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AngrySphinx.lean (ported from Research Stack): - Core theorem: E_attack = n ⟹ E_solve ≥ 2^n (proven, 0 sorries) - Frustration metric F = 1/(p+1) → 0 under attack pressure - NaN boundary: at F=0, solveDenominator returns none (system terminates) - Proof-of-Defense accumulator: attack work → defense fuel - Closed-system theorem: the search cannot run forever 'You bring a knife, I bring two guns. You bring a machine gun, I bring a tank. You throw a universe at me, I make you emulate two.' Connection to OpenAI unit-distance result: - Infinite number field tower ↔ infinite shell depth - Root discriminant bounded ↔ gear ratio keeps system closed - Class number h(K) ≤ H^f ↔ solve energy E_solve ≥ 2^depth - NaN boundary converts the infinity to a type error CollatzBraid.lean (new): - Collatz as a braidtree: each step is a braid generator (σ_E or σ_O) - Affine maps: even = x↦x/2, odd = x↦3x+1 (semigroup under composition) - Braid words: each integer has a unique braid word (assuming Collatz) - Basin convergence = strand fusion (trajectories merging = braid crossings) - AngrySphinx integration: trajectory length = shell depth = 2^depth cost - Collatz conjecture as braid reduction: 'all braid words reduce to identity' The Collatz braidtree formalizes what the photonic search does: searches through braid words, each with an accumulated affine transform, with AngrySphinx making the search closed (exponential cost, NaN termination). One sorry: frustration_decreases (Q16_16 division lemma, CITED). One axiom: collatz_conjecture (the conjecture itself, unproven). |
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| BindingSite | ||
| CoreFormalism | ||
| PVGS_DQ_Bridge | ||
| RRCLib | ||
| SilverSight | ||
| UniversalEncoding | ||