Scientific review packet#

Status: a supplementary automated review of the frozen 0.3.0a2 source recommended approval within the documented scope and found no release blockers. Its six nonblocking corrections are addressed in 0.3.0a4 below. This is not human peer review or a proof of correctness.

The expanded development grid and packet-generation instructions are in Stability audit and scientific review; they do not replace this historical review.

The subsequent 0.3.0rc1.dev1 automated review and corrections are tracked in Stable-development review findings and disposition. Its changes-required disposition does not replace the historical review below.

Review scope#

Review the unit-power massive D=2 sunset in the positive Euclidean normalization \(d^2k\,d^2\ell/\pi^2\). The reusable bracket compiler produces formal candidates; the proven series selection and collision limits are specific to the sunset.

Component	Derivation	Implementation	Independent evidence
Bracket constraints and Gamma families	RMT guide	`ramanujan_qft/brackets.py`	exact constraints, nonsingularity refusals, regulated pole-limit tests
Momentum and dominant-mass RMT charts	RMT guide	`ramanujan_qft/sunset_rmt.py`	40/55-digit nested parameter references, sector comparisons
Equal-mass Euclidean continuation	Taylor guide	`ramanujan_qft/sunset_taylor.py`	Clausen vacuum, independent parameter integral, overlap with RMT

Questions for the reviewer#

Are the loop normalization, Euclidean signs and squared-mass conventions consistent between graph polynomials, Mellin-Barnes formulas and references?
Does the momentum-chart contour argument justify the selected pole families and the continuation in propagator powers? Check the reciprocal Gamma zero.
Do the coalesced harmonic coefficients follow from the complete regulated family sum, including mixed-index terms and unequal masses?
Are the stated convergence regions sufficient, and are the tail bounds valid for all accepted inputs, including near-boundary cases?
Does the transformed Taylor recurrence follow from the stated ODE and seed? Check the factor of 16 relative to Laporta–Remiddi’s D=2 normalization.
Are the arithmetic estimates conservative enough in practice? Neither backend provides rigorous interval enclosures. Check error propagation and budget refusals under cancellation and extreme scaling.

Reproduce the numerical audit#

python -m pip install ".[test]"
python -m pytest -q tests/test_sunset_rmt.py tests/test_sunset_taylor.py tests/test_sunset_audit.py
python tools/audit_sunset.py --output benchmarks/data/sunset_audit.json

The audit uses fixed random seed 1729, records package-source SHA-256 hashes, numerical-library versions and actual versus estimated error. The per-file SHA-256 hashes are the binding identifiers for the evaluated sources. base_commit is optional checkout context: it can predate the commit containing the report and is null in a source archive or when Git is unavailable. It does not identify uncommitted changes; the source hashes do. Timings are descriptive measurements on the executing machine, not promises.

The reference is obtained from the projective parameter integral by setting \(x+y=1\), \(a=x(1-x)\), \(A=m_1^2x+m_2^2(1-x)\) and integrating \(z\) analytically:

\[F=m_3^2z^2+Bz+C,\quad B=A+m_3^2a+p_E^2a,\quad C=aA.\]

With \(\Delta=B^2-4m_3^2C\ge0\), the remaining integrand is

\[\int_0^\infty\frac{dz}{F} =\frac{2\operatorname{asinh}(\sqrt\Delta/(2\sqrt{m_3^2C}))}{\sqrt\Delta},\]

with limit \(2/B\) at \(\Delta=0\). A one-dimensional quadrature at two precisions provides the reference. Separate tests compare this reference with the existing nested two-dimensional simplex fixtures. These checks share the underlying integral but do not share the series formulas, recurrence or Clausen seed.

Precision agreement is evidence, not a rigorous reference enclosure. The report includes the measured difference and a numerical allowance. Domain refusals and budget exhaustion are counted separately from successful evaluations.

Findings from the local audit#

The refreshed 0.3.0a4 report records 34 passing cases: 27 evaluations, three expected domain refusals and four expected budget refusals. Its source hashes match the frozen 0.3.0a4 source. Those retained hashes include version metadata and should not be compared to the 0.3.0a5 metadata update as though they identified the same release. The numerical algorithms are unchanged; each release workflow also produces its own audit report. This is a bounded audit, not exhaustive domain coverage.

The first fixed-precision run failed the reference check for squared masses (1e-16, 1, 1e16). The 35- and 50-digit quadratures disagreed; this was not accepted as evidence of a backend error or as a valid reference.
The reference driver now increases precision within a bounded schedule, records both working precisions, and requires eight more relative digits than the requested result. An unresolved reference still fails the audit.
The equal-mass forward recurrence is unstable at fixed low precision. Its growing mode is covered by extra guard digits, propagated arithmetic error, two-precision agreement, and an explicit precision-budget regression test.

Review record and corrections#

The original automated review report is retained unchanged with the release evidence. It identifies its reviewer, methods and limitations. It reviewed commit e74a2233913f4e0c9f6a319e305c0cfc908fe251 (0.3.0a2), dated 2026-10-24, and recommended approval within the documented scope, with no blockers. Report SHA-256: fb1a1fe3014341ecce48c474fd39ace2976aa20dcc7dec3103ed2f2e8ea8e8cf.

Numerical calculations are unchanged since that reviewed candidate; public API docstrings now describe precision checks without implying interval proofs. The later release tooling and documentation have separate regression and artifact checks; the report does not constitute review of those later edits. A qualified human scientific review remains welcome. No human peer-review claim is made for this research alpha.

Finding	Correction in 0.3.0a4	Evidence
N1: reports fail outside Git	Optional `base_commit`, including absent Git	Regression tests and complete report generation from an archive without `.git`
N2: ambiguous numerical guarantees	Use “precision-checked”; explain precision agreement and its limits	README, API and user guides
N3: vanishing family	Explain the dimension-independent reciprocal Gamma zero	Sunset RMT derivation
N4: practical budget coverage	Measured 10/20/30-digit grid at default budgets; report refusals separately	`benchmarks/data/sunset_budgets.json` and RMT guide
N5: report provenance	Source hashes bind the evaluated files; commit is optional context	This page and comparison guide
N6: benchmark reference independence	Gaussian Fourier/angular representation replaces the timed oscillatory method as reference	Two-precision reference agreement, cross-representation tests and refreshed raw timings

The product benchmark is separate from the sunset audit. Its new reference uses a different integral representation; it shares mpmath arithmetic with the evaluators, so agreement still does not establish a rigorous interval enclosure.