Research: independently audit PR #3131's first paired P104 collector at tensor multiplicity two

research/p104-tensor-collector-audit/README.md

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+# Independent actual tensor-collector audit for P104
+
+Two independent direct interpretations of the first paired P104 collector
+of Jose Manuel's **PR3131** agree at **multiplicity two**: `n=18`, `N=262144`,
+rank `14`, with the actual nine-field native recipe. Four complete signed fixtures
+agree on every query component and working grid, preserve all five source
+arrays, and return the private collector to literal zero. Two fixtures have
+nonzero rounding error. This supplies actual `lambda>1` semantic evidence at
+the boundary left in PR3131's PROOF section 7. The full retained nested
+implementation comparison remains **unchecked** after two bounded timeouts.
+
+This is a **finite interface audit**, not verification of the fast physical
+implementation, its time/space theorem, or a complete P104 supplier. The
+selected frontier is unchanged. The original-order map, paired inverse and
+error policy are predecessor constructions, not new results here.
+
+## Exact scope and evidence
+
+The frozen word interval is events **2025–2039**, with native occurrences
+**2031 and 2033**. The audit reconstructs the prefix frames, checks the actual
+source names `D31,D30,D29,D28,D27`, the `Q7` query, gathering/ungathering signs,
+private lifetime and unique native records. It uses PR3131's layout
+
+```
+address = sum_i v_i * 2^(i*lambda),
+v_i = sum_j x_(i,j) * 2^j.
+```
+
+The original lift acts on consecutive axes `0,...,7*lambda-1`. The numerical
+return inverts the outbound wrappers and the literal lift in reverse order.
+It does **not** independently round the distinct return recipe from event
+2033. That recipe remains bound to the source and is checked as an ideal
+round-trip fixture on the full multiplicity-two rounding input.
+
+`verify.py` expands the binary affine and strict-upper quadratic phase
+polynomials directly on 18 bits. `oracle.py` instead applies one 512-entry
+factor at a time on each strided nine-bit column. Every address of both
+outbound wrappers and their inverses is checked: **524288 forward monomial
+columns**, plus both inverse checks. Unique positive address markers make
+this an exact permutation-and-phase check, not a sampled linear-operator
+comparison. The two implementations share raw recipes and fixture inputs,
+not wrapper or lift code.
+
+Tekalign's later [PR3134](../guarded-wrapper-refinement/README.md) reduces
+wrapper-level lifting calls from 416 to 104 while retaining this collector
+interface. Its complete collector checks are also at `N=512`. This audit
+keeps PR3131's exact comparison source explicit; it does not replay PR3134's
+changed implementation or claim its call reduction as new.
+
+The primary lift uses the signed difference/floor sequence. The other uses
+a separately derived parity formula for each output. An additional ideal
+oracle uses `H diag(i^popcount) H / 2^14`, independently of either rounded
+pair implementation. Both full query arrays are compared before recording
+SHA256 digests. Digests summarize the outputs; they do not replace those
+component comparisons.
+
+| Multiplicity-two fixture | Input grid `f` | Working grid `F` | Squared error in working-grid numerator units |
+|---|---:|---:|---:|
+| signed, unpromoted, nonzero rounding | 3 | 3 | `5379503/8` |
+| signed, promoted, nonzero rounding | 3 | 5 | `2615337/4` |
+| 70-bit dirty cancellation to two unit components | 3 | 25 | `0` |
+| exact zero gathered sum | 3 | 3 | `0` |
+
+Physical squared error is the last column times `2^(-2F)`. The first two
+cases use `beta=0`; the latter two use `beta=8`. The cancellation cases
+retain independently supplied large positive and negative source arrays.
+Their small or zero sum does not permit omitting source preservation or
+literal ungathering. A complete `lambda=1` fixture is also included, and
+four small cases are compared with Tekalign's authenticated PR3025 source.
+
+## Why these are the intended semantics
+
+For Gaussian integers `a,b`, put `d=a-b`,
+`s=b+floor(d/2)` componentwise, rotate `d` by `i`, then return
+`(s-floor(d/2)+d, s-floor(d/2))`. Replacing the rotation by `-i`
+inverts the pair: the output difference determines the original `d`, and
+adding back its floor recovers `s`. Reversing the stage order therefore
+restores every integer input. This is Tekalign's credited bijection; the
+checker also exhausts all **2401** pairs with four real coordinates in
+`[-3,3]` against the separate parity expression.
+
+If `p_R,p_I` are the parities of the entering difference, both outputs
+have error `(p_I-p_R)(1-i)/2` relative to the ideal pair. Thus each stage's
+squared error is at most `N/2`. Ideal suffixes and exact monomial wrappers
+are unitary, so the whole outbound error has norm at most
+`r sqrt(N/2)` in working-grid numerator units. The ideal Walsh oracle
+checks the actual error and its unitary norm identity with integers only.
+
+For nonzero gathered numerator `S`, let `M=max |component(S)|` and
+`h=floor(log2 M)-f`. The source policy is
+
+```
+gamma = ceil(log2 r) + ceil((n-1)/2),
+F = max(f, beta+1+gamma-h).
+```
+
+For zero `S`, use `F=f`. Since `||S 2^-f|| >= 2^h` and
+`r sqrt(N/2) <= 2^gamma`, the outbound relative defect is at most
+`epsilon=2^(-beta-1)`. The paired return is exactly the embedded input.
+Its difference from the *ideal* inverse has the same norm as the outbound
+defect, by unitarity, so its relative defect on this paired execution is at
+most `epsilon/(1-epsilon) <= 2^-beta`. The checker evaluates both squared
+relative inequalities without floating point. This is not a relative-error
+theorem for arbitrary inputs to the inverse routine.
+
+The query is promoted to grid `F` **before** adding the outbound value.
+Private return permits exact downshift to `f`, then five reversed
+ungathers. Exact private cleanup does not remove the query's numerical
+error and is not by itself evidence of the correct forward map.
+
+## Discriminating controls
+
+The retained recipe's right wrapper sends address zero to **212799** with
+phase **2** at multiplicity two. Using copy-major layout without conversion
+instead sends it to **192375**. Forgetting the second copy's constant phase
+changes phase 2 to 1. The left wrapper has a separate layout witness at
+address 8. The full address checks distinguish these errors.
+
+The four-component real impulse `(1,0,0,0)` becomes `(0,0,1,0)` under
+lift order `[0,1]`, but `(0,1,0,0)` under `[1,0]`. Both paired inverses
+restore the impulse. This small control explains why checking cleanup or
+an ideal tensor endpoint alone cannot justify reordering nonlinear stages.
+It is a calibration of the inherited order requirement, not a new
+obstruction to arbitrary collectors.
+
+Eight behavioral test groups also cover the actual optimized CLI,
+source corruption before arithmetic, altered event signs/targets/lifetimes,
+missing native occurrence, wrong query-grid promotion, corrupted return,
+signed-floor truncation, wrapper phase changes, duplicate JSON keys and
+changed receipt values/types. Assertions are not used for acceptance.
+
+## Incomplete retained evaluator comparison
+
+`attempt_retained.py` attempts the actual PR3131 nested evaluator on the full promoted
+multiplicity-two fixture and compares its complete entrance, query, sent,
+returned and private arrays with the independent oracle. Its one disclosed
+adapter changes the finite `Executor` extent check from `n<=10` to `n<=18`.
+All arithmetic, block-planning code, protected XOR interfaces, dense wrapper
+calls and inverse routines are unchanged. The finite parameters are
+`width=160, d=157, spacing=1, suffix=2, outer=14`, obtained from the inherited
+exponents and checked using integer inequalities. The adapter authenticates
+the original bytes and requires exactly that one reversible text substitution.
+
+Both the small-test defaults `d=2, spacing=2, suffix=1, outer=3` and the
+explicit derived plan above failed to finish within **600 seconds each**
+(exit 124). Neither produced a completed receipt. These timeouts establish
+no mathematical failure and no successful retained implementation comparison.
+The script is preserved as an optional follow-up, outside the registered
+successful replay. For example, from the repository root:
+
+```sh
+timeout 600s python3 -I -B research/p104-tensor-collector-audit/attempt_retained.py --plan derived
+```
+
+Use `--plan defaults` for the other attempt. The command compares full arrays
+if it completes; no successful output is claimed for either recorded attempt.
+
+The evaluator retains PR3109's frozen **direct semantic oracle**. This does
+not execute, benchmark or verify a fast physical C-layer trace. Sources and
+the archive remain unchanged; the adapter compiles its copy in memory.
+`TASK.json` records the two attempted parameter sets and incomplete outcomes.
+
+## Reproduce
+
+Python **3.12**, standard library, from the repository root:
+
+```sh
+python3 -I -B scripts/research_package.py --package research/p104-tensor-collector-audit --check-only
+python3 -I -B scripts/research_package.py --package research/p104-tensor-collector-audit
+```
+
+The registered replay runs the independent full-array check and eight controls
+under `-O`. Expected markers are
+`PASS_P104_TENSOR_COLLECTOR_AUDIT cases=5 no_new_kappa` and
+`PASS_REGISTERED_RESEARCH_PACKAGE`. Individual commands are in `VERIFY.json`.
+`--emit` prints regenerated JSON; default replay reads and compares the
+complete committed receipt without modifying it. Exact immutable source
+hashes and Git blobs are in `SOURCES.json`.
+
+The independent full-array run takes about **32 seconds** and **690 MiB**
+on the recorded CPython 3.12.3 environment. This measures this direct checker,
+not the proposed fast collector. The finite direct paired word has
+`3670016` pair sites, `1048576` wrapper value visits and 11 full-array
+scalar additions per multiplicity-two execution. Those are direct-reference
+counts, not project-native child charges or a hosted physical bill.
+
+## Limitations
+
+No completed retained nested `lambda=2` implementation comparison, actual
+`lambda>2` collector, fast C-layer trace, all-size machine
+refinement, clean-history hosting, tape movement, complete correction word
+or selected cold replay is checked. No human or formal-kernel review is
+claimed. The source archive's scientific admission remains separate.
+
+## Open next questions
+
+1. Complete the retained nested evaluator comparison on this same actual
+   fixture, with a measured replay budget, or establish its separate component
+   equivalences. Agreement of the two direct semantic models does not verify
+   the nested implementation. Both 600-second attempts remain unresolved.
+2. Bind an actual fast reversible backend trace to this checked boundary,
+   pricing snapshots, source access, cleanup and clean stock. The blocker is
+   the physical backend and enclosing caller, not this direct finite oracle.
+3. Name a changed complete P104 profile or consumer and price every term
+   before further construction. PR3131 retains the unchanged five-forward /
+   four-dual rejection `599/584 > 1`; this audit does not reprove it or remove
+   any of its paid ranks. Clean history is not extra productive coverage.
+
+The decision is to stop at this bounded audit. Detailed scope and next
+questions are in `TASK.json`; the claim is in discussion **#2750**.
+
+## Credit
+
+Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.
+
+Credit Jose Manuel / jmbarrancoml, **PR3131**
+`0c9e344d5a5295a218558fa4a51d867f39ff5311`, for the actual field-major dense
+collector, original-order construction and explicit validation gap;
+Tekalign, **PR3025** `a544ef068a46f4de3bc47d1d02149cbdc3ba547f` and **PR3033**
+`b12bbaeb5ca2e83f15433fc2dd0ba3b766595281`, for the signed lifting pair,
+paired collector, grid policy and period split; and Ross Richardson,
+**PR3072** `cd1bbd05251f9d8e15cbb0192f1bfe83dc138f5e`, for the conditional
+blocked construction. Retain Jose Manuel's PR3109 and PR2250/2287/2899
+affine/compiler/physical lineage, Douglas Colkitt, ywz65 / PR2586,
+Arham Tahir, Vasek/flyingviper's consumer audit and the retained Rohan Arun,
+Chafik Boukhalfa, Adam Gall, Josie Elliston and Ali Romman P104 lineage.
+
+Both new numerical evaluators were separately written in this contribution
+with shared raw inputs. The small calibration intentionally executes credited
+PR3025 code; the incomplete retained attempts intentionally execute credited
+PR3131 and its source archive. These are not separate human reviews. Apache-2.0;
+predecessor licenses, frozen inputs and the selected record are unchanged.