Benchmark Reproduction and Data Provenance
A bootstrap benchmark is reproduced only when a clean environment regenerates the stated observable from frozen scientific inputs and an independent evaluator confirms the certificate or residual within a preregistered tolerance. Matching a published number after manually adjusting conventions is useful diagnosis, but not yet a reproducible record.
Required background. Extremal Functionals, Navigators, and Spectrum Reconstruction define reconstructed observables. Precision, Convergence, and Numerical Error Budgets define refinement evidence. Helpful background. Solver Certificates and Independent Verification define certificate checks.
Evidence cutoff: 2026-08-23. Software versions, archived files, and published targets can change or disappear. Every real benchmark needs a dated, source-specific record. This page claims an executed exact-rational verifier fixture and a planned synthetic generalized-free-field protocol; it claims no production solver or interacting-CFT reproduction.
Freeze the scientific specification
Section titled “Freeze the scientific specification”Archive or regenerate from versioned source:
- the exact correlator and crossing convention;
- external data, spectral assumptions, sector and tensor-basis order;
- block-generator source revision and all parameters;
- canonical block tables and conic inputs with cryptographic hashes;
- solver source or release, build flags, dependencies, and container or environment digest;
- precision, deterministic seeds, resource-neutral settings, and stopping criteria;
- certificate, logs, convergence rows, reconstructed data, and output hashes; and
- license or rights information for code and archived inputs.
Hardware details matter when they change numerical ordering or performance, but a scientific acceptance target should be hardware-neutral: residuals, signs, hashes of deterministic artifacts, and observable tolerances rather than an exact wall time.
Clean reproduction protocol
Section titled “Clean reproduction protocol”The solver-level inputs and termination quantities that must be preserved are defined explicitly in Simmons-Duffin 2015, §§2–3.
- Verify downloaded or generated source hashes before execution.
- Build in a clean pinned environment and record the dependency graph.
- Regenerate crossing and block inputs rather than trusting copied solver files.
- Run at least two functional/block truncations and two precision values, with deterministic seeds where randomness is present.
- Evaluate the exported certificate or crossing residual using a separate implementation.
- Compare the observable to the preregistered target and decompose any difference by convention, truncation, solver, or environment.
- Publish machine-readable inputs, outputs, hashes, and a human-readable discrepancy report.
A byte-identical solver log is not required if parallel reductions are nondeterministic. The canonical scientific arrays and verified quantities must nonetheless agree within their declared rounding and tolerance policy. Release-aware conformal-block software and bootstrap frameworks are reviewed in Rychkov and Su 2024, §§2.1–2.2, pp. 2–3.
Durable fixtures and dated targets
Section titled “Durable fixtures and dated targets”The saved exact certificate contains the cone , a feasible control, a rational separator, its half-line Gram matrix, and the exact polynomial matrices for the derivative functional. The independent verification record binds the input and result hashes and records three rejected defects. This validates serialization, exact rational algebra, and the verifier’s fail-closed behavior without floating-point ambiguity.
The next fixture is a checksum-frozen generalized-free-boson correlator: regenerate blocks, verify crossing with a tail bound, construct a finite certificate, and recover selected low data within a declared truncation envelope. It remains prospective.
A three-dimensional Ising island or spectrum estimate is a different evidence class. It must name the precise paper and target table, translate conventions, freeze software and blocks, and record the evidence cutoff. No such reproduction is claimed here.
Numerical certificate and provenance table
Section titled “Numerical certificate and provenance table”| Problem | Approximation | Solver build | Precision | Certificate | Residual | Error budget | Input hash | Output hash | Independent rerun | Evidence cutoff |
|---|---|---|---|---|---|---|---|---|---|---|
| Rational cone and 1D lower-envelope fixture | no floating-point approximation; analytic inequality stated separately | independent exact-rational Node evaluator | exact fractions | finite Farkas separator, half-line SOS, normalized CFT functional, and Gram matrices | zero coefficient residuals; exact nonnegative PSD minors | none for serialized algebra; analytic lemma proved on the functional page | 25d2c0ba…0bc8 | 237dfc99…a4b1 | exact agreement; 3/3 defects rejected | executed 2026-08-23; no solver-version claim |
| Generalized-free-boson crossing | planned derivative, block, tail, and precision ladders | source revision and dependency digest required | at least two values | not yet produced | separate evaluator required | preregistered truncation envelope required | not yet recorded | not yet recorded | required | planned, unrun as of 2026-08-23 |
| Named interacting-CFT benchmark | absent until source-specific record exists | absent | absent | none | none | none | none | none | none | no reproduction claim as of 2026-08-09 |
The first row is an executed verifier fixture. It proves only its declared toy-cone and one-dimensional lower-envelope statements; the remaining rows are acceptance requirements, not completed computations.
Discrepancy classification
Section titled “Discrepancy classification”| Symptom | Likely class | First independent check |
|---|---|---|
| Crossing residual before solving | convention or generator mismatch | exact permutation and normalization identities |
| Correct blocks, different bound | assumption, sector, or search mismatch | diff canonical physical specifications |
| Same input, different termination | build, precision, scaling, or tolerance | verify certificate independently |
| Stable bound, unstable spectrum | extremal degeneracy or primal conditioning | track zeros and singular values across cutoffs |
| Matching headline number only | possible accidental agreement | compare full convergence and certificate records |
The generalized-free fixture above is the baseline for reproduction. A real three-dimensional benchmark should not be reported until a dated record satisfies the stated requirements.
Failure tests
Section titled “Failure tests”Mutable-input test. Replace a frozen block table by an unversioned download. Reproducibility status must be withdrawn.
Hash test. Change a sector order without changing numerical values. Canonical input hashes and the independent evaluator must detect the mismatch.
Headline test. Match one reported digit while convergence rows disagree. The reproduction fails its full target.