[AdaWorldAPI]

Research-only .arxiv shelf: QR256, elimination, rotation, proof traces

Adds six primary-source/reference excerpts and one consolidated preregistered 12-path hypothesis matrix.

Source notes

• arXiv:2201.06508: Gaussian/greedy GF(2) reversible circuit synthesis
• arXiv:2610.17934 (2026-10-13): chordal-code elimination and fill-in order
• arXiv:2610.08701 (2026-10-06): partial-pivoting growth, numerical-stability counterexamples
• arXiv:2609.28901 (2026-09-24): reversible finite-field quantum Gaussian circuit, analogy only
• arXiv:2304.04332: egglog Datalog + equality saturation and contemporary proof-store API
• Four Russians / M4RI and ISIT 2026 reverse-lookup work (IEEE source, not arXiv)

Preregistered hypotheses / negative controls

12 paths cover co-ordinal directory joins, many-to-many memberships, cross-ontology binding, GF(2) Four Russians, Boolean QR256 composition, million-fold egglog substitution, chordal PEO, numerical pivot growth, reversible sidecar, dirty masks, typed coordinate rotation, and binding amortization.

Exact rotation fixture:

1 2 3       3 6 9
4 5 6   ->  2 5 8
7 8 9       1 4 7

CCW 90° view new[r,c]=old[c,N-1-r]; 4 rotations identity. Negative test distinguishes image rotation from a consistent graph-node relabeling. Matrix remains an 8 KiB resident 256×256 bitset; sidecar is cold for replay/writeback and retains zero-copy SoA row references.

Explicit boundaries

• GF(2) XOR is not existential Boolean OR/AND; bag != set.
• The paper results are not Lance-graph benchmarks or production claims.
• ADMISSION B no-cross-table-value-gather remains in force, even during preparation.
• Stale source/codebook/coordinate witnesses must refuse; actual dirty vs committed dirty are separate.
• No C/GraphBLAS dependency, code, runtime, CE64 reinterpretation or production wiring added.
• No existing files changed, no code executed. Test paths are hypothetical and come with independent oracles and kill conditions.

Verification

Checked against source arXiv abstracts/HTML, existing .arxiv shelf conventions, D-RMAP-2 and unified relalg plan. GitHub compare confirms seven added Markdown files in one commit, no deletions.

Cross-PR implementation bridge: #1659 → #1660

The missing PowerShell-style ordinal template polyfill is mapped in D-QR-POLY bridge design, added in commit 311a8625.

• PR #1659 is the physical lab owner: refcounted ScalarBuffer lanes, Side {present,off,pos,lane}, Run::get as lane[pos[k]], and a one-slot prefetch hint. The physical code remains on Zero-copy joins: relations are lanes, a side is an index map $i (mork-pathmap-probe, crepe-plan-probe) #1659's separate branch and is NOT incorporated by this docs PR.
• PR #1660 is the logical/proof research owner: a typed 256×256 Boolean QR plane (8 KiB per full plane), palette8 methods, Boolean composition, typed rotations, M4RI/GF(2) controls, egglog shared proofs, cold BEFORE/AFTER replay. No implementation or benchmark added.
• Missing between them: the zero-heap "{0}{1}" -f $laneA[$i],$laneB[$i] declarative placeholder/ordinal compiler. This is a position template, not string concatenation or a tuple allocator. For separate source relations, use each side's own witnessed off/pos rather than assuming equal row indices signify equal entities.
• Materialized QR package: OrderedAddressView (refcounted borrowed lanes, present/off/pos, codebook and generation witnesses, prefetch) + QR256 (hot Boolean truth); separate cold ProofReplaySidecar (mapping, derivation DAG, dirty bits, authorized writeback). The entire package costs more than 8 KiB: 8 KiB describes the packed truth plane only. Reuse existing mask-risc/ndarray Boolean kernels and BlasGraph semantics/oracles, not its owned CSR/CSC as a falsely zero-copy tile.
• EXO-119 owns the proposed position-template/lens contract; EXO-120 contains the QR/BlasGraph/replay probes. Both are Backlog, unclaimed, research-gated. EXO-50 is the agent handoff bus.

Decision gates: #1659 still has an unpruned index-preparation failure on unordered input and cannot be declared production-ready. Key-order witness policy overlaps EXO-114; general global→focus binding admission overlaps EXO-46. #1640 ADMISSION B forbids cross-table value-driven positional gathers even in preparation. No new operator permission, copied SoA values, tuple decoder or production engine follows from this document.

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