From 9c73dc3a7ade3d1debcfde85f771e99e25619305 Mon Sep 17 00:00:00 2001 From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com> Date: Tue, 26 May 2026 14:30:39 -0500 Subject: [PATCH] archive: preserve duplicate PISTMachine search-space copy --- archive/2026-05-26/PISTMachine.lean.archived | 180 +++++++++++++++++++ 1 file changed, 180 insertions(+) create mode 100644 archive/2026-05-26/PISTMachine.lean.archived diff --git a/archive/2026-05-26/PISTMachine.lean.archived b/archive/2026-05-26/PISTMachine.lean.archived new file mode 100644 index 00000000..7e38f2a3 --- /dev/null +++ b/archive/2026-05-26/PISTMachine.lean.archived @@ -0,0 +1,180 @@ +# Archived from: 2-Search-Space/PIST/PISTMachine.lean +# Date: 2026-05-26 +# Reason: duplicate unreferenced copy of canonical Semantics.PISTMachine module. +# Active canonical module: 0-Core-Formalism/lean/Semantics/Semantics/PISTMachine.lean +# +# Original content follows. + +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