Reciprocity tower automated regression results

Synthesis

GitHub Actions workflow:

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 RECIPROCITY-TOWER-SHADOWS.md. The finite ranges below are regression/falsification evidence, not the proof itself.

Workflow provenance

GitHub Actions workflow:

CENTL Erdős-Straus reciprocity tower shadows

Completed run:

run id:      31852607474
head commit: 93ce84c8fb1fa795da2b4ed8f4f2add497f7d89f
conclusion:  success

Artifact:

artifact id: 9237972571
name:        reciprocity-tower-93ce84c8fb1fa795da2b4ed8f4f2add497f7d89f
sha256:      11344d55fdfcd5d77c46ff9f7bf18d1ce2d556e3b077ccbeedfe75ef058a1288

The artifact contains the JSON theorem-regression record, report, and SHA-256 manifest.

Jacobi-saturation regression

Every Type A/B layer through

k\le50,000

was checked by comparing the exact trap cardinality with one half of the reduced unit group.

Observed Jacobi-saturated layers:

\boxed{[1,2,4].}

No others appeared.

This agrees with the universal classification proved in RECIPROCITY-TOWER-SHADOWS.md:

\boxed{ T_j=\{u:(u/(4j-1))=-1\} \iff j\in\{1,2,4\}. }

Explicit tower regression

For each base

j\in\{1,2,4\}

the workflow checked every positive odd lift parameter

1\le c\le1001.

That is

501

lifts per base and

\boxed{1503}

total square-lift layers.

For every tested lift

K=\frac{(4j-1)c^2+1}{4},

the workflow explicitly enumerated the Type A/B trap residues at K, reduced them modulo the base modulus, and verified complete containment in the base trap set.

Result:

\boxed{1503/1503\text{ fully shadowed}.}

Reciprocity-lemma regression

Across those lifted depths, the workflow enumerated

\boxed{12,715}

divisors and independently checked

\left(\frac e{4j-1}\right)=+1

for every divisor e|K used in the lifted trap sets.

All 12,715 checks passed.

Range reached automatically

The largest lifted depth tested for each base was:

base 1, modulus 3:   K =   751,501
base 2, modulus 7:   K = 1,753,502
base 4, modulus 15:  K = 3,757,504

Thus the regression reaches several million in Type A/B depth even though the theorem itself is universal and requires no finite bound.

The three exact infinite families

Writing c=2n+1, the theorem gives the structural-gap families

\boxed{3n^2+3n+1,}

\boxed{7n^2+7n+2,}

and

\boxed{15n^2+15n+4,}

for every n>=1.

Every layer in the first family is fully shadowed by j=1; every layer in the second by j=2; every layer in the third by j=4.

Interpretation

The regression confirms that the infinite reciprocity theorem is not merely an algebraic curiosity. Its first 1,503 explicit target layers, extending to depth 3.75 million, behave exactly as predicted.

Together with the green dyadic-lattice regression, the shadow graph now contains multiple independently automated infinite theorem families generated by different arithmetic mechanisms.