Prime-child shadow automated regression results

Date: 2026-08-15

Status: completed green finite regression of proved theorem family

Project: Free Computation Foundation / CENTL

Claim boundary: the universal proofs are in PRIME-CHILD-SHADOWS.md. The finite enumeration below is regression/falsification evidence, not the proof itself.

Workflow provenance

Completed GitHub Actions run:

workflow:     CENTL Erdős-Straus prime-child shadows
run id:       31852969007
head commit:  76ad8a9df8890a3dd0f6048b0985076a6d1852f9
conclusion:   success
artifact id:  9238092721
artifact sha256:
21a22ccdb80e505d9cacbf9a8932e088f3721bfc62b55c249e984066bbbdb6e5

General ancestry-quotient regression

The analyzer tested every configured ancestry quotient

q = 5, 9, 13, ..., 101

with base depths

j <= 2000.

Whenever the ancestry child

was prime, the analyzer explicitly enumerated T_K, reduced it modulo 4j-1, and checked complete containment in T_j.

Result:

prime-child shadow checks passed.

No prime-child theorem regression failure occurred.

Quotient-5 rigidity regression

For

the workflow checked every

Counts:

prime children K:                   5,510
full unrestricted q=5 shadows:      5,510
prime/shadow mismatches:                0

Thus over all 50,000 tested bases,

\[ \boxed{ T_{5j-1}\bmod(4j-1)\subseteq T_j \iff 5j-1\text{ is prime} }

held exactly.

This agrees with the universal quotient-5 rigidity theorem.

Why this matters

The finite ancestry map's strong quotient-5 population is now split cleanly into two phenomena:

1. an unrestricted infinite prime-child family, proved exactly;
2. extra shadows that appear only after Mordell-hard-class / prime-compatibility conditioning removes target classes.

The unrestricted theorem no longer needs to be inferred from finite graph statistics.

Methodological note

The run hashes its JSON and report before artifact upload. The artifact digest above freezes the exact finite regression state.