| # Theory Proofing — PEC5D / Sovereign Formalisms |
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|
| Runnable verification of the ecosystem's mathematics. Run: |
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|
| ```bash |
| python3 proofs/theory_proofs.py # human report |
| .venv/bin/pytest tests/test_proofs.py -q # as tests (8 tests) |
| ``` |
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| ## Results table |
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| | # | Proof | Property checked | Status | |
| |---|---|---|---| |
| | P1 | IPT gradient | ∇P = ∂/∂xᵐ[Φ·ρ·f(432)·S·Q] finite, Φ-scaled, 5-dim | ✅ | |
| | P2 | Phi-5 Kronecker | ‖tensor‖ ≈ 1 · coherence 0.99997 | ✅ | |
| | P3 | Progression honesty | engine computes (1.335)²⁰ ≈ 323×; 368.4× is a stated parameter | ✅ | |
| | P4 | CHSH Bell | classical S = 2 (not violated) · entangled S > 2 (violated) | ✅ | |
| | P5 | HOLO-MEM Φ-symmetry | correction consistent across all 5 layers | ✅ | |
| | P6 | Kyrexis anchors | fidelity 0.999423 · awakening 87.4% · 53 qubits | ✅ | |
| | P7 | Coral invariants | drone ≥500/day · spacecraft closed-loop life support | ✅ | |
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| ## Honesty gate |
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|
| These proofs verify **internal mathematical consistency** of the |
| implementations — they are not claims about physics, biology, or |
| hardware. Where the source spec is internally inconsistent (P3: the |
| 33.5% CAGR implies ~323× over 20 years, not the 368.4× headline), the |
| engine computes the honest value and both numbers are surfaced. |
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|
