The Holographic Circlette: Part 19 — The F2 Pati-Salam Isomorphism and the Cosmological Cooling of the Error-Correcting Vacuum

Audit note. This paper predates the framework's methodology audit of 2026-05-30. The Pati-Salam isomorphism content is structural and largely unaffected by the audit's headline retractions. Specific scope considerations: (i) §16.3 search-space audit: the E_{R2} \sim 10^{15} GeV derivation from the Topological Type-I Seesaw + observed neutrino mass + Higgs VEV v = 246 GeV is at Proposition tier --- the order-of-magnitude convergence of E_{R2} with the standard proton-decay M_X \sim 10^{16} GeV is at §15 item 40 as ``order-of-magnitude consistent but factor-of-10 gap unresolved.'' (ii) Minor: the v = 246 GeV Higgs VEV is applied to the seesaw eigenvalues phenomenologically per §15 item 53 (Q6 dimensionalisation theorem open). The R1--R4 \leftrightarrow Pati-Salam mapping at the algebraic level is class-3 / Locked and survives unchanged; the precise GUT-scale identifications sit at Proposition tier pen

The four parity-check constraints R1-R4 are identified as the exact F2 binary generators of the Pati-Salam GUT (SU(4)_C x SU(2)_L x SU(2)_R). Parity checks activate sequentially as the universe cools past Landauer thresholds. The R2 constraint scale (~10^15 GeV) converges with the GUT scale.

2026-06-20 legacy canon revision: This is a canon-reconciled legacy version. Pati-Salam/broken-load status changed The paper retains its historical derivation trail but carries a 2026-06-20 canon revision note identifying current status and superseded claims.