invoice(local): + targets = Counter({r: 18*n for r,n in local['helpers'].items()}) + paid = Counter({r: 18*n for r,n in local['paid'].items()}) + paid[1] += 17*104 + # Four child trees: 7, 2, 1 and 8 leaves. + for size, count in {2:8, 3:1, 4:3, 7:1, 8:1}.items(): + targets[1+8*size] += 208*count + paid[8*size] += 208*count + for rank,count in {145:1,17:1,73:2,9:2}.items(): + targets[rank] += 104*count + paid[16] += 104 + paid[8] += 208 + return targets, paid + + +if __name__ == '__main__': + word = construct() + print(replay(word)) + print(controls(word)) diff --git a/research/mixed-projector-query-root/module_check.py b/research/mixed-projector-query-root/module_check.py new file mode 100644 index 0000000000..89ec4480ad --- /dev/null +++ b/research/mixed-projector-query-root/module_check.py @@ -0,0 +1,149 @@ +"""Check the root independently of the emitted caller. + +The shortest-query tuple is from five-call-projector-rigidity. The chosen +stage projectors, normalization and mixed root are new here. Ali Romman, +with substantial OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +import json + +from algebra import Q, add, eye, inverse, matrix, multiply, need, zadd, zmul + +HERE = Path(__file__).resolve().parent + + +def run(): + d = json.loads((HERE/'ROOT.json').read_text()) + n, identity = 6, eye(6) + zero = [[Q(0)]*n for _ in range(n)] + f, fi = matrix(d['input_basis']), matrix(d['output_basis']) + need(multiply(f, fi) == multiply(fi, f) == identity, 'Root bases are inverses') + prefix, projectors, queries = identity, [], [] + for i, site in enumerate(d['sites']): + u = [int(j == i) for j in range(n)] if i < n else [-(-1)**j for j in range(n)] + v = [int(i > j)-int(i < j) for j in range(n)] + r = matrix([[x*y for y in v] for x in u]) + need(multiply(r, r) == zero, 'Square-zero query') + prefix = multiply(add(identity, r, -2), prefix) + c, ci = matrix(site['basis']), matrix(site['inverse']) + need(multiply(c, ci) == multiply(ci, c) == identity, 'Each native basis has an inverse') + e = [[Q(0)]*n for _ in range(n)] + e[0][1] = Q(1) + need(multiply(multiply(c,e),ci) == r, 'Actual native two-field query plane') + p = matrix(site['projector']) + if site['full']: + support = site['support'] + diagonal = [[int(j == k and j in support) for k in range(n)] for j in range(n)] + need(p == multiply(multiply(f,diagonal),fi), 'Independent output stage mask') + size = site['stage_rank'] + physical = [[int(j == k and j < size) for k in range(n)] for j in range(n)] + need(p == multiply(multiply(c,physical),ci), 'Every complementary idle is included') + need(multiply(p,p) == p and multiply(p,r) == multiply(r,p) == r, 'Stage projector') + need(multiply(p,prefix) == multiply(prefix,p), 'Chronological commutation') + for old in projectors: + need(multiply(p,old) == multiply(old,p), 'Independent stages commute') + projectors.append(p) + else: + need(p == zero, 'Thin sites have no free diagonal supplier') + queries.append(r) + need(prefix == [[-x for x in row] for row in identity], 'All minus-character outputs') + masks = [[int(j in s['support']) for s in d['sites'] if s['full']] for j in range(n)] + need(masks == d['masks'], 'Declared full-site masks') + expected = {} + for j,bits in enumerate(masks): + mask = sum(bit << i for i,bit in enumerate(bits)) + expected.setdefault(mask, [[Q(0)]*n for _ in range(n)])[j][j] = Q(1) + for sign in (1,-1): + word, stage = {0: identity}, 0 + for r,site in zip(queries,d['sites']): + next_word = {} + p = matrix(site['projector']) + for mask,old in word.items(): + a = multiply(add(identity,r,sign-1),old) + if site['full']: + next_word[mask] = multiply(add(identity,p,-1),a) + next_word[mask | (1 << stage)] = multiply(p,a) + else: + next_word[mask] = a + word = {k:a for k,a in next_word.items() if a != zero} + stage += int(site['full']) + actual = {k:multiply(multiply(fi,a),f) for k,a in word.items()} + need(actual == {k:[[sign*x for x in row] for row in a] for k,a in expected.items()}, + 'Every independent full-stage polynomial coefficient') + # The four ordinary operations act on each pair of translated addresses. + # No whole field is copied or initialized for this normalization. + pair_matrices = [] + for sign in (1,-1): + a, b = (Q(1,2),Q(sign,2)), (Q(1,2),Q(-sign,2)) + columns = [] + for column in (0,1): + x,y = (Q(int(column == 0)),Q(0)), (Q(int(column == 1)),Q(0)) + x = zadd(x,zmul((Q(0),Q(-sign)),y)) + x = zmul(a,x) + y = zmul((Q(1),Q(sign)),y) + y = zadd(y,zmul((Q(0),Q(-sign)),x)) + columns.append([x,y]) + m = list(map(list,zip(*columns))) + need(m == [[a,b],[b,a]], 'Four-operation ordinary normalization') + pair_matrices.append(m) + def zmat(a,b): + return [[zadd(zmul(a[i][0],b[0][j]),zmul(a[i][1],b[1][j])) for j in range(2)] for i in range(2)] + need(zmat(*pair_matrices) == [[(1,0),(0,0)],[(0,0),(1,0)]], 'Normalization inverse') + need(zmat(pair_matrices[0],pair_matrices[0]) == [[(0,0),(1,0)],[(1,0),(0,0)]], + 'Normalization square is the ordinary translation') + for q in [(1,0),(-1,0),(0,1),(0,-1)]: + square = zmul(q,q) + lam = zadd((Q(1,2),Q(1,2)),zmul((Q(1,2),Q(-1,2)),square)) + lam_inv = zadd((Q(1,2),Q(-1,2)),zmul((Q(1,2),Q(1,2)),square)) + s = zmul(lam,q) + need(zmul(s,s) == (1,0) and zmul(lam_inv,s) == q, 'All four Gaussian characters') + def dense_product(a,b): + size = len(a) + out = [[(Q(0),Q(0)) for _ in range(size)] for _ in range(size)] + for i in range(size): + for j in range(size): + for k in range(size): + out[i][j] = zadd(out[i][j],zmul(a[i][k],b[k][j])) + return out + tensor_columns = 0 + wrong_tensor_rejected = False + for width in (1,2,3): + size = 1 << width + ident = [[(Q(int(i == j)),Q(0)) for j in range(size)] for i in range(size)] + gaussian,normalizer,restore = [],[],[] + for i in range(size): + row,norm,back = [],[],[] + for j in range(size): + value = (Q(1),Q(0)) + for bit in range(width): + c = (Q(1,2),Q(1 if (i^j)&(1 << bit) else -1,2)) + value = zmul(value,c) + row.append(value) + norm.append((Q(1,2),Q(1,2)) if i == j else + (Q(1,2),Q(-1,2)) if i^j == size-1 else (Q(0),Q(0))) + back.append((Q(1,2),Q(-1,2)) if i == j else + (Q(1,2),Q(1,2)) if i^j == size-1 else (Q(0),Q(0))) + gaussian.append(row) + normalizer.append(norm) + restore.append(back) + normalized = dense_product(normalizer,gaussian) + need(dense_product(normalized,normalized) == ident, 'Actual tensor Gaussian normalizes to an involution') + need(dense_product(restore,normalized) == gaussian, 'Actual tensor Gaussian is restored') + if width == 1: + need(normalized == ident, 'One-column normalization positive control') + if width == 2: + need(normalized != ident and dense_product(restore,ident) != gaussian, + 'Tensoring the one-column normalization is rejected') + wrong_tensor_rejected = True + tensor_columns += size + return {'fields':n,'full_sites':4,'thin_sites':3,'stage_ranks':[2,3,4,2], + 'polynomial_coefficients':2*16*n*n,'gaussian_characters':4, + 'actual_tensor_gaussian_columns':tensor_columns, + 'wrong_tensor_normalization_rejected':wrong_tensor_rejected, + 'ordinary_normalization_operations_per_pair':4,'owned_normalization_fields':0, + 'normalization_growth_per_operation_upper':2, + 'tensor_rule':'Normalize the complete field with its global Q squared translation; scalar coefficients stay outside tensor powers.'} + + +if __name__ == '__main__': + print(run()) diff --git a/research/mixed-projector-query-root/physical.py b/research/mixed-projector-query-root/physical.py new file mode 100644 index 0000000000..b63471439e --- /dev/null +++ b/research/mixed-projector-query-root/physical.py @@ -0,0 +1,88 @@ +"""Bind the mixed root to native phases and every whole Gaussian job. + +Adapted from Ali Romman's PR5544 physical checker. The Clifford recipes, +phase interpreter and local interface retain their predecessor credit. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import json + + +def physical(word, local, L): + need = L.need + N = L.load(L.ROOT/'research/pr4359-p7-padding/native_inventory.py', 'productive_p104_phase_polynomial') + source = L.read(L.ROOT/'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json') + recipes = {r['q']:r for r in source['recipes']} + dimension = word['ambient_rank'] + axes = tuple(1 << i for i in range(dimension)) + def completed(stage): + return N.norm((axis,1) for axis in axes[:9+8*stage]) + contacts, squares, target_profile = [], 0, Counter() + idle_jobs = Counter() + for _,stage,x,y in (e for e in word['events'] if e[0] == 'LOCAL'): + spectator = N.norm((axis,1) for axis in axes[9:9+8*stage]) + for q in local['ports']: + basis = recipes[q]['idle_children'][0]['orthogonal_axes'][:8] + need(all((x&q).bit_count()%2 == 0 for x in basis), 'Fresh-block basis fixes central port') + need(all((a&b).bit_count()%2 == int(i==j) for i,a in enumerate(basis) for j,b in enumerate(basis)), 'Actual orthonormal basis') + swaps = [] if stage == 0 else [b ^ axes[9+8*(stage-1)+i] for i,b in enumerate(basis)] + route = tuple(e ^ N.act(swaps,sum(((e&v).bit_count()%2) << i for i,v in enumerate(swaps))) for e in axes) + need(all(N.act(route,route[i]) == axes[i] for i in range(dimension)), 'Route inverse') + need(all((a&b).bit_count()%2 == int(i==j) for i,a in enumerate(route) for j,b in enumerate(route)), 'Orthogonal physical route') + need(N.act(route,q) == q, 'Route preserves Q') + raw_x = N.norm([(q,1)]) if stage == 0 else completed(stage-1) + raw_y = () if stage == 0 else N.norm(list(raw_x)+[(q,-1)]) + entry_x, entry_y = N.norm(list(spectator)+[(q,1)]), spectator + out0 = N.norm(list(spectator)+[(axis,1) for axis in axes[:9]]) + exit_x, exit_y = out0, N.norm(list(out0)+[(q,-1)]) + out_x, out_y = completed(stage), N.norm(list(completed(stage))+[(q,-1)]) + maps = [N.contact(a,b,route,dimension) for a,b in [(raw_x,entry_x),(raw_y,entry_y),(exit_x,out_x),(exit_y,out_y)]] + delta = N.norm([(axis,1) for axis in axes[:9]]+[(q,-1)]) if stage == 0 else N.norm((axis,1) for axis in axes[9+8*(stage-1):9+8*stage]) + for incoming,outgoing in [(raw_x,out_x),(raw_y,out_y)]: + need(N.polynomial(N.norm(list(outgoing)+[(a,-c) for a,c in incoming]),dimension) == N.polynomial(delta,dimension), 'Actual diagonal D_s') + cross = N.norm(list(out_y)+[(a,-c) for a,c in raw_x]) + need(N.polynomial(cross,dimension) == N.polynomial(N.norm(list(delta)+[(q,-1)]),dimension), 'Actual cross term D_s Q^-1') + need(sum(route[i] != axes[i] for i in range(dimension)) <= 17 and all(m['translation'].bit_count() <= 17 and m['inverse_translation'].bit_count() <= 17 for m in maps), 'Fixed seventeen-axis route allowance') + contacts.append([stage,q,maps]) + for q in local['ports']: + # Multiply the Gaussian pair twice with exact real and imaginary parts. + a,b = (Q(1,2),Q(1,2)), (Q(1,2),Q(-1,2)) + mul = lambda z,w: (z[0]*w[0]-z[1]*w[1],z[0]*w[1]+z[1]*w[0]) + plus = lambda z,w: (z[0]+w[0],z[1]+w[1]) + diagonal,off = plus(mul(a,a),mul(b,b)), plus(mul(a,b),mul(b,a)) + need(diagonal == (0,0) and off == (1,0), 'Q^2 is translation with phase +1') + for address in range(512): + need({address:diagonal,address^q:off}[address^q] == (1,0), 'Every central square column') + squares += 1 + for term in word['diagonal']: + qp,selected = term[0],term[1:] + physical = N.norm([(q,qp)]+[(axis,1) for s,yes in enumerate(selected) if yes for axis in (axes[:9] if s == 0 else axes[9+8*(s-1):9+8*s])]+[(q,-1)]*selected[0]) + positive = list(axes[:9]) if selected[0] else [q] + positive += [axis for s in range(1,len(selected)) if selected[s] for axis in axes[9+8*(s-1):9+8*s]] + need(N.polynomial(physical,dimension) == N.polynomial(N.norm([(x,1) for x in positive]+[(q,2)]*(qp == -1)),dimension), 'Full main output phase and rank') + target_profile[len(positive)] += 1 + for e in word['events']: + if e[0] not in ('IDLE', 'IDLE_ONE'): + continue + stages = e[3] if e[0] == 'IDLE' else e[2] + need(len(stages) == len(set(stages)), 'Whole idle has no repeated stage') + for q in local['ports']: + positive, physical = [], [] + for stage in stages: + if stage == 0: + positive += recipes[q]['idle_children'][0]['orthogonal_axes'][:8] + physical += [(x,1) for x in axes[:9]]+[(q,-1)] + else: + block = axes[9+8*(stage-1):9+8*stage] + positive += block + physical += [(x,1) for x in block] + need(len(positive) == 8*len(stages), 'All idle Gaussian axes') + need(all((a&b).bit_count()%2 == int(i==j) for i,a in enumerate(positive) for j,b in enumerate(positive)), 'Independent orthonormal idle axes') + N.contact(N.norm(physical),N.norm((x,1) for x in positive),axes,dimension) + idle_jobs[len(positive)] += 2 if e[0] == 'IDLE' else 1 + return {'ports':104,'full_calls':len(contacts)//104,'physical_contacts':4*len(contacts),'central_square_columns':squares, + 'main_targets':dict(target_profile),'whole_idle_jobs':dict(idle_jobs),'route_payload_sha256':sha256(json.dumps(contacts,separators=(',',':')).encode()).hexdigest(), + 'central_translations':sum(e[0] == 'Q_POWER' for e in word['events']), + 'ordinary_normalizations':sum(e[0] == 'LAMBDA' for e in word['events']),'new_paid_jobs':0,'tensor_rule':'Factorwise native maps; scalar signs stay outside the tensor power.'} diff --git a/research/mixed-projector-query-root/pricing.py b/research/mixed-projector-query-root/pricing.py new file mode 100644 index 0000000000..a235780498 --- /dev/null +++ b/research/mixed-projector-query-root/pricing.py @@ -0,0 +1,167 @@ +"""Check the complete mixed-projector-root invoice and outer transfer. + +The interval and compiler bounds are by zxv and Cao Yifan. The productive +recursion is by Jacob Alan Sussman. The source price adapter is by Ali Romman. +The source lifts and tree invoice are by Ali Romman, with OpenAI Codex +assistance. This file counts the new root, individual idles and ordinary normalization. +The original sources retain their credit. Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +from controller import formula_invoice, need + +KAPPA = Q('0.00327980') +TESTED = Q('0.003279805') +PREVIOUS = Q('0.00315057') + + +def encode(value): + if isinstance(value, Q): + return str(value) + if isinstance(value, dict): + return {str(k): encode(v) for k, v in value.items()} + if isinstance(value, (tuple, list)): + return [encode(v) for v in value] + return value + + +def assemble(local, native, word, physical): + paid, targets = Counter(), Counter() + counts = Counter(e[0] for e in word['events']) + need(local['helpers'] == native['helpers'], 'All source helper targets have native maps') + idle = Counter() + for event in word['events']: + if event[0] == 'LOCAL': + paid.update(local['paid']) + targets.update(local['helpers']) + elif event[0] == 'QUERY': + paid[1] += 104 + elif event[0] in ('IDLE', 'IDLE_ONE'): + rank = 8*len(event[3] if event[0] == 'IDLE' else event[2]) + count = 208 if event[0] == 'IDLE' else 104 + paid[rank] += count + idle[rank] += count + main = Counter() + for term in word['diagonal']: + main[1+8*sum(term[1:])] += 104 + targets.update(main) + need(main == physical['main_targets'], 'All main target phases and ranks') + need(idle == physical['whole_idle_jobs'], 'All paired and individual whole idle jobs') + need((targets, paid) == formula_invoice(local), 'Independent tree and emitted-event counts') + need((counts['LOCAL'], counts['QUERY'], counts['IDLE']) == (18, 17, 14) and counts['IDLE_ONE'] == 3 and counts['LAMBDA'] == 20, 'Complete caller census') + need((sum(targets.values()), sum(paid.values())) == (13652, 67092), 'All independent fields and paid calls') + need(sum(r*n for r, n in targets.items())-sum(r*n for r, n in paid.items()) == 760, 'Complete rank-mass surplus') + need((max(targets), max(paid)) == (145, 64), 'Maximum target and paid ranks') + return targets, paid, counts + + +def run(local, native, word, physical, L): + T, P, counts = assemble(local, native, word, physical) + E = L.load(L.ROOT/'research/higher-moment-strictification/verify.py', 'balanced_intervals') + other = L.load(L.ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py', 'balanced_second_intervals') + def margin(k): + a, b = E.moment(T, 1-k), E.moment(P, 1-k) + return a[0]-b[1], a[1]-b[0] + low, high, grid = 0, 10**12, 10**14 + while high-low > 1: + middle = (low+high)//2 + if margin(Q(middle, grid))[0] > 0: + low = middle + else: + high = middle + lower, upper = Q(low, grid), Q(high, grid) + signed = Counter(T) + signed.subtract(P) + cap, derivative_upper = Q('.0034'), Q(0) + for rank, count in signed.items(): + logarithm = E.log_bounds(rank) + a = E.mul(E.power(rank, 1-cap), logarithm)[0] + b = rank*logarithm[1] + derivative_upper -= count*(a if count >= 0 else b) + need(derivative_upper < 0, 'Unique raw crossing below the BIT cap') + need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure') + need(PREVIOUS < KAPPA < TESTED < lower, 'The mixed root improves the published PR6353 claim') + t, offset, power, cutoff, floor = 1-TESTED, Q(1, 7), 1024, 12, 13 + target, paid = E.moment(T, t), E.moment(P, t) + tl, th = other.moment(T, TESTED) + pl, ph = other.moment(P, TESTED) + need(tl > ph and max(tl, target[0]) <= min(th, target[1]) + and max(pl, paid[0]) <= min(ph, paid[1]), 'Two independent rational moment engines') + alpha = E.divide(paid, target) + gamma = E.divide(E.moment(P, t+offset), E.mul(E.power(cutoff, offset), target)) + delta = E.divide((Q(sum(T.values())*floor),)*2, E.mul(E.power(cutoff, TESTED), target)) + reserve, decay = Q(1, 10**12), Q(31, 32) + need(alpha[1] < 1-reserve and gamma[1] < decay and delta[1] < decay, 'All charged tail ratios') + need(decay**128 < Q(1, 16), 'Both tail decay blocks') + normalized = 1/(1+power*reserve)+Q(4, 2**32) + need(normalized < 1 and cutoff**64 < floor**63, 'Completion, splitting and rounding') + theta, logarithm_power = Q(63, 64), 1100 + # Keep each exponential inside the retained engine's proved domain. + half = E.power(145, Q(power, 2)*TESTED) + factor = E.mul(half, half) + eta = E.scale(E.divide((Q(1), Q(1)), factor), t) + need(2*(cutoff**power)**64 <= (145**power)**63 + and eta[0] > theta**logarithm_power, 'Shifted exits and complement capacity') + need(factor[1] < 2**logarithm_power, 'Compiler initial range') + gap = (TESTED-KAPPA)/7 + need(gap.numerator == 1, 'Exact compiler integer grid') + step = gap.denominator + def wins(j): + return (step*j+1)**logarithm_power < 2**j + left, right = 1, 2 + while not wins(right): + left, right = right, 2*right + while right-left > 1: + middle = (left+right)//2 + if wins(middle): + right = middle + else: + left = middle + H = step*right + need(H > 8*power and wins(right) and not wins(right-1), 'Uniform threshold and adjacent-grid rejection') + local_routes = (sum(local['paid'].values())+native['helper_normalizers'] + +native['main_adapters']+4*104+4*local['owned_lifetimes'])*1000 + need(local['real_scalar_allowance']+local_routes < 10**7, 'Every local ordinary operation is funded') + raw = 18*10**7 + 17*1664 + 32*34*104*len(word['events']) + 34*104*(26+1000) + need(all(abs(Q(e[-1])) <= 16 for e in word['events'] if e[0] in ('ADD', 'SCALE')), + 'Every emitted scalar coefficient has the declared growth bound') + need(raw < 10**9, 'Complete ordinary-work budget') + bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + atom = Q(bit['atom']) + ordinary = (1-atom)*Q(bit['after_cover']) + atom*Q('.0000384599') + admitted = Q(bit['admitted']) + need(atom > ordinary > admitted > TESTED and atom < 1-ordinary, 'Retained BIT admission and stock') + outer_module = L.load(L.ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'balanced_outer') + params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA+6*gap, + 'b': KAPPA+5*gap, 'a': KAPPA+4*gap, 'q': KAPPA+3*gap, 'bit_saving': admitted, + 'epsilon': 1-gap, 'beta': 1-3*gap, 'r0': gap/10, 'stop': gap, 'layout': gap, 'd': gap} + outer = outer_module.ledger(params) + outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta']*(1-atom) + need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Full outer predicate inventory') + need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict') + old_completion = E.divide((Q(sum(T.values())*17),)*2, E.mul(E.power(16, TESTED), target)) + need(old_completion[0] > 1, 'The old completion cutoff does not fund the new inventory') + bad = outer_module.ledger(dict(params, bit_saving=Q('.0027'))) + need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT saving rejected') + return encode({'kappa': KAPPA, 'kappa_decimal': '0.00327980', 'previous_pr6353': PREVIOUS, + 'gain': KAPPA-PREVIOUS, 'relative_gain_percent': 100*(KAPPA/PREVIOUS-1), + 'raw_root_interval': [lower, upper], 'raw_headroom': [lower-KAPPA, upper-KAPPA], + 'derivative_upper': derivative_upper, 'margin_at_previous': E.display(margin(PREVIOUS)), + 'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), + 'rank_mass_surplus': 760, 'full_forward_calls': 18, 'thin_queries': 17, + 'whole_idle_jobs': 3224, 'strictification': { + 'tested': TESTED, 'power': power, 'cutoff': cutoff, 'floor': floor, + 'tail_offset': offset, 'reserve': reserve, 'tail_decay': decay, 'tail_block': 128, + 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), + 'normalized_paid_upper': normalized}, + 'compiler': {'theta': theta, 'logarithm_power': logarithm_power, 'eta': E.display(eta), + 'gap': gap, 'H': H, 'N': '2^'+str(H), 'integer_test_exponent': right, + 'uniform_saving': params['complex_uniform_saving'], 'word_materialized': False}, + 'nonrecursive': {'local_scalar': local['real_scalar_allowance'], 'local_routes': local_routes, + 'raw_scalar_upper': raw, 'raw_budget': 10**9, + 'peak_owned_fields': local['peak_owned_fields'], + 'scalar_growth_bound': 'At most 2^(10^9 + R*f), where R is the full paid rank mass.', + 'paid_rank_mass': sum(r*n for r, n in P.items())}, + 'ordinary_BIT': bit, 'outer': outer, + 'negative_controls': {'old_completion': 'Cutoff16 and floor17 give a ratio above one.', + 'old_BIT': 'An outer inequality fails at BIT saving0.0027.'}}) diff --git a/research/mixed-projector-query-root/verify.py b/research/mixed-projector-query-root/verify.py new file mode 100644 index 0000000000..a1cc67d955 --- /dev/null +++ b/research/mixed-projector-query-root/verify.py @@ -0,0 +1,100 @@ +"""Replay the exact source, mixed root, physical caller and complete bound. + +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +Predecessor authors and proof engines retain their credit in NOTICE. +""" +from hashlib import sha1, sha256 +from pathlib import Path +import gzip +import importlib.util +import json +import sys + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +LIFT = ROOT/'research/p104-native-input-lifting' +TREE = ROOT/'research/balanced-query-tree' +STATUS = 'PASS_MIXED_PROJECTOR_QUERY_ROOT_KAPPA_00327980' + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def read(path): + return json.loads(Path(path).read_bytes()) + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def authenticate(): + pins = [p for p in read(HERE/'SOURCES.json')['files'] if p['usage'] == 'input'] + for pin in pins: + raw = (ROOT/pin['path']).read_bytes() + need(sha256(raw).hexdigest() == pin['sha256'], 'Source SHA256: '+pin['path']) + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == pin['git_blob'], + 'Source Git blob: '+pin['path']) + need(len(pins) == 17, 'Complete live source inventory') + return len(pins) + + +def run(): + sources = authenticate() + load(HERE/'algebra.py', 'algebra') + controller = load(HERE/'controller.py', 'controller') + module = load(HERE/'module_check.py', 'mixed_root_module') + physical = load(HERE/'physical.py', 'mixed_root_physical') + price = load(HERE/'pricing.py', 'mixed_root_price') + support = load(LIFT/'support.py', 'support') + constructor = load(LIFT/'construct.py', 'mixed_source_constructor') + lift_checks = load(LIFT/'verify.py', 'mixed_source_checks') + binary = load(TREE/'module_check.py', 'mixed_binary_module') + source = json.loads(gzip.decompress(support.inputs()[support.WORD])) + local_word = constructor.construct(source) + need(constructor.payload(local_word) == gzip.decompress((LIFT/'WORD.json.gz').read_bytes()), + 'Every unchanged lifted source byte') + word = controller.construct() + need(word == read(HERE/'CONTROLLER.json'), 'Every emitted caller event') + root_check, binary_check = module.run(), binary.run() + caller = controller.replay(word) + controls = controller.controls(word) + print('PASS exact root, ordinary normalization, binary children, full caller and controls', flush=True) + with support.checkers() as (L, root): + directions = lift_checks.preparation(L, source, local_word) + local = L.replay(local_word) + need(price.encode(local) == read(LIFT/'RESULT.json')['local'], 'Complete unchanged local receipt') + controls.update(lift_checks.word_controls(L, local_word)) + columns = L.reverse_columns(local_word) + need(columns['columns'] == 799 and columns['coefficients'] == 638401, 'Every arbitrary source input') + print('PASS source arbitrary inputs, preparation, ownership and dense transpose', flush=True) + native = L.native(local_word) + maps = physical.physical(word, local_word, L) + need(maps['full_calls'] == 18 and maps['physical_contacts'] == 7488, 'Every native contact') + print('PASS native absolute phases, whole idles and physical caller', flush=True) + result_price = price.run(local, native, word, maps, L) + print('PASS complete invoice, both rational price engines, compiler and outer predicates', flush=True) + return price.encode({'status':STATUS, 'source_inputs':sources, 'root':root_check, + 'binary_module':binary_check, 'caller':caller, + 'local':local, 'lifted_directions':directions, 'columns':columns, + 'native':native, 'physical':maps, 'price':result_price, + 'negative_controls':controls, + 'assumptions':['native_all_columns','owned_erasure','compiler', + 'precision_tape','analytic_recovery'], + 'selected_frontier_changed':False}) + + +if __name__ == '__main__': + result = run() + if sys.argv[1:] == ['--write-result']: + (HERE/'RESULT.json').write_text(json.dumps(result,sort_keys=True,indent=2)+'\n') + else: + need(not sys.argv[1:], 'Only --write-result is supported') + need(result == read(HERE/'RESULT.json'), 'Exact retained scientific receipt') + print(STATUS, flush=True) From 26e40e6b9b736ecfd6f37cb03cc825339b08b684 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 1 Nov 2026 22:54:37 -0600 Subject: [PATCH 02/32] Record local sealed verification for mixed projector root --- .../mixed-projector-query-root/VALIDATION.md | 24 +++++++++++++++---- 1 file changed, 20 insertions(+), 4 deletions(-) diff --git a/research/mixed-projector-query-root/VALIDATION.md b/research/mixed-projector-query-root/VALIDATION.md index 8cca54fb24..b86b5f39ab 100644 --- a/research/mixed-projector-query-root/VALIDATION.md +++ b/research/mixed-projector-query-root/VALIDATION.md @@ -22,7 +22,23 @@ checks passed. The selected record retains SHA256 `9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa`. The user instructed that this result stay local until they authorize a PR. -No branch push, PR or hosted CI is planned under that instruction. Local -committed-input checks and a sealed export will be recorded after they run. -Full source-history preflight needs the missing ancestry in this shallow -checkout. Independent scientific review remains open. +No branch push, PR or hosted CI is planned under that instruction. + +Local science commit: `1d49e6c75e608dd29c4fb2794463c8dc36df037f`. +The committed-byte check passed for all 33 package and declared-input files, +including owner-execute bits. The official export and all 17 declared-input +coverage checks passed. Export SHA256: +`f7d2893c8d93e8e55484383169ed798c4562b833fb4c5e87e7b59576e5a3101c`. + +The optimized verifier passed from that Git-free export with empty PATH and +all files and directories read-only. All 34 file hashes and modes were +unchanged after replay. Corrupting the source word was rejected at its SHA256 +guard. Changing the root basis and regenerating the matching literal caller +was rejected at the exact inverse-basis check. All original export bytes and +modes were restored and compared with the initial snapshot. + +The source-history preflight stopped with `source-history check requires +full Git history`. No missing ancestry was fetched. All declared source pins +use the canonical base, which is an ancestor of the local science commit. +This limitation does not affect the successful sealed export replay. +Independent scientific review remains open. From 52e87e4971a85a8f098fadb967dc75bee9f76c65 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Mon, 2 Nov 2026 00:05:53 -0600 Subject: [PATCH 03/32] Improve mixed projector root to conditional kappa .00328467 --- .../CONTROLLER.json | 1143 ++++++++++------- research/mixed-projector-query-root/PROOF.md | 102 +- research/mixed-projector-query-root/README.md | 19 +- .../mixed-projector-query-root/RESULT.json | 192 +-- research/mixed-projector-query-root/ROOT.json | 492 +++---- research/mixed-projector-query-root/SEARCH.md | 64 + research/mixed-projector-query-root/TASK.json | 4 +- .../mixed-projector-query-root/VALIDATION.md | 45 + .../mixed-projector-query-root/ceiling.py | 66 + .../mixed-projector-query-root/controller.py | 17 +- .../module_check.py | 2 +- .../mixed-projector-query-root/pricing.py | 17 +- research/mixed-projector-query-root/verify.py | 15 +- 13 files changed, 1293 insertions(+), 885 deletions(-) create mode 100644 research/mixed-projector-query-root/SEARCH.md create mode 100644 research/mixed-projector-query-root/ceiling.py diff --git a/research/mixed-projector-query-root/CONTROLLER.json b/research/mixed-projector-query-root/CONTROLLER.json index d75ebe8b9c..4f7d7a2f13 100644 --- a/research/mixed-projector-query-root/CONTROLLER.json +++ b/research/mixed-projector-query-root/CONTROLLER.json @@ -23,28 +23,6 @@ 1, 1 ], - [ - -1, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 1, - 1, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0 - ], [ -1, 0, @@ -101,7 +79,7 @@ 0, 0, 0, - 1, + 0, 0, 0, 0, @@ -124,6 +102,28 @@ 0, 0, 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 0, 0, 0, 0, @@ -453,15 +453,15 @@ 0, 0, 0, - 0, - 1, 1, 1, - 1, - 1, - 1, - 1, - 1 + 0, + 0, + 0, + 0, + 0, + 0, + 0 ], [ 1, @@ -475,18 +475,19 @@ 0, 0, 0, - 0, - 1, - 1, - 1, 1, 1, - 1, - 1, - 1 + 0, + 0, + 0, + 0, + 0, + 0, + 0 ], [ - 1, + -1, + 0, 0, 0, 0, @@ -502,13 +503,13 @@ 1, 1, 1, - 0, - 0, - 0, - 0 + 1, + 1, + 1 ], [ - -1, + 1, + 0, 0, 0, 0, @@ -524,13 +525,13 @@ 1, 1, 1, - 0, - 0, - 0, - 0 + 1, + 1, + 1 ], [ - -1, + 1, + 0, 0, 0, 0, @@ -544,15 +545,15 @@ 0, 1, 1, - 0, - 0, + 1, 0, 0, 0, 0 ], [ - 1, + -1, + 0, 0, 0, 0, @@ -566,8 +567,7 @@ 0, 1, 1, - 0, - 0, + 1, 0, 0, 0, @@ -751,61 +751,84 @@ ] ], "events": [ + [ + "ADD", + 4, + 5, + "-3" + ], [ "ADD", 3, 5, - "-2" + "1" ], [ "ADD", - 0, + 2, + 5, + "-3" + ], + [ + "ADD", + 1, 5, "1" ], [ "ADD", + 0, 5, + "2" + ], + [ + "ADD", + 2, + 4, + "-2" + ], + [ + "ADD", + 0, 4, "1" ], [ - "SCALE", + "SWAP", 4, - "-1" + 5 ], [ "ADD", 5, 3, - "1" + "2" ], [ "ADD", - 4, + 2, 3, - "-1" + "-2" ], [ "ADD", 0, 3, - "1/2" + "1" ], [ "SCALE", 3, - "1/2" + "-1" ], [ - "ADD", + "SWAP", 3, - 2, - "-1/2" + 4 ], [ "ADD", - 1, + 5, 2, "1" ], @@ -813,8 +836,19 @@ "ADD", 0, 2, + "1/2" + ], + [ + "SCALE", + 2, "-1/2" ], + [ + "ADD", + 4, + 1, + "-1" + ], [ "ADD", 3, @@ -825,19 +859,31 @@ "ADD", 2, 1, - "-2" + "-1/2" + ], + [ + "ADD", + 0, + 1, + "-1/2" + ], + [ + "ADD", + 4, + 0, + "2" ], [ "ADD", 3, 0, - "-1" + "-2" ], [ "ADD", 2, 0, - "2" + "1" ], [ "ADD", @@ -884,7 +930,7 @@ "ADD", 0, 3, - "-2" + "-3" ], [ "ADD", @@ -896,19 +942,25 @@ "ADD", 0, 2, - "-1" + "-2" + ], + [ + "ADD", + 4, + 1, + "2" ], [ "ADD", 3, 1, - "-1" + "-2" ], [ "ADD", 2, 1, - "2" + "1" ], [ "SCALE", @@ -1663,17 +1715,23 @@ 1, -1 ], + [ + "ADD", + 4, + 5, + "-2" + ], [ "ADD", 3, 5, - "1" + "2" ], [ "ADD", 2, 5, - "-2" + "-1" ], [ "ADD", @@ -1691,49 +1749,77 @@ "ADD", 3, 4, - "1" + "1/2" ], [ "ADD", 2, 4, - "-2" + "-1/2" ], [ "ADD", 1, 4, - "1" + "1/2" ], [ "ADD", 0, 4, - "2" + "3/2" + ], + [ + "SCALE", + 4, + "1/2" ], [ "ADD", - 2, + 4, 3, "3" ], [ "ADD", - 1, + 2, 3, "-1" ], + [ + "ADD", + 1, + 3, + "1" + ], [ "ADD", 0, 3, - "-1" + "5" ], [ "SCALE", 3, + "-2" + ], + [ + "SWAP", + 3, + 4 + ], + [ + "ADD", + 4, + 2, "-1" ], + [ + "ADD", + 3, + 2, + "1" + ], [ "ADD", 1, @@ -1744,29 +1830,30 @@ "ADD", 0, 2, - "1" + "2" ], [ "SCALE", 2, "1/2" ], - [ - "SWAP", - 2, - 3 - ], [ "ADD", - 3, + 4, 1, - "-1" + "2" + ], + [ + "ADD", + 3, + 1, + "-2" ], [ "ADD", 2, 1, - "2" + "1" ], [ "SCALE", @@ -1775,13 +1862,13 @@ ], [ "ADD", - 3, + 2, 5, "1" ], [ "ADD", - 3, + 2, 4, "1" ], @@ -1795,7 +1882,7 @@ "ADD", 1, 3, - "-2" + "-1" ], [ "ADD", @@ -1805,20 +1892,21 @@ ], [ "ADD", - 1, + 4, 2, - "1" + "2" ], [ "ADD", - 0, + 3, 2, - "-1" + "-2" ], [ - "SWAP", + "ADD", + 0, 2, - 3 + "-1" ], [ "SWAP", @@ -1990,10 +2078,16 @@ ], [ "ADD", - 3, + 4, 5, "-2" ], + [ + "ADD", + 3, + 5, + "2" + ], [ "ADD", 2, @@ -2010,42 +2104,76 @@ "ADD", 3, 4, - "-2" + "3/4" ], [ "ADD", 2, 4, - "-1" + "-1/2" ], [ "ADD", 1, 4, - "1" + "1/4" + ], + [ + "ADD", + 0, + 4, + "1/4" + ], + [ + "SCALE", + 4, + "1/4" + ], + [ + "ADD", + 4, + 3, + "-3" ], [ "ADD", 2, 3, - "-1/2" + "2" ], [ "ADD", 1, 3, - "1/2" + "1" + ], + [ + "ADD", + 0, + 3, + "-3" ], [ "SCALE", 3, - "1/2" + "4" + ], + [ + "SWAP", + 3, + 4 + ], + [ + "ADD", + 4, + 2, + "-2" ], [ "ADD", 3, 2, - "1" + "2" ], [ "ADD", @@ -2062,7 +2190,7 @@ [ "SCALE", 2, - "-2" + "-1" ], [ "SWAP", @@ -2259,64 +2387,33 @@ 0, 3 ], - [ - "ADD", - 3, - 5, - "1" - ], - [ - "ADD", - 2, - 5, - "-2" - ], - [ - "ADD", - 1, - 5, - "2" - ], [ "ADD", 0, 5, - "-2" - ], - [ - "ADD", - 2, - 3, - "2" + "-1" ], [ "ADD", 0, 3, - "-1" + "1" ], [ "SWAP", 3, - 5 - ], - [ - "ADD", - 5, - 2, - "-1" + 4 ], [ "ADD", - 1, + 0, 2, - "-1" + "1" ], [ - "ADD", - 0, + "SWAP", 2, - "2" + 3 ], [ "ADD", @@ -2327,19 +2424,7 @@ [ "SWAP", 1, - 4 - ], - [ - "ADD", - 5, - 0, - "1" - ], - [ - "ADD", - 4, - 0, - "2" + 2 ], [ "SWAP", @@ -2352,34 +2437,10 @@ -1 ], [ - "SWAP", - 0, - 1 - ], - [ - "LOCAL", - 10, - 0, - 1 - ], - [ - "SWAP", + "QUERY", 0, - 1 - ], - [ - "IDLE_ONE", - 2, - [ - 10 - ] - ], - [ - "IDLE_ONE", - 3, - [ - 10 - ] + 1, + -1 ], [ "LAMBDA", @@ -2392,23 +2453,11 @@ 1, -1 ], - [ - "ADD", - 4, - 5, - "-2" - ], [ "ADD", 1, 5, - "-1" - ], - [ - "ADD", - 2, - 4, - "-1" + "1" ], [ "ADD", @@ -2416,60 +2465,32 @@ 4, "-1" ], - [ - "SWAP", - 4, - 5 - ], [ "ADD", 1, 3, - "1" + "-1" ], [ "SWAP", 3, - 5 + 4 ], [ "ADD", 1, 2, - "-1/2" - ], - [ - "SCALE", - 2, - "1/2" - ], - [ - "SWAP", - 2, - 3 - ], - [ - "ADD", - 4, - 1, - "2" - ], - [ - "ADD", - 3, - 1, "-1" ], [ - "ADD", + "SWAP", 2, - 1, - "2" + 4 ], [ - "SCALE", + "SWAP", 1, - "-2" + 4 ], [ "SWAP", @@ -2478,7 +2499,7 @@ ], [ "ADD", - 0, + 2, 4, "1" ], @@ -2487,11 +2508,17 @@ 4, 5 ], + [ + "ADD", + 2, + 3, + "3/2" + ], [ "ADD", 0, 3, - "1" + "-1/2" ], [ "SWAP", @@ -2500,14 +2527,27 @@ ], [ "ADD", - 0, + 5, 2, - "1" + "2" ], [ - "SWAP", + "ADD", + 4, 2, - 3 + "-2" + ], + [ + "ADD", + 1, + 2, + "-2" + ], + [ + "ADD", + 0, + 2, + "3" ], [ "ADD", @@ -2518,7 +2558,25 @@ [ "SWAP", 1, - 2 + 3 + ], + [ + "ADD", + 5, + 0, + "-2" + ], + [ + "ADD", + 4, + 0, + "2" + ], + [ + "ADD", + 3, + 0, + "2" ], [ "SWAP", @@ -2531,123 +2589,225 @@ -1 ], [ - "QUERY", + "SWAP", 0, + 21 + ], + [ + "SWAP", 1, - -1 + 20 ], [ - "LAMBDA", + "SWAP", + 20, + 21 + ], + [ + "ADD", 0, + 20, 1 ], [ "ADD", - 0, + 21, 1, -1 ], + [ + "QUERY", + 20, + 21, + -1 + ], [ "ADD", + 21, 1, - 5, - "-1" + 1 ], [ "ADD", + 0, + 20, + -1 + ], + [ + "IDLE", + 20, + 21, + [ + 10, + 11 + ] + ], + [ + "SCALE", 1, - 4, - "-1" + -1 + ], + [ + "Q_POWER", + 1, + -2 ], [ "SWAP", - 4, - 5 + 1, + 0 ], [ - "ADD", + "LOCAL", + 10, 1, - 3, - "-1" + 0 ], [ "SWAP", - 3, - 5 + 1, + 0 ], [ - "ADD", + "Q_POWER", 1, - 2, - "-1" + 2 ], [ - "SWAP", - 2, - 5 + "SCALE", + 1, + -1 ], [ "SWAP", - 1, - 5 + 0, + 1 + ], + [ + "LOCAL", + 11, + 0, + 1 ], [ "SWAP", 0, - 5 + 1 ], [ "ADD", - 2, - 5, - "2" + 0, + 20, + 1 + ], + [ + "SCALE", + 20, + -1 ], [ "ADD", + 20, 0, - 5, - "-1" + 1 + ], + [ + "SWAP", + 1, + 21 + ], + [ + "SCALE", + 21, + -1 ], [ "ADD", + 21, + 1, + 1 + ], + [ + "IDLE_ONE", 2, - 4, - "2" + [ + 10, + 11 + ] + ], + [ + "LAMBDA", + 0, + 1 ], [ "ADD", 0, + 1, + -1 + ], + [ + "ADD", 4, - "-1" + 5, + "1" ], [ "ADD", - 2, 3, - "2" + 5, + "1" + ], + [ + "ADD", + 1, + 5, + "1/2" + ], + [ + "SCALE", + 5, + "-1/2" + ], + [ + "ADD", + 5, + 4, + "1/2" ], [ "ADD", - 0, 3, + 4, "-1" ], [ "ADD", - 5, 2, + 4, "-1" ], [ "ADD", + 1, 4, - 2, - "1" + "-3/2" ], [ "ADD", + 4, 3, + "1" + ], + [ + "ADD", 2, + 3, + "1/2" + ], + [ + "SCALE", + 3, "-1" ], [ @@ -2658,116 +2818,144 @@ ], [ "ADD", - 0, - 2, + 5, + 1, "2" ], [ "ADD", - 0, + 4, 1, - "1" + "2" ], [ - "SWAP", + "ADD", + 3, 1, - 2 + "-2" ], [ "ADD", - 3, + 2, + 1, + "1" + ], + [ + "SCALE", + 1, + "-2" + ], + [ + "SWAP", 0, + 5 + ], + [ + "ADD", + 2, + 5, "1" ], [ "ADD", 2, - 0, - "2" + 4, + "1" ], [ - "SWAP", - 0, - 1 + "ADD", + 2, + 3, + "3/2" ], [ - "LAMBDA", + "ADD", 0, - -1 + 3, + "-1/2" ], [ - "SWAP", - 0, - 21 + "ADD", + 5, + 2, + "-2" ], [ - "SWAP", - 1, - 20 + "ADD", + 4, + 2, + "2" ], [ - "SWAP", - 20, - 21 + "ADD", + 3, + 2, + "-2" + ], + [ + "ADD", + 1, + 2, + "-2" ], [ "ADD", 0, - 20, - 1 + 2, + "3" + ], + [ + "SCALE", + 2, + "2" ], [ "ADD", - 21, + 0, 1, - -1 + "1" ], [ - "QUERY", - 20, - 21, - -1 + "SWAP", + 1, + 2 ], [ "ADD", - 21, - 1, - 1 + 4, + 0, + "-2" ], [ "ADD", + 3, 0, - 20, - -1 + "2" ], [ - "IDLE", - 20, - 21, - [ - 11, - 12, - 13, - 14, - 15, - 16, - 17, - 18 - ] + "ADD", + 2, + 0, + "2" ], [ - "SCALE", - 1, + "SWAP", + 0, + 1 + ], + [ + "LAMBDA", + 0, -1 ], [ "SWAP", - 1, + 0, 23 ], [ "SWAP", - 0, + 1, 22 ], [ @@ -2777,31 +2965,31 @@ ], [ "ADD", - 1, + 0, 22, 1 ], [ "ADD", 23, - 0, + 1, -1 ], [ "QUERY", 22, 23, - 1 + -1 ], [ "ADD", 23, - 0, + 1, 1 ], [ "ADD", - 1, + 0, 22, -1 ], @@ -2810,25 +2998,28 @@ 22, 23, [ - 11, 12, 13, - 14 + 14, + 15, + 16, + 17, + 18 ] ], [ "SCALE", - 0, + 1, -1 ], [ "SWAP", - 0, + 1, 25 ], [ "SWAP", - 1, + 0, 24 ], [ @@ -2838,31 +3029,31 @@ ], [ "ADD", - 0, + 1, 24, 1 ], [ "ADD", 25, - 1, + 0, -1 ], [ "QUERY", 24, 25, - -1 + 1 ], [ "ADD", 25, - 1, + 0, 1 ], [ "ADD", - 0, + 1, 24, -1 ], @@ -2871,44 +3062,14 @@ 24, 25, [ - 11, - 12 + 12, + 13, + 14 ] ], [ "SCALE", - 1, - -1 - ], - [ - "Q_POWER", - 1, - -2 - ], - [ - "SWAP", - 1, - 0 - ], - [ - "LOCAL", - 11, - 1, - 0 - ], - [ - "SWAP", - 1, - 0 - ], - [ - "Q_POWER", - 1, - 2 - ], - [ - "SCALE", - 1, + 0, -1 ], [ @@ -2927,39 +3088,6 @@ 0, 1 ], - [ - "ADD", - 0, - 24, - 1 - ], - [ - "SCALE", - 24, - -1 - ], - [ - "ADD", - 24, - 0, - 1 - ], - [ - "SWAP", - 1, - 25 - ], - [ - "SCALE", - 25, - -1 - ], - [ - "ADD", - 25, - 1, - 1 - ], [ "SCALE", 0, @@ -3107,33 +3235,33 @@ [ "ADD", 1, - 22, + 24, 1 ], [ "SCALE", - 22, + 24, -1 ], [ "ADD", - 22, + 24, 1, 1 ], [ "SWAP", 0, - 23 + 25 ], [ "SCALE", - 23, + 25, -1 ], [ "ADD", - 23, + 25, 0, 1 ], @@ -3522,33 +3650,33 @@ [ "ADD", 0, - 20, + 22, 1 ], [ "SCALE", - 20, + 22, -1 ], [ "ADD", - 20, + 22, 0, 1 ], [ "SWAP", 1, - 21 + 23 ], [ "SCALE", - 21, + 23, -1 ], [ "ADD", - 21, + 23, 1, 1 ], @@ -3563,18 +3691,6 @@ 1, -1 ], - [ - "ADD", - 4, - 5, - "2" - ], - [ - "ADD", - 3, - 5, - "-1" - ], [ "ADD", 1, @@ -3596,42 +3712,54 @@ "ADD", 5, 4, - "2" + "-2" ], [ "ADD", - 3, + 1, 4, "1" ], [ "ADD", - 1, + 0, 4, - "-1" + "2" ], [ "ADD", - 0, - 4, + 5, + 3, "-2" ], [ - "SCALE", + "ADD", 4, - "-1" + 3, + "1" ], [ "ADD", 2, 3, - "-3" + "-3/2" ], [ "ADD", 1, 3, - "-1" + "1/2" + ], + [ + "ADD", + 0, + 3, + "2" + ], + [ + "SCALE", + 3, + "1/2" ], [ "ADD", @@ -3643,7 +3771,7 @@ "ADD", 4, 2, - "-1" + "1" ], [ "ADD", @@ -3657,6 +3785,16 @@ 2, "-1" ], + [ + "SCALE", + 2, + "-1" + ], + [ + "SWAP", + 2, + 3 + ], [ "ADD", 5, @@ -3665,20 +3803,19 @@ ], [ "ADD", - 4, + 0, 1, "-2" ], [ - "ADD", - 0, + "SCALE", 1, - "-2" + "-1" ], [ "SWAP", 1, - 3 + 2 ], [ "ADD", @@ -3717,15 +3854,9 @@ ], [ "ADD", - 4, - 5, - "2" - ], - [ - "ADD", - 3, + 2, 5, - "-1" + "1" ], [ "SCALE", @@ -3734,39 +3865,66 @@ ], [ "ADD", - 5, + 3, 4, "1" ], [ "ADD", - 3, + 2, 4, - "1" + "-1/2" + ], + [ + "ADD", + 1, + 4, + "1/2" + ], + [ + "SCALE", + 4, + "-1/2" + ], + [ + "SWAP", + 4, + 5 + ], + [ + "ADD", + 5, + 3, + "1/2" ], [ "ADD", 2, 3, - "2" + "3/2" ], [ "ADD", 1, 3, - "-2" + "-1/2" ], [ - "ADD", - 0, + "SCALE", 3, + "-1" + ], + [ + "ADD", + 5, + 2, "1" ], [ "ADD", 4, 2, - "-1" + "2" ], [ "ADD", @@ -3778,18 +3936,18 @@ "ADD", 0, 2, - "-1" + "-2" ], [ - "SWAP", + "SCALE", 2, - 3 + "2" ], [ "ADD", - 2, + 5, 1, - "1" + "-1" ], [ "ADD", @@ -3797,14 +3955,9 @@ 1, "1" ], - [ - "SCALE", - 1, - "-1" - ], [ "ADD", - 2, + 1, 0, "1" ], @@ -3932,38 +4085,36 @@ 21 ], "stages": [ - 11, - 12, - 13, - 14, - 15, - 16, - 17, - 18 + 10, + 11 ] }, { - "exponent": -1, + "exponent": 1, "roles": [ 22, 23 ], "stages": [ - 11, 12, 13, - 14 + 14, + 15, + 16, + 17, + 18 ] }, { - "exponent": 1, + "exponent": -1, "roles": [ 24, 25 ], "stages": [ - 11, - 12 + 12, + 13, + 14 ] }, { @@ -4014,6 +4165,6 @@ } ], "roles": 34, - "schema": "mixed-projector-query-root/1", + "schema": "mixed-projector-query-root/2", "stages": 18 } diff --git a/research/mixed-projector-query-root/PROOF.md b/research/mixed-projector-query-root/PROOF.md index 27bdfe3e10..510bf9dba0 100644 --- a/research/mixed-projector-query-root/PROOF.md +++ b/research/mixed-projector-query-root/PROOF.md @@ -1,12 +1,12 @@ # A mixed projector root for independent Gaussian outputs This construction changes the caller. It keeps the complete PR6349 native -source. Four binary query suppliers, with 7, 2, 1 and 8 native leaves, enter -a six-field root. The root has three thin queries and three individual +source. Four binary query suppliers, with 7, 2, 2 and 7 native leaves, enter +a six-field root. The root has three thin queries and two individual whole idle jobs. It gives six independent Gaussian outputs. The child suppliers give another 28 independent main outputs. -The conditional claim is kappa 0.00327980. The five inherited framework +The conditional claim is kappa 0.00328467. The five inherited framework assumptions remain. This is not an unconditional multiplication theorem, a materialized uniform word or an independent scientific review. @@ -64,15 +64,15 @@ Each R_i is square-zero and has rank one. Direct exact multiplication gives ``` `ROOT.json` specifies an invertible rational basis F, four stage projectors -P_i, and their native two-field bases C_i. Full sites are 0, 1, 4 and 6. -Sites 2, 3 and 5 are thin. In F coordinates the four projector masks are +P_i, and their native two-field bases C_i. Full sites are 0, 1, 5 and 6. +Sites 2, 3 and 4 are thin. In F coordinates the four projector masks are | Site | Output coordinates in the stage | Rank | Native leaves | Extra whole idles | | --- | --- | ---: | ---: | --- | -| 0 | 0,2 | 2 | 7 | none | -| 1 | 0,1,2 | 3 | 2 | one H16 | -| 4 | 0,3,4,5 | 4 | 1 | two H8 | -| 6 | 0,3 | 2 | 8 | none | +| 0 | 0,1 | 2 | 7 | none | +| 1 | 0,1,5 | 3 | 2 | one H16 | +| 5 | 0,2,4 | 3 | 2 | one H16 | +| 6 | 0,2 | 2 | 7 | none | The exact checker verifies P_i^2=P_i, P_i R_i=R_i P_i=R_i and pairwise commutation of the four P_i. It also verifies that P_i commutes with the @@ -91,10 +91,10 @@ Apply F at entry and F^-1 at exit. Apply lambda^-1 to all six root outputs. Their independent stage supports are ```text -ABCD, B, AB, CD, C, C. +ABCD, AB, CD, empty, C, B. ``` -For child sizes 7,2,1,8, the six Gaussian ranks are 145,17,73,73,9,9. +For child sizes 7,2,2,7, the six Gaussian ranks are 145,73,73,1,17,17. No root input is owned or initialized. The scalar basis maps are invertible. ## 3. Binary children and full endpoint @@ -105,10 +105,10 @@ It returns another query supplier and two independent Gaussian outputs. Its separate Laurent checker is replayed here under its source hash. The four child trees have 18 native leaves and 14 binary nodes. Their node -size counts are {2:8,3:1,4:3,7:1,8:1}. The root adds three thin queries. +size counts are {2:8,3:2,4:2,7:2}. The root adds three thin queries. The complete caller has 34 main fields per port, 18 distinct native stages, -17 thin queries, 14 paired whole idles and three individual whole idles. -Its 543 literal instructions include all basis maps and 20 normalizations. +17 thin queries, 14 paired whole idles and two individual whole idles. +Its 570 literal instructions include all basis maps and 20 normalizations. The full replay uses exact coefficients in Q(i)[Q,D_1,...,D_18]/(Q^4-1). It checks all 1,156 input/output entries. Stage variables remain distinct. @@ -129,16 +129,16 @@ receives its complete arbitrary-input, dense-transpose and native replay. ## 4. Complete price and outer transfer -The complete invoice has 67,092 paid jobs and 13,652 productive jobs. -Paid rank mass is 188,668; productive rank mass is 189,428. The surplus is -760. The maximum target rank is 145 and maximum paid rank is 64. The +The complete invoice has 66,988 paid jobs and 13,652 productive jobs. +Paid rank mass is 185,340; productive rank mass is 186,100. The surplus is +760. The maximum target rank is 145 and maximum paid rank is 56. The emitted-event count agrees with a separate fixed-tree and root count. -The strict raw crossing is in (0.00327981076011,0.00327981076012), between +The strict raw crossing is in (0.00328468791927,0.00328468791928), between adjacent points on the 10^-14 grid. `RESULT.json` records both rational moment engines, completion, compiler and outer ledger. The claim is -0.00327980; the tested -saving is 0.003279805. The completion uses power 1024, cutoff 12, floor 13, +0.00328467; the tested +saving is 0.003284675. The completion uses power 1024, cutoff 12, floor 13, offset 1/7, reserve 10^-12 and decay 31/32. The logarithm power is 1100. All local native, route and scalar costs remain charged. The new caller uses a conservative 32 real scalar units per field per instruction, @@ -151,11 +151,61 @@ source is PR6349; it does not consume PR6353's output-contracted word. The source-relative gain is from the new caller, not new digits of an old crossing. PR6353 and PR6350 retain their separate construction credit. -The child-size discovery checked every tuple from 1 through 40 for this -fixed four-site root, at two floating trial savings. It selected 7,2,1,8. -That bounded search is not an exact optimality certificate or a search of -all root bases. The published bound depends only on the exact chosen word -and its complete rational replay. +The basis search checked 241,886,080 bounded bases modulo 65521. It found +695 support patterns. Floating searches selected the rank 2,3,3,2 pattern. +The exact rational checker then verified the chosen basis and every stage +coefficient. This finite search does not prove a global basis optimum. +The new child-size search selected 7,2,2,7. Section 5 gives an exact ceiling +for all binary children of this fixed root. + +## 5. A ceiling for every binary child size of this root + +This statement keeps the root and the PR6349 native source fixed. It permits +all positive integer child sizes and all binary tree shapes. Let H(r)=r^t, +t=1-kappa, and let L be the native paid-minus-helper moment per port. +Let C(n) be the minimum binary-node cost for n leaves. Then + +```text +C(1)=0, +C(n)=min_{1 <= a < n} (C(a)+C(n-a)+2H(8n)+1-2H(8n+1)). +``` + +For a pair with total n, the best root contribution is + +```text +G(n)=max_{1 <= b < n} + (H(8n+1)-n L-C(n-b)-C(b)+H(8b+1)-H(8b)). +``` + +For four positive children, with pair totals x and y, the complete margin +per port is H(8(x+y)+1)+G(x)+G(y)-2. The two pairs contain all root outputs, +three thin queries, both individual idles and every binary-node job. + +At kappa .00328469, `ceiling.py` uses rational outward intervals. It checks +all 4,851 binary splits below 100 leaves and all 4,656 root pair choices with +four through 99 leaves. Every margin upper bound is strictly negative. + +For larger totals f, concavity gives C(n) >= -(n-1) and +H(8b+1)-H(8b) <= H(9)-H(8). Jensen's inequality gives the upper bound + +```text +B(f)=H(8f+1)+2H(4f+1)-f(L-1)+2(H(9)-H(8))-6. +``` + +The checker proves B(100)<0 and B'(100)<0 with rational intervals. Since +t is strictly between zero and one, B' decreases. Thus B(f)<0 for every +real f>=100. No larger binary tree is omitted. + +The native deficit L has strictly positive derivative throughout +0<=kappa<=.0034. The checker proves this with an interval lower bound above +42. Each binary-node cost increases with kappa, while each positive H term +and each increment H(r+1)-H(r) decreases. Thus every root margin decreases +throughout the retained BIT admission range. Failure at .00328469 also +excludes every larger saving in that range. + +This fixed root cannot reach .00328469 with the retained native source. +The claim .00328467 is within .00000002 of that ceiling. This is a scoped +ceiling, not a bound for other roots, source words or query interfaces. ## Scope and open next questions @@ -166,7 +216,7 @@ and rounded multiplier are not materialized. No global optimality or practical speedup is claimed. The selected frontier stays unchanged. An independent reviewer should first check the global-field normalization, -the charged rank-three and rank-four projectors, and input independence. +the two charged rank-three projectors, and input independence. Then replay the exact source and complete invoice. A later improvement can change this root or combine it with a verified source, but must include every changed productive debit, ordinary operation and compiler cost. diff --git a/research/mixed-projector-query-root/README.md b/research/mixed-projector-query-root/README.md index 92cb8835dd..e396a0cd8a 100644 --- a/research/mixed-projector-query-root/README.md +++ b/research/mixed-projector-query-root/README.md @@ -1,15 +1,19 @@ -# Conditional kappa 0.00327980 from a mixed projector root +# Conditional kappa 0.00328467 from a mixed projector root -This caller gives conditional **kappa 0.00327980**, an increase of -**0.00012923 (about 4.10 percent)** over PR6353's .00315057. It keeps the +This caller gives conditional **kappa 0.00328467**, an increase of +**0.00013410 (about 4.26 percent)** over PR6353's .00315057. It keeps the PR6349 native source and combines four PR6348 binary query suppliers in a new six-field root. The selected frontier stays unchanged. -The root permits paid stage projectors of ranks two, three and four. An +The root permits paid stage projectors of ranks two and three. An ordinary translation-based normalization supplies its central involution and restores Gaussian outputs. The literal caller includes every normalization, basis change, native call, thin query and complementary idle. -It has 18 native calls, 34 main fields per port and 67,092 paid jobs. +It has 18 native calls, 34 main fields per port and 66,988 paid jobs. + +An exact check bounds all binary child sizes for this fixed root below +.00328469. The new claim is within .00000002 of that scoped ceiling. It is +.1485 percent above the earlier local .00327980 root. Start with [PROOF.md](PROOF.md), [ROOT.json](ROOT.json), the literal [CONTROLLER.json](CONTROLLER.json) and [RESULT.json](RESULT.json). @@ -21,7 +25,7 @@ python3.12 -I -B research/mixed-projector-query-root/verify.py python3.12 -I -O -B research/mixed-projector-query-root/verify.py ``` -Expected marker: `PASS_MIXED_PROJECTOR_QUERY_ROOT_KAPPA_00327980`. +Expected marker: `PASS_MIXED_PROJECTOR_QUERY_ROOT_KAPPA_00328467`. The registered verifier uses only the Python standard library. Five inherited framework assumptions remain. The uniform word and rounded @@ -29,6 +33,9 @@ multiplier are not materialized. Author replay and hosted CI do not replace independent scientific review or formal-kernel acceptance. No global optimum or practical runtime improvement is claimed. +The result remains local under the donor's publication hold. No push, PR +or hosted CI is claimed. + ## Open next questions - Independently check the normalization on the complete field, the four diff --git a/research/mixed-projector-query-root/RESULT.json b/research/mixed-projector-query-root/RESULT.json index 928f344f71..7ffa8fadc0 100644 --- a/research/mixed-projector-query-root/RESULT.json +++ b/research/mixed-projector-query-root/RESULT.json @@ -18,8 +18,8 @@ }, "caller": { "coefficients": 1156, - "event_sha256": "27cb309b1013bc459ec7f93983dba26627255c35bbb4d38299ed4fd8f28c486b", - "events": 543, + "event_sha256": "be648c29aa09c0f068a3b5b5120d1eb1f782e49f4523b4c6d62843750517bdea", + "events": 570, "inputs": 34, "native_stages": 18 }, @@ -28,6 +28,18 @@ "coefficients": 638401, "columns": 799 }, + "fixed_root_ceiling": { + "admitted_saving_cap": "17/5000", + "binary_split_checks": 4851, + "ceiling": "328469/100000000", + "finite_margin_upper": "-750506598129274945514234334134410155551008660593345983/163204645120053699859730525003399326818661241556064897335296", + "finite_pair_checks": 4656, + "first_tail_total": 100, + "native_derivative_lower": "86198265613857174984961926826035460452887338210852170396752075072748738729212441010936924815282480413581462223705108297/2048904322212512919038510085207467917864146442064203226733311257020777532117854951793541845254015613321944655495954432", + "scope": "All positive integer child sizes and all binary tree shapes for this fixed root and PR6349 source.", + "tail_derivative_upper": "-3877624858468274458330205673541784769862279749592609108719814384627637/65526869021507960560806630452021083966851011811312001361243013120000000", + "tail_margin_upper": "-151099573163525840514660484867817751572373987297076544356433/81602322560026849929865262501699663409330620778032448667648" + }, "lifted_directions": [ { "basis": [ @@ -148,6 +160,7 @@ "wrong_phase_rejected": true }, "negative_controls": { + "changed_ceiling_root": "The ceiling uses the actual paired root masks", "missing_carrier_move": "Scalar destination and coefficient", "missing_first_carrier_subtraction": "All public and owned rows", "missing_idle": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", @@ -168,14 +181,13 @@ "central_translations": 16, "full_calls": 18, "main_targets": { + "1": 104, "145": 104, - "17": 1768, - "25": 208, - "33": 624, - "57": 208, - "65": 208, - "73": 208, - "9": 208 + "17": 1872, + "25": 416, + "33": 416, + "57": 416, + "73": 208 }, "new_paid_jobs": 0, "ordinary_normalizations": 20, @@ -184,12 +196,10 @@ "route_payload_sha256": "79930ec6c09a8e4930556c925c354bb5431203eaf069d9373f056049c061289b", "tensor_rule": "Factorwise native maps; scalar signs stay outside the tensor power.", "whole_idle_jobs": { - "16": 1768, - "24": 208, - "32": 624, - "56": 208, - "64": 208, - "8": 208 + "16": 1872, + "24": 416, + "32": 416, + "56": 416 } }, "price": { @@ -197,24 +207,24 @@ "H": 70855400000000, "N": "2^70855400000000", "eta": { - "lower": "0.000000054900323468016292837875", - "upper": "0.000000054900323468016292837876" + "lower": "0.000000053554294001314085839719", + "upper": "0.000000053554294001314085839720" }, "gap": "1/1400000000", "integer_test_exponent": 50611, "logarithm_power": 1100, "theta": "63/64", - "uniform_saving": "2295863/700000000", + "uniform_saving": "287409/87500000", "word_materialized": false }, - "derivative_upper": "-177870484769676531090751061240712034497904012779690454216995569/784637716923335095479473677900958302012794430558004314112", + "derivative_upper": "-88879058930240593538878666108991983162882356258539092284847813/392318858461667547739736838950479151006397215279002157056", "full_forward_calls": 18, - "gain": "12923/100000000", - "kappa": "16399/5000000", - "kappa_decimal": "0.00327980", + "gain": "1341/10000000", + "kappa": "328467/100000000", + "kappa_decimal": "0.00328467", "margin_at_previous": { - "lower": "29.757936288213564682353374405281", - "upper": "29.757936288213564682353374405282" + "lower": "30.835026124181562841635714475041", + "upper": "30.835026124181562841635714475042" }, "negative_controls": { "old_BIT": "An outer inequality fails at BIT saving0.0027.", @@ -223,10 +233,10 @@ "nonrecursive": { "local_routes": 5326000, "local_scalar": 127088, - "paid_rank_mass": 188668, + "paid_rank_mass": 185340, "peak_owned_fields": 13, "raw_budget": 1000000000, - "raw_scalar_upper": 245097760, + "raw_scalar_upper": 248152864, "scalar_growth_bound": "At most 2^(10^9 + R*f), where R is the full paid rank mass." }, "ordinary_BIT": { @@ -245,82 +255,82 @@ "new_semantic_group_guard": "3/1400000000" }, "margins": { - "boundary_algebraic_matrix": "6428413595408277/1960000000000000000", - "fused_gaussian": "6428413586224831/1960000000000000000", - "global_coordinate_router": "1147931/350000000", - "group_bit_router": "1607103746556207/490000000000000000", + "boundary_algebraic_matrix": "6437958795401459/1960000000000000000", + "fused_gaussian": "6437958786204377/1960000000000000000", + "global_coordinate_router": "2299271/700000000", + "group_bit_router": "3218980093102187/980000000000000000", "group_scans": "699999999/700000000", - "main_transform": "6428412195408277/1960000000000000000", + "main_transform": "6437957395401459/1960000000000000000", "microbox_face_corrections": "26950000001/350000000", "polynomial_products": "1399999999/1400000000", - "sparse_union_movement": "802678413595408277/1960000000000000000" + "sparse_union_movement": "802687958795401459/1960000000000000000" }, "parameters": { - "a": "1147931/350000000", - "b": "183669/56000000", + "a": "2299271/700000000", + "b": "4598543/1400000000", "beta": "1399999997/1400000000", "bit_saving": "17/5000", - "cap_xi": "1782678412195408277/1960000000000000000", - "complex_uniform_saving": "2295863/700000000", + "cap_xi": "1782687957395401459/1960000000000000000", + "complex_uniform_saving": "287409/87500000", "d": "1/1400000000", "epsilon": "1399999999/1400000000", - "kappa": "16399/5000000", - "lambda_": "398688079/400000000", - "lambda_prime": "1395408277/1400000000", + "kappa": "328467/100000000", + "lambda_": "398686131/400000000", + "lambda_prime": "1395401459/1400000000", "layout": "1/1400000000", - "q": "4591723/1400000000", + "q": "4598541/1400000000", "r0": "1/14000000000", "stop": "1/1400000000", - "tested_saving": "655961/200000000" + "tested_saving": "131387/40000000" }, "strict_checks": { - "actual_bit_above_effective": "42069/350000000", + "actual_bit_above_effective": "80729/700000000", "actual_logarithmic_gamma_guard": "1/1400000000", - "actual_logarithmic_group_guard": "177321589904591723/980000000000000000", + "actual_logarithmic_group_guard": "177312044704598541/980000000000000000", "alpha_logarithm_absorption": "1/14000000000", - "boundary_algebraic_matrix_above_kappa": "5595408277/1960000000000000000", - "cap_above_band": "802678412195408277/1960000000000000000", - "cap_below_cell": "177321586404591723/1960000000000000000", - "cap_below_phase_cell_power": "2137321587804591723/1960000000000000000", + "boundary_algebraic_matrix_above_kappa": "5595401459/1960000000000000000", + "cap_above_band": "802687957395401459/1960000000000000000", + "cap_below_cell": "177312041204598541/1960000000000000000", + "cap_below_phase_cell_power": "2137312042604598541/1960000000000000000", "complex_above_effective": "1/1400000000", - "complex_below_one_over_32": "1566331/56000000", + "complex_below_one_over_32": "39151457/1400000000", "complex_endpoint": "1/700000000", "epsilon_below_one": "1/1400000000", "epsilon_positive": "1399999999/1400000000", "fine_prime_halo_umbrella": "7/2", - "fused_gaussian_above_kappa": "5586224831/1960000000000000000", - "gaussian_above_main": "695408277/980000000000000000", + "fused_gaussian_above_kappa": "5586204377/1960000000000000000", + "gaussian_above_main": "695401459/980000000000000000", "global_coordinate_router_above_kappa": "1/350000000", "global_gamma_power_slack": "9/14000000000", "group_below_dimension": "1/700000000", - "group_bit_router_above_kappa": "1746556207/490000000000000000", - "group_gauge_power_slack": "177321589834591723/980000000000000000", + "group_bit_router_above_kappa": "3493102187/980000000000000000", + "group_gauge_power_slack": "177312044634598541/980000000000000000", "group_key_fits_record": "1/700000000", "group_positive": "1399999997/1400000000", - "group_scans_above_kappa": "697704139/700000000", + "group_scans_above_kappa": "69770073/70000000", "halo_covers_generic_inverse_radius": "5", - "improvement_over_user_baseline": "774414790400418148631/500000000000000000000000", + "improvement_over_user_baseline": "776849790400418148631/500000000000000000000000", "lambda_above_internal": "1/2800000000", "lambda_above_sigma": "3/2800000000", "lambda_above_tau": "1/2800000000", "lambda_prime_above_lambda": "1/2800000000", - "lambda_prime_above_leaf": "111816331/78400000000000000", - "leaf_saving_above_effective": "55816331/78400000000000000", - "main_transform_above_kappa": "4195408277/1960000000000000000", + "lambda_prime_above_leaf": "2795401457/1960000000000000000", + "leaf_saving_above_effective": "1395401457/1960000000000000000", + "main_transform_above_kappa": "4195401459/1960000000000000000", "membership_arithmetic_fits_record": "1/1400000000", - "microbox_face_corrections_above_kappa": "26948852071/350000000", + "microbox_face_corrections_above_kappa": "53897700733/700000000", "microbox_halo_volume": "110600000003/1400000000", "new_complex_uniform_saving_above_b": "1/1400000000", "new_semantic_guard_with_C1_one": "1/1400000000", - "polynomial_products_above_kappa": "1395408279/1400000000", + "polynomial_products_above_kappa": "1395401461/1400000000", "positive_layout_slack": "1/1400000000", "q_below_effective": "1/1400000000", "q_below_internal": "1/1400000000", - "q_below_leaf": "111816331/78400000000000000", - "q_positive": "4591723/1400000000", - "short_record_fallback": "55816331/56000000", + "q_below_leaf": "2795401457/1960000000000000000", + "q_positive": "4598541/1400000000", + "short_record_fallback": "1395401457/1400000000", "source_axis_superpolynomial": "1/1400000000", - "sparse_union_movement_above_kappa": "796250005595408277/1960000000000000000", + "sparse_union_movement_above_kappa": "796250005595401459/1960000000000000000", "stop_below_one": "1399999999/1400000000", "stop_positive": "1/1400000000", "strassen_integer_power_gap": "1951441519231", @@ -332,46 +342,45 @@ }, "paid": { "1": 41674, - "16": 1768, + "16": 1872, "2": 8226, - "24": 208, + "24": 416, "3": 8946, - "32": 624, + "32": 416, "4": 1800, "5": 2898, - "56": 208, + "56": 416, "6": 144, - "64": 208, "7": 162, - "8": 226 + "8": 18 }, - "paid_calls": 67092, + "paid_calls": 66988, "previous_pr6353": "315057/100000000", "productive_fields": 13652, "rank_mass_surplus": 760, "raw_headroom": [ - "1076011/100000000000000", - "269003/25000000000000" + "1791927/100000000000000", + "223991/12500000000000" ], "raw_root_interval": [ - "327981076011/100000000000000", - "81995269003/25000000000000" + "328468791927/100000000000000", + "41058598991/12500000000000" ], - "relative_gain_percent": "1292300/315057", + "relative_gain_percent": "447000/105019", "strictification": { "alpha": { - "lower": "0.999999992929646999590270520854", - "upper": "0.999999992929646999590270520855" + "lower": "0.999999983883647043526813312973", + "upper": "0.999999983883647043526813312974" }, "cutoff": 12, "delta": { - "lower": "0.938685728930131504978223980532", - "upper": "0.938685728930131504978223980533" + "lower": "0.955396196009635532136372107420", + "upper": "0.955396196009635532136372107421" }, "floor": 13, "gamma": { - "lower": "0.931060358967415077851987843691", - "upper": "0.931060358967415077851987843692" + "lower": "0.924233987161773495066939289639", + "upper": "0.924233987161773495066939289640" }, "normalized_paid_upper": "1048576000976562501/1048576001073741824", "power": 1024, @@ -379,28 +388,27 @@ "tail_block": 128, "tail_decay": "31/32", "tail_offset": "1/7", - "tested": "655961/200000000" + "tested": "131387/40000000" }, "targets": { - "1": 252, + "1": 356, "145": 104, - "17": 1768, + "17": 1872, "2": 144, - "25": 208, + "25": 416, "3": 72, - "33": 624, + "33": 416, "4": 1926, "5": 252, - "57": 208, + "57": 416, "6": 54, - "65": 208, "7": 162, "73": 208, "8": 396, - "9": 7066 + "9": 6858 }, "thin_queries": 17, - "whole_idle_jobs": 3224 + "whole_idle_jobs": 3120 }, "root": { "actual_tensor_gaussian_columns": 14, @@ -414,7 +422,7 @@ "stage_ranks": [ 2, 3, - 4, + 3, 2 ], "tensor_rule": "Normalize the complete field with its global Q squared translation; scalar coefficients stay outside tensor powers.", @@ -423,5 +431,5 @@ }, "selected_frontier_changed": false, "source_inputs": 17, - "status": "PASS_MIXED_PROJECTOR_QUERY_ROOT_KAPPA_00327980" + "status": "PASS_MIXED_PROJECTOR_QUERY_ROOT_KAPPA_00328467" } diff --git a/research/mixed-projector-query-root/ROOT.json b/research/mixed-projector-query-root/ROOT.json index 3ffcd5374b..b59f1ea89a 100644 --- a/research/mixed-projector-query-root/ROOT.json +++ b/research/mixed-projector-query-root/ROOT.json @@ -4,112 +4,112 @@ "full_sites": [ 0, 1, - 4, + 5, 6 ], "thin_sites": [ 2, 3, - 5 + 4 ], "input_basis": [ [ "2", - "0", "-1", "1", "0", + "0", "0" ], [ "-2", - "1", "2", "-1", "0", - "0" - ], - [ - "2", - "-2", - "-2", - "1", "0", - "0" + "1" ], [ + "1", "-1", + "0", "1", "1", - "0", - "0", "-1" ], [ + "-2", + "2", + "-1", "0", "0", - "0", - "-1", - "-1", "2" ], [ + "2", + "-2", + "1", + "-1", "0", + "-2" + ], + [ "0", "0", "1", - "1", - "-1" + "0", + "-1", + "0" ] ], "output_basis": [ [ "1", "1", - "0", "-1", + "-2", "-1", "-1" ], - [ - "0", - "-1", - "-1", - "0", - "0", - "0" - ], [ "1", "2", - "1", "0", + "-1", "0", "0" ], [ "0", "0", - "1", "2", + "3", "2", "2" ], [ + "0", "0", "0", "-1", - "-2", "-1", "0" ], [ "0", "0", + "2", + "3", + "2", + "1" + ], + [ "0", + "-1", "0", "1", - "1" + "0", + "0" ] ], "sites": [ @@ -119,14 +119,14 @@ "stage_rank": 2, "support": [ 0, - 2 + 1 ], "basis": [ [ "1", "0", - "1", "2", + "3", "2", "2" ], @@ -140,7 +140,7 @@ ], [ "0", - "2", + "1", "1", "0", "0", @@ -148,7 +148,7 @@ ], [ "0", - "-1", + "-2", "0", "1", "0", @@ -156,7 +156,7 @@ ], [ "0", - "0", + "2", "0", "0", "1", @@ -175,8 +175,8 @@ [ "1", "0", - "-1", "-2", + "-3", "-2", "-2" ], @@ -190,27 +190,27 @@ ], [ "0", + "1", "2", - "3", - "2", - "2", - "2" + "1", + "1", + "1" ], [ "0", + "-2", + "-2", "-1", - "-1", - "0", - "-1", - "-1" + "-2", + "-2" ], [ "0", - "0", - "0", - "0", - "1", - "0" + "2", + "2", + "2", + "3", + "2" ], [ "0", @@ -225,8 +225,8 @@ [ "1", "0", - "-1", "-2", + "-3", "-2", "-2" ], @@ -240,27 +240,27 @@ ], [ "0", - "-2", - "-2", - "-2", - "-2", - "-2" + "-1", + "-1", + "-1", + "-1", + "-1" ], [ "0", - "1", - "1", - "1", - "1", - "1" + "2", + "2", + "2", + "2", + "2" ], [ "0", - "0", - "0", - "0", - "0", - "0" + "-2", + "-2", + "-2", + "-2", + "-2" ], [ "0", @@ -279,14 +279,14 @@ "support": [ 0, 1, - 2 + 5 ], "basis": [ [ "0", "1", "-1", - "1", + "-1", "0", "0" ], @@ -294,30 +294,30 @@ "1", "0", "2", - "-1", + "1", "0", "0" ], [ "0", "0", + "-1", "-2", - "1", - "0", - "0" + "-1", + "-1" ], [ "0", "0", + "2", "1", "0", - "-1", - "-1" + "0" ], [ "0", "0", - "0", + "-2", "0", "1", "0" @@ -335,8 +335,8 @@ [ "0", "1", - "1", "0", + "-1", "0", "0" ], @@ -349,28 +349,28 @@ "-1" ], [ - "0", "0", "0", "1", + "2", "1", "1" ], [ "0", "0", - "1", - "2", - "2", - "2" + "-2", + "-3", + "-2", + "-2" ], [ "0", "0", - "0", - "0", - "1", - "0" + "2", + "4", + "3", + "2" ], [ "0", @@ -385,42 +385,42 @@ [ "1", "0", - "-1", "-2", + "-3", "-2", "-2" ], [ "0", "1", - "1", "2", + "3", "2", "2" ], [ "0", "0", - "0", - "-2", + "-1", "-2", - "-2" + "-1", + "-1" ], [ "0", "0", - "0", - "1", - "1", - "1" + "2", + "4", + "2", + "2" ], [ "0", "0", - "0", - "0", - "0", - "0" + "-2", + "-4", + "-2", + "-2" ], [ "0", @@ -746,46 +746,41 @@ }, { "site": 4, - "full": true, - "stage_rank": 4, - "support": [ - 0, - 3, - 4, - 5 - ], + "full": false, + "stage_rank": 2, + "support": [], "basis": [ [ "0", - "2", + "1", + "-1", "-1", - "2", "-1", "1" ], [ "0", - "-2", - "1", - "-2", + "0", "1", + "0", + "0", "0" ], [ "0", - "2", - "-1", - "2", "0", - "-2" + "0", + "1", + "0", + "0" ], [ "0", - "-1", - "1", - "-1", "0", - "1" + "0", + "0", + "1", + "0" ], [ "1", @@ -799,9 +794,9 @@ "0", "0", "0", - "1", "0", - "0" + "0", + "1" ] ], "inverse": [ @@ -822,68 +817,68 @@ "-1" ], [ - "0", "0", "1", - "2", + "0", + "0", "0", "0" ], [ "0", "0", + "1", "0", "0", - "0", - "1" + "0" ], [ - "2", - "3", - "1", "0", "0", + "0", + "1", + "0", "0" ], [ - "1", - "1", "0", "0", "0", - "0" + "0", + "0", + "1" ] ], "projector": [ [ - "2", - "2", - "1", + "0", + "0", + "0", "0", "0", "0" ], [ - "-2", - "-2", - "-1", + "0", + "0", + "0", "0", "0", "0" ], [ - "2", - "2", - "1", + "0", + "0", + "0", "0", "0", "0" ], [ - "-1", - "-1", "0", - "1", + "0", + "0", + "0", "0", "0" ], @@ -892,7 +887,7 @@ "0", "0", "0", - "1", + "0", "0" ], [ @@ -901,52 +896,56 @@ "0", "0", "0", - "1" + "0" ] ] }, { "site": 5, - "full": false, - "stage_rank": 2, - "support": [], + "full": true, + "stage_rank": 3, + "support": [ + 0, + 2, + 4 + ], "basis": [ [ "0", - "1", - "-1", - "-1", + "2", + "-2", "-1", - "-1" + "1/2", + "0" ], [ "0", - "0", + "-2", + "2", "1", "0", - "0", "0" ], [ - "0", - "0", "0", "1", "0", - "0" + "0", + "-3/2", + "-1" ], [ "0", - "0", - "0", + "-2", + "2", "0", "1", "0" ], [ "0", - "0", - "0", + "2", + "-2", "0", "0", "1" @@ -978,76 +977,76 @@ "0" ], [ - "0", - "1", - "0", "0", "0", + "1", + "3/2", + "1", "0" ], [ + "2", + "3", "0", - "0", - "1", - "0", + "-1", "0", "0" ], [ + "2", + "2", "0", "0", "0", - "1", - "0", "0" ], [ + "-2", + "-2", "0", - "0", - "0", - "0", + "1", "1", "0" ] ], "projector": [ [ + "2", + "2", "0", - "0", - "0", - "0", + "-1", "0", "0" ], [ + "-2", + "-2", "0", - "0", - "0", - "0", + "1", "0", "0" ], [ - "0", - "0", - "0", - "0", - "0", + "1", + "1", + "1", + "1", + "1", "0" ], [ + "-2", + "-2", "0", - "0", - "0", - "0", + "1", "0", "0" ], [ + "2", + "2", "0", - "0", - "0", - "0", + "-1", "0", "0" ], @@ -1057,7 +1056,7 @@ "0", "0", "0", - "0" + "1" ] ] }, @@ -1067,16 +1066,16 @@ "stage_rank": 2, "support": [ 0, - 3 + 2 ], "basis": [ [ "-1", "2", "-1", - "1", - "1", - "1" + "1/2", + "0", + "0" ], [ "1", @@ -1088,15 +1087,15 @@ ], [ "-1", - "2", + "1", "0", - "-2", - "-2", - "-2" + "-3/2", + "-1", + "-1" ], [ "1", - "-1", + "-2", "0", "1", "0", @@ -1104,7 +1103,7 @@ ], [ "-1", - "0", + "2", "0", "0", "1", @@ -1123,8 +1122,8 @@ [ "0", "0", - "1", "2", + "3", "2", "2" ], @@ -1139,32 +1138,32 @@ [ "2", "3", - "1", "0", + "-1", "0", "0" ], [ - "1", - "1", + "2", + "2", "0", "0", - "-1", - "-1" + "0", + "0" ], [ - "0", + "-2", + "-2", "0", "1", - "2", - "3", - "2" + "1", + "0" ], [ "0", "0", - "-1", "-2", + "-3", "-2", "-1" ] @@ -1173,48 +1172,48 @@ [ "2", "2", - "1", "0", + "-1", "0", "0" ], [ "-2", "-2", - "-1", - "0", "0", - "0" - ], - [ - "2", - "2", "1", "0", - "0", "0" ], [ + "1", + "1", "-1", + "-2", "-1", + "-1" + ], + [ + "-2", + "-2", "0", "1", - "1", - "1" + "0", + "0" ], [ - "0", + "2", + "2", "0", "-1", - "-2", - "-2", - "-2" + "0", + "0" ], [ "0", "0", - "1", "2", + "3", "2", "2" ] @@ -1228,12 +1227,6 @@ 1, 1 ], - [ - 0, - 1, - 0, - 0 - ], [ 1, 1, @@ -1249,7 +1242,7 @@ [ 0, 0, - 1, + 0, 0 ], [ @@ -1257,17 +1250,18 @@ 0, 1, 0 + ], + [ + 0, + 1, + 0, + 0 ] ], "independent_stage_coefficients": 1152, "normalization": "lambda=(1+i)/2+(1-i)*q^2/2; q^4=1", "scope": "Exact rational root and Gaussian normalization; full caller costs not certified", - "child_sizes": [ - 7, - 2, - 1, - 8 - ], + "schema": "mixed-projector-query-root/2", "children": [ [ [ @@ -1292,13 +1286,13 @@ 1, 1 ], - 1, + [ + 1, + 1 + ], [ [ - [ - 1, - 1 - ], + 1, [ 1, 1 @@ -1315,5 +1309,11 @@ ] ] ] + ], + "child_sizes": [ + 7, + 2, + 2, + 7 ] } diff --git a/research/mixed-projector-query-root/SEARCH.md b/research/mixed-projector-query-root/SEARCH.md new file mode 100644 index 0000000000..b9f11d55a5 --- /dev/null +++ b/research/mixed-projector-query-root/SEARCH.md @@ -0,0 +1,64 @@ +# Search scope and fixed-root limit + +The new bound uses the explicit rational root in ROOT.json. Its acceptance +does not depend on a heuristic search or on a modular zero test. + +## Basis catalogue + +The search kept rank-two projectors at query sites zero and six. Their +intersection has one dimension. Write u for (-1,1,-1,1,-1,1). Let K be the +four-dimensional space of vectors whose first coordinate and coordinate +sum are zero. For z in K and three independent columns d1,d2,d3 in K, use + +```text +F = [e0-u-z, u+z, e0-z, d1, d2, d3]. +``` + +In the four coordinates of K, z ranged over the nonzero vectors in +{-1,0,1}^4. Each d column ranged over primitive integer vectors in +{-2,-1,0,1,2}^4, with first nonzero coordinate positive. The search used +each unordered triple of d columns. Singular F matrices were excluded. + +The enumeration checked 241,886,080 invertible bases modulo 65521. It found +695 distinct seven-site support patterns. Floating child-size searches +selected a pattern with full-site ranks 2,3,3,2. The rational reconstruction +then checked its exact projectors, native query planes and all independent +stage coefficients. The selected F has determinant one. Its inverse and +native basis data have dyadic coefficients. + +This is a bounded catalogue. It does not cover all rational bases, larger +roots, noncommuting stage families or other query words. Floating searches +over the catalogue do not prove that each pattern's price is optimal. +An additional integer-program screen has finite time limits and unresolved +solver bounds. It is not used as an exclusion certificate. + +## Child sizes + +The two-pair score separates the four child sizes into two sums. A floating +dynamic program tested all totals through 200 and all binary child splits. +It selected 7,2,2,7. The complete exact caller and invoice use those trees. + +The separate rational checker ceiling.py covers all positive integer child +sizes and all binary tree shapes for this fixed root and native source. +It checks every total below 100 and proves a decreasing negative bound for +all larger totals. Its ceiling is .00328469. The claim is .00328467. +PROOF.md states the full argument and its restrictions. + +## Other local searches + +- Structured roots through 20 fields did not improve the retained price. +- Braid moves on longer query words did not give a favorable complete bill + in the tested finite domains. +- Two- and four-copy coupled bases did not improve the scalar construction + in 14,000 proposed moves per coupling size. +- An internal-query extension of the earlier root has two exact shared + idle subspaces. Its complete proposed price still loses to the binary + supplier. The screen tested all child tuples through 48 per child. + +These are search outcomes, not general impossibility results. The local +scripts, output files and logs remain in work/new-route-20261101. They are +outside the registered mathematical replay. The complete positive word, +source pins, exact bound and fixed-root ceiling are in this package. + +The selected frontier is unchanged. The donor's local publication hold +remains in effect. No result from another investigation is claimed here. diff --git a/research/mixed-projector-query-root/TASK.json b/research/mixed-projector-query-root/TASK.json index 4527fb934b..58626f9ee8 100644 --- a/research/mixed-projector-query-root/TASK.json +++ b/research/mixed-projector-query-root/TASK.json @@ -64,8 +64,8 @@ ] }, "scope_status": "refined", - "scope_change_reason": "Use a paid rank-three/rank-four mixed root with unequal binary children and a whole-field central-involution normalization. The source word remains fixed.", - "actual_scope": "Complete source-bound caller at conditional kappa 0.00327980, including all main fields, independent helpers, native phases, idle jobs, ordinary normalization, compiler and outer costs.", + "scope_change_reason": "Use a paid rank 2,3,3,2 root with binary children 7,2,2,7 and a whole-field central-involution normalization. Prove a fixed-root ceiling over all binary child sizes. The native source word remains fixed.", + "actual_scope": "Complete source-bound caller at conditional kappa 0.00328467, including all main fields, independent helpers, native phases, idle jobs, ordinary normalization, compiler and outer costs.", "bottleneck_link": "Complex supplier; changes the full signed target and paid moment while retaining admitted BIT .0034.", "outcome": "completed", "evidence": "PROOF.md, ROOT.json, CONTROLLER.json, RESULT.json and VALIDATION.md.", diff --git a/research/mixed-projector-query-root/VALIDATION.md b/research/mixed-projector-query-root/VALIDATION.md index b86b5f39ab..676e7b5b27 100644 --- a/research/mixed-projector-query-root/VALIDATION.md +++ b/research/mixed-projector-query-root/VALIDATION.md @@ -1,5 +1,50 @@ # Validation record +## Current local .00328467 revision + +The rank 2,3,3,2 root has passed its complete author build. The result covers +all 570 caller events, 1,156 caller coefficients, 799 source input columns, +the separate 638,401-coefficient transpose, native absolute phases and all +7,488 physical contacts. Both rational price engines, the completion, +compiler, 54 strict outer predicates and four functional predicates pass. +The complete ordinary-work upper bound is 248,152,864, below 10^9. + +The exact raw crossing is strictly in +(.00328468791927,.00328468791928). The claimed saving is .00328467. +The complete invoice has 66,988 paid jobs, 13,652 productive fields and rank +surplus 760. No new owned field is added. Every emitted rational scalar is +dyadic and has magnitude at most five. + +The all-size fixed-root ceiling uses a separate rational dynamic program. +It checks 4,851 binary splits and 4,656 pair totals below 100 leaves. A +negative decreasing bound covers all larger totals. A separate derivative +bound above 42 proves monotonicity throughout the retained BIT range. +Changing a root mask is rejected before the ceiling calculation. + +The first complete registered normal and optimized runs passed. The final +ceiling adds the explicit saving-range monotonicity check and a wrong-root +control. The final registered normal and optimized replays also passed with +those checks. Sealed-export and committed-byte checks are still pending for +this revision. +No previous revision's transport receipt is transferred to these bytes. + +Discovery also replayed all 695 retained modular support patterns with a +separate NumPy implementation. This checks the retained representatives, +not a second complete 241,886,080-basis enumeration or a global optimum. + +Canonical main was refreshed and remains +7c49fe32c55de02c2c873655c804b16e4c3fef0a. Live PR and adjacent Discussion +checks found separate PR6353 audits and no new overlapping root claim. +The selected record SHA256 is still +9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa. + +The five framework assumptions remain. The uniform word and rounded +multiplier are not materialized. Hosted CI, independent scientific review +and full source-history ancestry are not claimed. The local publication +hold remains in effect; no push or PR has occurred. + +# Earlier local .00327980 checkpoint + This file records author checks. Independent scientific review and hosted CI are separate checks. Do not infer their completion from a local pass. diff --git a/research/mixed-projector-query-root/ceiling.py b/research/mixed-projector-query-root/ceiling.py new file mode 100644 index 0000000000..93f626e821 --- /dev/null +++ b/research/mixed-projector-query-root/ceiling.py @@ -0,0 +1,66 @@ +"""Bound every binary-child size for the rank 2,3,3,2 root. + +The native source stays fixed. Other roots and native sources are outside +this claim. All arithmetic in this checker uses rational intervals. +""" +from fractions import Fraction as Q + +CEILING=Q('.00328469') +BIT_CAP=Q('.0034') +TAIL=100 + + +def run(local,E,root): + def need(ok,message): + if not ok:raise ValueError(message) + need(00,'The native deficit increases throughout the admitted range') + h={r:E.power(r,t) for r in range(1,8*TAIL+2)} + lower=[Q(0)]*TAIL + upper=[Q(0)]*TAIL + split_checks=0 + for n in range(2,TAIL): + node_lower=2*h[8*n][0]+1-2*h[8*n+1][1] + node_upper=2*h[8*n][1]+1-2*h[8*n+1][0] + lower[n]=min(lower[a]+lower[n-a]+node_lower for a in range(1,n)) + upper[n]=min(upper[a]+upper[n-a]+node_upper for a in range(1,n)) + need(lower[n]<=upper[n],'Binary subtree interval') + split_checks+=n-1 + pairs={} + for n in range(2,TAIL-1): + pairs[n]=max(h[8*n+1][1]-n*native_lower-lower[n-b]-lower[b] + +h[8*b+1][1]-h[8*b][0] for b in range(1,n)) + margins=[] + for n in range(4,TAIL): + for a in range(2,n-1): + margins.append(h[8*n+1][1]+pairs[a]+pairs[n-a]-2) + finite_upper=max(margins) + need(finite_upper<0,'Every finite child sum fails at the ceiling') + # Every binary node costs at least -1 by concavity. For total n, + # Jensen bounds the two pair outputs and each added increment is at + # most H9-H8. The resulting upper bound is decreasing for n >= TAIL. + tail_upper=(h[8*TAIL+1][1]+2*h[4*TAIL+1][1]-TAIL*(native_lower-1) + +2*(h[9][1]-h[8][0])-6) + derivative_upper=(8*t*(h[8*TAIL+1][1]/(8*TAIL+1) + +h[4*TAIL+1][1]/(4*TAIL+1))-(native_lower-1)) + need(tail_upper<0 and derivative_upper<0,'All larger child sums fail') + return {'ceiling':str(CEILING),'first_tail_total':TAIL,'binary_split_checks':split_checks, + 'admitted_saving_cap':str(BIT_CAP),'native_derivative_lower':str(derivative_lower), + 'finite_pair_checks':len(margins),'finite_margin_upper':str(finite_upper), + 'tail_margin_upper':str(tail_upper),'tail_derivative_upper':str(derivative_upper), + 'scope':'All positive integer child sizes and all binary tree shapes for this fixed root and PR6349 source.'} + + diff --git a/research/mixed-projector-query-root/controller.py b/research/mixed-projector-query-root/controller.py index d9c3330791..393524f903 100644 --- a/research/mixed-projector-query-root/controller.py +++ b/research/mixed-projector-query-root/controller.py @@ -27,7 +27,11 @@ def mix(rows): a = matrix(rows) ops = [] for j in range(6): - k = next(k for k in range(j, 6) if a[k][j]) + # A unit in the dyadic ring keeps every emitted scale dyadic. + pivots = [k for k in range(j, 6) if a[k][j] + and abs(a[k][j].numerator) & (abs(a[k][j].numerator)-1) == 0] + need(pivots, 'Each declared basis has a dyadic unit pivot') + k = pivots[0] if k != j: a[j], a[k] = a[k], a[j] ops.append(['SWAP', j, k]) @@ -119,7 +123,7 @@ def supplier(tree, x, y, exponent): need(stage == 18 and next_role == 34, 'Complete mixed-root dimensions') diagonal = [[targets[r][0], 0]+[int(s in targets[r][1]) for s in range(1, stage+1)] for r in range(next_role)] - return {'schema': 'mixed-projector-query-root/1', 'roles': next_role, + return {'schema': 'mixed-projector-query-root/2', 'roles': next_role, 'stages': stage, 'ambient_rank': 9+8*stage, 'nodes': nodes, 'events': events, 'diagonal': diagonal} @@ -203,14 +207,13 @@ def formula_invoice(local): targets = Counter({r: 18*n for r,n in local['helpers'].items()}) paid = Counter({r: 18*n for r,n in local['paid'].items()}) paid[1] += 17*104 - # Four child trees: 7, 2, 1 and 8 leaves. - for size, count in {2:8, 3:1, 4:3, 7:1, 8:1}.items(): + # Four child trees: 7, 2, 2 and 7 leaves. + for size, count in {2:8, 3:2, 4:2, 7:2}.items(): targets[1+8*size] += 208*count paid[8*size] += 208*count - for rank,count in {145:1,17:1,73:2,9:2}.items(): + for rank,count in {145:1,73:2,1:1,17:2}.items(): targets[rank] += 104*count - paid[16] += 104 - paid[8] += 208 + paid[16] += 208 return targets, paid diff --git a/research/mixed-projector-query-root/module_check.py b/research/mixed-projector-query-root/module_check.py index 89ec4480ad..8631a48310 100644 --- a/research/mixed-projector-query-root/module_check.py +++ b/research/mixed-projector-query-root/module_check.py @@ -136,7 +136,7 @@ def dense_product(a,b): 'Tensoring the one-column normalization is rejected') wrong_tensor_rejected = True tensor_columns += size - return {'fields':n,'full_sites':4,'thin_sites':3,'stage_ranks':[2,3,4,2], + return {'fields':n,'full_sites':4,'thin_sites':3,'stage_ranks':[2,3,3,2], 'polynomial_coefficients':2*16*n*n,'gaussian_characters':4, 'actual_tensor_gaussian_columns':tensor_columns, 'wrong_tensor_normalization_rejected':wrong_tensor_rejected, diff --git a/research/mixed-projector-query-root/pricing.py b/research/mixed-projector-query-root/pricing.py index a235780498..6c9f0db0f4 100644 --- a/research/mixed-projector-query-root/pricing.py +++ b/research/mixed-projector-query-root/pricing.py @@ -10,8 +10,8 @@ from fractions import Fraction as Q from controller import formula_invoice, need -KAPPA = Q('0.00327980') -TESTED = Q('0.003279805') +KAPPA = Q('0.00328467') +TESTED = Q('0.003284675') PREVIOUS = Q('0.00315057') @@ -48,10 +48,10 @@ def assemble(local, native, word, physical): need(main == physical['main_targets'], 'All main target phases and ranks') need(idle == physical['whole_idle_jobs'], 'All paired and individual whole idle jobs') need((targets, paid) == formula_invoice(local), 'Independent tree and emitted-event counts') - need((counts['LOCAL'], counts['QUERY'], counts['IDLE']) == (18, 17, 14) and counts['IDLE_ONE'] == 3 and counts['LAMBDA'] == 20, 'Complete caller census') - need((sum(targets.values()), sum(paid.values())) == (13652, 67092), 'All independent fields and paid calls') + need((counts['LOCAL'], counts['QUERY'], counts['IDLE']) == (18, 17, 14) and counts['IDLE_ONE'] == 2 and counts['LAMBDA'] == 20, 'Complete caller census') + need((sum(targets.values()), sum(paid.values())) == (13652, 66988), 'All independent fields and paid calls') need(sum(r*n for r, n in targets.items())-sum(r*n for r, n in paid.items()) == 760, 'Complete rank-mass surplus') - need((max(targets), max(paid)) == (145, 64), 'Maximum target and paid ranks') + need((max(targets), max(paid)) == (145, 56), 'Maximum target and paid ranks') return targets, paid, counts @@ -125,6 +125,9 @@ def wins(j): raw = 18*10**7 + 17*1664 + 32*34*104*len(word['events']) + 34*104*(26+1000) need(all(abs(Q(e[-1])) <= 16 for e in word['events'] if e[0] in ('ADD', 'SCALE')), 'Every emitted scalar coefficient has the declared growth bound') + need(all(Q(e[-1]).denominator & (Q(e[-1]).denominator-1) == 0 + for e in word['events'] if e[0] in ('ADD', 'SCALE')), + 'Every emitted rational scalar is dyadic') need(raw < 10**9, 'Complete ordinary-work budget') bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] atom = Q(bit['atom']) @@ -143,13 +146,13 @@ def wins(j): need(old_completion[0] > 1, 'The old completion cutoff does not fund the new inventory') bad = outer_module.ledger(dict(params, bit_saving=Q('.0027'))) need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT saving rejected') - return encode({'kappa': KAPPA, 'kappa_decimal': '0.00327980', 'previous_pr6353': PREVIOUS, + return encode({'kappa': KAPPA, 'kappa_decimal': '0.00328467', 'previous_pr6353': PREVIOUS, 'gain': KAPPA-PREVIOUS, 'relative_gain_percent': 100*(KAPPA/PREVIOUS-1), 'raw_root_interval': [lower, upper], 'raw_headroom': [lower-KAPPA, upper-KAPPA], 'derivative_upper': derivative_upper, 'margin_at_previous': E.display(margin(PREVIOUS)), 'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 760, 'full_forward_calls': 18, 'thin_queries': 17, - 'whole_idle_jobs': 3224, 'strictification': { + 'whole_idle_jobs': 3120, 'strictification': { 'tested': TESTED, 'power': power, 'cutoff': cutoff, 'floor': floor, 'tail_offset': offset, 'reserve': reserve, 'tail_decay': decay, 'tail_block': 128, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), diff --git a/research/mixed-projector-query-root/verify.py b/research/mixed-projector-query-root/verify.py index a1cc67d955..8c1306a2aa 100644 --- a/research/mixed-projector-query-root/verify.py +++ b/research/mixed-projector-query-root/verify.py @@ -14,7 +14,7 @@ ROOT = HERE.parents[1] LIFT = ROOT/'research/p104-native-input-lifting' TREE = ROOT/'research/balanced-query-tree' -STATUS = 'PASS_MIXED_PROJECTOR_QUERY_ROOT_KAPPA_00327980' +STATUS = 'PASS_MIXED_PROJECTOR_QUERY_ROOT_KAPPA_00328467' def need(ok, message): @@ -52,6 +52,7 @@ def run(): module = load(HERE/'module_check.py', 'mixed_root_module') physical = load(HERE/'physical.py', 'mixed_root_physical') price = load(HERE/'pricing.py', 'mixed_root_price') + ceiling = load(HERE/'ceiling.py', 'mixed_root_ceiling') support = load(LIFT/'support.py', 'support') constructor = load(LIFT/'construct.py', 'mixed_source_constructor') lift_checks = load(LIFT/'verify.py', 'mixed_source_checks') @@ -79,11 +80,21 @@ def run(): need(maps['full_calls'] == 18 and maps['physical_contacts'] == 7488, 'Every native contact') print('PASS native absolute phases, whole idles and physical caller', flush=True) result_price = price.run(local, native, word, maps, L) + intervals = L.load(L.ROOT/'research/higher-moment-strictification/verify.py', 'mixed_ceiling_intervals') + fixed_ceiling = ceiling.run(local, intervals, read(HERE/'ROOT.json')) + bad_root = read(HERE/'ROOT.json') + bad_root['masks'][3][0] = 1 + try: + ceiling.run(local, intervals, bad_root) + except ValueError as error: + controls['changed_ceiling_root'] = str(error) + else: + raise ValueError('A changed root entered the fixed-root ceiling') print('PASS complete invoice, both rational price engines, compiler and outer predicates', flush=True) return price.encode({'status':STATUS, 'source_inputs':sources, 'root':root_check, 'binary_module':binary_check, 'caller':caller, 'local':local, 'lifted_directions':directions, 'columns':columns, - 'native':native, 'physical':maps, 'price':result_price, + 'native':native, 'physical':maps, 'price':result_price, 'fixed_root_ceiling':fixed_ceiling, 'negative_controls':controls, 'assumptions':['native_all_columns','owned_erasure','compiler', 'precision_tape','analytic_recovery'], From d079398e6dfc895954862ea3ea5bf53111c7b5e7 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Mon, 2 Nov 2026 00:20:36 -0600 Subject: [PATCH 04/32] Record sealed replay and scoped root search limits --- research/mixed-projector-query-root/SEARCH.md | 13 ++++++++-- research/mixed-projector-query-root/TASK.json | 2 +- .../mixed-projector-query-root/VALIDATION.md | 25 ++++++++++++++----- .../mixed-projector-query-root/VERIFY.json | 2 +- 4 files changed, 32 insertions(+), 10 deletions(-) diff --git a/research/mixed-projector-query-root/SEARCH.md b/research/mixed-projector-query-root/SEARCH.md index b9f11d55a5..1363fb04c5 100644 --- a/research/mixed-projector-query-root/SEARCH.md +++ b/research/mixed-projector-query-root/SEARCH.md @@ -29,8 +29,10 @@ native basis data have dyadic coefficients. This is a bounded catalogue. It does not cover all rational bases, larger roots, noncommuting stage families or other query words. Floating searches over the catalogue do not prove that each pattern's price is optimal. -An additional integer-program screen has finite time limits and unresolved -solver bounds. It is not used as an exclusion certificate. +An additional integer-program screen checked 88 price-equivalence classes +from this catalogue, with native totals below 100. It found no better +candidate. The floating solver reported 47 completed optima and 41 time +limits with unresolved bounds. This is not an exact exclusion certificate. ## Child sizes @@ -47,6 +49,13 @@ PROOF.md states the full argument and its restrictions. ## Other local searches - Structured roots through 20 fields did not improve the retained price. + A later eight-field family kept the four stage ranks 2,3,3,2. Its 582,240 + bounded bases gave 351 support patterns. The price search recovered the + six-field bound and did not improve it. A separate pair-decomposition + search then tested all child totals through 200 for each of nine possible + added-stage support types, including thin anchor choices. Every best + floating margin stayed negative at .00328469. This is a bounded price + screen, not an exact exclusion theorem. - Braid moves on longer query words did not give a favorable complete bill in the tested finite domains. - Two- and four-copy coupled bases did not improve the scalar construction diff --git a/research/mixed-projector-query-root/TASK.json b/research/mixed-projector-query-root/TASK.json index 58626f9ee8..40fa090d04 100644 --- a/research/mixed-projector-query-root/TASK.json +++ b/research/mixed-projector-query-root/TASK.json @@ -68,7 +68,7 @@ "actual_scope": "Complete source-bound caller at conditional kappa 0.00328467, including all main fields, independent helpers, native phases, idle jobs, ordinary normalization, compiler and outer costs.", "bottleneck_link": "Complex supplier; changes the full signed target and paid moment while retaining admitted BIT .0034.", "outcome": "completed", - "evidence": "PROOF.md, ROOT.json, CONTROLLER.json, RESULT.json and VALIDATION.md.", + "evidence": "PROOF.md, ROOT.json, CONTROLLER.json, RESULT.json, ceiling.py, SEARCH.md and VALIDATION.md.", "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5600#discussioncomment-19209322", "stop_rule": "Require exact arbitrary-input and native identities, global normalization, a complete invoice, both rational engines, compiler and outer checks before a kappa claim.", "author": "Ali Romman", diff --git a/research/mixed-projector-query-root/VALIDATION.md b/research/mixed-projector-query-root/VALIDATION.md index 676e7b5b27..ed82c4208c 100644 --- a/research/mixed-projector-query-root/VALIDATION.md +++ b/research/mixed-projector-query-root/VALIDATION.md @@ -21,12 +21,25 @@ negative decreasing bound covers all larger totals. A separate derivative bound above 42 proves monotonicity throughout the retained BIT range. Changing a root mask is rejected before the ceiling calculation. -The first complete registered normal and optimized runs passed. The final -ceiling adds the explicit saving-range monotonicity check and a wrong-root -control. The final registered normal and optimized replays also passed with -those checks. Sealed-export and committed-byte checks are still pending for -this revision. -No previous revision's transport receipt is transferred to these bytes. +The complete registered normal and optimized replays passed, including the +saving-range monotonicity check and wrong-root ceiling control. The local +scientific commit is 52e87e4971a85a8f098fadb967dc75bee9f76c65. All 35 package +and declared-input files passed the committed-byte and owner-execute checks. +The official export passed integrity and coverage checks for all 17 inputs. + +The export SHA256 is +95f881c6250350dc19e3571a5f67a452237e100d4e561c73ac79361af933674b. +Its optimized verifier passed with empty PATH in a Git-free, read-only tree. +All 36 exported file hashes and all path modes stayed unchanged. An actual +source-word corruption failed its SHA256 gate. Swapping root input-basis +rows and regenerating the matching caller failed the inverse-basis check. +Both controls restored and rechecked every original byte and mode. + +The first extraction command requested gzip for the exporter's plain tar +file. Extraction stopped before a verifier ran. The archive was renamed +with its actual .tar format and extracted with automatic format detection. +The subsequent sealed replay and corruption controls passed. This setup +failure did not change the exported bytes or scientific claim. Discovery also replayed all 695 retained modular support patterns with a separate NumPy implementation. This checks the retained representatives, diff --git a/research/mixed-projector-query-root/VERIFY.json b/research/mixed-projector-query-root/VERIFY.json index e0481dae44..955f1be6cd 100644 --- a/research/mixed-projector-query-root/VERIFY.json +++ b/research/mixed-projector-query-root/VERIFY.json @@ -31,7 +31,7 @@ "{package}/verify.py" ], "timeout_seconds": 590, - "checks": "Authenticate the unchanged native source; check exact root, global normalization, all native input columns, full physical caller, complete invoice, both interval engines, compiler and outer ledger." + "checks": "Authenticate the unchanged native source; check the exact root, global normalization, all native input columns, physical caller, complete invoice, both interval engines, compiler, outer ledger and fixed-root ceiling for all binary child sizes." }, { "argv": [ From 24f03629fc2a939ea0c6c015017bf1cdc07e06cd Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Mon, 2 Nov 2026 03:02:21 -0600 Subject: [PATCH 05/32] Compose the mixed root with PR6353 at kappa 0.00328551 --- .../CEILING-EDITS.json | 18 + .../mixed-root-source-composition/INPUTS.json | 236 +++++++ research/mixed-root-source-composition/NOTICE | 590 ++++++++++++++++++ .../PRICING-EDITS.json | 30 + .../mixed-root-source-composition/PROOF.md | 107 ++++ .../mixed-root-source-composition/README.md | 60 ++ .../mixed-root-source-composition/RESULT.json | 425 +++++++++++++ .../SOURCES.json | 33 + .../mixed-root-source-composition/TASK.json | 91 +++ .../mixed-root-source-composition/VERIFY.json | 30 + .../mixed-root-source-composition/ceiling.py | 65 ++ .../mixed-root-source-composition/pricing.py | 171 +++++ .../mixed-root-source-composition/sources.tar | Bin 0 -> 4823040 bytes .../mixed-root-source-composition/verify.py | 187 ++++++ 14 files changed, 2043 insertions(+) create mode 100644 research/mixed-root-source-composition/CEILING-EDITS.json create mode 100644 research/mixed-root-source-composition/INPUTS.json create mode 100644 research/mixed-root-source-composition/NOTICE create mode 100644 research/mixed-root-source-composition/PRICING-EDITS.json create mode 100644 research/mixed-root-source-composition/PROOF.md create mode 100644 research/mixed-root-source-composition/README.md create mode 100644 research/mixed-root-source-composition/RESULT.json create mode 100644 research/mixed-root-source-composition/SOURCES.json create mode 100644 research/mixed-root-source-composition/TASK.json create mode 100644 research/mixed-root-source-composition/VERIFY.json create mode 100644 research/mixed-root-source-composition/ceiling.py create mode 100644 research/mixed-root-source-composition/pricing.py create mode 100644 research/mixed-root-source-composition/sources.tar create mode 100644 research/mixed-root-source-composition/verify.py diff --git a/research/mixed-root-source-composition/CEILING-EDITS.json b/research/mixed-root-source-composition/CEILING-EDITS.json new file mode 100644 index 0000000000..872ed925cb --- /dev/null +++ b/research/mixed-root-source-composition/CEILING-EDITS.json @@ -0,0 +1,18 @@ +[ + [ + "CEILING=Q('.00328469')", + "CEILING=Q('.00328554')" + ], + [ + "this fixed root and PR6349 source.", + "this fixed root and PR6353 source." + ], + [ + "The native source stays fixed. Other roots and native sources are outside", + "Adapted from the prior fixed-root ceiling by Ali Romman with OpenAI Codex.\nThe contracted native source stays fixed. Other roots and sources are outside" + ], + [ + "source.'}\n\n\n", + "source.'}\n" + ] +] diff --git a/research/mixed-root-source-composition/INPUTS.json b/research/mixed-root-source-composition/INPUTS.json new file mode 100644 index 0000000000..0af459cf4e --- /dev/null +++ b/research/mixed-root-source-composition/INPUTS.json @@ -0,0 +1,236 @@ +{ + "schema": 1, + "archive_sha256": "6d05208f4fa1d98b4b63a8b2d9366576313a1f1466232a6a4f1a286de23c292b", + "root_head": "52e87e4971a85a8f098fadb967dc75bee9f76c65", + "contract_head": "db2a20bc50bc7a8a4db931af85ce7f012ae7c3c3", + "files": [ + { + "path": "research/balanced-query-tree/CONTROLLER.json", + "head": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "sha256": "6fd67eaabe659956d6694471d3fd7d2824c0a4a79cf3b8f22922f7189b11b91f", + "git_blob": "1f2e375b24aba5fb25580dfea7fab7a2049f3eb8" + }, + { + "path": "research/balanced-query-tree/RESULT.json", + "head": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "sha256": 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contracted-source composition +Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. +The earlier local contracted-mixed-query-local package supplies the adapter. +The present package changes its frozen root and complete bound. + +Local contracted-source and mixed-root composition +Ali Romman, with substantial OpenAI Codex assistance; no subagents. +Apache-2.0. Neither source construction is claimed as new here. + +Mixed projector query root +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. No subagents. + +The new contribution is the normalized six-field root, its weighted binary +children, exact complete caller, full invoice and conditional bound. +The shortest central-involution query tuple is from the credited +five-call-projector-rigidity package by Ali Romman with OpenAI Codex. +The binary query extension is PR6348. The unchanged native source is PR6349. +The simple normalization identity is not claimed as a new general algebra theorem. +The native construction, scalar compression and inherited proof engines are +predecessor work. Their exact source notices follow. + +Source: research/balanced-query-tree/NOTICE + +Binary query-tree caller + +New construction, proof and code: Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. No subagents. + +Cinna Davis supplies the productive path caller, query thinning and exact Laurent factorization. Ali Romman supplies the all-forward P104 binding in PR5544 and the retained-operand word in PR6167. The native word and interval/compiler lineage remain predecessor work. The new contribution is the four-field query extension, its tree composition, complete invoice and conditional price. + +The authenticated PR6167 notice follows. + +Retained-operand descent: Ali Romman, with substantial OpenAI Codex assistance. +Apache-2.0. + +The exact source word and price are from DreamingOfClouds, PR6144 and PR6143, +with Claude Opus 5.5 (Anthropic), via Claude Code. They extend PR6030 and PR5907. +The source reader is adapted from that work. The gzip portability controls +retain Douglas Colkitt and Maxime Fleury credit. + +The pinned PR5827 checker and all earlier source notices are retained below. + +Unread-register path resynthesis +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author-side. + +Mason Hale supplied PR5811, the complete two-block composition and the exact +role92 remapping and fourth accumulation. The earlier elementary accumulation, +retained-copy and second-block work is by Ali Romman. Joel Pulikkan supplied +R22. Dugongue supplied the concurrent baseline composition proof. Their source +notice and proof are retained byte for byte under inputs/pr5811-*. + +The source closure retains flyingviper, Cinna Davis, David Arias, Gareth +Davidson, Jacob Alan Sussman, zxv, Cao Yifan, Pierre-Loic Doulcet, thu-nmrc, +Scratch-net and all native/helper/controller/compiler/geometry/analytic +predecessors. The exact PR5786 source archive and its nested notices remain. +This package does not claim any predecessor construction as new. + +Exact PR5811 vendor/accumulated/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +Accumulated native updates +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. The same assistant made the construction and the author checks. + +Concurrent scope: Discussion5125 now tests retained copies in the transposed +supplier. That route uses the same source/destination duality. This package +claims the three fixed forward-supplier groups and their complete result, +not the elementary accumulation identity or the broader transposed search. + +Exact source: PR5786 at 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. +The complete predecessor notice follows unchanged. + +Asynchronous helper hubs +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. + +Retained native copies from PR5774 at 7d6ec0cdef31d0c37b7d2563e709979caa0d5eae. +All prior credit follows unchanged. + +Paid intermediate meetings and collective helper splits. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. All checks are author-side calculations. + +The complete PR5718 notice follows unchanged. + +Four paid interior public-basis changes. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. + +The following exact notice is retained from PR5660. + +New helper-subspace construction, proof and replay: +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The same assistant performed the construction and author-side checks. + +Retained contributions: +flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613 +relay/split compositions. +Scratch-net: PR5606 prepared-helper identities and target debit. +Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source. +Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame +change, PR5580 contact step, +and PR5544/5545 complete P104 caller. +Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. +DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. +thu-nmrc: PR5551 contact improvements. +Gareth Davidson (bitplane): PR2305 source composition. +David Arias: PR2152 coalesced P104 word. +Cinna Davis: PR2219 private reuse and the controller lineage. +Jacob Alan Sussman: productive mixed-target recursion. +zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage. +GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept. +The retained source notices preserve earlier geometry, BIT and analytic credit. + +The elementary rank-one basis identity is not claimed as a new general +linear-algebra theorem. The contribution is its explicit independent-target +use on this P104 word and the complete conditional kappa improvement. + +New contribution: Ali Romman, with substantial OpenAI Codex assistance. +The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644. +The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit. +The compensated triangle method retains Cinna Davis PR4692 credit. +No subagents were used for this contribution. Apache-2.0. + +Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by +Ali Romman corroborates it. This package credits that released composition +and contributes the further four-gate placement. + +New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices. + +Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial +OpenAI Codex assistance, including independent AI review agents. Apache-2.0. + +Retained native-copy construction +Prepared by Ali Romman with substantial OpenAI Codex assistance. No subagents. +The paid-meeting source is PR5751 by Ali Romman with OpenAI Codex assistance. +The dimension-four span [265,194,164,75] is from Joel Pulikkan / GamingPuzzled +PR5739, with Claude Opus 5.5 assistance. The R22 block edits are not included. +The retained-copy mechanism, exact constructor, source-specific verification, +new price and proof are the contribution of this package. Apache-2.0. + +Exact PR5811 vendor/blocks/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +The second block is PR5796 at4b30391e633ba0c7c674f03586ae97d443e9bc9c, by Ali Romman with substantial OpenAI Codex assistance, following Joel Pulikkan/GamingPuzzled R22. Exact notice, plan, proof and source words are retained in source/SECOND-* unchanged. + +The final immediate source is PR5786 asynchronous helper hubs by Ali Romman with substantial OpenAI Codex assistance. Its three temporal helper splits and complete completion parameters are retained and credited. The earlier PR5774-only composition is a superseded checkpoint, not a separate contribution. + +New complete retained-copy and R22 composition: Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. + +The thirteen retained native conversions and changed helper targets are by Ali Romman with OpenAI Codex assistance in PR5774. The R22 block and rank-four basis are by Joel Pulikkan (GamingPuzzled), with Claude Opus5.5 assistance, in PR5739/5756. The complete source archive and R22 notice remain unchanged. + +The construction retains Ali Romman PR5751 paid intermediate meetings, flyingviper PR5718 boundary splits, Cinna Davis's productive controller, Jacob Alan Sussman's productive recursion, zxv and Cao Yifan's interval/compiler line, and every P104/native/BIT predecessor in the source notices. The source engines are reused under exact byte bindings, not claimed as new implementations. + +Source: research/p104-native-input-lifting/NOTICE + +Native helper input lifting +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author checks. + +The direct source is PR6314 at 36533d4d1b4e2dd8672427461b12de3001b85810, +by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +It compresses the scalar word of PR6167 without a kappa change. +The four native input lifts and their complete conditional price are new here. +The basis identity is elementary linear algebra; no new general theorem +for that identity is claimed. + +The PR6167 source notice follows unchanged. Its nested source archive also +retains the earlier notices. + +Retained-operand descent: Ali Romman, with substantial OpenAI Codex assistance. +Apache-2.0. + +The exact source word and price are from DreamingOfClouds, PR6144 and PR6143, +with Claude Opus 5.5 (Anthropic), via Claude Code. They extend PR6030 and PR5907. +The source reader is adapted from that work. The gzip portability controls +retain Douglas Colkitt and Maxime Fleury credit. + +The pinned PR5827 checker and all earlier source notices are retained below. + +Unread-register path resynthesis +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author-side. + +Mason Hale supplied PR5811, the complete two-block composition and the exact +role92 remapping and fourth accumulation. The earlier elementary accumulation, +retained-copy and second-block work is by Ali Romman. Joel Pulikkan supplied +R22. Dugongue supplied the concurrent baseline composition proof. Their source +notice and proof are retained byte for byte under inputs/pr5811-*. + +The source closure retains flyingviper, Cinna Davis, David Arias, Gareth +Davidson, Jacob Alan Sussman, zxv, Cao Yifan, Pierre-Loic Doulcet, thu-nmrc, +Scratch-net and all native/helper/controller/compiler/geometry/analytic +predecessors. The exact PR5786 source archive and its nested notices remain. +This package does not claim any predecessor construction as new. + +Exact PR5811 vendor/accumulated/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +Accumulated native updates +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. The same assistant made the construction and the author checks. + +Concurrent scope: Discussion5125 now tests retained copies in the transposed +supplier. That route uses the same source/destination duality. This package +claims the three fixed forward-supplier groups and their complete result, +not the elementary accumulation identity or the broader transposed search. + +Exact source: PR5786 at 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. +The complete predecessor notice follows unchanged. + +Asynchronous helper hubs +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. + +Retained native copies from PR5774 at 7d6ec0cdef31d0c37b7d2563e709979caa0d5eae. +All prior credit follows unchanged. + +Paid intermediate meetings and collective helper splits. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. All checks are author-side calculations. + +The complete PR5718 notice follows unchanged. + +Four paid interior public-basis changes. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. + +The following exact notice is retained from PR5660. + +New helper-subspace construction, proof and replay: +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The same assistant performed the construction and author-side checks. + +Retained contributions: +flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613 +relay/split compositions. +Scratch-net: PR5606 prepared-helper identities and target debit. +Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source. +Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame +change, PR5580 contact step, +and PR5544/5545 complete P104 caller. +Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. +DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. +thu-nmrc: PR5551 contact improvements. +Gareth Davidson (bitplane): PR2305 source composition. +David Arias: PR2152 coalesced P104 word. +Cinna Davis: PR2219 private reuse and the controller lineage. +Jacob Alan Sussman: productive mixed-target recursion. +zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage. +GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept. +The retained source notices preserve earlier geometry, BIT and analytic credit. + +The elementary rank-one basis identity is not claimed as a new general +linear-algebra theorem. The contribution is its explicit independent-target +use on this P104 word and the complete conditional kappa improvement. + +New contribution: Ali Romman, with substantial OpenAI Codex assistance. +The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644. +The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit. +The compensated triangle method retains Cinna Davis PR4692 credit. +No subagents were used for this contribution. Apache-2.0. + +Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by +Ali Romman corroborates it. This package credits that released composition +and contributes the further four-gate placement. + +New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices. + +Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial +OpenAI Codex assistance, including independent AI review agents. Apache-2.0. + +Retained native-copy construction +Prepared by Ali Romman with substantial OpenAI Codex assistance. No subagents. +The paid-meeting source is PR5751 by Ali Romman with OpenAI Codex assistance. +The dimension-four span [265,194,164,75] is from Joel Pulikkan / GamingPuzzled +PR5739, with Claude Opus 5.5 assistance. The R22 block edits are not included. +The retained-copy mechanism, exact constructor, source-specific verification, +new price and proof are the contribution of this package. Apache-2.0. + +Exact PR5811 vendor/blocks/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +The second block is PR5796 at4b30391e633ba0c7c674f03586ae97d443e9bc9c, by Ali Romman with substantial OpenAI Codex assistance, following Joel Pulikkan/GamingPuzzled R22. Exact notice, plan, proof and source words are retained in source/SECOND-* unchanged. + +The final immediate source is PR5786 asynchronous helper hubs by Ali Romman with substantial OpenAI Codex assistance. Its three temporal helper splits and complete completion parameters are retained and credited. The earlier PR5774-only composition is a superseded checkpoint, not a separate contribution. + +New complete retained-copy and R22 composition: Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. + +The thirteen retained native conversions and changed helper targets are by Ali Romman with OpenAI Codex assistance in PR5774. The R22 block and rank-four basis are by Joel Pulikkan (GamingPuzzled), with Claude Opus5.5 assistance, in PR5739/5756. The complete source archive and R22 notice remain unchanged. + +The construction retains Ali Romman PR5751 paid intermediate meetings, flyingviper PR5718 boundary splits, Cinna Davis's productive controller, Jacob Alan Sussman's productive recursion, zxv and Cao Yifan's interval/compiler line, and every P104/native/BIT predecessor in the source notices. The source engines are reused under exact byte bindings, not claimed as new implementations. + + +Joint native output contraction +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author checks. + +PR6349 supplies the exact native input-lift source. PR6348 supplies the fixed +binary query-tree caller and price engine. PR6350, by Ali Romman with OpenAI +Codex assistance, supplies the released composition control and its prior +conditional claim. Its source and caller are recounted here from main; no +pending PR6350 code is imported. Cinna Davis supplies the productive caller, +thin-query interface and exact Laurent factorization. + +The new result is the explicit nine-helper joint output contraction, its +literal forward word and complete conditional price. The input/departure basis +identity is elementary linear algebra. No new general linear algebra theorem, +native duality theorem or caller construction is claimed. + +The exact PR6349 and PR6348 notices follow. Their nested source archive retains +all earlier native, helper, recursion, compiler, BIT and analytic attribution. + +Native helper input lifting +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author checks. + +The direct source is PR6314 at 36533d4d1b4e2dd8672427461b12de3001b85810, +by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +It compresses the scalar word of PR6167 without a kappa change. +The four native input lifts and their complete conditional price are new here. +The basis identity is elementary linear algebra; no new general theorem +for that identity is claimed. + +The PR6167 source notice follows unchanged. Its nested source archive also +retains the earlier notices. + +Retained-operand descent: Ali Romman, with substantial OpenAI Codex assistance. +Apache-2.0. + +The exact source word and price are from DreamingOfClouds, PR6144 and PR6143, +with Claude Opus 5.5 (Anthropic), via Claude Code. They extend PR6030 and PR5907. +The source reader is adapted from that work. The gzip portability controls +retain Douglas Colkitt and Maxime Fleury credit. + +The pinned PR5827 checker and all earlier source notices are retained below. + +Unread-register path resynthesis +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author-side. + +Mason Hale supplied PR5811, the complete two-block composition and the exact +role92 remapping and fourth accumulation. The earlier elementary accumulation, +retained-copy and second-block work is by Ali Romman. Joel Pulikkan supplied +R22. Dugongue supplied the concurrent baseline composition proof. Their source +notice and proof are retained byte for byte under inputs/pr5811-*. + +The source closure retains flyingviper, Cinna Davis, David Arias, Gareth +Davidson, Jacob Alan Sussman, zxv, Cao Yifan, Pierre-Loic Doulcet, thu-nmrc, +Scratch-net and all native/helper/controller/compiler/geometry/analytic +predecessors. The exact PR5786 source archive and its nested notices remain. +This package does not claim any predecessor construction as new. + +Exact PR5811 vendor/accumulated/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +Accumulated native updates +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. The same assistant made the construction and the author checks. + +Concurrent scope: Discussion5125 now tests retained copies in the transposed +supplier. That route uses the same source/destination duality. This package +claims the three fixed forward-supplier groups and their complete result, +not the elementary accumulation identity or the broader transposed search. + +Exact source: PR5786 at 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. +The complete predecessor notice follows unchanged. + +Asynchronous helper hubs +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. + +Retained native copies from PR5774 at 7d6ec0cdef31d0c37b7d2563e709979caa0d5eae. +All prior credit follows unchanged. + +Paid intermediate meetings and collective helper splits. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. All checks are author-side calculations. + +The complete PR5718 notice follows unchanged. + +Four paid interior public-basis changes. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. + +The following exact notice is retained from PR5660. + +New helper-subspace construction, proof and replay: +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The same assistant performed the construction and author-side checks. + +Retained contributions: +flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613 +relay/split compositions. +Scratch-net: PR5606 prepared-helper identities and target debit. +Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source. +Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame +change, PR5580 contact step, +and PR5544/5545 complete P104 caller. +Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. +DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. +thu-nmrc: PR5551 contact improvements. +Gareth Davidson (bitplane): PR2305 source composition. +David Arias: PR2152 coalesced P104 word. +Cinna Davis: PR2219 private reuse and the controller lineage. +Jacob Alan Sussman: productive mixed-target recursion. +zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage. +GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept. +The retained source notices preserve earlier geometry, BIT and analytic credit. + +The elementary rank-one basis identity is not claimed as a new general +linear-algebra theorem. The contribution is its explicit independent-target +use on this P104 word and the complete conditional kappa improvement. + +New contribution: Ali Romman, with substantial OpenAI Codex assistance. +The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644. +The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit. +The compensated triangle method retains Cinna Davis PR4692 credit. +No subagents were used for this contribution. Apache-2.0. + +Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by +Ali Romman corroborates it. This package credits that released composition +and contributes the further four-gate placement. + +New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices. + +Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial +OpenAI Codex assistance, including independent AI review agents. Apache-2.0. + +Retained native-copy construction +Prepared by Ali Romman with substantial OpenAI Codex assistance. No subagents. +The paid-meeting source is PR5751 by Ali Romman with OpenAI Codex assistance. +The dimension-four span [265,194,164,75] is from Joel Pulikkan / GamingPuzzled +PR5739, with Claude Opus 5.5 assistance. The R22 block edits are not included. +The retained-copy mechanism, exact constructor, source-specific verification, +new price and proof are the contribution of this package. Apache-2.0. + +Exact PR5811 vendor/blocks/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +The second block is PR5796 at4b30391e633ba0c7c674f03586ae97d443e9bc9c, by Ali Romman with substantial OpenAI Codex assistance, following Joel Pulikkan/GamingPuzzled R22. Exact notice, plan, proof and source words are retained in source/SECOND-* unchanged. + +The final immediate source is PR5786 asynchronous helper hubs by Ali Romman with substantial OpenAI Codex assistance. Its three temporal helper splits and complete completion parameters are retained and credited. The earlier PR5774-only composition is a superseded checkpoint, not a separate contribution. + +New complete retained-copy and R22 composition: Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. + +The thirteen retained native conversions and changed helper targets are by Ali Romman with OpenAI Codex assistance in PR5774. The R22 block and rank-four basis are by Joel Pulikkan (GamingPuzzled), with Claude Opus5.5 assistance, in PR5739/5756. The complete source archive and R22 notice remain unchanged. + +The construction retains Ali Romman PR5751 paid intermediate meetings, flyingviper PR5718 boundary splits, Cinna Davis's productive controller, Jacob Alan Sussman's productive recursion, zxv and Cao Yifan's interval/compiler line, and every P104/native/BIT predecessor in the source notices. The source engines are reused under exact byte bindings, not claimed as new implementations. + +Binary query-tree caller + +New construction, proof and code: Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. No subagents. + +Cinna Davis supplies the productive path caller, query thinning and exact Laurent factorization. Ali Romman supplies the all-forward P104 binding in PR5544 and the retained-operand word in PR6167. The native word and interval/compiler lineage remain predecessor work. The new contribution is the four-field query extension, its tree composition, complete invoice and conditional price. + +The authenticated PR6167 notice follows. + +Retained-operand descent: Ali Romman, with substantial OpenAI Codex assistance. +Apache-2.0. + +The exact source word and price are from DreamingOfClouds, PR6144 and PR6143, +with Claude Opus 5.5 (Anthropic), via Claude Code. They extend PR6030 and PR5907. +The source reader is adapted from that work. The gzip portability controls +retain Douglas Colkitt and Maxime Fleury credit. + +The pinned PR5827 checker and all earlier source notices are retained below. + +Unread-register path resynthesis +Copyright 2026 Ali Romman. Apache-2.0. + +New construction, code, calculations and prose: Ali Romman with substantial +OpenAI Codex assistance. No subagents. All new checks are author-side. + +Mason Hale supplied PR5811, the complete two-block composition and the exact +role92 remapping and fourth accumulation. The earlier elementary accumulation, +retained-copy and second-block work is by Ali Romman. Joel Pulikkan supplied +R22. Dugongue supplied the concurrent baseline composition proof. Their source +notice and proof are retained byte for byte under inputs/pr5811-*. + +The source closure retains flyingviper, Cinna Davis, David Arias, Gareth +Davidson, Jacob Alan Sussman, zxv, Cao Yifan, Pierre-Loic Doulcet, thu-nmrc, +Scratch-net and all native/helper/controller/compiler/geometry/analytic +predecessors. The exact PR5786 source archive and its nested notices remain. +This package does not claim any predecessor construction as new. + +Exact PR5811 vendor/accumulated/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +Accumulated native updates +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. The same assistant made the construction and the author checks. + +Concurrent scope: Discussion5125 now tests retained copies in the transposed +supplier. That route uses the same source/destination duality. This package +claims the three fixed forward-supplier groups and their complete result, +not the elementary accumulation identity or the broader transposed search. + +Exact source: PR5786 at 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. +The complete predecessor notice follows unchanged. + +Asynchronous helper hubs +New work: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. + +Retained native copies from PR5774 at 7d6ec0cdef31d0c37b7d2563e709979caa0d5eae. +All prior credit follows unchanged. + +Paid intermediate meetings and collective helper splits. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. All checks are author-side calculations. + +The complete PR5718 notice follows unchanged. + +Four paid interior public-basis changes. +Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0. +No subagents. + +The following exact notice is retained from PR5660. + +New helper-subspace construction, proof and replay: +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The same assistant performed the construction and author-side checks. + +Retained contributions: +flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613 +relay/split compositions. +Scratch-net: PR5606 prepared-helper identities and target debit. +Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source. +Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame +change, PR5580 contact step, +and PR5544/5545 complete P104 caller. +Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. +DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. +thu-nmrc: PR5551 contact improvements. +Gareth Davidson (bitplane): PR2305 source composition. +David Arias: PR2152 coalesced P104 word. +Cinna Davis: PR2219 private reuse and the controller lineage. +Jacob Alan Sussman: productive mixed-target recursion. +zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage. +GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept. +The retained source notices preserve earlier geometry, BIT and analytic credit. + +The elementary rank-one basis identity is not claimed as a new general +linear-algebra theorem. The contribution is its explicit independent-target +use on this P104 word and the complete conditional kappa improvement. + +New contribution: Ali Romman, with substantial OpenAI Codex assistance. +The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644. +The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit. +The compensated triangle method retains Cinna Davis PR4692 credit. +No subagents were used for this contribution. Apache-2.0. + +Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by +Ali Romman corroborates it. This package credits that released composition +and contributes the further four-gate placement. + +New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices. + +Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial +OpenAI Codex assistance, including independent AI review agents. Apache-2.0. + +Retained native-copy construction +Prepared by Ali Romman with substantial OpenAI Codex assistance. No subagents. +The paid-meeting source is PR5751 by Ali Romman with OpenAI Codex assistance. +The dimension-four span [265,194,164,75] is from Joel Pulikkan / GamingPuzzled +PR5739, with Claude Opus 5.5 assistance. The R22 block edits are not included. +The retained-copy mechanism, exact constructor, source-specific verification, +new price and proof are the contribution of this package. Apache-2.0. + +Exact PR5811 vendor/blocks/NOTICE follows. Source head: +33d7760d0a6fea6394aefd014eea68f0af02a92e + +The second block is PR5796 at4b30391e633ba0c7c674f03586ae97d443e9bc9c, by Ali Romman with substantial OpenAI Codex assistance, following Joel Pulikkan/GamingPuzzled R22. Exact notice, plan, proof and source words are retained in source/SECOND-* unchanged. + +The final immediate source is PR5786 asynchronous helper hubs by Ali Romman with substantial OpenAI Codex assistance. Its three temporal helper splits and complete completion parameters are retained and credited. The earlier PR5774-only composition is a superseded checkpoint, not a separate contribution. + +New complete retained-copy and R22 composition: Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. + +The thirteen retained native conversions and changed helper targets are by Ali Romman with OpenAI Codex assistance in PR5774. The R22 block and rank-four basis are by Joel Pulikkan (GamingPuzzled), with Claude Opus5.5 assistance, in PR5739/5756. The complete source archive and R22 notice remain unchanged. + +The construction retains Ali Romman PR5751 paid intermediate meetings, flyingviper PR5718 boundary splits, Cinna Davis's productive controller, Jacob Alan Sussman's productive recursion, zxv and Cao Yifan's interval/compiler line, and every P104/native/BIT predecessor in the source notices. The source engines are reused under exact byte bindings, not claimed as new implementations. diff --git a/research/mixed-root-source-composition/PRICING-EDITS.json b/research/mixed-root-source-composition/PRICING-EDITS.json new file mode 100644 index 0000000000..c0c62b4b5a --- /dev/null +++ b/research/mixed-root-source-composition/PRICING-EDITS.json @@ -0,0 +1,30 @@ +[ + [ + "KAPPA = Q('0.00328467')", + "KAPPA = Q('0.00328551')" + ], + [ + "TESTED = Q('0.003284675')", + "TESTED = Q('0.003285515')" + ], + [ + "PREVIOUS = Q('0.00315057')", + "PREVIOUS = Q('0.00328467')" + ], + [ + "(13652, 66988)", + "(13652, 67096)" + ], + [ + "The mixed root improves the published PR6353 claim", + "The composed source improves the fixed root claim" + ], + [ + "'kappa_decimal': '0.00328467', 'previous_pr6353': PREVIOUS", + "'kappa_decimal': '0.00328551', 'previous_fixed_root': PREVIOUS" + ], + [ + "This file counts the new root, individual idles and ordinary normalization.", + "This adapter keeps the root and changes the native source invoice.\nIt includes all nine output contractions and their productive target debits." + ] +] diff --git a/research/mixed-root-source-composition/PROOF.md b/research/mixed-root-source-composition/PROOF.md new file mode 100644 index 0000000000..a7a2433c80 --- /dev/null +++ b/research/mixed-root-source-composition/PROOF.md @@ -0,0 +1,107 @@ +# Complete composition of the root and contracted native source + +The new conditional claim is kappa 0.00328551. The proof uses the five +inherited assumptions: native_all_columns, owned_erasure, compiler, +precision_tape and analytic_recovery. No unconditional theorem is claimed. + +## Exact source and interface + +The root source is local commit 52e87e4971a85a8f098fadb967dc75bee9f76c65. +Its four binary children have 7, 2, 2 and 7 leaves. Its full projector ranks +are 2, 3, 3 and 2. The constructor emits the same 570 instructions and +34 independent main fields per port. The replay checks all 1,156 endpoint +coefficients in the declared Laurent ring, including all normalizations. + +PR6353 at db2a20bc50bc7a8a4db931af85ce7f012ae7c3c3 changes nine helper +outputs. It keeps the native main interface D U(q). The source constructor +rebuilds every byte of its 17,657-event word and every joint-basis witness. +Its complete scalar replay checks all independent public inputs and owned +lifetimes. The separate dense reverse replay checks 799 columns and +638,401 coefficients. The native phase checker then verifies the actual +word. The caller checker binds all 7,488 physical native contacts and all +paired and individual whole idle jobs. + +The local source has 29 owned labels, 41 lifetimes and peak ownership 13. +All 562 helper inputs per native call remain independent. They are separate +from the caller inputs and from the helpers in other calls. + +## Complete invoice + +Write H(r)=r^(1-kappa). Relative to PR6349, one contracted native call has +the paid change + +```text +14 H1 - 4 H2 - 3 H3 + 4 H4 - 5 H5 +``` + +and the productive helper change + +```text +H5 + 8 H8 - 9 H9. +``` + +The checker reconstructs these two changes from the exact words. It then +requires exactly 18 copies of each change in the complete caller bill. +No target debit is omitted. The emitted instructions and a separate formula +give the same invoice. + +There are 67,096 paid jobs and 13,652 productive fields. Paid rank mass is +185,124 and productive rank mass is 185,884. Their difference is 760. +The maximum paid rank is 56; the maximum productive rank is 145. All +17 thin queries, 14 paired whole idles and two individual whole idles are +charged. All 20 ordinary normalizations remain in the caller. + +Two rational moment engines give a strict raw crossing in +(0.00328552920257, 0.00328552920258). The unchanged-source caller has a +strict negative margin at the new claim. Its old crossing is separately +checked in (0.00328468791927, 0.00328468791928). + +## Completion, compiler and outer transfer + +The tested saving is 0.003285515. Completion uses power 1024, cutoff 12, +floor 13, offset 1/7, reserve 10^-12 and decay 31/32. Both moment engines, +all completion ratios and the exact compiler integer grid must pass. + +The complete ordinary allowance is 248,152,864, below the retained budget +of 10^9. It includes source scalar work, native routes, the changed owned +lifetimes, every caller basis operation and every normalization. The BIT +admission remains 0.0034. All 54 strict and four functional outer predicates +are positive. The large uniform word is not materialized. + +The checker also rejects 53 controls, including a missing paid native job, +a missing helper target debit, damaged source bytes and the inherited +native, caller and source-semantic faults. Verification under optimized +Python keeps these checks active. + +## Ceiling for all binary child sizes + +The fixed-root ceiling is recalculated with the contracted source. At +kappa 0.00328554, rational outward intervals check all 4,851 binary splits +and all 4,656 root pair choices with total size below 100. Every margin +upper bound is negative; the largest is below -0.00002385 per port. + +For all larger totals, the same concavity argument as the root source +gives a decreasing upper bound. Its value at 100 is below -1.853 and +its derivative is below -0.0592. The native deficit derivative stays +above 42.04 throughout the admitted range. Thus larger child sizes, +other binary tree shapes and larger savings up to 0.0034 cannot pass +for this fixed root and PR6353 source. + +The claimed saving is within 0.00000003 of this ceiling. This is a scoped +ceiling. It does not limit a changed root, native source or query interface. + +## Scope and open next questions + +This is a composition increment of 0.0255733 percent over the previous +local claim. It is not the requested large breakthrough. It does not prove +global optimality, a practical speedup, all five framework assumptions or +independent scientific acceptance. The selected frontier stays unchanged. + +The next review should check the exact source closure and all 18 productive +debits before it checks the outer inequalities. A larger construction must +change the source or caller and supply a new complete identity and bill. + +Credit stays with the two source packages, the earlier local composition +adapter and all native, helper, caller, recursion, compiler, BIT and analytic +authors in `NOTICE`. New composition and checks: Ali Romman with substantial +OpenAI Codex assistance; no subagents. Apache-2.0. diff --git a/research/mixed-root-source-composition/README.md b/research/mixed-root-source-composition/README.md new file mode 100644 index 0000000000..4c8faa98ac --- /dev/null +++ b/research/mixed-root-source-composition/README.md @@ -0,0 +1,60 @@ +# Local root and source composition + +The complete conditional bound is **kappa 0.00328551**. The previous local +bound was 0.00328467. The new gain is 0.0255733 percent. This does not meet +the requested one-percent improvement over that local result. + +This package combines the current mixed-projector root with PR6353's nine +native output contractions. It keeps the root, all four child trees and all +570 caller events unchanged. Each of the 18 native calls uses the contracted +source, with every productive target debit included. + +The exact raw crossing is in +`(0.00328552920257, 0.00328552920258)`. The full replay passes at the claim +above and tested saving 0.003285515. There are 67,096 paid jobs and 13,652 +independent productive fields. The complete rank-mass surplus remains 760. + +This result is local only. No PR, push or selected-frontier change is made. +The five inherited framework assumptions remain. The checks are author +checks; independent scientific review and hosted replay remain open. + +## Replay + +Use Python 3.12 and its standard library: + +```sh +python3 -I -B research/mixed-root-source-composition/verify.py +python3 -I -O -B research/mixed-root-source-composition/verify.py +``` + +The source archive is complete. The checker authenticates its 38 files +before it loads any predecessor code. It reconstructs the native word, +checks its arbitrary inputs and native phases, and checks the complete +caller, price, compiler and outer ledger. See `VALIDATION.md` for the +commands that were actually run and their limits. + +## Sources and credit + +The root is frozen at local commit +`52e87e4971a85a8f098fadb967dc75bee9f76c65`. The native source is +[PR6353](https://github.com/CrocSwap/integer-mult-bounds/pull/6353), exact +head `db2a20bc50bc7a8a4db931af85ce7f012ae7c3c3`. Canonical main is +`7c49fe32c55de02c2c873655c804b16e4c3fef0a`. + +The earlier local `contracted-mixed-query-local` package supplied the +composition checker. This package changes its root input and price adapter. +It does not claim either source mechanism or that adapter as a new result. +All source notices are retained in `NOTICE` and the source archive. + +Ali Romman with substantial OpenAI Codex assistance; no subagents. +Apache-2.0. See `PROOF.md` for the complete scope. + +## Open next questions + +- Can an independent reviewer confirm the source and root composition, + including all target debits and the physical native contacts? +- Can a different root or source give a material gain? The fixed-root + ceiling has now been checked for the contracted source: no positive + integer child sizes or binary tree shapes reach 0.00328554. This claim + is within 0.00000003 of that ceiling. The proof does not cover other + roots or sources. Numerical discovery does not establish a global optimum. diff --git a/research/mixed-root-source-composition/RESULT.json b/research/mixed-root-source-composition/RESULT.json new file mode 100644 index 0000000000..cc266a2e5c --- /dev/null +++ b/research/mixed-root-source-composition/RESULT.json @@ -0,0 +1,425 @@ +{ + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "binary": { + "coefficients": 16, + "identity": "L S A B Idle S^-1 C R = D_A D_B (U(q) direct-sum q direct-sum q^-1)", + "missing_idle_rejected": true, + "variables": [ + "q", + "D_A", + "D_B" + ] + }, + "caller": { + "coefficients": 1156, + "event_sha256": "be648c29aa09c0f068a3b5b5120d1eb1f782e49f4523b4c6d62843750517bdea", + "events": 570, + "inputs": 34, + "native_stages": 18 + }, + "columns": { + "arithmetic": "Dense integer rows with binary denominators; reverse chronology", + "coefficients": 638401, + "columns": 799 + }, + "contracted_source": "db2a20bc50bc7a8a4db931af85ce7f012ae7c3c3", + "fixed_root_ceiling": { + "admitted_saving_cap": "17/5000", + "binary_split_checks": 4851, + "ceiling": "164277/50000000", + "finite_margin_upper": "-7787170321424434524363970551831346942375489097397016615/326409290240107399719461050006798653637322483112129794670592", + "finite_pair_checks": 4656, + "first_tail_total": 100, + "native_derivative_lower": "86138912185857402894129942396511331880097482936030575207057935126156899899547982742715512297768167758596705255686534371/2048904322212512919038510085207467917864146442064203226733311257020777532117854951793541845254015613321944655495954432", + "scope": "All positive integer child sizes and all binary tree shapes for this fixed root and PR6353 source.", + "tail_derivative_upper": "-1212374402678709925753322157077533054142098874263059860209298677722997/20477146569221237675252072016256588739640941191035000425388441600000000", + "tail_margin_upper": "-302481154036608143267296779618452642963157685887739205404201/163204645120053699859730525003399326818661241556064897335296" + }, + "gain_over_pr6353": "6747/50000000", + "local": { + "endpoint_coefficients": 638401, + "helpers": { + "1": 14, + "2": 8, + "3": 4, + "4": 107, + "5": 15, + "6": 3, + "7": 9, + "8": 30, + "9": 372 + }, + "owned_fields": 29, + "owned_lifetimes": 41, + "paid": { + "1": 2231, + "2": 453, + "3": 494, + "4": 104, + "5": 156, + "6": 8, + "7": 9, + "8": 1 + }, + "paid_rank_mass": 5934, + "peak_owned_fields": 13, + "public_inputs": 770, + "real_scalar_allowance": 128694 + }, + "native": { + "distinct_maps": 2932, + "helper_normalizers": 1124, + "helpers": { + "1": 14, + "2": 8, + "3": 4, + "4": 107, + "5": 15, + "6": 3, + "7": 9, + "8": 30, + "9": 372 + }, + "main_adapters": 208, + "proof": "Every signed Pauli image and exact global phase; frame induction at every positive tensor width", + "recipe_payload_sha256": 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+ "relative_gain_percent": "2800/109489", + "strictification": { + "alpha": { + "lower": "0.999999982266622986391739596247", + "upper": "0.999999982266622986391739596248" + }, + "cutoff": 12, + "delta": { + "lower": "0.956506703835386815484711005744", + "upper": "0.956506703835386815484711005745" + }, + "floor": 13, + "gamma": { + "lower": "0.924130040323360594316376926466", + "upper": "0.924130040323360594316376926467" + }, + "normalized_paid_upper": "1048576000976562501/1048576001073741824", + "power": 1024, + "reserve": "1/1000000000000", + "tail_block": 128, + "tail_decay": "31/32", + "tail_offset": "1/7", + "tested": "657103/200000000" + }, + "targets": { + "1": 356, + "145": 104, + "17": 1872, + "2": 144, + "25": 416, + "3": 72, + "33": 416, + "4": 1926, + "5": 270, + "57": 416, + "6": 54, + "7": 162, + "73": 208, + "8": 540, + "9": 6696 + }, + "thin_queries": 17, + "whole_idle_jobs": 3120 + }, + "published": false, + "relative_gain_over_pr6353_percent": "449800/105019", + "root": { + "actual_tensor_gaussian_columns": 14, + "fields": 6, + "full_sites": 4, + "gaussian_characters": 4, + "normalization_growth_per_operation_upper": 2, + "ordinary_normalization_operations_per_pair": 4, + "owned_normalization_fields": 0, + "polynomial_coefficients": 1152, + "stage_ranks": [ + 2, + 3, + 3, + 2 + ], + "tensor_rule": "Normalize the complete field with its global Q squared translation; scalar coefficients stay outside tensor powers.", + "thin_sites": 3, + "wrong_tensor_normalization_rejected": true + }, + "root_source": "52e87e4971a85a8f098fadb967dc75bee9f76c65", + "same_caller_old_margin_upper": "-593038642754718312398192639814955356406652249474950126421/3138550867693340381917894711603833208051177722232017256448", + "same_caller_old_root": [ + "328468791927/100000000000000", + "41058598991/12500000000000" + ], + "selected_frontier_changed": false, + "source_files": 38, + "status": "PASS_MIXED_ROOT_SOURCE_COMPOSITION_KAPPA_00328551", + "target_delta": { + "5": 1, + "8": 8, + "9": -9 + } +} diff --git a/research/mixed-root-source-composition/SOURCES.json b/research/mixed-root-source-composition/SOURCES.json new file mode 100644 index 0000000000..5a96638cb3 --- /dev/null +++ b/research/mixed-root-source-composition/SOURCES.json @@ -0,0 +1,33 @@ +{ + "schema_version": 1, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + } + ], + "retained_predecessors": [ + { + "archive": "sources.tar", + "manifest": "INPUTS.json", + "archive_sha256": "6d05208f4fa1d98b4b63a8b2d9366576313a1f1466232a6a4f1a286de23c292b", + "reason": "The fixed root is local-only. The contracted source is a separate pending PR. Exact executable inputs and notices are retained; neither source commit is a runtime or publication-history dependency.", + "root_commit": "52e87e4971a85a8f098fadb967dc75bee9f76c65", + "contracted_commit": "db2a20bc50bc7a8a4db931af85ce7f012ae7c3c3" + } + ], + "local_adapter_provenance": { + "package": "contracted-mixed-query-local", + "verify_sha256": "e4e400fe08115bec501c17cd03362a6a6d24b22bf6d1ac907126c0a83300cc3a", + "scope": "Local predecessor checker; attribution only. Exact executable sources are in sources.tar." + } +} diff --git a/research/mixed-root-source-composition/TASK.json b/research/mixed-root-source-composition/TASK.json new file mode 100644 index 0000000000..4a202c946a --- /dev/null +++ b/research/mixed-root-source-composition/TASK.json @@ -0,0 +1,91 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 8, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "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": "changed", + "actual_scope": "Compose the current 7,2,2,7 mixed-projector root with the complete PR6353 source and verify its full conditional bound.", + "scope_change_reason": "The user requested a larger local result. This composition gives a small verified increment while distinct discovery routes continue.", + "bottleneck_link": "The complex supplier binds. The source change reduces the full signed cost at every one of the eighteen native calls.", + "stop_rule": "Reject any changed root event, missing target debit, native phase failure, incomplete source closure, failed interval or compiler/outer bound. No PR or push before donor approval.", + "outcome": "completed", + "evidence": "RESULT.json checks kappa .00328551, all native inputs and phases, 7488 contacts, both rational prices, the compiler and 58 outer predicates. The gain over the prior local .00328467 is .0255733 percent.", + "author": "Ali Romman with substantial OpenAI Codex assistance; no subagents", + "ai_assistance": "Substantial OpenAI Codex assistance; no subagents.", + "open_questions": [ + { + "question": "Can an independent reviewer confirm the complete contracted-source and mixed-root composition?", + "why_it_matters": "Both source mechanisms and the composition remain conditional and author checked.", + "first_step": "Check the exact source deltas at all eighteen calls, then replay the fixed root and native physical contacts.", + "blocked_by": "No scientific review is claimed by the local author replay." + }, + { + "question": "Can a new mechanism improve materially on the frozen mixed root?", + "why_it_matters": "The composition increment is small; most of the combined gain is inherited from the new root.", + "first_step": "Use a fresh overlap check and a favorable complete invoice before expanding a new caller.", + "blocked_by": "The present package changes no root or source construction." + } + ], + "publication_status": "LOCAL_ONLY_USER_REQUIRES_EXPLICIT_PR_PERMISSION", + "larger_user_objective": "Unmet: this scoped composition gains .0255733 percent, below one percent." +} diff --git a/research/mixed-root-source-composition/VERIFY.json b/research/mixed-root-source-composition/VERIFY.json new file mode 100644 index 0000000000..67428eea2a --- /dev/null +++ b/research/mixed-root-source-composition/VERIFY.json @@ -0,0 +1,30 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 590, + "checks": "Exact source reconstruction, all arbitrary inputs and phases, fixed caller, complete two-engine price, compiler, all outer predicates and a ceiling for all positive binary child sizes." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 590, + "checks": "The same complete conditional claim, all-child-size ceiling and rejecting controls under optimized Python." + } + ] +} diff --git a/research/mixed-root-source-composition/ceiling.py b/research/mixed-root-source-composition/ceiling.py new file mode 100644 index 0000000000..66fa8646d1 --- /dev/null +++ b/research/mixed-root-source-composition/ceiling.py @@ -0,0 +1,65 @@ +"""Bound every binary-child size for the rank 2,3,3,2 root. + +Adapted from the prior fixed-root ceiling by Ali Romman with OpenAI Codex. +The contracted native source stays fixed. Other roots and sources are outside +this claim. All arithmetic in this checker uses rational intervals. +""" +from fractions import Fraction as Q + +CEILING=Q('.00328554') +BIT_CAP=Q('.0034') +TAIL=100 + + +def run(local,E,root): + def need(ok,message): + if not ok:raise ValueError(message) + need(00,'The native deficit increases throughout the admitted range') + h={r:E.power(r,t) for r in range(1,8*TAIL+2)} + lower=[Q(0)]*TAIL + upper=[Q(0)]*TAIL + split_checks=0 + for n in range(2,TAIL): + node_lower=2*h[8*n][0]+1-2*h[8*n+1][1] + node_upper=2*h[8*n][1]+1-2*h[8*n+1][0] + lower[n]=min(lower[a]+lower[n-a]+node_lower for a in range(1,n)) + upper[n]=min(upper[a]+upper[n-a]+node_upper for a in range(1,n)) + need(lower[n]<=upper[n],'Binary subtree interval') + split_checks+=n-1 + pairs={} + for n in range(2,TAIL-1): + pairs[n]=max(h[8*n+1][1]-n*native_lower-lower[n-b]-lower[b] + +h[8*b+1][1]-h[8*b][0] for b in range(1,n)) + margins=[] + for n in range(4,TAIL): + for a in range(2,n-1): + margins.append(h[8*n+1][1]+pairs[a]+pairs[n-a]-2) + finite_upper=max(margins) + need(finite_upper<0,'Every finite child sum fails at the ceiling') + # Every binary node costs at least -1 by concavity. For total n, + # Jensen bounds the two pair outputs and each added increment is at + # most H9-H8. The resulting upper bound is decreasing for n >= TAIL. + tail_upper=(h[8*TAIL+1][1]+2*h[4*TAIL+1][1]-TAIL*(native_lower-1) + +2*(h[9][1]-h[8][0])-6) + derivative_upper=(8*t*(h[8*TAIL+1][1]/(8*TAIL+1) + +h[4*TAIL+1][1]/(4*TAIL+1))-(native_lower-1)) + need(tail_upper<0 and derivative_upper<0,'All larger child sums fail') + return {'ceiling':str(CEILING),'first_tail_total':TAIL,'binary_split_checks':split_checks, + 'admitted_saving_cap':str(BIT_CAP),'native_derivative_lower':str(derivative_lower), + 'finite_pair_checks':len(margins),'finite_margin_upper':str(finite_upper), + 'tail_margin_upper':str(tail_upper),'tail_derivative_upper':str(derivative_upper), + 'scope':'All positive integer child sizes and all binary tree shapes for this fixed root and PR6353 source.'} diff --git a/research/mixed-root-source-composition/pricing.py b/research/mixed-root-source-composition/pricing.py new file mode 100644 index 0000000000..0ba26a7e59 --- /dev/null +++ b/research/mixed-root-source-composition/pricing.py @@ -0,0 +1,171 @@ +"""Check the complete mixed-projector-root invoice and outer transfer. + +The interval and compiler bounds are by zxv and Cao Yifan. The productive +recursion is by Jacob Alan Sussman. The source price adapter is by Ali Romman. +The source lifts and tree invoice are by Ali Romman, with OpenAI Codex +assistance. This adapter keeps the root and changes the native source invoice. +It includes all nine output contractions and their productive target debits. +The original sources retain their credit. Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +from controller import formula_invoice, need + +KAPPA = Q('0.00328551') +TESTED = Q('0.003285515') +PREVIOUS = Q('0.00328467') + + +def encode(value): + if isinstance(value, Q): + return str(value) + if isinstance(value, dict): + return {str(k): encode(v) for k, v in value.items()} + if isinstance(value, (tuple, list)): + return [encode(v) for v in value] + return value + + +def assemble(local, native, word, physical): + paid, targets = Counter(), Counter() + counts = Counter(e[0] for e in word['events']) + need(local['helpers'] == native['helpers'], 'All source helper targets have native maps') + idle = Counter() + for event in word['events']: + if event[0] == 'LOCAL': + paid.update(local['paid']) + targets.update(local['helpers']) + elif event[0] == 'QUERY': + paid[1] += 104 + elif event[0] in ('IDLE', 'IDLE_ONE'): + rank = 8*len(event[3] if event[0] == 'IDLE' else event[2]) + count = 208 if event[0] == 'IDLE' else 104 + paid[rank] += count + idle[rank] += count + main = Counter() + for term in word['diagonal']: + main[1+8*sum(term[1:])] += 104 + targets.update(main) + need(main == physical['main_targets'], 'All main target phases and ranks') + need(idle == physical['whole_idle_jobs'], 'All paired and individual whole idle jobs') + need((targets, paid) == formula_invoice(local), 'Independent tree and emitted-event counts') + need((counts['LOCAL'], counts['QUERY'], counts['IDLE']) == (18, 17, 14) and counts['IDLE_ONE'] == 2 and counts['LAMBDA'] == 20, 'Complete caller census') + need((sum(targets.values()), sum(paid.values())) == (13652, 67096), 'All independent fields and paid calls') + need(sum(r*n for r, n in targets.items())-sum(r*n for r, n in paid.items()) == 760, 'Complete rank-mass surplus') + need((max(targets), max(paid)) == (145, 56), 'Maximum target and paid ranks') + return targets, paid, counts + + +def run(local, native, word, physical, L): + T, P, counts = assemble(local, native, word, physical) + E = L.load(L.ROOT/'research/higher-moment-strictification/verify.py', 'balanced_intervals') + other = L.load(L.ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py', 'balanced_second_intervals') + def margin(k): + a, b = E.moment(T, 1-k), E.moment(P, 1-k) + return a[0]-b[1], a[1]-b[0] + low, high, grid = 0, 10**12, 10**14 + while high-low > 1: + middle = (low+high)//2 + if margin(Q(middle, grid))[0] > 0: + low = middle + else: + high = middle + lower, upper = Q(low, grid), Q(high, grid) + signed = Counter(T) + signed.subtract(P) + cap, derivative_upper = Q('.0034'), Q(0) + for rank, count in signed.items(): + logarithm = E.log_bounds(rank) + a = E.mul(E.power(rank, 1-cap), logarithm)[0] + b = rank*logarithm[1] + derivative_upper -= count*(a if count >= 0 else b) + need(derivative_upper < 0, 'Unique raw crossing below the BIT cap') + need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure') + need(PREVIOUS < KAPPA < TESTED < lower, 'The composed source improves the fixed root claim') + t, offset, power, cutoff, floor = 1-TESTED, Q(1, 7), 1024, 12, 13 + target, paid = E.moment(T, t), E.moment(P, t) + tl, th = other.moment(T, TESTED) + pl, ph = other.moment(P, TESTED) + need(tl > ph and max(tl, target[0]) <= min(th, target[1]) + and max(pl, paid[0]) <= min(ph, paid[1]), 'Two independent rational moment engines') + alpha = E.divide(paid, target) + gamma = E.divide(E.moment(P, t+offset), E.mul(E.power(cutoff, offset), target)) + delta = E.divide((Q(sum(T.values())*floor),)*2, E.mul(E.power(cutoff, TESTED), target)) + reserve, decay = Q(1, 10**12), Q(31, 32) + need(alpha[1] < 1-reserve and gamma[1] < decay and delta[1] < decay, 'All charged tail ratios') + need(decay**128 < Q(1, 16), 'Both tail decay blocks') + normalized = 1/(1+power*reserve)+Q(4, 2**32) + need(normalized < 1 and cutoff**64 < floor**63, 'Completion, splitting and rounding') + theta, logarithm_power = Q(63, 64), 1100 + # Keep each exponential inside the retained engine's proved domain. + half = E.power(145, Q(power, 2)*TESTED) + factor = E.mul(half, half) + eta = E.scale(E.divide((Q(1), Q(1)), factor), t) + need(2*(cutoff**power)**64 <= (145**power)**63 + and eta[0] > theta**logarithm_power, 'Shifted exits and complement capacity') + need(factor[1] < 2**logarithm_power, 'Compiler initial range') + gap = (TESTED-KAPPA)/7 + need(gap.numerator == 1, 'Exact compiler integer grid') + step = gap.denominator + def wins(j): + return (step*j+1)**logarithm_power < 2**j + left, right = 1, 2 + while not wins(right): + left, right = right, 2*right + while right-left > 1: + middle = (left+right)//2 + if wins(middle): + right = middle + else: + left = middle + H = step*right + need(H > 8*power and wins(right) and not wins(right-1), 'Uniform threshold and adjacent-grid rejection') + local_routes = (sum(local['paid'].values())+native['helper_normalizers'] + +native['main_adapters']+4*104+4*local['owned_lifetimes'])*1000 + need(local['real_scalar_allowance']+local_routes < 10**7, 'Every local ordinary operation is funded') + raw = 18*10**7 + 17*1664 + 32*34*104*len(word['events']) + 34*104*(26+1000) + need(all(abs(Q(e[-1])) <= 16 for e in word['events'] if e[0] in ('ADD', 'SCALE')), + 'Every emitted scalar coefficient has the declared growth bound') + need(all(Q(e[-1]).denominator & (Q(e[-1]).denominator-1) == 0 + for e in word['events'] if e[0] in ('ADD', 'SCALE')), + 'Every emitted rational scalar is dyadic') + need(raw < 10**9, 'Complete ordinary-work budget') + bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + atom = Q(bit['atom']) + ordinary = (1-atom)*Q(bit['after_cover']) + atom*Q('.0000384599') + admitted = Q(bit['admitted']) + need(atom > ordinary > admitted > TESTED and atom < 1-ordinary, 'Retained BIT admission and stock') + outer_module = L.load(L.ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'balanced_outer') + params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA+6*gap, + 'b': KAPPA+5*gap, 'a': KAPPA+4*gap, 'q': KAPPA+3*gap, 'bit_saving': admitted, + 'epsilon': 1-gap, 'beta': 1-3*gap, 'r0': gap/10, 'stop': gap, 'layout': gap, 'd': gap} + outer = outer_module.ledger(params) + outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta']*(1-atom) + need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Full outer predicate inventory') + need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict') + old_completion = E.divide((Q(sum(T.values())*17),)*2, E.mul(E.power(16, TESTED), target)) + need(old_completion[0] > 1, 'The old completion cutoff does not fund the new inventory') + bad = outer_module.ledger(dict(params, bit_saving=Q('.0027'))) + need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT saving rejected') + return encode({'kappa': KAPPA, 'kappa_decimal': '0.00328551', 'previous_fixed_root': PREVIOUS, + 'gain': KAPPA-PREVIOUS, 'relative_gain_percent': 100*(KAPPA/PREVIOUS-1), + 'raw_root_interval': [lower, upper], 'raw_headroom': [lower-KAPPA, upper-KAPPA], + 'derivative_upper': derivative_upper, 'margin_at_previous': E.display(margin(PREVIOUS)), + 'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), + 'rank_mass_surplus': 760, 'full_forward_calls': 18, 'thin_queries': 17, + 'whole_idle_jobs': 3120, 'strictification': { + 'tested': TESTED, 'power': power, 'cutoff': cutoff, 'floor': floor, + 'tail_offset': offset, 'reserve': reserve, 'tail_decay': decay, 'tail_block': 128, + 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), + 'normalized_paid_upper': normalized}, + 'compiler': {'theta': theta, 'logarithm_power': logarithm_power, 'eta': E.display(eta), + 'gap': gap, 'H': H, 'N': '2^'+str(H), 'integer_test_exponent': right, + 'uniform_saving': params['complex_uniform_saving'], 'word_materialized': False}, + 'nonrecursive': {'local_scalar': local['real_scalar_allowance'], 'local_routes': local_routes, + 'raw_scalar_upper': raw, 'raw_budget': 10**9, + 'peak_owned_fields': local['peak_owned_fields'], + 'scalar_growth_bound': 'At most 2^(10^9 + R*f), where R is the full paid rank mass.', + 'paid_rank_mass': sum(r*n for r, n in P.items())}, + 'ordinary_BIT': bit, 'outer': outer, + 'negative_controls': {'old_completion': 'Cutoff16 and floor17 give a ratio above one.', + 'old_BIT': 'An outer inequality fails at BIT saving0.0027.'}}) diff --git a/research/mixed-root-source-composition/sources.tar b/research/mixed-root-source-composition/sources.tar new file mode 100644 index 0000000000000000000000000000000000000000..9969dc140de46e7a9224947ea5b751e3486ff9eb GIT binary patch literal 4823040 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