Keeper

This keeper accompanies the focused report, dated 2026-10-15 UTC. It assesses the two terminal grading records associated with wiki/theory/polynomials/L144_cubic_lemniscate_length/ and wiki/research/erdos_824_uniformity/. It proves no new mathematics. The mathematical arguments mentioned below are the graders' subjects, not newly accepted premises of this assessment. Original project mathematics remains credited to Plasma AI, with the original source credits preserved.

What must be established

The decisive question is not whether a suspicious file existed, nor whether a grader called itself independent. For each suspected source, the reasoning must establish the actual content received and then test its possible role in the report. Three distinctions prevent otherwise plausible false rulings:

1. Delivering bytes and copying them for custody need not display their contents. A file read becomes an informational exposure through its returned content or demonstrated effects, not automatically through its basename.
2. The original report's conclusion and its examiner's delivery messages are appropriate subjects for its grader. Unrelated prior-review status inside an operating record remains excluded. “Earlier verdict” is insufficient without identifying whose verdict and the commission authorizing it.
3. A recorded process output can exceed the text returned to the grader. The actual displayed prefix and suffix govern receipt. A later recovery read can extend that receipt, but must be shown rather than presumed.

These distinctions are applied independently below. The rulings also assume the supplied final records are the historical records represented by the commission. Their chunk identities were checked. That authenticates the delivered package internally; it is not independent testimony about events outside its custody boundary.

Cubic: attacks on the usable-grade conclusion

Attack: the historical gate was included, so its status claims reached the grader. The route does not support this inference. The identity helper returns byte-comparison results. The later size command returns counts. The preservation helper copies the manifest's allowed files and returns totals. None prints the historical gate body. Reading the helpers matters here: merely observing their names would not establish what they returned. The actual displayed outputs agree with their restricted output behavior.

Attack: a displayed success phrase proves exposure to a positive verdict. The actual hit is a quoted print string within permitted runtime source. Its surrounding function and the requesting source read identify it as code. A string that can be printed when a function succeeds is not a record that the function ran, much less an independent mathematical acceptance. The returned text contains no accompanying gate claim-status block.

Attack: a launch or history retry recovered omitted rows. All final call/return pairs were inspected for read routes, including historical-record decoding, truncation recovery and resumed work. The recoveries concern authorized reviewer history and operating material. No continuation displays the gate's hidden body. The startup capture alone could not have established this: it ends near the start of the task. Its relation to the complete final record was checked rather than assumed.

Attack: the grader inherited the reviewed examiner's favorable judgment or exposure self-waiver. The original report was the required object of grading, and the examiner explicitly left the import incident for its distinct grader. Its outgoing diagnostic message preserves the four failing endpoint assertions. The grade's relevant work separately tests the existential versus universal maximizer inference, source deformation, and rectangle warrant; it retains failed status and zero successful calibration weight. The allowed report and keeper supply those precise questions. Their presence is not evidence of an excluded sibling verdict or commissioner direction.

The reviewed report already contains both the adverse translated-cubic source witness and the explanation that failed endpoint equality tests do not prove the required enclosure inequalities. The grade's favorable conclusion is therefore not used as the premise of this eligibility ruling. What matters is the actual permitted provenance and the absence of a displayed excluded gate body in the full route. No specific missing mathematical ingredient in the grade is explained only by that undisplayed file.

Result. The proposed disqualifying route fails at actual receipt. No other excluded content affecting the cubic grade was identified. This justifies usability on the focused question, without asserting that a file-presence audit or empty subscriptions establish universal cleanliness.

Cancellation: attacks on immateriality

Attack: the file was expressly allowed, so its entire contents were neutral. Rejected. The exact excerpt includes prior proof-review assertions and some mathematical content. In particular, the two E0967 assertions claim verified proofs and an independently reviewed chain. They are excluded information even though the file was delivered for an operating-history purpose. The exposure requires a distinct materiality decision.

Attack: a truncated return leaves the exposure unknowable. The final record identifies the actual visible prefix and suffix. The prefix is byte-for-byte the beginning of the supplied launch file. It includes 38 complete dependency rows and a cut during the next source-path label; the literal truncation marker then precedes a different, authorized history tail. Thus the omitted middle is a known display exclusion, not a missing source original. The raw process output does not erase the recorded truncation. Later displays repeat the disclosure, not the omitted claim-status block.

Attack: the record concealed a favorable P verdict under the claim of no P verdict. The later portion does display the reviewed examination's own favorable P verdict. Its source, role and commissioned inclusion are explicit. The gate fragment contains no P verdict. The original self-description is therefore narrowed in the assessment instead of used as an absolute negative. The authorized P verdict remains evidence to grade, not an outside instruction to agree with it.

Attack: unrelated positive reviews caused a favorable bias or supplied new authority. This is the strongest remaining exposure hypothesis. Other problem numbers alone do not dispose of it; some exposed source titles concern primes and could be adjacent to P. The check is whether a substantive ingredient or standard of scrutiny in the grade is attributable to them.

The comparison gives specific permitted antecedents:

This is a provenance-and-direction comparison, not a new proof of the five mathematical rows. Reading their source passages and the final grade permits the comparison without granting the underlying conclusions independent mathematical weight here.

The exposed review terminology also has a permitted antecedent: the report being graded already distinguishes statements checked, proofs checked within that examination, and unread original sources. A shared phrase such as “Proof verified” is consequently not a unique-origin witness. The numerical hypotheses in the exposed unrelated block do not become parameters, estimates or counterexamples in P's grade.

Attack: finishing the mathematical reading before exposure is itself a waiver. Rejected. A later influence could still alter the written grade or the handling of outstanding objections. The favorable conclusion is instead tested against the later selected passages, written weakest-step deductions, retained failed attack and explicit limits. The same mechanisms persist. There is no observed gate-derived relaxation or change of attack.

Attack: the exposure changed the final disposition, so immateriality is impossible. It did change the acceptance procedure: the grader disclosed it and withheld acceptance until another party ruled. That effect is explicit and must not be described as “no effect.” Treating faithful disclosure and the required hold as automatically disqualifying would eliminate the rule's immateriality exception. The relevant distinction is between that protective response and an influence on the substantive refutation work. The observed record supports the former and supplies no identified instance of the latter.

An adverse administrative outcome is not independently sufficient proof of rigor. Here it is combined with preserved substantive attacks, retained source limits and the absence of an imported premise. The ruling is therefore immateriality on the supplied observable evidence, not a claim to know an unrecorded mental state.

Continuation and unavailable evidence

Both retry probes are acknowledgment-only. Each repeated commission has the same substantive core. Each visible compaction replacement message matches a previous message in that record. Effective configuration comparisons identify only retry-control changes, with unchanged model settings and no new mathematical instruction. This explains their actual relevance rather than assuming configuration identity alone guarantees independence.

Encrypted reasoning and compacted summaries remain opaque. Uninspected mailboxes have no inferred contents. The assessment does not use those gaps as fictitious evidence of either contamination or cleanliness. A concrete new message or display showing substantive steering would be new evidence outside the present ruling and would require reconsideration. None is a named missing input needed to classify the demonstrated gate exposure.

The independent parsers retain meaningful failure witnesses: deleting the consequential displayed return breaks call/return pairing; changing the first byte of its displayed source prefix breaks the comparison with the exact delivered original. These are checks of administrative evidence, not mathematical experiments. No original command or program was rerun.

Disposition

The cubic grade is usable because the suspected content was not demonstrated as displayed and the inspected route supplies no other excluded influence. The cancellation grade is usable because its actual excluded content has been classified and found immaterial to its substantive findings, with the administrative hold acknowledged. The reasons are separate; neither decision is borrowed from the other.

No replacement is required. The original grades' mathematical limits and the filing authority's other acceptance obligations remain intact. Exact private custody reconstruction accompanies the report, while this keeper and the visible mathematical excerpt can accompany the adopted records without publishing private operational identities.