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: 2026-08-09. Software versions, archived files, and published targets can change or disappear. Every real benchmark needs a dated, source-specific record; this page claims only an exact rational fixture and a planned synthetic generalized-free-field protocol.

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

The solver-level inputs and termination quantities that must be preserved are defined explicitly in Simmons-Duffin 2015, §§2–3.

1. Verify downloaded or generated source hashes before execution.
2. Build in a clean pinned environment and record the dependency graph.
3. Regenerate crossing and block inputs rather than trusting copied solver files.
4. Run at least two functional/block truncations and two precision values, with deterministic seeds where randomness is present.
5. Evaluate the exported certificate or crossing residual using a separate implementation.
6. Compare the observable to the preregistered target and decompose any difference by convention, truncation, solver, or environment.
7. 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 numerical-bootstrap software and reproducibility considerations are reviewed in Rychkov and Su 2024, §§II.C–II.D.

Durable fixtures and dated targets

The exact cone $v(x)=(1,x,x^2)$ at $x=0,1,2$ has a rational feasible target and rational separating functional, so it tests the full serialization path 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.

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

Problem	Approximation	Solver build	Precision	Certificate	Residual	Error budget	Input hash	Output hash	Independent rerun	Evidence cutoff
Rational cone fixture	exact generators $x=0,1,2$	exact rational evaluator	exact	feasible weights for $v(1)$ and $\alpha=(1,-2,1)$ for $t_{\rm out}$	exact equality and sign checks	none	canonical hash required	evaluation-record hash required	exact agreement required	stable mathematical fixture
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 2026-08-09
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

This table contains an exact algebraic fixture and acceptance requirements. It does not substitute intended values for executed results.

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

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.

References

• Rychkov, Slava, and Ning Su. “New Developments in the Numerical Conformal Bootstrap.” Reviews of Modern Physics 96 (2024): 045004. DOI. Open PDF
• Simmons-Duffin, David. “A Semidefinite Program Solver for the Conformal Bootstrap.” Journal of High Energy Physics 06 (2015): 174. DOI. Open PDF