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- Prover-Integrated Orchestration Layers (L0-L3): Goedel-Prover-V2 watchdog, BFS-Prover-V2 swarm consensus, bf4prover topology adaptation - FAMM Verilator benchmark: uniform vs preshaped delay comparison (4.4x speedup) - Swarm topological device prober: 11 agents probing traces, caps, delays, errors, vias, PDN - Spec sheet puller: 10 components with key params and topological relevance - Virtual FPGA system tests: 6/6 passed, 134K ops/s throughput - Fixed merge conflicts in AI-Newton test_experiment.ipynb
70 lines
2 KiB
Text
70 lines
2 KiB
Text
Derive 12 equations. The numbers have values. Formalize them in Lean 4.
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F01: 7 numbers — 121.567, 102.572, 97.254, 94.974, 93.780, 93.074, 93.622
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- Encode as Q16.16 fixed-point
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- Define: encode(x) = floor(x * 65536 + 0.5) / 65536
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- Verify with Wolfram Alpha
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- File: F01.lean
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F02: 8-level constraint hierarchy
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- Define compression operator C: (input, constraint) → output
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- Information rate: R(D) = I(input; output) given distortion D
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- 8 levels with cumulative compression ratio
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- File: F02.lean
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F03: Continuous information metric
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- Fisher-Rao metric: g_ij(θ) = E[∂log p(x;θ)/∂θ_i · ∂log p(x;θ)/∂θ_j]
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- Differential entropy: h(X) = -∫ p(x) log p(x) dx
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- File: F03.lean
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F04: Game-theoretic strategy encoding
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- Policy function: π: State → Action
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- ESS condition: π* = argmax E[payoff | π*, population]
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- File: F04.lean
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F05: Rate-distortion for biological encoding
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- R(D) = min_{p(x̂|x)} I(X;X̂) subject to E[d(X,X̂)] ≤ D
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- File: F05.lean
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F06: Evolutionary dynamics on manifold
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- Replicator: dx_i/dt = x_i((Ax)_i - x^TAx)
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- Lyapunov: dV/dt ≤ 0
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- File: F06.lean
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F07: Cancer as compression failure
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- Entropy increase: H_cancer > H_healthy
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- Threshold: H > H_critical → failure mode
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- File: F07.lean
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F08: Robustness-compression relation
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- R = f(C) where R = error correction capacity, C = compression ratio
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- Trade-off: dR/dC < 0
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- File: F08.lean
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F09: Compression dynamics
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- dC/dt = -∇_C L(total) where L = loss function
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- Fixed point: dC/dt = 0
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- File: F09.lean
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F10: Possibility space cardinality
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- |G| = 4^L for genome length L
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- Viable subset |V| << |G|
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- Ratio: |V|/|G| ≈ 10^(-6×10^8)
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- File: F10.lean
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F11: Adjacent possible expansion
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- d(AP)/dt = α · diversity + β · innovation
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- α, β = coupling constants
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- File: F11.lean
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F12: Master unification equation
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- S_{t+1} = Master(S_t, environment, constraints)
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- Integrate F01-F11
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- File: F12.lean
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Requirements:
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- Q16.16 fixed-point arithmetic only
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- #eval example for every def
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- Wolfram Alpha verification in comments
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- Theorem proving totality for every operation
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- lake build must pass
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