Allaun Silverfox
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13a1683b8e
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experiment(radial): 5-domain expert design — self-finding on S⁷
The experiment: use the Φ-corkscrew system to search its own manifold
for the direction that maximizes compression ratio. 5 domain experts
designed their components in parallel.
EXPERIMENT: EXPERIMENT_RADIAL_SELF_FIND.md
- Hypothesis: ∃ d* on S⁷: walking γ_{d*} monotonically increases C(n)
- Method: Self-referential geodesic search with radial exploration
- Predictions: gradient exists, ascent converges, self-encoding helps
AGENT 1 — GeometricPhysicist: experiment_geodesic_search.md
- Geodesic: γ_d(t) = cos(t)·x + sin(t)·d (great circles on S⁷)
- Gradient ascent: exponential map + parallel transport
- Direction sampling: uniform, Φ-guided, gradient-biased
- 3 core functions: geodesic_search, gradient_ascent_step, sample_directions
AGENT 2 — InformationTheorist: experiment_compression_metric.md
- C(n) = L_S / |RLE(DNA(phinary(n)))|
- Bounds: Ω(L_S/log n) ≤ C(n) ≤ O(L_S/log log n)
- Key insight: phinary constraint inherently favors compressibility
- Entropy H(n), Kolmogorov K(n), spectral radius analysis
AGENT 3 — SystemsEngineer: experiment_feedback_loop.md (2,033 lines!)
- 12-state, 15-transition state machine
- 3-layer strange loop containment (bounded, contractive, depth cap)
- Radial exploration: OUTWARD/INWARD/OSCILLATE modes
- Full FAMM-DAG integration with meltdown recovery
- 7 convergence criteria
AGENT 4 — FormalVerifier: experiment_formal_verification.md
- 8 Lean 4 theorems + master theorem
- Key: Bijection Preservation (search transform preserves injectivity)
- Paradox Prevention theorem (self-referential safety)
- 10 invariants, 5 verification conditions
- Integrates with ChentsovFinite.lean, quine.py proofs
AGENT 5 — MetaMathematician: experiment_meta_analysis.md
- Strange loop converges (C(n) is Lyapunov function, S⁷ compact)
- Fixed points exist (Brouwer + Kleene recursion theorem)
- Gödel boundary is epistemological, not ontological
- System finds itself but cannot prove global optimality
- 12 formal theorems
Total: 6 files, ~6,000 lines of experiment design
Refs: PHI_CORKSCREW_PERFECT_RECOVERY.md, PROOF_SELFSIGHT.md,
ChentsovFinite.lean, GoldenSpiralManifold.lean
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2026-06-23 02:13:42 -05:00 |
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