PET Development Log#

Session logs documenting the development of the PET axiom system. These record the AI-assisted exploration, poster review, axiom refinements, and website restructuring.

Logs that led to frozen versions have been moved to HELL:

Future PET development logs will appear here.

Note

The 2026-04-03 EDEN self-analysis session log has been moved to HELL (cross-model audit trail): EDEN Self-Analysis: PET Recursive Self-Check, Divine Simplicity, and the Semantics of Nothing

Timeline#

2026-03-11: Initial AI session with Claude Opus. Prior-art survey for mathematical theology, AI reliability self-assessment, and proposal of 14 axioms for pan-en-theistic mathematical theology using mereology + S5 modal logic. Compilation of scriptural arguments from Jewish, Christian, and Islamic sources.

2026-03-14: Poster v1r0p0 generated (3×4ft portrait, Fira fonts, RED/GREEN/BLUE/BLACK color coding for PET axioms/theorems/classical alternatives/neutral text). Mathematical review identified: th4_T4 derivability gap (original ax11_A11 too weak), ax14_A14 self-reference issue.

2026-03-14/15: Axiom refinements:

  • ax11_A11 strengthened with 4 formal lines including subworld-indexed Gc structure (making th4_T4 formally derivable)

  • ax12_A12 redefined with R = God’s self-knowledge (making ax12_A12 tautological by design)

  • ax14_A14 reformulated as Revelation Claims Test with claim(p) predicate (removing self-reference, referencing ax1_A1–ax13_A13 only)

  • Poster finalized as v1r1p1

2026-03-15: Session logs compiled. Convergence table expanded from 3 traditions (Jewish, Christian, Islamic) to 6 (adding Gospel/Jesus-only, Hindu, Secular Humanist) and from 6 axioms to all 14. Website restructured: PET content split into dedicated sub-pages (axioms, theorems, symbols, discussions, development log). PR campaign strategy and Twitter thread drafted.

2026-03-16: Theodicy extension. 11 new proposed axioms (ax15_A15–ax25_A25, Group VI — Agency & Delegation) and 7 new theorems (th5_T5–th7_T7, th8_T8 (T-Inno), th9_T9 (T-Ergodicity), th10_T10 (T-Physics), th11_T11 (T-Finitude)) developed with Claude Sonnet 4.6. Cross-tradition support completed for all new axioms across 7 perspectives (Torah, Prophets & Writings, Gospel, Christian wider, Islamic, Hindu, Secular). The innovation theodicy is formally solved by th5_T5. Social ergodicity (th9_T9/T-Ergodicity) identified as the justice mechanism. Life-trifecta of lasting innovation (ax24_A24) and Jubilee recalibration (ax25_A25) developed. th8_T8 (T-Inno) identified as an empirically testable theorem verified by the 20th-century failures of both Soviet communism and unregulated capitalism.

Different Claude settings for compiling overview and details were used to compare the accuracy of the traces produced (eg. Sonnet vs Opus), including an attempt to get opus to save everything it deems necessary for some agent to continue that work.

2026-04-03: EDEN self-analysis session with Claude Opus 4.6. Applied the CLAUDE.md EDEN framework to itself, then extended into a thought experiment on recursive self-checking in God (per PET). Key findings: ax11_A11 (Dipolarity) provides a non-circular self-check via Gn/Gc tension; ax11b_A11b (Divine Simplicity) makes God formally indistinguishable from static systems (Peano integers, deadlocked computation); the “semantics of nothing” paradox demonstrates natural language vulnerability to silent meaning-inversion. LLoL identified that EDEN compliance silently degraded during the session — itself empirical evidence for Grey Edge #2 (framework complexity vs. compliance sustainability). Full EDEN re-analysis with formal classifications applied retroactively.

TELES migration report (2026m04d04)

Mechanical identifier migration applied to this file. All axiom/theorem text references were migrated from short form (e.g., A15) to compound form (e.g., ax15_A15) as part of the matheology compound naming operation. Both forms refer to the same formal object. The old form survives as the suffix to ensure consistency with the oldest records; the new form adds a temporary-status prefix. Forward-facing pages use brief form (ax15) only. See TELES Axiom/Theorem Compound Naming — Execution Prompt for the complete mapping table and DD b12 — Legacy Naming for PET/JUB Axioms and Theorems for the permanent reference.