Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/Atoms.lean

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import Semantics.FixedPoint
namespace Semantics
open Semantics.Q16_16
-- ═══════════════════════════════════════════════════════════════════════════
-- §0 Hardware-Native Semantic Atom Structures (from HachimojiPipeline improvements)
-- ═══════════════════════════════════════════════════════════════════════════
/-- Discrete semantic state using Q16_16 for hardware-native computation -/
structure DiscreteSemanticState where
activation : Q16_16 -- Semantic activation level
salience : Q16_16 -- Semantic salience
coherence : Q16_16 -- Semantic coherence
entropy : Q16_16 -- Semantic entropy
deriving Repr, Inhabited
/-- Semantic grid for spatial discretization -/
structure SemanticGrid where
dimension : Nat -- Grid dimension
spacing : Q16_16 -- Grid spacing
values : Array DiscreteSemanticState -- State values at grid points
deriving Repr
/-- Semantic manifold for geometric phase evolution -/
structure SemanticManifold where
dimension : Nat -- Manifold dimension
curvature : Q16_16 -- Scalar curvature (affects semantic field)
torsion : Q16_16 -- Torsion (semantic deviation)
metric : Array Q16_16 -- Metric tensor diagonal elements
deriving Repr
/-- Christoffel symbols for semantic geometric phase -/
structure SemanticChristoffel where
dimension : Nat -- Manifold dimension
symbols : Array Q16_16 -- Flattened symbol array [i][j][k]
deriving Repr, Inhabited
/-- Semantic lock pattern for frustration computation -/
structure SemanticLockPattern where
activation : Q16_16
salience : Q16_16
coherence : Q16_16
deriving Repr, Inhabited
/-- Semantic frustration wave parameters -/
structure SemanticFrustrationWave where
waveVector : Array Q16_16 -- k_r wave vector
weight : Q16_16 -- w_r weight from anisotropy
deriving Repr, Inhabited
/-- Compute semantic Christoffel symbols -/
def computeSemanticChristoffel (manifold : SemanticManifold) : SemanticChristoffel :=
let n := manifold.dimension
let symbolCount := n * n * n
let symbols := Array.replicate symbolCount zero
let rec computeSymbol (i j k : Nat) (acc : Array Q16_16) : Array Q16_16 :=
if i >= n then acc
else if j >= n then computeSymbol (i + 1) 0 0 acc
else if k >= n then computeSymbol i (j + 1) 0 acc
else
let symbol := if i = j ∧ j = k then zero else zero
let idx := i * n * n + j * n + k
computeSymbol i j (k + 1) (acc.set! idx symbol)
let result := computeSymbol 0 0 0 symbols
{ dimension := n, symbols := result }
/-- Compute cosine using Taylor series for Q16_16 -/
def semanticCos (x : Q16_16) : Q16_16 :=
let x2 := mul x x
let term2 := mul x2 (div (ofNat 1) (ofNat 2))
one - term2
/-- Compute semantic frustration W(z;A) = Σ_r w_r(A)(1 - cos(k_r·z)) -/
def computeSemanticFrustration (z : SemanticLockPattern) (waves : Array SemanticFrustrationWave) : Q16_16 :=
let zArray := #[z.activation, z.salience, z.coherence, zero]
let rec sumWaves (i : Nat) (acc : Q16_16) : Q16_16 :=
if i >= waves.size then acc
else
let wave := waves[i]!
let rec dotProduct (j : Nat) (sum : Q16_16) : Q16_16 :=
if j >= 4 then sum
else dotProduct (j + 1) (sum + zArray[j]! * wave.waveVector[j]!)
let dot := dotProduct 0 zero
let cosine := semanticCos dot
let contribution := mul wave.weight (one - cosine)
sumWaves (i + 1) (acc + contribution)
sumWaves 0 zero
/-- Compute semantic locking energy for stability -/
def computeSemanticLockingEnergy (currentPattern previousPattern : SemanticLockPattern) (waves : Array SemanticFrustrationWave) : Q16_16 :=
let z := {
activation := currentPattern.activation - previousPattern.activation,
salience := currentPattern.salience - previousPattern.salience,
coherence := currentPattern.coherence - previousPattern.coherence
}
computeSemanticFrustration z waves
/-- Update discrete semantic state from geometry -/
def updateSemanticStateFromGeometry (state : DiscreteSemanticState) (manifold : SemanticManifold) : DiscreteSemanticState :=
let newActivation := state.activation + manifold.curvature
let newSalience := state.salience + manifold.torsion
{
activation := newActivation,
salience := newSalience,
coherence := state.coherence,
entropy := state.entropy
}
/-- Update discrete semantic state from Christoffel symbols -/
def updateSemanticStateFromChristoffel (state : DiscreteSemanticState) (symbols : SemanticChristoffel) (i j k : Nat) : DiscreteSemanticState :=
let symbol := symbols.symbols[i * symbols.dimension * symbols.dimension + j * symbols.dimension + k]!
let entropyIncrement := if symbol > ofNat 100 then one else zero
{
activation := state.activation,
salience := state.salience,
coherence := state.coherence,
entropy := state.entropy + entropyIncrement
}
-- ═══════════════════════════════════════════════════════════════════════════
-- §1 Original Semantic Atoms (NSM theory primitives)
-- ═══════════════════════════════════════════════════════════════════════════
/--
Universal Semantic Primes (Atoms).
These are the irreducible primitives of human thought according to NSM theory.
-/
inductive Atom : Type
| someone
| something
| do_
| happen
| move
| cause
| die
| want
| know
| feel
| think
| good
| bad
| because
| not
deriving Repr, DecidableEq
/-- Enhanced atom with discrete semantic state tracking -/
structure AtomWithState where
atom : Atom
semanticState : DiscreteSemanticState
deriving Repr
end Semantics