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c44a01df3b
- New: InformationManifold.lean — tensor integration module - Update: SLUQ.lean — proof refinements - New: chentsov_fusion.py — Chentsov fusion bridge - New: tdoku_16d.py — 16-dimensional TDoku solver - New: validate_docs.py — documentation validation script - New: negative_tests.json + test_negative_suite.py — negative test fixtures - Update: flac_dsp_node.py — DSP node refinements - Update: CITATION.cff — citation metadata - Docs: GEOMETRIC_SUBSTANCE_CANONICAL_RECONCILIATION, LITERATURE_MAPPING, GROTHENDIECKIAN_ORGANIZATIONAL_ROTATION_PROPOSAL, formula extraction suite - New: package/ — public-apis npm metadata
27 lines
1.1 KiB
Text
27 lines
1.1 KiB
Text
import Mathlib.Data.Real.Basic
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-- The Information Manifold Φ structure
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structure Phi where
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feature : ℕ -- F ∈ {0..7}
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tau : ℝ -- Torsion/Complexity
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consistency : ℕ -- c ∈ {0..5}
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delta : ℝ -- Local variance
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-- Similarity flow based on Fisher-Rao gradient and torsion correction
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-- SimFlowPhi = (Fisher-Rao Distance) + (τ * Consistency)
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def simFlowPhi (p1 p2 : Phi) : ℝ :=
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let fisherRao := (p1.tau - p2.tau).sqr -- Simplified Fisher-Rao for this context
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(fisherRao + (p1.tau * toReal p1.consistency)) - (p2.tau * toReal p2.consistency)
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-- Convergence predicate: Is the state stable?
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def isConvergent (p : Phi) : Prop :=
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p.consistency > 0 && p.delta < 1.0
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-- Example instances of S1-S4 specializations
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def s1_phi : Phi := {feature := 0, tau := 0, consistency := 1, delta := 0}
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def s2_phi : Phi := {feature := 1, tau := 8, consistency := 1, delta := 0.5}
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def s3_phi : Phi := {feature := 2, tau := 4, consistency := 1, delta := 0.2}
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def s4_phi : Phi := {feature := 3, tau := 8, consistency := 1, delta := 0.8}
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-- Example usage: check if S2 is convergent
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example (p : Phi) : Prop := isConvergent p2_phi
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