# Four-language reproduction report

2026-09-20T16:07:16.593943+00:00

All eight executions passed 21 check groups and matched `expected.txt` byte for byte.

Reference transcript: 5683 bytes; SHA-256 `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662`.

| Runtime | Version |
|---|---|
| Python | 3.12.14 (main, Aug 25 2026, 14:00:49) [Clang 22.1.3 ] |
| Julia | julia version 1.10.10 |
| Rust | rustc 1.85.0 (4d91de4e4 2025-02-17) |
| Cargo | cargo 1.85.0 (d73d2caf9 2024-12-31) |
| Java | openjdk version "17.0.20" 2026-07-21 |

| Execution | Transcript SHA-256 |
|---|---|
| python | `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662` |
| python-optimized | `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662` |
| julia | `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662` |
| julia-optimized | `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662` |
| rust-debug | `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662` |
| rust-release | `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662` |
| java | `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662` |
| java-assertions-disabled | `7ef550cb3f03d5032769024b9cbeb47f5c143ef45f709a0f1b785128684fd662` |

The transcript distinguishes exact `VALUE` records from its one `APPROX` record.
Rust builds used the bundled dependencies in offline mode with an isolated Cargo cache.
Written proofs establish the parameter-wide statements; these runs reproduce their computational checks.

## Scope

The package reproduces the supplied mathematical note in four native implementations. It includes formal polynomial identity checks, exact field computations, independent moment solving, positive-support search, recovery checks, and rational enclosures for the one-arcsecond seed and contraction. See README.md for the theorem-to-code mapping and supplementary algorithm proofs.

Each source computes its answers itself. This cross-language agreement is an implementation result; the all-parameter mathematical proofs remain in PROOFS.md.