The main historical statements were compared with their proofs. Two original Lean files were rebuilt. Five old calculation scripts ran unchanged. Separate checks covered algebra, quadrature, modular products, coupling running and the scalar energy matrix. This is not a complete reproduction of every historical experiment or external peer review.
| Component | Assessment | Precise scope |
|---|---|---|
| Exponential core | Formal pass | Kern.lean rebuilt. Half-line s≥0; λ≥0. |
| Four symmetry theorems | Formal pass | Chain rule, critical orbits and Hessian null directions. No proof of S=A+K+I. |
| Kraft, Bayes and Pareto | Conditionally derived | Proofs and examples restored; code, prior and positive weights explicit. |
| Laplace weights | Derived and recalculated | Nondegenerate minima plus measure and tail conditions; example tends to 0.6339745962. |
| Born exponent p=2 | Conditionally derived | Norm-preserving splitting and additive branch weights are inputs. |
| K3: χ, σ, a₄, ζ(0) | Exact within the geometry | 24, −16, 4/15 and −11/15. Scalar operator and Ricci-flatness where required. |
| Modular η calculation | Numerically reproduced | Modular invariance explained; not complete α matching. |
| 56 constant-j patterns | Count reproduced | Pattern types, not a finite list of individual metrics. |
| Old spectra and ζ′(0) | Not reliably confirmed | Constant null mode fails in the energy matrix; renewed convergence checks required. |
| α normalisation | Internal error found | Factor two between the stated equation and implementation. |
| Coupling running | Model calculation reproduced | Independent solver confirms mismatch; measured couplings are inputs. |
| 42 modes / 9 LISA lines | Not restored as a prediction | Old group script runs, but a physical spectrum needs fields, masses and couplings. |
| Standard-model selection and exact bit prices | Not fully reproduced | Search space, description language and observer conditions still need justification. |
| EEML ⇒ K3 ⇒ α(0) | Open | The valid intermediate results do not close the physical chain. |
The check used Lean 4.34.0-rc1 and Mathlib commit e2d86c683b522c3f887029ed2335a0838cb71b8c. Both files completed with exit code 0. Their printed axiom dependencies are propext, Classical.choice and Quot.sound. These sources contain no sorry proof gaps or new axiom declarations.
Lean checks the theorem statement, not physical interpretations in comments. The additional step from symmetry to a universal decomposition of costs is therefore not proved. The core source already correctly restricted its claim to nonnegative values when the old website spoke more broadly.
The recalculation uses NumPy, SciPy, SymPy and mpmath. Modular products use high working precision. Integral examples and the ODE check use independent numerical routines. These are checks, not certified interval proofs.
The saved k=3,…,6 spectra were inspected; the full expensive spectra were not regenerated. Their heat-kernel fit in the chosen window gives a₄≈−3.56,…,−1.02 versus the target metric's exact 4/15. This can mix truncation, model and discretisation errors. Together with the separately demonstrated matrix error, it gives no basis to reaffirm the old small uncertainty on ζ′(0).
The higher-order a₆ curvature project, all classification searches and the full prediction register were not reproduced in full. A script completing does not prove its broader conclusion. The independent spectrum check shares the original point and metric data, but rebuilds energy through real gradients.
A short description or self-representation alone does not establish physical truth, uniqueness or low complexity of all reality. An available description provides at most an upper bound dependent on its own length. Frequencies of axiom use in a software library likewise do not determine metaphysical truth.
The bundle contains selected original sources, stored spectra, new checks, raw results, compilation logs, versions and SHA-256 hashes. Old code is labelled as historical material, including the errors found. The README explains how to rerun the checks.
Download the verification bundle · Reproduction and scope
Algebra and numerics: raw results · Null-mode check: raw results · File hashes
The complete old site backup remains outside the public webroot. The historical mathematics page can still be read verbatim.
Read the restored mathematics →v0.24 · 16 September 2026