From 1d0a9dad8fa3b0502f5616f7db225f038cfa9609 Mon Sep 17 00:00:00 2001 From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com> Date: Tue, 26 May 2026 14:31:44 -0500 Subject: [PATCH] archive: remove duplicate PISTMachine search-space copy --- 2-Search-Space/PIST/PISTMachine.lean | 173 --------------------------- 1 file changed, 173 deletions(-) delete mode 100644 2-Search-Space/PIST/PISTMachine.lean diff --git a/2-Search-Space/PIST/PISTMachine.lean b/2-Search-Space/PIST/PISTMachine.lean deleted file mode 100644 index 0ad02372..00000000 --- a/2-Search-Space/PIST/PISTMachine.lean +++ /dev/null @@ -1,173 +0,0 @@ -import Semantics.FixedPoint -import Mathlib.Data.Nat.Sqrt - -namespace Semantics.PISTMachine - -/-! # PIST State Machine — Formal Core -Revised and Neutralized Language Specification. -Anchored to: ChatGPT-Making_It_Rigorous.md (Definitions 1-11) --/ - -/-- Phase Sort: Energy bands for machine orchestration. -/ -inductive Phase - | grounded -- m(n) = 0 (Anchor/Square) - | drift -- Low tension - | seismic -- High tension -deriving Repr, BEq, DecidableEq - -/-- Transfer Move Flags: Admissible transition events. -/ -inductive MoveFlag - | linearStep -- n_{t+1} = n_t ± 1 - | resonanceJump -- mass preservation - | rejected -- P_perp violation - | crystallized -- m(n) hits 0 -deriving Repr, BEq, DecidableEq - -/-- State Vector: Formal machine configuration. -/ -structure State where - n : Nat -- Active coordinate - phase : Phase -- Coarse energy class - friction : Nat -- Loss register - mass : Nat -- Hyperbola Index m(n) -deriving Repr, BEq, DecidableEq - -/-- Square Anchoring: Distance to lower square boundary. -/ -def a (n : Nat) : Nat := - let k := Nat.sqrt n - n - k^2 - -/-- Square Anchoring: Distance to upper square boundary. -/ -def b (n : Nat) : Nat := - let k := Nat.sqrt n - (k + 1)^2 - n - -/-- Hyperbola Index: Symmetric square-gap tension. -/ -def hyperbolaIndex (n : Nat) : Nat := - (a n) * (b n) - -/-- Normalized Tension Ratio: ρ(n) ∈ [0, 1]. -/ -def rho (n : Nat) : Float := - let k := Nat.sqrt n - let maxMass := ((2 * k + 1)^2 : Nat).toFloat / 4.0 - if maxMass == 0 then 0.0 - else (hyperbolaIndex n).toFloat / maxMass - -/-- Phase Classifier: Maps mass to coarse energy bands. -/ -def classifyPhase (n : Nat) (alpha : Float := 0.5) : Phase := - let m := hyperbolaIndex n - if m == 0 then Phase.grounded - else if rho n < alpha then Phase.drift - else Phase.seismic - -/-- Mirror Involution: Symmetry-preserving resonance jump. -/ -def mirror (n : Nat) : Nat := - let k := Nat.sqrt n - (k + 1)^2 + k^2 - n - -/-- Lyapunov Functional: Scalar energy for strict descent. -/ -def lambda (s : State) : Nat := - s.mass + s.friction - -/-! # Theorems -/ - -/-- Theorem: Mirror preserves mass. -/ -theorem mirror_preserves_mass (n : Nat) : - hyperbolaIndex (mirror n) = hyperbolaIndex n := by - let k := Nat.sqrt n - have ha : a (mirror n) = b n := by - simp [a, mirror, k] - omega - have hb : b (mirror n) = a n := by - simp [b, mirror, k] - omega - simp [hyperbolaIndex, ha, hb, Nat.mul_comm] - -/-- Theorem: Zero-mass iff square. -/ -theorem zero_mass_iff_square (n : Nat) : - hyperbolaIndex n = 0 ↔ (Nat.sqrt n)^2 = n := by - simp [hyperbolaIndex, a, b] - constructor - · intro h - cases Nat.eq_zero_or_pos (Nat.sqrt n + 1)^2 with - | inl h_zero => - have h_pos : (Nat.sqrt n + 1)^2 > 0 := Nat.pos_of_ne_zero (by intro h_z; injection h_z) - exact False.elim (Nat.lt_irrefl 0 (h_pos.trans_le (Nat.zero_le _))) - | inr _h_pos => - have hn : n < (Nat.sqrt n + 1)^2 := Nat.lt_succ_sqrt n - have hb_pos : (Nat.sqrt n + 1)^2 - n > 0 := Nat.sub_pos_of_lt hn - have ha_zero : n - (Nat.sqrt n)^2 = 0 := by - exact Nat.eq_zero_of_mul_eq_zero_left h (Nat.ne_of_gt hb_pos) - exact Nat.eq_of_sub_eq_zero ha_zero - · intro h - simp [h] - -/-! ## MNLOG-001 Mass Number Valuations for PISTMachine Theorems - - Doctrine: Logic can have a mass-number value only after we say which reality is weighing it. - These valuations are field-local under the PIST machine reality contract. --/ - -/-- Reality contract for PIST machine theorems -/ -structure PISTRealityField where - domain := "PIST state machine" - contract := "hyperbola index preservation and square boundary invariants" - validator := "algebraic proof (omega tactics)" - -/-- Residual model for PIST machine theorems -/ -structure PISTResidualModel where - uncertainty : Nat -- Unresolved edge cases - assumptions : Nat -- Axiomatic dependencies (sqrt properties) - cost : Nat -- Proof complexity - -/-- Projection rule for PIST machine theorems -/ -structure PISTProjectionRule where - name := "linear projection" - scaling := 256 -- Q8_8 approximation - -/-- Logical mass structure for PIST theorems -/ -structure PISTLogicalMass where - field : PISTRealityField - admissible : Nat -- Proof strength, invariant preservation - residual : PISTResidualModel - projection : PISTProjectionRule - -/-- Compute mass number for PIST theorem -/ -def PISTLogicalMass.massNumber (lm : PISTLogicalMass) : Q0_16 := - let totalResidual := lm.residual.uncertainty + lm.residual.assumptions + lm.residual.cost - let denom := 1 + totalResidual - let maxVal : Nat := 32767 - if denom = 0 then Q0_16.zero - else - let scaled := if lm.admissible ≥ maxVal then maxVal else lm.admissible - let denomScaled := if denom ≥ maxVal then maxVal else denom - let result := scaled * lm.projection.scaling / denomScaled - ⟨result.toUInt16⟩ - -/-- Mass number for mirror_preserves_mass theorem -/ -def mirrorPreservesMassMass : PISTLogicalMass := - { - field := { domain := "PIST state machine", contract := "hyperbola index preservation", validator := "algebraic proof" }, - admissible := 80, - residual := { uncertainty := 2, assumptions := 3, cost := 5 }, - projection := { name := "linear projection", scaling := 256 } - } - -/-- Mass number for zero_mass_iff_square theorem -/ -def zeroMassIffSquareMass : PISTLogicalMass := - { - field := { domain := "PIST state machine", contract := "square boundary invariants", validator := "algebraic proof" }, - admissible := 75, - residual := { uncertainty := 3, assumptions := 3, cost := 7 }, - projection := { name := "linear projection", scaling := 256 } - } - -/- Demonstrate MNLOG-001: PIST theorems have field-local numerical valuations -/ -#eval! mirrorPreservesMassMass.massNumber --- Note: This valuation means "high admissibility under algebraic proof validator" --- It does NOT mean "this theorem is universally true". Truth is proven by the theorem itself. - -#eval! zeroMassIffSquareMass.massNumber --- Note: This valuation means "moderate admissibility with higher proof cost" --- Truth still requires the formal proof provided in the theorem. - -end Semantics.PISTMachine