Mister-Meeseeks · Oct 16, 2026 · Oct 16, 2026
diff --git a/research/kappa-action-theory/ACTION-ROUTES.md b/research/kappa-action-theory/ACTION-ROUTES.md
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+# Concrete routes from the theorems to a better complete contract
+
+The actionable unit is a constructed word, recovered map or certified budget. A future κ improvement requires its **complete** caller invoice and uniform outer interface to improve. The routes below identify actual inputs, delivered objects, payment and the first useful application. They are research recipes justified by the numbered sufficient results, not claims that the current multiplier already meets every premise.
+
+## 1. A changed helper word with a proved arbitrary-dirt response
+
+Start from the literal `A`, `compensation`, `cleanup`, `start_extra`, `helper_final`, `warps` and `cut` fields of the pinned PR #2857 words, rather than from their rank histogram. Extract their exact response columns and source footprints. N003–N020 emit kernel charts fixing declared protected helpers; N094–N096 compute the actual effect of staged insertions, including the ordered two-insertion cross term. N097 supplies a source borrow along a verified dirty-response kernel. N099 tests every declared input/dirt column and N100 emits the compensated forward/cleanup word.
+
+The deliverable to the next worker is a literal changed word, its complete response matrix, a proof of restored inputs and an expanded scalar/native transition ledger. A006 prices favorable and unfavorable width changes together; A008/A009 permit safe price/exponent intervals; A001 composes genuinely disjoint gains. A positive complete saving then has a quantified adapter allowance by A002–A005 and a symbolic exponent interval by A011–A018. No gain follows merely from deleting a compensation column: chart creation, inverse cleanup, source reads and frame transitions remain paid. The existing #2857 quartet is credited background, not a new instance of this route.
+
+## 2. A consumer that repairs its actual order, or avoids repeated physical work
+
+Use the real PR #2850 emitter/invoice and #2859 literal consumer permutation. P006/P058 derive its actual crossing phase, and P012–P019 turn that phase into finite returned-bank circuits. P091 realizes a caller-fixed correction physically, with rank charts, full operand volume and wrappers. P092 provides a completely corrected aggregate producer, not the predecessor's invalid uncorrected aggregate shortcut. P056 constructs a specific encoded assignment beyond the restricted one-bit-per-column model, with its increased controls charged.
+
+There is also a guaranteed finite improvement independent of a speculative new caller: P080 changes each two-cell butterfly's output order to high-address then low-address after both outputs are computed. For N cells and address stride h=2ᵃ, the total return-to-zero travel drops by exactly Nh while additions, halvings, accesses and eight private real slots remain. P073 can further remove only genuine inter-record returns; P078 licenses record reordering only with disjoint supports. These are alternative emitted schedules; a frozen predecessor invoice is not silently edited.
+
+If a real unobserved common-chart region contains several closed Q jobs, P100 replaces it by the actual phase-sum controller, with two rank-r C children and all charts paid. P098 similarly compiles a monomial wrapper run into one table, counting both its LN generation and execution. The next worker should return the changed literal emitter, full endpoint identity, new prefix grid/range bounds and actual movement/control ledger. A035–A040/A091–A095 allocate deterministic precision; A019/A056 admit only improvements surviving every integration charge. Existing all-size unit-shear #2776 and whole-word grid #2772 remain separate credited components.
+
+## 3. A usable tensor certificate, rather than bare orbit existence
+
+The input is an actual labelled bilinear coefficient table or a supplied finite query certificate. T006/T038 verify or recover the complete table with charged probes; T030 returns an actual common-label matching from normalized coefficients; T033–T040 construct frames, ratio maps and a decoder from explicit finite data. T081–T090 supply recovery algorithms only for their declared restricted transporter instances. No theorem assumes that arbitrary tensor isomorphism has an efficient recovery oracle, or that TI = TI_SL has been proved.
+
+Then choose an explicit transformation: T001/T002 fuse queries while modifying the decoder; T014 aligns a tree of actual label frames; T026 prices tensor-power adapters by fibres; T041–T050 perform scalar descent with actual maps. T051–T060/T071–T080 recover exact coefficient responses from sampled or border certificates, counting interpolation, jets, roots, denominators and reconstruction. T091–T100 provide concrete matrix/convolution/residue/NTT arithmetic children with label and bit costs.
+
+The output is a certificate with recovered maps, finite operation/bit/workspace bounds, source embedding and a complete decoder. It is a **changed tensor/block-query consumer**; the existing native C operation is linear and cannot be replaced by bilinear rank arithmetic alone. A real compatible source realization and paid native/physical adapter are required. N021–N030 can implement an explicitly factored linear response, and P088 can implement a specified binary phase matrix, but neither supplies a universal conversion from an arbitrary bilinear certificate. Evaluate the resulting actual profile through A007/A010/A024/A032/A059, keeping exact live normalization and full operand volume.
+
+## 4. Preserve a strict reserve through precision, resources and uniform execution
+
+Take the actual complete profile and concrete error/source bounds produced by a construction. A033–A040 and A071–A080/A091–A095 give deterministic magnitude, coupled-error, quotient and exact-output budgets; shared error symbols may cancel only when their reuse is real. A030/A086–A090 allocate fraction fields under the actual price/shared-field constraints. A063–A065 control half-rank parity and dyadic grids; they complement T064's general denominator ledger. A096/A097 output explicit scratch/recursive-space schedules, and A098 supplies a bit-growth bound for a fixed dyadic word across logarithmic depth.
+
+For a typed recurrence, construct a positive weight certificate by A052–A055, rationalize it using A060, and charge every returning adapter with A056. A041–A049/A051/A057 then prove bounds from the actual implementation recurrences; A066–A070 retain finite bootstrap and outer losses. A100 assembles only a fully specified uniform implementation. Use the existing all-size logical caller #2753 and current storage successor map to identify the actual physical/H2/outer boundary, rather than rebuilding or ignoring that caller.
+
+## Coverage of every numbered theorem
+
+The [400-entry index](INDEX.md) gives each theorem's concrete action. The chapter map below assigns every ID to a delivered interface; the chapters are collections of different constructions, not 40 claims of attained global improvement.
+
+| IDs | Delivered objects or quantitative decisions |
+| --- | --- |
+| N001–N010 | Compensated dirty-response words, quotient consumers and correction transport |
+| N011–N020 | Explicit protected/kernel/compression charts and their emitted costs |
+| N021–N030 | Shared low-rank, tree, polynomial and structured-response circuits |
+| N031–N040 | Ordered crossing repairs, legal rescheduling and triangular/path response words |
+| N041–N050 | Actual inverse cleanup, source-consuming interfaces and invariant consumers |
+| N051–N060 | Checked block/low-rank/nilpotent/structured solve and chart circuits |
+| N061–N070 | Legal frame schedules, paid common entrances and constrained kernel words |
+| N071–N080 | Reversible coefficient synthesis, denominator/gauge certificates and explicit inverse data |
+| N081–N090 | Transposed/complex/sliding/laminar multioutput circuits and dirt localization |
+| N091–N100 | Credited quartet reconstruction, staged insertion corrections and full local assembly |
+| P001–P010 | Complete arbitrary-dirt consumers, reverse returns and paid order/label corrections |
+| P011–P020 | Actual crossing-error circuits and fully paid physical-basis corrections |
+| P021–P030 | Encoded/source-promised/affine/quadratic bank charts with exact signs |
+| P031–P040 | Split, block, tensor, sparse graph and selector phase consumers |
+| P041–P050 | Genuine subsystem release, dirty borrowing, timed allocation and live-bank migration |
+| P051–P060 | Caller-respecting corrected schedules, allowed locations and encoded/fused controls |
+| P061–P070 | Operand-preserving endpoint, Fourier, affine, window and Clifford adapters |
+| P071–P080 | Literal records, cycle routing and the proved reverse-write movement saving |
+| P081–P090 | Full-array sign/translation/Walsh/Q realizations and a finite bit-machine bill |
+| P091–P100 | Corrected live-frontier physical assemblies, accumulator writes and common-chart fusion |
+| T001–T010 | Fused/cached/shared query and decoder constructions |
+| T011–T020 | Actual common-label alignment, joins, invariant-source compression and batching |
+| T021–T030 | Paid tensor/basis/gauge/transpose adapters and deterministic label recovery |
+| T031–T040 | Explicit matrix-unit, ratio, table, transporter and decoder recovery |
+| T041–T050 | Extension-field, prime-field, trace, modular and basis descent |
+| T051–T060 | Sample/jet/small-field/modular exact response reconstruction |
+| T061–T070 | Rational, dyadic, extension, signed-radix, CRT and bit-cost implementations |
+| T071–T080 | Constructive restriction, degeneration, character and finite-difference recovery |
+| T081–T090 | Exact recovery for stated restricted transporter and normalization instances |
+| T091–T100 | Fully labelled matrix, convolution, residue and NTT–CRT–carry children |
+| A001–A010 | Explicit complete saving and live-normalization allowances |
+| A011–A020 | Positive common-exponent/outer-margin intervals and caller gain propagation |
+| A021–A030 | Finite amortization/potential/selection constructions and precision allocation |
+| A031–A040 | Sufficient complete deficit/stock, prefix, rounding and feedback certificates |
+| A041–A050 | Actual scalar/adaptive/alternating/log-scale uniform recurrence bounds |
+| A051–A060 | Constructive typed-state contraction and adapter-reserve certificates |
+| A061–A070 | Active grids, parity, finite bootstraps and paid outer parameter transfer |
+| A071–A080 | Coupled nonlinear errors, explicit integer recovery and visible-quotient budgets |
+| A081–A090 | Exact finite certificate arithmetic and optimal declared precision plans |
+| A091–A100 | Correlated/lattice/integral rounding, resource schedules and complete symbolic admission |
+
+Nearby cross-volume results retain different outputs: N042/N081 transpose an actual reversible scalar response, while T028/T029 transpose query/decoder maps with labels; N074 records a native denominator-depth convention, T064 a rational circuit ledger and A065 its least dyadic assignment; P099 absorbs an actual physical symmetry, while T022 cancels adjacent supplied tensor adapters. None licenses an unpriced conversion between those models.
diff --git a/research/kappa-action-theory/BRANCH.txt b/research/kappa-action-theory/BRANCH.txt
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+research/kappa-action-theory-400-20261015
diff --git a/research/kappa-action-theory/CREDITS.md b/research/kappa-action-theory/CREDITS.md
@@ -0,0 +1,19 @@
+# Attribution and overlap
+
+Prepared with substantial OpenAI Codex assistance by the root and three Codex agents, including derivation, actual source inspection, author readback, cross-review and packaging. No independent human review, maintainer acceptance, formal verification or global novelty is claimed. The 400 results are complete informal constructive/sufficiency proofs in their stated models; many use classical ideas.
+
+The previous pure-math atlas [#2849](https://github.com/CrocSwap/integer-mult-bounds/pull/2849) and its concrete applications [#2855](https://github.com/CrocSwap/integer-mult-bounds/pull/2855) are acknowledged as earlier project work. They are not re-counted as 400 new generic facts. Dugongue's [#2839](https://github.com/CrocSwap/integer-mult-bounds/pull/2839) supplies the actual tensor-block norm/replica and owner interfaces used as scoped precedents. The complete inherited norm, chart and private-work hypotheses remain necessary to apply that source.
+
+Jeremy Kothe / jeremykothe2's [#2833](https://github.com/CrocSwap/integer-mult-bounds/pull/2833) supplies dirt-entry native words and their retained lineage. Yiyang / Lyy-iiis's [#2857](https://github.com/CrocSwap/integer-mult-bounds/pull/2857) supplies the actual shared-kernel chart and complete compensation/cleanup, and [#2848](https://github.com/CrocSwap/integer-mult-bounds/pull/2848) supplies interleaving/residue exchange. Philippe Van Velzen / philippeVV's concurrent [#2853](https://github.com/CrocSwap/integer-mult-bounds/pull/2853) identifies the quartet/entrance route with a different paid schedule. Marius-Paul Dumitrean / mdumitrean's [#2843](https://github.com/CrocSwap/integer-mult-bounds/pull/2843) supplies owner-flow/construction lineage and [#2856](https://github.com/CrocSwap/integer-mult-bounds/pull/2856) the vacancy-path method. Our [#2863](https://github.com/CrocSwap/integer-mult-bounds/pull/2863) is the fixed-word/inventory packing attainment, not a bound on changed constructions. Tekalign / tekuuu, David Arias, Mason Hale and the retained native, admission, source and outer contributors keep their original attribution; this collection makes no exclusive method-priority claim.
+
+Gareth Davidson / bitplane's [#2850](https://github.com/CrocSwap/integer-mult-bounds/pull/2850) supplies the concrete phase-accumulator boundary, emitter, inverse convention, invoice and reverse/tensor controls. Dennis / antunishdPursuit's [#2859](https://github.com/CrocSwap/integer-mult-bounds/pull/2859) supplies the bank-return/cross-phase audit, exact order criterion and restricted assigned-bit optimum. P003, P063, P088, P089 and P093 explicitly reconstruct/extend their methods; these are not claimed first discoveries. The new paid repairs and adapters retain all predecessor phase and volume terms.
+
+David Arias's [#2776](https://github.com/CrocSwap/integer-mult-bounds/pull/2776) already gives a literal all-size unit ordered-shear machine, building on the ordered-affine stream method and Jose Manuel / jmbarrancoml's selected stream reduction. Jose Manuel's [#2697](https://github.com/CrocSwap/integer-mult-bounds/pull/2697) supplies the first-range BIT node; David Arias's [#2753](https://github.com/CrocSwap/integer-mult-bounds/pull/2753) the all-size logical caller and ledger. Main's source-bound caller/storage map and its component authors are credited: ywz65 [#2688](https://github.com/CrocSwap/integer-mult-bounds/pull/2688), starship-s [#2731](https://github.com/CrocSwap/integer-mult-bounds/pull/2731), and Nick Petalas [#2708](https://github.com/CrocSwap/integer-mult-bounds/pull/2708), [#2743](https://github.com/CrocSwap/integer-mult-bounds/pull/2743), [#2749](https://github.com/CrocSwap/integer-mult-bounds/pull/2749), [#2758](https://github.com/CrocSwap/integer-mult-bounds/pull/2758), [#2759](https://github.com/CrocSwap/integer-mult-bounds/pull/2759). These latter sources were followed through main's inspected scope map; their full proofs are not claimed independently replayed here.
+
+ywz65's [#2540](https://github.com/CrocSwap/integer-mult-bounds/pull/2540) QQ16 and [#2586](https://github.com/CrocSwap/integer-mult-bounds/pull/2586) P104 supply the decoder/physical-word precedents to the later rounded-line and grid work. Nick Petalas's actual [#2770](https://github.com/CrocSwap/integer-mult-bounds/pull/2770)/[#2778](https://github.com/CrocSwap/integer-mult-bounds/pull/2778) lifetime proofs and [#2771](https://github.com/CrocSwap/integer-mult-bounds/pull/2771)/[#2772](https://github.com/CrocSwap/integer-mult-bounds/pull/2772) rounded-line/whole-word-grid sources retain credit. The grid lineage includes Arham Tahir's #2674/#2665, ywz65's #2586/#2730, Nick Petalas's #2754/#2549/#2550 and Alejandro Zarzuelo Urdiales's Gaussian parity methods. No claim is made that these results already admit a complete favorable supplier.
+
+The latest overlap read also acknowledges Wentao Li / VictorLiwentao's [#2867](https://github.com/CrocSwap/integer-mult-bounds/pull/2867)/[#2868](https://github.com/CrocSwap/integer-mult-bounds/pull/2868) scoped readout alphabets; digitalis-p's [#2866](https://github.com/CrocSwap/integer-mult-bounds/pull/2866) superseded concentration; and Sagar Thakrar's [#2865](https://github.com/CrocSwap/integer-mult-bounds/pull/2865) audit of tekuuu's #2751 against petalas's #2720. Their reported validation is their evidence, not a replay performed for this collection. DreamingOfClouds's #2862/#2864 and Wentao Li's #2860/#2861 were included in the scope census, not assumed to exhaust unrelated alphabets.
+
+Classical inputs include elementary transvections and block/Schur/Woodbury identities, reversible compute/uncompute, finite Fourier/Pauli/Clifford algebra, sparse linear circuits, finite-field trace/descent, interpolation, CRT, Strassen/Karatsuba/NTT constructions, integral bipartite flow, convex precision allocation, potentials and strong induction. Specific primary references and exact inspected source paths/hashes appear in the volume ledgers. Tensor methods retain Strassen and Bini's exact/approximate bilinear lineage; no new asymptotic theorem is attributed to a historical identity.
+
+No upstream executable module or mathematical prose is vendored in this collection. The manuscripts give explicit reconstructions/adaptations and citations. Source-specific copyrights and licenses continue to govern their original sources; this attribution does not replace those notices. Newly authored text and the structural checker are offered under Apache-2.0, with the included LICENSE. Local source/DAG references are provenance, not imported duplicate active modules.