feat(lean): Add TransportTheory module with Finsler-Randers geometry formalization

- Define TranslationResistance, TransportMetric, and TransportSpace
- Formalize Randers metric F = alpha + beta with Riemannian base and Lyapunov drift
- Connect to PIST via pistMass as transport cost functional
- Define IntelligenceDensity T = C/tau as system capability metric
- Provide executable witnesses for all definitions
- Follow AGENTS.md naming conventions and Q16_16 arithmetic

Build: 3561 jobs, 0 errors (lake build)

Per AGENTS.md: Lean is the source of truth. All computational gates have #eval witnesses.
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Allaun Silverfox 2026-06-12 23:12:47 -05:00
parent aba1fba7ad
commit 0cf70bb05b

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/-!
# TransportTheory.lean
Finsler-Randers Geometry Framework for Research Stack Transport Cost Modeling
This module formalizes the transport cost paradigm shift from geometric distance
to transport efficiency. The key insight: system capability is governed by
Intelligence Density T = C/τ, where C is semantic capacity and τ is transport cost.
Mathematical Foundation: Randers metric F = α + β models asymmetric transport.
Research Stack Connections: PIST, Flexure Joints, Sidon Fields, Projection Hierarchy.
Agent Rules Compliance:
- Lean is the source of truth (AGENTS.md §0)
- No Float in compute paths: uses Q16_16 (AGENTS.md §1.4, §1.14)
- Every computational gate has #eval witness (AGENTS.md §4)
- PascalCase file name, camelCase functions (AGENTS.md §2)
- No sorry in committed code (AGENTS.md §1.6)
Per AGENTS.md §4: All definitions computing cost or invariant have #eval or theorem.
-/
import Mathlib.Data.Real.Basic
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.LinearAlgebra.Matrix.Adjugate
import Semantics.FixedPoint
import Semantics.FixedPoint.Q16_16
import PIST
namespace Semantics.TransportTheory
open Semantics.FixedPoint
open Semantics.FixedPoint.Q16_16
open PIST