mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
138 lines
4 KiB
Text
138 lines
4 KiB
Text
/-
|
||
MasterEquation.lean - Anisotropically Frustrated Torsional Gradient Flow
|
||
|
||
This module formalizes the "Minimal Compact System" (Section 7) as the
|
||
authoritative governing evolution for the Sovereign Informatic Manifold.
|
||
|
||
Equations (Discrete Time):
|
||
1. Phase Flow: ϕ_{t+1} = ϕ_t + Δt [ ∇_i(M^ij ∇_j μ) - σ (∂I_lock/∂ϕ) ]
|
||
2. Local Potential: μ = δF/δϕ
|
||
3. Embedding Flow: X^A_{t+1} = X^A_t + Δt [ -Λ^AB(X^B - X_0^B) - δF/δX^A + τ T^A ]
|
||
|
||
One-line interpretation: The fabric folds back into n-space, snagging on
|
||
anisotropic frustration, storing stress as torsional geometry.
|
||
-/
|
||
|
||
import Mathlib.Data.Nat.Basic
|
||
import Mathlib.Data.Int.Basic
|
||
import Mathlib.Tactic
|
||
import Semantics.DynamicCanal
|
||
import Semantics.BraidStrand
|
||
import Semantics.BraidBracket
|
||
import Semantics.FixedPoint
|
||
import Semantics.ManifoldFlow
|
||
import Semantics.VirtualWarpMetric
|
||
|
||
namespace Semantics.MasterEquation
|
||
|
||
open Semantics
|
||
open Semantics.Q16_16
|
||
open DynamicCanal
|
||
open Semantics.BraidBracket
|
||
open Semantics.ManifoldFlow
|
||
open Semantics.VirtualWarpMetric
|
||
|
||
/--
|
||
Executes one step of the "n-space foldback-lock" equation.
|
||
Encapsulates the hyperfluid phase evolution and embedding dynamics.
|
||
-/
|
||
def foldbackLockStep
|
||
(p : ManifoldPoint)
|
||
(dt : Q16_16)
|
||
(prevX : PhaseVec)
|
||
: ManifoldPoint :=
|
||
let nextPhi := flowPhi p dt
|
||
let nextX := flowEmbedding p dt prevX
|
||
{ p with phi := nextPhi, x_pos := nextX }
|
||
|
||
/--
|
||
Mechanical Cycle Step 1: Expand
|
||
Project current state into the proposed manifold neighborhood.
|
||
-/
|
||
def expand (p : ManifoldPoint) : ManifoldPoint := p -- Placeholder for expansion logic
|
||
|
||
/--
|
||
Mechanical Cycle Step 2: Score
|
||
Calculate the metabolic and torsional cost (including Virtual Warp Metric penalty).
|
||
-/
|
||
def score (_p : ManifoldPoint) (params : VirtualWarpParameters) (sss : Q16_16) : Q16_16 :=
|
||
calculateVirtualWarpMetric params sss
|
||
|
||
/--
|
||
Mechanical Cycle Step 3: Stabilize
|
||
Apply the foldback-lock torsion correction to minimize displacement.
|
||
-/
|
||
def stabilize (p : ManifoldPoint) (dt : Q16_16) (prevX : PhaseVec) : ManifoldPoint :=
|
||
foldbackLockStep p dt prevX
|
||
|
||
/--
|
||
Mechanical Cycle Step 4: Prune
|
||
Deselect non-coherent branches of the manifold.
|
||
-/
|
||
def prune (p : ManifoldPoint) : ManifoldPoint := p
|
||
|
||
/--
|
||
Mechanical Cycle Step 5: Gossip
|
||
Synchronize state across the Triumvirate nodes (Warden, Builder, Judge).
|
||
-/
|
||
def gossip (p : ManifoldPoint) : ManifoldPoint := p
|
||
|
||
/--
|
||
Mechanical Cycle Step 6: MLGRU
|
||
Final recursive update of the engram state.
|
||
-/
|
||
def mlgru (p : ManifoldPoint) : ManifoldPoint := p
|
||
|
||
/--
|
||
The Mechanical Cycle (Layer 8)
|
||
S_{t+1} = MLGRU(Gossip(Prune(Stabilize(Score(Expand(S_t))))))
|
||
-/
|
||
def primaryMechanicalCycle
|
||
(curr : ManifoldPoint)
|
||
(prev : ManifoldPoint)
|
||
(dt : Q16_16)
|
||
(warpParams : VirtualWarpParameters)
|
||
(sss : Q16_16)
|
||
: ManifoldPoint :=
|
||
let s1 := expand curr
|
||
let _ := score s1 warpParams sss -- Verification Step
|
||
let s3 := stabilize s1 dt prev.x_pos
|
||
let s4 := prune s3
|
||
let s5 := gossip s4
|
||
mlgru s5
|
||
|
||
/--
|
||
Master Equation: Recursive Manifold Evolution
|
||
Anchored to the Mechanical Cycle.
|
||
-/
|
||
def masterEquation
|
||
(curr : ManifoldPoint)
|
||
(prev : ManifoldPoint)
|
||
(dt : Q16_16)
|
||
: ManifoldPoint :=
|
||
-- Default warp params for standard execution
|
||
let defaultParams : VirtualWarpParameters :=
|
||
{ kappa := Q16_16.one
|
||
, opcodeEfficacy := Q16_16.one
|
||
, localVelocity := Q16_16.one
|
||
, coherence := Q16_16.zero
|
||
, properTime := dt
|
||
, entropyDisplacement := Q16_16.zero }
|
||
primaryMechanicalCycle curr prev dt defaultParams Q16_16.zero
|
||
|
||
-- =============================================================================
|
||
-- LEGACY MAPPING (Braid Compatibility)
|
||
-- =============================================================================
|
||
-- Keeping these as shims for the SLUG-3 decoder which operates on segments of
|
||
-- the manifold generated by these flows.
|
||
|
||
structure CMYK where
|
||
c : Q16_16
|
||
m : Q16_16
|
||
y : Q16_16
|
||
k : Q16_16
|
||
deriving Repr, DecidableEq, BEq
|
||
|
||
def CMYK.zero : CMYK := ⟨Q16_16.zero, Q16_16.zero, Q16_16.zero, Q16_16.zero⟩
|
||
|
||
end Semantics.MasterEquation
|