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Construct fast dense execution of the original paired collector - #3131

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jmbarrancoml:research/dense-paired-collector
Oct 17, 2026
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jmbarrancoml:research/dense-paired-collector

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I supply a conditional fast execution of the original paired P104 collector, including its dense Gaussian monomial wrappers. For n=9lambda, N=2^n and linear working precision, I derive time O(N lambda^(2-8003/6000000)) and additional clean space O(N lambda^(5991997/3000000))+F. I charge both calls, four wrappers, grid handling, source/query access and cleanup.

I use the credited scalar-period identity to turn PR3109's changed-order lift into an exact dense scaled-linear backend. On a sufficient power-of-two input scale, standard character conjugation then supplies whole-field CNOTs and toggles with exact shifts and literal inverse cleanup. A second residue partition preserves the original consecutive nonlinear word. I bind the construction to PR2586 events 2025–2039 through Tekalign's PR3025/3033 paired interface.

I passed eight registered cold commands on Python 3.12.13/macOS arm64. Checks include 512 ideal native columns, 2,048 affine address cases, 2,610 interval plans, original-word payloads through 257 bits, and four complete N=512 collectors matching the predecessor's query, grid and private return. I included large dirty-source cancellation, a zero sum, synthetic tensor wrappers and guard/phase controls; algebra and consumer checks also pass under -O.

The finite executable uses direct semantic backends. It does not benchmark or emit the fast physical C trace; the time/space result is a written construction under the retained C-layer/compiler premises. The input contract uses explicit field-major serialization and charged clean history. I claim no linear-space host, width-one Boolean speedup, new multiplication exponent or full P104 supplier. The frozen five-forward/four-dual profile still has zero-saving bill at least599/584.

Reproduce: python3.12 scripts/research_package.py --package research/dense-paired-collector.

I credit Tekalign's PR3025/3033, Ross Richardson's PR3072, Douglas Colkitt's Fourier-conjugation analysis, ywz65's physical dual, the PR2250/2287/2899/3109 framework and Vasek/flyingviper's frozen-consumer audit. Tekalign's concurrent PR3122 reduces core history and explicitly leaves the wrapper/collector scope open; I retain a conservative collector-space bound and import none of that new code. SOURCES.json retains exact pins and source notices. Canonical coordination: 2750#18986640.

Jose Manuel (jmbarrancoml), with substantial OpenAI Codex assistance, including analysis subagents. I claim no hosted CI, independent human or proof-assistant verification. Apache-2.0. I leave the selected frontier unchanged.

@Mister-Meeseeks
Mister-Meeseeks merged commit 7db27e8 into CrocSwap:main Oct 17, 2026
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Mister-Meeseeks pushed a commit that referenced this pull request Oct 17, 2026
…at tensor multiplicity two

Checks the first paired P104 collector of PR #3131 at actual tensor
multiplicity two (n = 18, N = 262144, rank 14, events 2025-2039, native
events 2031 and 2033), beyond the predecessor's complete N = 512 tests.
Two separately written exact evaluators agree on the entire outgoing
value, promoted query and working grid of four deterministic signed
fixtures; the five dirty sources are preserved and the private collector
returns to literal zero. Both actual wrappers are checked on every
address (524,288 forward columns) and inverted. Two fixtures have
nonzero rounding error, 5379503/8 and 2615337/4 in working-grid
numerator units (grids 3 and 5), inside the exact forward and
paired-inverse relative bounds; the cancellation and zero fixtures
(grids 25 and 3) have none. The original return recipe passes an ideal
round-trip fixture, and layout, phase, lift-order, promotion,
restoration, source and receipt controls reject.

PR #3131's own nested evaluator did not finish on this fixture in two
600-second attempts; the optional script is kept outside the registered
replay and is not claimed as evidence. PR #3134's implementation,
lambda > 2, the fast physical trace, clean-stock hosting, all-size
refinement and the consumer bill remain open, and the inherited 599/584
screen is unchanged. No new kappa or selected-frontier change.

Adds research/p104-tensor-collector-audit/ only.

Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex
research and implementation; packaged with Claude Code).

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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