Remove tensor padding (199.32× smaller uniform-rank exponent)

research/compact-joint-compiler/.gitattributes

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+* -text

research/compact-joint-compiler/FRONTIER.json

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+{
+  "canonical_main": "2a13eb1827784206202db90e5dc8327cf8a250db",
+  "source_pr": 4470,
+  "source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363",
+  "strongest_observed_open_conditional_kappa": "0.00302015",
+  "new_kappa_claim": false,
+  "selected_frontier_changed": false,
+  "recent_checkpoint_coverage": {
+    "pr_updates": 917,
+    "since": "2026-10-18T23:40:10Z",
+    "complete": true,
+    "latest_refresh_includes": 4477
+  },
+  "initial_candidate": {
+    "kappa": "0.00300428",
+    "status": "superseded by PR4470 during the session"
+  },
+  "overlap_limit": "No exhaustive historical code/Discussion search or global novelty claim.",
+  "checked_at_utc": "2026-10-21T23:56:00Z"
+}

research/compact-joint-compiler/PROOF.md

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+# Sufficient compact compilation at the retained saving
+
+**Proposition.** Under precisely the conditional contracts retained by PR #4470, its unchanged source-bound p16 supplier has a sufficient uniform local rank N = 2^558100005581 at declared κ = 0.00302015. This replaces the previous sufficient local rank 2^64215200000000.
+
+**Proof.** Keep C = 0.00302016 and t = 1 − C. The literal controller yields the same target and paid histograms as PR #4470; independent event counting retains all 18 full native calls, 15 copied-query shears and 3,360 whole idle jobs. All 408 helpers remain independent arbitrary fields, including nonzero dirty entry values. Native and phase replay are independent required gates, rather than being inferred from an arithmetic receipt.
+
+For the same complete histograms T and P choose v = 682, c = 17, b = 21 and u = 1/8. Exact rational intervals give
+
+α = P_t/T_t < 1 − 31/(5·10^9),
+γ = P_(t+u)/(17^u T_t) < 98102/100000,
+δ = 10928·21/(17^C T_t) < 959/1000.
+
+The retained paid-completion and splitting theorem therefore bounds the normalized final paid moment by
+
+1/(1 + 682·31/(5·10^9)) + 2(98102/100000)^682 + 2(959/1000)^682 < 1.
+
+This includes both the original paid tail and the completion tail. No new padded target has unpaid axes. The same conservative bound rejects v = 681; this is a control for the displayed choices, not a global minimum theorem.
+
+Use θ = 94/101 and logarithm power 143 in the credited general majorant. The exact checks are 17^101 < 21^94, 128(17^682)^101 ≤ (145^682)^94, and, for η = (1 − C)145^(−682C), η > θ^143 and 145^(682C) < 2^143. These supply the same shifted-exit, complement-capacity and initial-range hypotheses as in the predecessor theorem. Power 142 fails the displayed η control.
+
+Allocate compiler gap g = 1/100000001 and outer slack d = (C − κ − g)/6 = 1/60000000600000000. The elementary identity C − g = κ + 6d with d > 0 leaves the strict chain
+
+κ < q = κ + 3d < a = κ + 4d < b = κ + 5d < C − g.
+
+The exact current ledger independently checks the remaining conditions; the chain alone is not substituted for those checks. In particular, all 54 strict predicates and four functional guards pass, as do all 63 legacy predicates and equality of all nine cost rows. Ordinary BIT saving 0.0034 is retained. The legacy decimal grid is refined to 10^20 to resolve the smaller positive margins.
+
+The integer majorant test (100000001j + 1)^143 < 2^j holds at j = 5581 and fails at j = 5580. The retained sufficient logarithmic compiler theorem consequently gives N = 2^(100000001·5581) = 2^558100005581 for the uniform local supplier. Every scalar and route remains within the retained finite bound; the enormous resulting word is specified algorithmically and not materialized. This proves the conditional proposition. ∎
+
+The smaller local rank is not a higher saving exponent. Nor does it prove an improved overall multiplication threshold: the smaller outer slack may worsen that separate threshold. All inherited physical, analytic, precision, tape, stock, prime and recovery premises remain.
+
+Credit PR #4470 for the native construction and controller, PR #4447 for the missing span, PR #4440/#4441 for query thinning and helper retiming, zxv for higher-moment and logarithmic-majorant work, Jacob Alan Sussman for the mixed-target compiler, and all source scalar/Clifford/BIT/outer-ledger contributors. The legacy ledger retains Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe, Vlado Vojdanovski and its full source attribution. This contribution changes the sufficient completion and compiler parameters; it does not claim these general methods were invented here.

research/compact-joint-compiler/README.md

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+# Compact finite compiler for the joint-helper supplier
+
+Retain PR #4470's conditional κ = 0.00302015 while reducing its sufficient **local uniform-supplier rank** from 2^64215200000000 to **2^558100005581**. The exponent is about 115.06 times smaller. This is a new sufficient compiler construction at the same κ, not a higher κ, a practical speedup or a smaller overall multiplication input threshold.
+
+The native words and complete p16 controller are unchanged: 408 independent productive helpers, 10,928 productive fields, 64,620 paid calls, rank surplus 752, all owned-center work, 15 copied-query shears and 3,360 whole idle jobs. The verifier freshly checks both native orientations, 632 arbitrary columns, Clifford tableaux and absolute phases, as well as the parent construction's exact source admissions.
+
+Two changes contribute to the smaller local bound: a newly priced completion/splitting choice reduces the tensor power and logarithmic majorant; separate compiler and outer-transfer slack makes a much larger compiler gap available. Both paid tails, every outer row and all inherited charges remain checked. The smaller outer slack may increase the eventual full-algorithm input threshold; no bound or improvement of that threshold is asserted.
+
+Run Python 3.12, standard library only:
+
+```sh
+python -B scripts/research_package.py --package research/compact-joint-compiler
+```
+
+The three registered gates can also be run separately with `verify.py --part dependencies`, `--part native`, and `--part arithmetic`. See PROOF.md, arithmetic/PROOF.txt, VALIDATION.md and REUSE.md.
+
+This branch is stacked on PR #4470 at b9a13c1673e0e9697de410de16e8bbf3207a7363; inherited files are predecessor contributions. Retain the conditional native lift, primitive semantics, owned erasure, whole-job matching, finite-template closure, precision, fixed-tape, stock, analytic decomposition, prime-avoidance and exact-recovery premises. No formal-kernel check, human acceptance, global optimum or selected-frontier promotion is claimed.
+
+Prepared for Dugongue with substantial OpenAI Codex assistance, root plus three agents. Apache-2.0 for new code; original source notices remain applicable.
+
+## Open next questions
+
+Can changed warp charts or general nonmonotone contact moves improve the complete PR #4470 paid invoice? Any successful successor must emit and check the physical operators including absolute phase, replay all arbitrary input columns and reprice the complete construction. Can a sharper sufficient recurrence reduce the local supplier rank without shrinking outer slack?

research/compact-joint-compiler/REPLAY.json

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+{
+  "status": "PASS_ALL_FOUR_REQUIRED_GATES",
+  "source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363",
+  "scope": "Exact operator and rational/integer arithmetic replay, not kernel or human acceptance.",
+  "execution": "Three registered dependency/native/arithmetic gates completed together. The separately added read-only independent gate completed under isolated optimized Python; final four-command metadata/pins check passed.",
+  "gates": [
+    "PASS_COMPACT_JOINT_COMPILER_DEPENDENCIES",
+    "PASS_COMPACT_JOINT_COMPILER_NATIVE",
+    "PASS_COMPACT_JOINT_COMPILER_ARITHMETIC",
+    "PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER"
+  ],
+  "kappa": "0.00302015",
+  "new_kappa_claim": false,
+  "local_uniform_rank": "2^558100005581",
+  "hosted_CI_claim": false
+}

research/compact-joint-compiler/REUSE.md

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+# Discovery reuse and predecessor credit
+
+The root and three workers queried the registered source catalog and the canonical typed DAG, then read selected relevant source bodies. This is a broad catalog search, not a claim that every registered proof body was read or that none of these concepts has previously been used. No new Lean formalization or fresh Lean kernel/axiom audit is claimed. Source reads and Python/operator certificates are distinguished throughout.
+
+| Worker | Retrieved precedents | Implemented ideas and outcome |
+| --- | --- | --- |
+| Root | `Mathproof.Meta.TISLTransvectionWord20260908`, `External.TenProofs.ConnesRigidity`, `Mathproof.Meta.RationalLPCertificate20260908`, and the Schur-complement wrapper in `ArXiv200902452_20260903` | Constructive quotient reconstruction for commuting contact rewrites; common-chart block elimination; exact general-Clifford distance retiming outside monotone flags. All were implemented and bounded tests found no gain over PR #4470. The Schur wrapper restates standard matrix algebra and is not credited as a new discovery. |
+| Native worker | `TISLTransvectionWord20260908`, adapted subspace/quotient coordinates in the Problem18/anchor modules | Joint contact/helper-boundary retiming; overlap-compatible patch assembly; exact free-warp chart changes with priced neighbors. The first two produced an all-column checked κ = 0.00300428 stepping stone, superseded by PR #4470. |
+| Controller/audit worker | `UniversalChartMomentRank20260831.hasTruncatedMoment_iff_factors`, quotient-kernel monotonicity and two-sided Woodbury sources | Arbitrary-subset Laurent specialization and fully charged rank-factor batch queries; diagonal scalar-gauge normalization and transvection folding. These preserve exact arbitrary-column semantics. They did not produce a higher complete saving in this session. |
+| Moment/compiler worker | `Computability.IntegerKappaMomentTransfer20261015`, `Mathproof.ConvexSlope`, the prior `MULTITYPE-MOMENT.md` and prefix-majorization sources | Exact support-hypergraph subset dynamic programming; separately allocated compiler/outer slack; newly priced two-tail/logarithmic majorant parameters. The latter two give the sufficient local-rank improvement certified here. |
+
+No positive recurrence result from a source containing an unresolved `sorry` is used. The numerical search programs nominate candidates only; exact frozen receipts and proofs establish the retained sufficient result. The new public package contains the compact compiler, not an assertion that all discovery experiments are novel research contributions. The larger session archive preserves failed and interrupted searches separately.
+
+## Direct source lineage
+
+- PR #4470 supplies the unchanged joint-helper native words, productive inventory, p16 controller and κ = 0.00302015. It deserves the saving-exponent credit.
+- PR #4447 supplies the missing-span contact; PR #4440 supplies query thinning; PR #4441 supplies its helper-retiming combination. PR #4446 and #4453 are overlapping certificates, with #4453 also informing compact finite compilation. Their source contracts differ from older packing interfaces and are not conflated.
+- PR #4359 supplies the selected productive-job/mixed-target framework. zxv's higher-moment and logarithmic work, including the general majorant used by PR #4433, and Jacob Alan Sussman's finite mixed-target compiler remain essential premises.
+- The ordinary BIT, scalar, Clifford, geometry, owner/erasure, fixed-tape and outer-ledger lineage remains credited in the unchanged source files and their manifests. The legacy ledger explicitly retains Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe and Vlado Vojdanovski, among the credited predecessors.
+- PR #4474 records stacked p17 content and documentation conflicts; PR #4477 records the distinct direct-flow chain. Neither disposition is treated as mathematical acceptance or rejection of the source κ claim.
+
+The first 917 PR updates since the previous local checkpoint were collected in full. Repeated newest-100 refreshes included PR #4470 and subsequently #4477. Older overlap was additionally searched for native/Clifford fusion, including PR #4002's phase-tag warning and PR #4074's distinct caller fusion. This bounded coverage does not establish global novelty. The canonical selected result remains unchanged.