Research: two-block native-query encoding theorem and paid boundary obstructions

research/native-query-boundary/CLAIM.md

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+# Local research claim
+
+Route 6: native fused DATA queries and the ordinary BIT supplier boundary.
+
+Base: `abdc6a7002abdbcd9e21bfc5e1a795784deacfdf`.
+Branch: `codex/k9-native-query`.
+Claim time: 2026-10-13 18:08 UTC. Expected finish: 2026-10-13 20:15 UTC.
+No fixed user time limit applies. This time is a work estimate.
+
+A fresh GraphQL check found no pinned issue. The shared open-PR list and a
+fresh 40-PR update list through PR1099 were checked before this claim. No
+matching native boundary result was found in those lists.
+
+## Three candidate tasks
+
+1. Use the PR840 centered DATA shear in a direct ordinary-interchange word.
+   First test the ADDRESS orbit action on every genuine DATA role.
+2. Convert one completed fused block by a paid binary linear encoding.
+   First test exact conjugacy invariants on the complete ADDRESS domain.
+3. Prove a uniform obstruction for the conversion classes in items 1 and 2.
+   Count native orbits over all odd prime powers, derive full-array ranks,
+   and compare them with the exact ordinary supplier boundary.
+
+The first two tests fail in their stated classes. The native powers preserve
+separate ADDRESS orbits. The ordinary endpoint exchanges some of those
+orbits. One centered block has a binary rank that differs from any positive
+number of full ordinary-interchange rows. This comparison holds under an
+encoding and its inverse. Different entry and exit adapters are not covered
+by that conjugacy statement. Item 3 is the selected task.
+
+## Exact object and method
+
+Use PR840 at `da2cd0dd2229e08b61b174a8835a2c2bb99d2230`, with its unchanged
+PR521 and PR677 inputs. Use the actual six-field ADDRESS push map on
+`(Z/p^b)^6`, every odd prime p, every b >= 1, and every spectator volume.
+Do not infer full-array rank from rational ADDRESS rank. Compute the orbit
+quotient, prove its count, and test the formulas with independent full-domain
+and binary-matrix checks. Also price complete fused blocks after arbitrary
+separate conjugations.
+
+A second-block escape will be constructed on the complete order-three domain.
+It implements one ordinary DATA-row interchange with two restored dirty helper
+rows. The favorable bill is six full-volume children at one-third width. This
+already fails the positive-saving test, before the encoders are charged.
+
+Expected deliverable: a scoped negative theorem, an exact finite escape,
+standalone checks, rejection controls, and complete typed costs. No new kappa
+or selected-supplier change is planned. A later extension below resolves
+the algebraic two-block question for three genuine rows. Cheap paid encoders
+that mix native orbits remain open.
+
+## Predecessors and overlap
+
+PR521 gives the native map. PR677 gives restored DATA boundaries. PR840 gives
+the three-child centered shear. PR990 uses the same map in a private batch;
+its full endpoint was read. Its lifetime and batching result stay valid.
+PR955 closes fixed complex register words. PR720 concerns an abelian formal
+rational model. PR836 concerns complex unitary mixing. None supplies this
+full finite ADDRESS-domain rank comparison.
+
+The earlier private archive fixes a seven-map core plus an eighth rank-one
+map. Its one-negative and mod-4 results were read. This task does not repeat
+that screen. The present conversion class differs.
+
+This work uses one CPU thread. It uses no solver, random search, large install,
+or new agent. It leaves `upstream/` and the selected frontier unchanged.
+
+## Completed result and final overlap check
+
+At 2026-10-13 18:46 UTC, the final read found no pinned coordination issue.
+The 45 most recently updated open PRs, through PR1125, had no matching
+native-query boundary result. This is the inspected metadata scope, not a
+claim to have read every concurrent submission. PR840 and PR990 are still
+open at the exact heads above. Main is
+`ba82555c64e1879e4b7decce28186f208fcb8262`; its selected PR1042 differs from
+the stated base. The base and all construction pins remain unchanged.
+
+The one-block full-domain rank obstruction and the same-h orbit-quotient
+obstruction are proved. The exact two-block construction on one genuine row
+and two restored dirty rows is emitted and checked on all input columns,
+with an actual two-fiber spectator lift. Its six full-volume children fail
+the positive-saving recurrence even before its encoders are charged.
+
+The second-block experiment suggested a stronger extension. For three genuine
+rows and every odd prime power m>=11, complementary square-zero factors give
+exactly two complete fused blocks under free arbitrary binary encodings.
+This is a constructive proof, not a failed search or a conjecture. Its six
+children each retain one-third of the total DATA volume. The favorable child
+coefficient is two. The supplied scan-per-bit encoder still fails the full
+tape budget. The orbit quotient gives a quantitative lower charge for that
+specific emission. Structured encoders that group transfers remain open.
+
+The work stopped at that explicit implementation boundary. A large dense
+encoder replay would not remove its proved time cost, so no such enumeration
+was run. The completed package gives the universal algebra, full-domain
+obstructions, exact finite escape, all cost terms, and executable controls.
+It claims neither a new supplier nor a new kappa. The final quarter of this
+session was reserved for proof review, source/receipt checks and handoff.

research/native-query-boundary/LICENSE

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research/native-query-boundary/NOTICE.md

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+# Attribution and scope
+
+Contributed by Ali Romman. Substantial AI assistance from OpenAI Codex was
+used for research, mathematics, implementation, verification and writing.
+No independent human review or full formal verification is claimed.
+New code and prose are under the repository's Apache-2.0 license.
+
+- Karl Appel / @applecrusher, PR521 at
+  `a190fdb39f31647fc6f651625353710624627348`, supplies the native unipotent
+  ADDRESS map and the seven-event lowering. `query_events` is an attributed
+  transcription of that lowering. Its rational matrix is checked separately.
+- @commdata2338, PR677 at `613c02b8b4411f991f108dcc1481b3f9100b996f`,
+  supplies restored DATA-shear contracts, query-model distinctions and typed
+  costs. Its source notice and AI-assistance disclosure are retained.
+- Wentao Li / @VictorLiwentao, PR840 at
+  `da2cd0dd2229e08b61b174a8835a2c2bb99d2230`, supplies the centered dyadic
+  fused block with three ordinary children. `fused_events` transcribes its
+  event order. This work addresses the ordinary boundary left open there.
+- Sagar Thakrar / @thakrarsagar, PR990 at
+  `1c3ddf6bbbe1d8f0227de6726bb8273b2cb03711`, supplies the private native
+  batch and its distinct lifetime contract. Its source notice is retained.
+- OpenAI #109 and the upstream contributors supply the ordinary interchange,
+  stream, tape, restoration and head-return contracts. Their copied source
+  and license are unchanged. Those contracts remain premises.
+- Jonathan Capalbo's selected PR942 assembly, the later PR1042 assembly,
+  their complex lineage, and DreamingOfClouds' PR589 on eumemic's PR555 BIT
+  supplier retain their existing attribution. No selected artifact is changed.
+- The archived native-fusion521 application screens and PR955, PR720 and
+  PR836 were checked for overlap. Their narrower negative results retain
+  their stated scopes. This package does not rerun those searches.
+
+Exact copied bytes, source paths, Git blobs and hashes are in SOURCES.json.
+The vendor files preserve predecessor text and notices without edits.
+The full-domain orbit/rank argument, adapter charge, complementary-factor
+construction, literal encoder emission, independent complete VALUE replay,
+and cost comparison are the new contribution.
+
+No priority is claimed for binary Jordan form, Gaussian elimination, rank
+subadditivity, or the elementary complementary companion blocks. Their use
+here closes a specific native-query encoding question. A fast uniform tape
+encoder and a complete recursive supplier remain open.