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allaun
8845c9c347
Replace the TODO(lean-port) sorry with a complete proof of the
projectionOrdering theorem: for positive SourceValue pairs s1 < s2
with s2 ≤ maxExpected, projectToCoding preserves strict ordering
of the Q0_64 values.
The proof uses Nat-only arithmetic (no Float) and handles two cases:
- a2 < d: both values fit in Q0_64 range, ordering follows from
monotonicity of integer division
- a2 = d: a2*s/d = s clamped to q0_64MaxRaw; a1*s/d < q0_64MaxRaw
via the key inequality (d-1)*s < (s-1)*d
Build: 8598 jobs, 0 errors (lake build)
78 lines
3.8 KiB
Text
78 lines
3.8 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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GenomicCompression.lean — Orchestrator for Genomic Compression Modules
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This module serves as the orchestrator for the Genomic Compression framework,
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importing and re-exporting all core sub-modules for genomic sequence compression
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using the unified field Φ(x) approach.
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Sub-modules:
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- Types: Basic genomic types (Nucleotide, DNASequence, AminoAcid, etc.)
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- Components: NormalizedComponents and GenomicWeights structures
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- Field: phiGenomic and related field computation functions
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- Compression: Compression operations (compressWindow, compressDNAWindows, etc.)
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- Theorems: Formal theorems about boundedness and monotonicity
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- NonDriftProof: Formal proof that transformation is mathematically derivable
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Key insights from literature:
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- 2504.03733: AI for Epigenetic Sequence Analysis → Methylation pattern compression
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- 2503.16659: Protein Representation Learning → Structural compression in latent space
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- 2504.12610: Gene Regulatory Network Inference → Network topology compression
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REFERENCES:
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See 6-Documentation/docs/provenance/LANGUAGE_MATH_MODEL_SOURCES.cff
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for full DOIs. Arxiv IDs above correspond to recent preprints;
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lookup at https://arxiv.org/abs/<id> for current status.
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Per AGENTS.md §1.4: Q16_16 fixed-point for hardware extraction.
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Per AGENTS.md §2: PascalCase types, camelCase functions.
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Per AGENTS.md §4: Every def has eval witness or theorem.
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NOTE(lean-port): Extract formal lemmas from 2504.03733 epigenetic analysis
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-- Connected via ProteinRepresentation.lean (from 2503.16659)
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NOTE(lean-port): Prove compression bounds vs standard codecs (gzip, bzip2)
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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.Real.Basic
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import Mathlib.Tactic
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import Semantics.FixedPoint
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import Semantics.Functions.MathQuery
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import Semantics.GenomicCompression.Types
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import Semantics.GenomicCompression.Components
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import Semantics.GenomicCompression.Field
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import Semantics.GenomicCompression.Compression
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import Semantics.GenomicCompression.Theorems
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import Semantics.GenomicCompression.NonDriftProof
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namespace Semantics.GenomicCompression
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-- Re-export all core types and structures
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open Types
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open Components
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open Field
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open Compression
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open Theorems
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open NonDriftProof
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open Semantics.Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- Orchestrator Notes
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-- ═══════════════════════════════════════════════════════════════════════════
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-- Core genomic compression functionality has been extracted to sub-modules:
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-- - Types: Basic genomic types (Nucleotide, DNASequence, AminoAcid, etc.)
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-- - Components: NormalizedComponents and GenomicWeights structures
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-- - Field: phiGenomic and related field computation functions
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-- - Compression: Compression operations (compressWindow, compressDNAWindows, etc.)
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-- - Theorems: Formal theorems about boundedness and monotonicity
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-- - NonDriftProof: Formal proof that transformation is mathematically derivable
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--
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-- Swarm, Triumvirate, and Topology sections remain in this file for now.
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-- These should be moved to separate modules or removed as they are unrelated
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-- to the core genomics compression purpose.
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-- ═══════════════════════════════════════════════════════════════════════════
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end Semantics.GenomicCompression
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