# Independent adversarial panel: source adjudication notes This is supporting evidence for the single final report in `../outputs/`. Provider outputs are proposals for checking, rather than proof certificates. The initial independent prompts contain source packets and error criteria only; they contain no Sol/Astra verdicts or findings from another panel member. ## Gemini 3.1 Pro: marked moment, first pass - Validated result: `gemini/marked_moment_section17/review.json`. - Native Google HIGH thinking, 32,768 shared output budget; one captured wire request. Reported usage: 64,847 prompt, 22,591 thinking, 700 answer tokens. - It proposes no objections and reports `no_demonstrated_error_found`. Its positive audit covers priority assignments, retained cube labels, canonical child data, exponent identities, finite propagation and amplification. - Its numeric equation references are unreliable. For example, its first positive row cites (17.13)–(17.14) as inclusion/exclusion and priority identities. In the compiled PDF those are terminal reflected-energy bounds (TeX `old-eq:4.10` and `old-eq:4.11`). Its retained-cube-label discussion cites (17.26)–(17.27), which actually give the enlarged first-frequency scale and first-prefactor comparison. Its amplification row cites (17.60)–(17.61), which belong to the second Cauchy/fibre-count calculation. - These mismatches are defects of the model's audit references, not identified mathematical defects in the paper. The descriptions can be associated with corresponding manuscript identities, but the seven short summaries do not supply a complete independent reconstruction of the masked Gauss coefficients. Its positive assessment therefore cannot certify the full Lemma 17.2 proof. ## Grok 4.7: fourth moment, first pass - Validated result: `grok-4.7/fourth_moment_section18/review.json`. - Native xAI high effort; one captured request. Reported usage is 47,781 prompt tokens, 61,312 reasoning tokens and 1,579 visible tokens. The provider reports 110,672 total tokens; its completion field counts the visible portion here. - No objections were proposed. The model gives eight source-anchored positive checks and leaves five prerequisite/citation obligations unverified. - Its `old-eq:2.6` calculation matches the local unequal-common-prime argument: with positive common valuations i >= j >= 1 and r=1 when their difference is not six-divisible, the excess gap in the positive branch is `(3i+11j-12-5r)/6`. The smallest r=1 case i=2,j=1 gives equality; the stated inequality is consistent. Extending this to j=0 would disregard its common support hypotheses and would not be a counterexample. - Its width/F2/centered-deficit checks agree with the displayed manuscript ledger and the independent checks already recorded in the final report. They are algebra checks conditional on the actual transformed coefficient. - The model explicitly leaves the primitive functional-equation proof, fixed-numerator ray reduction, uniform radial-kernel bounds, fixed-extension prime counting input, and underlying reciprocity table proof unseen. Several are internal prerequisites whose proofs were intentionally not in the packet, rather than missing manuscript hypotheses. No conductor-uniform external prime-counting error is claimed by the source at this fixed-data stage. - Its short summaries do not provide an exhaustive reconstruction of every complete-support/artificial-extension/amplifier coefficient. The absence of an objection adds an independent adversarial check within this scope; it does not certify all of Lemma 18.1 or the overall zero-free theorem. ## Trace coverage Fable, Gemini and Grok inference wire payloads and responses are recorded before adapter/schema processing. The initial Qwen job used a dedicated Alibaba Maas hostname outside the initial tracer allowlist. Its complete invocation/prompt is recorded, and its returned text is saved before JSON parsing. The first logical request payload is explicitly reconstructed in `qwen/reflection_external/initial_request.reconstructed.json`; original wire bytes, usage and internal retry counts for that job are not claimed captured. The corrected runner includes the Maas hostname for subsequent requests. ## Fable combined request: no verdict The combined 459,270-byte critical-gates source request failed after 1,020.175 seconds. Both the 32,768 and automatic 65,536 shared output budgets ended with `stop_reason=max_tokens`, and each reported its entire output budget as thinking, with no visible answer. Each attempt used 230,629 input tokens and reported no cache hits. Both complete SSE responses, native payloads, request IDs and the explicit adapter error are preserved. This is a recorded budget failure, not a mathematical review or an independent vote. Recovery uses separate source-only reflection, §17 and §18 requests, retaining high effort and the 32,768 initial budget. Each has a bounded falsification focus and permits an incomplete conclusion with explicit obligations. No model findings were included. Three successful packet reports would count as one provider's targeted coverage rather than three independent providers. ## Qwen bounded workflow: no verdict The initial Qwen reflection job used native `qwen3.8-max`, with requested high mapped to Alibaba xhigh and a 32,768 visible-answer budget. It returned no visible answer before the client workflow was interrupted near its first 30-minute SDK deadline. The execution session exited 130. This is recorded as `client_cancelled`, not a native timeout, mathematical objection, or completed review. OpenAI SDK 2.31.0 defaults to two retries; the adapter did not override that setting. Actual native retry count, usage and server billing/completion remain unknown because of the initial tracer-host omission. No independent Qwen rerun was launched. The reported elapsed time includes brief recording delay and is not a measured model latency. ## Readable content in failed Fable attempts Completed first-attempt SSE streams provide empty `thinking_delta` strings and opaque signatures, with usage metadata. They contain no readable candidate counterexample to adjudicate and no visible answer. The budget failure is not converted to a model mathematical conclusion. ## Fable reflection split: completed and adjudicated The validated high-effort result completed in 858.789 seconds across two native attempts. It supplies 14 source-anchored checks, two `unverified_step` objections and six prerequisite obligations, and explicitly finds no demonstrated error. Attempt one exhausted 32,768 thinking tokens; attempt two reported 51,526 output tokens, of which 44,959 were thinking. Each used 60,649 input tokens and no cache hits. The first failed budget is not an additional independent review. Its uncertainty about the imported automorphy direction and shared-prime support does not exhibit a mismatch. Direct native DR source `chidef` states the unconjugated `(c/a)_3`, homomorphic extension to Gamma2 and trivial restriction to SL2(Z); its coefficient domain and conjugation match the manuscript as established in the independent source check. Patterson's underlying proof was not rederived. Its unseen `eq:pointwise-mellin-tail` concern is a packet omission: original source lines1164–1177 give the estimate by repeated logarithmic integration by parts. For the stated V and derivative decay at both ends, the weighted boundary terms vanish uniformly on each compact real strip. A derivative order above the polynomial growth exponent of T therefore removes the horizontal joins. An independent algebra check also confirms the reflected/direct Mellin scalar ratio: `-i·3^(-5/2)(2pi)^(4s-2)27^(-s)` at `s=1/2-t` becomes `(-i/81)[(2pi)^4/27]^(-t)`. The gamma quotient correspondingly becomes the stated R(t). This checks that displayed normalization, not every moving-prime cusp matrix or the full later reflected energy estimate. The model's detailed local calculations support the reflection component but do not replace the remaining independently unclosed global gates. ## Fable §17 split: partial answer, no completed verdict The job failed explicitly after 1,058.188 seconds and two native attempts. The first exhausted 32,768 thinking tokens. The second reported 65,536 output tokens, with 62,303 thinking and 3,233 visible, and stopped inside an audit-step JSON string. Each attempt used 99,597 input tokens with no cache hits. The raw SSE is preserved and its partial visible answer is separately extracted as `fable/marked_moment_section17/response.partial.txt`. Missing schema fields and a mathematical verdict are not manufactured. Its seven complete visible audit entries cover the masked-Poisson derivation, first conductor/support data, eight local exponent cases, first frequency budgets, second primitive character, extraction/child character identity and margin decrease. Their displayed local identities agree with independently checked arithmetic in the principal report. No candidate counterexample or objection occurs in the surviving partial answer. The interrupted answer does not supply a completed global reconstruction or a no-error-found assessment. ## Fable §18 split: partial answer, no completed verdict The job failed explicitly after 1,146.418 seconds and two native attempts. The first used 32,768 thinking tokens; the second used 65,536 output tokens, including 63,472 thinking and 2,064 visible. Each attempt used 72,582 input tokens with no cache hits. Its visible JSON stops inside the seventh audit entry. The six complete entries examine CRT/amplification, valuation-1/6/7 coefficients, preservation of the centered coefficient, width decrease and two local exponent ledgers. Those displayed identities agree with the source and checks in this report; the surviving partial text has no candidate counterexample. It is not a completed assessment of the whole invariant. Raw SSE and `fable/fourth_moment_section18/response.partial.txt` are preserved. No additional recovery call was made after the three split outcomes.