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