Exact shared-error arithmetic with bounded large-integer output

The first qualification stopped at its twelfth charged identity because Python's 4,300-digit decimal conversion cap rejected an exact rational result. The eight independent dense checks and the 32/64/128-epoch prefixes passed. Preserve that freeze, its charged failure and four unstarted identities; never resume it.

This separate version reuses the unchanged mathematical implementation, all sixteen generated identities and every numerical/work acceptance limit from the original plan. Its only change is a local 50,000-digit decimal-output cap, restored after each identity. This finite cap accommodates the existing 131,072-bit rational precision limit without globally disabling Python's protection. It does not change equations, floating-point endpoints, covariance, reference space or acceptance criteria.

Limits remain sixteen identities, 1,072 innovation epochs, ten cooperative seconds per identity, 120 seconds overall, four reserved numerical threads, zero native calls, optimizer starts or archive reads, and no retries/signals. Each identity and its full epoch reservation are charged before calculation. The worker freezes source/environment hashes and a separate versioned allowance.

All sixteen must pass before a separate recorded-source assessment is prepared. Gaussian error applicability and the excessive nonlinear prediction widths remain unqualified. No observed Earth-model fit follows.