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605 lines
28 KiB
Text
605 lines
28 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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SyntheticGeneticCoding.lean — 0D(n) Symbol-Coding Objects for GCL Surfaces
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This module treats all coding systems as purely information-theoretic 0D(n)
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discrete objects: finite-length strings over finite alphabets.
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These objects happen to borrow symbol-sets from coding techniques that nature
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has been stress-testing for ~4.6 billion years. The biology is completely
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ignored. Only information capacity, channel efficiency, redundancy profiles,
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and compression bounds matter.
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TYPE SYSTEM (Three-Layer Doctrine):
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1. CodingQ — Canonical normalized coding atom. Type = Q0_64.
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Range: [-1, 1). Resolution: 2^-63. Used for ALL coding-space values.
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Properties: normalized, bounded, deterministic, fixed-point, comparable.
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2. BioParamQ — Physical-ish fixed-point parameter, NOT a coding atom.
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Type = Q16_16. Range: [-32768, 32767]. Resolution: 2^-16.
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Used for raw source measurements: dimensions, charge, rigidity, temperature.
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These values are >1, dimensioned, or negative — cannot be raw Q0_64.
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3. BioCodingProjection — A normalized biological parameter projected into coding space.
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Contains: optional raw BioParamQ + normalized CodingQ + scaleReceipt.
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The projection map must be explicit and receipted.
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WARDEN RULES:
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- If field is marked coding_atom: type must be Q0_64.
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- If field is raw physical/geometric/thermodynamic: type must not pretend to be
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Q0_64 unless a normalization scale is declared.
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- If Q0_64 value was produced from a raw parameter: require scale_receipt.
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- If any canonical constructor uses Float: block promotion.
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No float in canonical coding. Decimal constants enter as rational literals
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or pre-scaled integers via ofRatio.
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Per AGENTS.md §1.4: Q0_64 fixed-point for maximum precision dimensionless.
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Per AGENTS.md §1.5: No float in canonical hot-path code.
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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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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.Real.Basic
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import Semantics.FixedPoint
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namespace Semantics.SyntheticGeneticCoding
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open Semantics.Q16_16.Q0_64
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open Semantics.Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 THREE-LAYER TYPE SYSTEM (CodingQ / BioParamQ / BioCodingProjection)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Canonical normalized coding atom. Range [-1, 1). All coding values. -/
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structure CodingQ where
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value : Q0_64
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deriving Repr, Inhabited, BEq, DecidableEq
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/-- Physical-ish fixed-point parameter. NOT a coding atom.
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Used for source-side measurements: dimensions, charge, rigidity, etc. -/
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structure BioParamQ where
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value : Q16_16
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deriving Repr, Inhabited, BEq, DecidableEq
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/-- A normalized biological parameter projected into coding space.
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The projection map (raw → normalized) must be explicit and receipted. -/
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structure BioCodingProjection where
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raw? : Option BioParamQ -- Optional source measurement
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normalized : CodingQ -- Projected value in Q0_64
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scaleReceipt : String -- Provenance of normalization map
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deriving Repr, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 PROJECTION FUNCTIONS (Source → Coding)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Direct rational projection: num/den → CodingQ with receipt.
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No Float used. Receipt documents the normalization provenance. -/
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def projectRatioToCodingQ (num : Nat) (den : Nat) (receipt : String) : BioCodingProjection :=
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{ raw? := none,
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normalized := CodingQ.mk (Q0_64.ofRatio num den),
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scaleReceipt := receipt
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 ALPHABET TYPE HIERARCHY (Pure Symbol Sets)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Standard 4-symbol alphabet -/
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inductive StandardAlphabet4 where
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| A | C | G | T
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deriving BEq, DecidableEq, Repr, Inhabited
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/-- Expanded 8-symbol alphabet -/
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inductive Alphabet8 where
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| A | C | G | T | P | Z | B | S
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deriving BEq, DecidableEq, Repr, Inhabited
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/-- Encoding family identifier (pure channel type, no biology) -/
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inductive EncodingFamily where
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| fourSymbolBlock -- 4-symbol block codes
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| eightSymbolBlock -- 8-symbol block codes
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| sixteenSymbolBlock -- 16-symbol block codes
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| binaryBlock -- 2-symbol binary codes
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| custom : Nat → EncodingFamily -- N-symbol custom alphabet
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deriving BEq, DecidableEq, Repr, Inhabited
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/-- Base pairing constraint (structural compatibility, not chemistry) -/
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inductive PairConstraint where
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| strictComplement -- Must pair A↔T, C↔G style
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| fourWay -- 4 orthogonal pairs (8-symbol)
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| unrestricted -- Any symbol can follow any symbol
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deriving BEq, DecidableEq, Repr
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 CODE SPACE (Information Theory)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Block code configuration: alphabet size and block length -/
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structure BlockCodeConfig where
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alphabetSize : Nat
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blockLength : Nat
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proofPositive : alphabetSize > 0 ∧ blockLength > 0
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deriving Repr
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/-- Number of possible codewords = |A|^L -/
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def codeSpaceSize (alphabetSize : Nat) (blockLength : Nat) : Nat :=
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alphabetSize ^ blockLength
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/-- Standard 4^3 = 64 codewords -/
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def code64 : Nat := codeSpaceSize 4 3
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/-- Expanded 8^3 = 512 codewords -/
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def code512 : Nat := codeSpaceSize 8 3
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/-- Quadruplet 4^4 = 256 codewords -/
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def code256 : Nat := codeSpaceSize 4 4
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/-- Binary 2^8 = 256 bytes -/
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def codeByte : Nat := codeSpaceSize 2 8
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/-- Normalized information capacity per symbol = log2(N) / 8
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For comparison across alphabet sizes, normalized to [0, 1] in CodingQ.
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Uses pre-computed rational values — NO FLOAT in canonical code.
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With max alphabet = 256 (byte), log2(256) = 8 bits:
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- 2-symbol: log2(2)/8 = 1/8 = 0.125
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- 4-symbol: log2(4)/8 = 2/8 = 0.25
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- 8-symbol: log2(8)/8 = 3/8 = 0.375
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- 16-symbol: log2(16)/8 = 4/8 = 0.5
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- 256-symbol: log2(256)/8 = 8/8 = 1.0
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All results as CodingQ (Q0_64). -/
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def normalizedCapacity (alphabetSize : Nat) : CodingQ :=
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match alphabetSize with
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| 0 => CodingQ.mk zero
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| 1 => CodingQ.mk zero -- log2(1) = 0
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| 2 => CodingQ.mk (Q0_64.ofRatio 1 8) -- 0.125
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| 4 => CodingQ.mk (Q0_64.ofRatio 2 8) -- 0.25
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| 8 => CodingQ.mk (Q0_64.ofRatio 3 8) -- 0.375
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| 16 => CodingQ.mk (Q0_64.ofRatio 4 8) -- 0.5
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| 32 => CodingQ.mk (Q0_64.ofRatio 5 8) -- 0.625
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| 64 => CodingQ.mk (Q0_64.ofRatio 6 8) -- 0.75
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| 128 => CodingQ.mk (Q0_64.ofRatio 7 8) -- 0.875
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| 256 => CodingQ.mk one -- 1.0
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| _ => CodingQ.mk (Q0_64.ofRatio 1 8) -- default: conservative 2-symbol
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/-- 4-symbol normalized capacity = 0.25 -/
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def cap4 : CodingQ := normalizedCapacity 4
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/-- 8-symbol normalized capacity = 0.375 -/
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def cap8 : CodingQ := normalizedCapacity 8
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/-- 2-symbol normalized capacity = 0.125 -/
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def cap2 : CodingQ := normalizedCapacity 2
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/-- 16-symbol normalized capacity = 0.5 -/
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def cap16 : CodingQ := normalizedCapacity 16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 CHANNEL PARAMETERS (Noise/Constraint Model — All CodingQ)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Channel noise parameters for a given encoding family.
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ALL values are CodingQ (Q0_64) normalized dimensionless quantities [0, 1).
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No biological meaning — purely information-theoretic channel properties. -/
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structure ChannelParameters where
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encodingFamily : EncodingFamily
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-- Symbol reliability: probability of correct transmission per symbol
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symbolReliability : CodingQ
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-- Pairing constraint strictness: 0 = no pairing, 1 = strict complement
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pairConstraintStrength : CodingQ
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-- Sequence stability: resistance to random mutation/insertion/deletion
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stabilityScore : CodingQ
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-- Copy fidelity: accuracy of replication/transcription equivalent
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copyFidelity : CodingQ
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-- Decoding efficiency: fraction of codewords usable (accounting for degeneracy)
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decodingEfficiency : CodingQ
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deriving Repr, Inhabited
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/-- High-stability channel -/
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def highStabilityChannel : ChannelParameters := {
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encodingFamily := EncodingFamily.fourSymbolBlock,
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symbolReliability := CodingQ.mk (Q0_64.ofRatio 999 1000), -- 0.999
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pairConstraintStrength := CodingQ.mk (Q0_64.ofRatio 95 100), -- 0.95
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stabilityScore := CodingQ.mk (Q0_64.ofRatio 99 100), -- 0.99
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copyFidelity := CodingQ.mk (Q0_64.ofRatio 999 1000), -- 0.999
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decodingEfficiency := CodingQ.mk (Q0_64.ofRatio 95 100) -- 0.95
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}
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/-- Flexible channel -/
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def flexibleChannel : ChannelParameters := {
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encodingFamily := EncodingFamily.fourSymbolBlock,
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symbolReliability := CodingQ.mk (Q0_64.ofRatio 85 100), -- 0.85
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pairConstraintStrength := CodingQ.mk (Q0_64.ofRatio 30 100), -- 0.30
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stabilityScore := CodingQ.mk (Q0_64.ofRatio 70 100), -- 0.70
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copyFidelity := CodingQ.mk (Q0_64.ofRatio 85 100), -- 0.85
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decodingEfficiency := CodingQ.mk (Q0_64.ofRatio 90 100) -- 0.90
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}
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/-- Neutral channel -/
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def neutralChannel : ChannelParameters := {
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encodingFamily := EncodingFamily.fourSymbolBlock,
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symbolReliability := CodingQ.mk (Q0_64.ofRatio 90 100), -- 0.90
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pairConstraintStrength := CodingQ.mk (Q0_64.ofRatio 50 100), -- 0.50
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stabilityScore := CodingQ.mk (Q0_64.ofRatio 99 100), -- 0.99
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copyFidelity := CodingQ.mk (Q0_64.ofRatio 95 100), -- 0.95
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decodingEfficiency := CodingQ.mk (Q0_64.ofRatio 85 100) -- 0.85
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 CODE EXPANSION (Block Length Extension)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Non-standard symbol for expanded codes -/
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structure ExtendedSymbol where
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symbolId : String
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properties : List String
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blockAssignment : Option String
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deriving Repr, Inhabited
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/-- Code expansion strategy -/
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inductive ExpansionStrategy where
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| reservedBlockRecoding : String → ExpansionStrategy
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| blockLengthExtension : ExpansionStrategy
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| senseBlockReassignment : String → ExpansionStrategy
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deriving Repr
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/-- Code system definition (pure combinatorics, no translation) -/
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structure CodeSystem where
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name : String
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alphabetSize : Nat
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blockLength : Nat
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totalBlocks : Nat
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senseBlocks : Nat
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stopBlocks : Nat
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extendedSymbols : List ExtendedSymbol
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orthogonalDecoder : Bool
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deriving Repr, Inhabited
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/-- Standard 64-block system (4^3) -/
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def standardCodeSystem : CodeSystem := {
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name := "Standard 64-Block",
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alphabetSize := 4,
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blockLength := 3,
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totalBlocks := 64,
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senseBlocks := 61,
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stopBlocks := 3,
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extendedSymbols := [],
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orthogonalDecoder := false
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}
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/-- Extended 320-block system (4^4 with overlap) -/
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def extendedCodeSystem : CodeSystem := {
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name := "Extended 320-Block",
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alphabetSize := 4,
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blockLength := 4,
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totalBlocks := 320,
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senseBlocks := 300,
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stopBlocks := 20,
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extendedSymbols := [
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{ symbolId := "AzF", properties := ["click-chemistry", "photocrosslinker"], blockAssignment := some "AGGA" },
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{ symbolId := "AcF", properties := ["ketone-reactive"], blockAssignment := some "AGGG" }
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],
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orthogonalDecoder := true
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}
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/-- 512-block system (8^3) -/
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def expanded512CodeSystem : CodeSystem := {
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name := "Expanded 512-Block",
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alphabetSize := 8,
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blockLength := 3,
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totalBlocks := 512,
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senseBlocks := 480,
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stopBlocks := 32,
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extendedSymbols := [],
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orthogonalDecoder := false
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 COMPRESSION FUNCTIONS (Information Theory — All CodingQ)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Compute compression potential of a symbol sequence.
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Returns CodingQ [0, 1]. Higher info density → lower redundancy → higher compression. -/
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def compressionPotential
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(alphabetSize : Nat)
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(_sequenceLength : Nat)
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(redundancyFactor : CodingQ) : CodingQ :=
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let infoContent := (normalizedCapacity alphabetSize).value
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let oneMinusRedundancy := Q0_64.sub one redundancyFactor.value
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CodingQ.mk (Q0_64.mul infoContent oneMinusRedundancy)
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/-- Channel stability score: combines reliability and stability -/
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def channelStabilityScore (ch : ChannelParameters) : CodingQ :=
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let r1 := Q0_64.mul ch.symbolReliability.value (Q0_64.ofRatio 3 10) -- weight 0.3
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let r2 := Q0_64.mul ch.stabilityScore.value (Q0_64.ofRatio 4 10) -- weight 0.4
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let r3 := Q0_64.mul ch.copyFidelity.value (Q0_64.ofRatio 3 10) -- weight 0.3
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CodingQ.mk (Q0_64.add (Q0_64.add r1 r2) r3)
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/-- Block optimization score: penalize low-efficiency codes -/
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def blockOptimizationScore
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(blockUsageTable : Array CodingQ)
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(desiredBlock : Nat)
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(rareBlockThreshold : CodingQ) : CodingQ :=
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if desiredBlock >= blockUsageTable.size then CodingQ.mk zero
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else
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let frequency := blockUsageTable[desiredBlock]!.value
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if frequency < rareBlockThreshold.value
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then CodingQ.mk (Q0_64.ofRatio 5 10) -- penalize: 0.5
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else CodingQ.mk one
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 GCL SURFACE BIND FUNCTIONS (All return CodingQ)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Information-theoretic bind: measures coding efficiency -/
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def informationalBind (code : CodeSystem) : CodingQ :=
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let capacity := (normalizedCapacity code.alphabetSize).value
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let efficiency := Q0_64.ofRatio code.senseBlocks code.totalBlocks
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CodingQ.mk (Q0_64.mul capacity efficiency)
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/-- Stability bind: noise resilience as CodingQ -/
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def stabilityBind (ch : ChannelParameters) : CodingQ :=
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channelStabilityScore ch
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/-- Control bind: decoder orthogonality and expansion capability -/
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def controlBind (code : CodeSystem) : CodingQ :=
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if code.orthogonalDecoder then CodingQ.mk (Q0_64.ofRatio 8 10) -- 0.8
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else CodingQ.mk (Q0_64.ofRatio 4 10) -- 0.4
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §9 DELTA-PHI-GAMMA-LAMBDA AUDIT GRAMMAR (v3 Delta Definitions)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Delta (Δ): Residual change — what was lost, distorted, or left over.
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Magnitude is CodingQ [0, 1]: normalized residual. -/
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structure DeltaResidual where
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changeDescription : String
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magnitude : CodingQ
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receipt : Option String
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deriving Repr, Inhabited
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/-- Phi (φ): Invariant structure — what must survive transformation -/
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structure PhiInvariant where
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invariantDescription : String
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preserved : Bool
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proofReceipt : Option String
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deriving Repr, Inhabited
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/-- Gamma (γ): Compression pressure — force toward collapse/abstraction.
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Normalized pressure level [0, 1] in CodingQ. -/
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structure GammaPressure where
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pressureLevel : CodingQ
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description : String
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deriving Repr, Inhabited
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/-- Lambda (λ): Scale band — resolution of comparison -/
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structure LambdaScale where
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scaleDescription : String
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byteSpan : Option Nat
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temporalWindow : Option Nat
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deriving Repr, Inhabited
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/-- Complete Delta-Phi-Gamma-Lambda audit record.
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All dimensionless quantities are CodingQ (Q0_64). -/
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structure DeltaPhiGammaLambdaAudit where
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delta : DeltaResidual
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phi : PhiInvariant
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gamma : GammaPressure
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lambda : LambdaScale
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auditPassed : Bool
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deriving Repr, Inhabited
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/-- Audit check: Did phi survive within bounded delta under gamma at lambda? -/
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def dpglAuditCheck (audit : DeltaPhiGammaLambdaAudit) : Bool :=
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audit.phi.preserved &&
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audit.delta.magnitude.value < Q0_64.ofRatio 1 10 && -- threshold 0.1
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audit.auditPassed
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §10 AUTHORITY STATES (v3 Delta Definitions)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- GCL separates existence from authority. Objects exist but must earn authority. -/
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inductive AuthorityState where
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| U_scope -- Unscoped: exploratory, no authority
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| HOLD -- Important but unresolved; preserve but do not promote
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| V_scope -- Valid under declared local scope only
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| REVIEWED -- Review or audit receipts exist
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| CANONICAL_LEAN -- Formal artifact builds without hidden gaps
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| QUARANTINE -- Unsafe, misleading, or category-confused
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deriving BEq, DecidableEq, Repr, Inhabited
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/-- Check if authority state permits promotion -/
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def canPromote (auth : AuthorityState) : Bool :=
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match auth with
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| AuthorityState.CANONICAL_LEAN => true
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| AuthorityState.REVIEWED => true
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| _ => false
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §11 COMBINED GCL CODING OBJECT (v3 Delta Definitions)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Combined GCL Coding Object for unified inspection across regimes.
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All coding values are CodingQ. Raw measurements use BioCodingProjection. -/
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structure CombinedGCLCodingObject where
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gclId : String
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preferredName : String
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aliases : List String
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codingVariant : String
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kind : String
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claimState : String
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authorityScope : AuthorityState
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definition : String
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genotype : String
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expression : String
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expansionSlots : List String
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gates : List String
|
||
receipts : List String
|
||
projections : List String
|
||
mutationHistory : List String
|
||
repairPaths : List String
|
||
blockedUsages : List String
|
||
dpglAudit : Option DeltaPhiGammaLambdaAudit
|
||
deriving Repr, Inhabited
|
||
|
||
/-- Convert EncodingFamily to String for genotype field -/
|
||
def encodingFamilyToString (ef : EncodingFamily) : String :=
|
||
match ef with
|
||
| EncodingFamily.fourSymbolBlock => "4sym"
|
||
| EncodingFamily.eightSymbolBlock => "8sym"
|
||
| EncodingFamily.sixteenSymbolBlock => "16sym"
|
||
| EncodingFamily.binaryBlock => "bin"
|
||
| EncodingFamily.custom n => s!"c{n}"
|
||
|
||
/-- Create a synthetic genetic coding object with GCL v3 structure.
|
||
All normalized values are CodingQ. -/
|
||
def makeSyntheticGCLObject
|
||
(name : String)
|
||
(encFamily : EncodingFamily)
|
||
(alphabetSize : Nat)
|
||
(auth : AuthorityState) : CombinedGCLCodingObject :=
|
||
{ gclId := s!"gcl_synthetic_{name}",
|
||
preferredName := name,
|
||
aliases := [],
|
||
codingVariant := match encFamily with
|
||
| EncodingFamily.fourSymbolBlock => "4-symbol"
|
||
| EncodingFamily.eightSymbolBlock => "8-symbol"
|
||
| EncodingFamily.sixteenSymbolBlock => "16-symbol"
|
||
| EncodingFamily.binaryBlock => "binary"
|
||
| EncodingFamily.custom n => s!"custom-{n}",
|
||
kind := "synthetic_genetic",
|
||
claimState := "experimental",
|
||
authorityScope := auth,
|
||
definition := s!"Block code with {alphabetSize}-symbol alphabet",
|
||
genotype := s!"family={encodingFamilyToString encFamily}, alphabet={alphabetSize}",
|
||
expression := "surface_projection_pending",
|
||
expansionSlots := ["epigenetic_marks", "modified_bases"],
|
||
gates := ["channel_stability_gate", "decoding_efficiency_gate"],
|
||
receipts := [],
|
||
projections := [],
|
||
mutationHistory := [],
|
||
repairPaths := ["reverse_collapse_to_binary"],
|
||
blockedUsages := if auth == AuthorityState.QUARANTINE then ["therapeutic_use"] else [],
|
||
dpglAudit := none
|
||
}
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §12 WARDEN VALIDATION RULES (v3 Delta Definitions)
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Warden emission types for combined surface validation -/
|
||
inductive WardenEmission where
|
||
| bioOverclaim -- Biological analogy presented as evidence
|
||
| aliasBoundaryBlur -- Aliases collapse incompatible meanings
|
||
| projectionProofConfusion -- Surface used as proof
|
||
| missingTestReceipt -- Algorithmic collapse lacks behavior tests
|
||
| recursiveAbstractionWithoutGround -- No reverse-collapse target
|
||
| fixedPointViolation -- Floats in fixed-point hot path
|
||
| codingAtomTypeViolation -- Field marked coding_atom but not CodingQ
|
||
| deltaUnbounded -- Residual change exceeds threshold
|
||
| phiNotPreserved -- Invariant failed under compression
|
||
deriving BEq, DecidableEq, Repr, Inhabited
|
||
|
||
/-- Warden validation result -/
|
||
structure WardenValidation where
|
||
passed : Bool
|
||
emissions : List WardenEmission
|
||
requiredHolds : Bool
|
||
deriving Repr, Inhabited
|
||
|
||
/-- Check if emissions list is empty -/
|
||
def emissionsEmpty (emissions : List WardenEmission) : Bool :=
|
||
match emissions with
|
||
| [] => true
|
||
| _ => false
|
||
|
||
/-- Validate a synthetic genetic object against Warden rules -/
|
||
def wardenValidateSynthetic (obj : CombinedGCLCodingObject) : WardenValidation :=
|
||
let emissions : List WardenEmission := []
|
||
-- Check 1: If claiming biological relevance, need external receipts
|
||
let emissions := if obj.claimState == "biological_evidence" && obj.receipts == []
|
||
then WardenEmission.bioOverclaim :: emissions else emissions
|
||
-- Check 2: If aliases present but no repair paths
|
||
let emissions := if obj.aliases != [] && obj.repairPaths == []
|
||
then WardenEmission.aliasBoundaryBlur :: emissions else emissions
|
||
-- Check 3: If no reverse collapse path
|
||
let emissions := if obj.repairPaths == []
|
||
then WardenEmission.recursiveAbstractionWithoutGround :: emissions else emissions
|
||
-- Check 4: Authority state check
|
||
let passed := emissionsEmpty emissions && canPromote obj.authorityScope
|
||
{ passed := passed,
|
||
emissions := emissions,
|
||
requiredHolds := !emissionsEmpty emissions
|
||
}
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §13 REVERSE COLLAPSE SAFETY
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Reverse collapse path: can abstraction unfold back to concrete anchor? -/
|
||
structure ReverseCollapsePath where
|
||
targetAbstraction : String
|
||
concreteAnchor : String
|
||
collapseSteps : Nat
|
||
recoveryTest : Option String
|
||
deriving Repr, Inhabited
|
||
|
||
/-- Verify reverse collapse is possible -/
|
||
def verifyReverseCollapse
|
||
(obj : CombinedGCLCodingObject)
|
||
(path : ReverseCollapsePath) : Bool :=
|
||
path.collapseSteps > 0 && path.recoveryTest != none && obj.repairPaths != []
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §14 THEOREMS (Formal Verification)
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Theorem: 512-block space is 8x larger than 64-block -/
|
||
theorem block512vs64 :
|
||
code512 = 8 * code64 := by
|
||
rfl
|
||
|
||
/-- Theorem: Extended 4-block system has 4x more blocks than 3-block -/
|
||
theorem block256vs64 :
|
||
code256 = 4 * code64 := by
|
||
rfl
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §15 #eval WITNESSES
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
#eval code64 -- 64
|
||
#eval code512 -- 512
|
||
#eval code256 -- 256
|
||
#eval codeByte -- 256
|
||
|
||
#eval cap4 -- CodingQ with ~0.25
|
||
#eval cap8 -- CodingQ with ~0.375
|
||
#eval cap2 -- CodingQ with ~0.125
|
||
#eval cap16 -- CodingQ with ~0.5
|
||
|
||
#eval highStabilityChannel.stabilityScore
|
||
#eval flexibleChannel.stabilityScore
|
||
#eval neutralChannel.copyFidelity
|
||
|
||
#eval compressionPotential 4 1000 (CodingQ.mk (Q0_64.ofRatio 3 10))
|
||
#eval channelStabilityScore highStabilityChannel
|
||
#eval informationalBind standardCodeSystem
|
||
#eval controlBind extendedCodeSystem
|
||
|
||
#eval canPromote AuthorityState.CANONICAL_LEAN
|
||
#eval canPromote AuthorityState.HOLD
|
||
|
||
#eval (makeSyntheticGCLObject "test_4sym" EncodingFamily.fourSymbolBlock 4 AuthorityState.HOLD).authorityScope
|
||
|
||
#eval (wardenValidateSynthetic (makeSyntheticGCLObject "test_xna" EncodingFamily.eightSymbolBlock 8 AuthorityState.U_scope)).passed
|
||
|
||
end Semantics.SyntheticGeneticCoding
|