/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Research Stack Team

SyntheticGeneticCoding.lean — 0D(n) Symbol-Coding Objects for GCL Surfaces

This module treats all coding systems as purely information-theoretic 0D(n)
discrete objects: finite-length strings over finite alphabets.

These objects happen to borrow symbol-sets from coding techniques that nature
has been stress-testing for ~4.6 billion years. The biology is completely
ignored. Only information capacity, channel efficiency, redundancy profiles,
and compression bounds matter.

TYPE SYSTEM (Three-Layer Doctrine):

1. CodingQ — Canonical normalized coding atom. Type = Q0_64.
   Range: [-1, 1). Resolution: 2^-63. Used for ALL coding-space values.
   Properties: normalized, bounded, deterministic, fixed-point, comparable.

2. BioParamQ — Physical-ish fixed-point parameter, NOT a coding atom.
   Type = Q16_16. Range: [-32768, 32767]. Resolution: 2^-16.
   Used for raw source measurements: dimensions, charge, rigidity, temperature.
   These values are >1, dimensioned, or negative — cannot be raw Q0_64.

3. BioCodingProjection — A normalized biological parameter projected into coding space.
   Contains: optional raw BioParamQ + normalized CodingQ + scaleReceipt.
   The projection map must be explicit and receipted.

WARDEN RULES:
- If field is marked coding_atom: type must be Q0_64.
- If field is raw physical/geometric/thermodynamic: type must not pretend to be
  Q0_64 unless a normalization scale is declared.
- If Q0_64 value was produced from a raw parameter: require scale_receipt.
- If any canonical constructor uses Float: block promotion.

No float in canonical coding. Decimal constants enter as rational literals
or pre-scaled integers via ofRatio.

Per AGENTS.md §1.4: Q0_64 fixed-point for maximum precision dimensionless.
Per AGENTS.md §1.5: No float in canonical hot-path code.
Per AGENTS.md §2: PascalCase types, camelCase functions.
Per AGENTS.md §4: Every def has #eval witness or theorem.
-/

import Mathlib.Data.Nat.Basic
import Mathlib.Data.Real.Basic
import Semantics.FixedPoint

namespace Semantics.SyntheticGeneticCoding

open Semantics.Q16_16.Q0_64
open Semantics.Q16_16

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  THREE-LAYER TYPE SYSTEM (CodingQ / BioParamQ / BioCodingProjection)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Canonical normalized coding atom. Range [-1, 1). All coding values. -/
structure CodingQ where
  value : Q0_64
  deriving Repr, Inhabited, BEq, DecidableEq

/-- Physical-ish fixed-point parameter. NOT a coding atom.
    Used for source-side measurements: dimensions, charge, rigidity, etc. -/
structure BioParamQ where
  value : Q16_16
  deriving Repr, Inhabited, BEq, DecidableEq

/-- A normalized biological parameter projected into coding space.
    The projection map (raw → normalized) must be explicit and receipted. -/
structure BioCodingProjection where
  raw? : Option BioParamQ      -- Optional source measurement
  normalized : CodingQ       -- Projected value in Q0_64
  scaleReceipt : String        -- Provenance of normalization map
  deriving Repr, Inhabited

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  PROJECTION FUNCTIONS (Source → Coding)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Direct rational projection: num/den → CodingQ with receipt.
    No Float used. Receipt documents the normalization provenance. -/
def projectRatioToCodingQ (num : Nat) (den : Nat) (receipt : String) : BioCodingProjection :=
  { raw? := none,
    normalized := CodingQ.mk (Q0_64.ofRatio num den),
    scaleReceipt := receipt
  }

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  ALPHABET TYPE HIERARCHY (Pure Symbol Sets)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Standard 4-symbol alphabet -/
inductive StandardAlphabet4 where
  | A | C | G | T
  deriving BEq, DecidableEq, Repr, Inhabited

/-- Expanded 8-symbol alphabet -/
inductive Alphabet8 where
  | A | C | G | T | P | Z | B | S
  deriving BEq, DecidableEq, Repr, Inhabited

/-- Encoding family identifier (pure channel type, no biology) -/
inductive EncodingFamily where
  | fourSymbolBlock    -- 4-symbol block codes
  | eightSymbolBlock   -- 8-symbol block codes
  | sixteenSymbolBlock -- 16-symbol block codes
  | binaryBlock        -- 2-symbol binary codes
  | custom : Nat → EncodingFamily  -- N-symbol custom alphabet
  deriving BEq, DecidableEq, Repr, Inhabited

/-- Base pairing constraint (structural compatibility, not chemistry) -/
inductive PairConstraint where
  | strictComplement  -- Must pair A↔T, C↔G style
  | fourWay           -- 4 orthogonal pairs (8-symbol)
  | unrestricted      -- Any symbol can follow any symbol
  deriving BEq, DecidableEq, Repr

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  CODE SPACE (Information Theory)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Block code configuration: alphabet size and block length -/
structure BlockCodeConfig where
  alphabetSize : Nat
  blockLength : Nat
  proofPositive : alphabetSize > 0 ∧ blockLength > 0
  deriving Repr

/-- Number of possible codewords = |A|^L -/
def codeSpaceSize (alphabetSize : Nat) (blockLength : Nat) : Nat :=
  alphabetSize ^ blockLength

/-- Standard 4^3 = 64 codewords -/
def code64 : Nat := codeSpaceSize 4 3

/-- Expanded 8^3 = 512 codewords -/
def code512 : Nat := codeSpaceSize 8 3

/-- Quadruplet 4^4 = 256 codewords -/
def code256 : Nat := codeSpaceSize 4 4

/-- Binary 2^8 = 256 bytes -/
def codeByte : Nat := codeSpaceSize 2 8

/-- Normalized information capacity per symbol = log2(N) / 8
    For comparison across alphabet sizes, normalized to [0, 1] in CodingQ.
    Uses pre-computed rational values — NO FLOAT in canonical code.

    With max alphabet = 256 (byte), log2(256) = 8 bits:
    - 2-symbol: log2(2)/8 = 1/8 = 0.125
    - 4-symbol: log2(4)/8 = 2/8 = 0.25
    - 8-symbol: log2(8)/8 = 3/8 = 0.375
    - 16-symbol: log2(16)/8 = 4/8 = 0.5
    - 256-symbol: log2(256)/8 = 8/8 = 1.0
    All results as CodingQ (Q0_64). -/
def normalizedCapacity (alphabetSize : Nat) : CodingQ :=
  match alphabetSize with
  | 0 => CodingQ.mk zero
  | 1 => CodingQ.mk zero  -- log2(1) = 0
  | 2 => CodingQ.mk (Q0_64.ofRatio 1 8)     -- 0.125
  | 4 => CodingQ.mk (Q0_64.ofRatio 2 8)     -- 0.25
  | 8 => CodingQ.mk (Q0_64.ofRatio 3 8)     -- 0.375
  | 16 => CodingQ.mk (Q0_64.ofRatio 4 8)    -- 0.5
  | 32 => CodingQ.mk (Q0_64.ofRatio 5 8)    -- 0.625
  | 64 => CodingQ.mk (Q0_64.ofRatio 6 8)    -- 0.75
  | 128 => CodingQ.mk (Q0_64.ofRatio 7 8)   -- 0.875
  | 256 => CodingQ.mk one                      -- 1.0
  | _ => CodingQ.mk (Q0_64.ofRatio 1 8)     -- default: conservative 2-symbol

/-- 4-symbol normalized capacity = 0.25 -/
def cap4 : CodingQ := normalizedCapacity 4

/-- 8-symbol normalized capacity = 0.375 -/
def cap8 : CodingQ := normalizedCapacity 8

/-- 2-symbol normalized capacity = 0.125 -/
def cap2 : CodingQ := normalizedCapacity 2

/-- 16-symbol normalized capacity = 0.5 -/
def cap16 : CodingQ := normalizedCapacity 16

-- ═══════════════════════════════════════════════════════════════════════════
-- §5  CHANNEL PARAMETERS (Noise/Constraint Model — All CodingQ)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Channel noise parameters for a given encoding family.
    ALL values are CodingQ (Q0_64) normalized dimensionless quantities [0, 1).
    No biological meaning — purely information-theoretic channel properties. -/
structure ChannelParameters where
  encodingFamily : EncodingFamily
  -- Symbol reliability: probability of correct transmission per symbol
  symbolReliability : CodingQ
  -- Pairing constraint strictness: 0 = no pairing, 1 = strict complement
  pairConstraintStrength : CodingQ
  -- Sequence stability: resistance to random mutation/insertion/deletion
  stabilityScore : CodingQ
  -- Copy fidelity: accuracy of replication/transcription equivalent
  copyFidelity : CodingQ
  -- Decoding efficiency: fraction of codewords usable (accounting for degeneracy)
  decodingEfficiency : CodingQ
  deriving Repr, Inhabited

/-- High-stability channel -/
def highStabilityChannel : ChannelParameters := {
  encodingFamily := EncodingFamily.fourSymbolBlock,
  symbolReliability := CodingQ.mk (Q0_64.ofRatio 999 1000),    -- 0.999
  pairConstraintStrength := CodingQ.mk (Q0_64.ofRatio 95 100),    -- 0.95
  stabilityScore := CodingQ.mk (Q0_64.ofRatio 99 100),          -- 0.99
  copyFidelity := CodingQ.mk (Q0_64.ofRatio 999 1000),          -- 0.999
  decodingEfficiency := CodingQ.mk (Q0_64.ofRatio 95 100)        -- 0.95
}

/-- Flexible channel -/
def flexibleChannel : ChannelParameters := {
  encodingFamily := EncodingFamily.fourSymbolBlock,
  symbolReliability := CodingQ.mk (Q0_64.ofRatio 85 100),         -- 0.85
  pairConstraintStrength := CodingQ.mk (Q0_64.ofRatio 30 100),    -- 0.30
  stabilityScore := CodingQ.mk (Q0_64.ofRatio 70 100),           -- 0.70
  copyFidelity := CodingQ.mk (Q0_64.ofRatio 85 100),             -- 0.85
  decodingEfficiency := CodingQ.mk (Q0_64.ofRatio 90 100)        -- 0.90
}

/-- Neutral channel -/
def neutralChannel : ChannelParameters := {
  encodingFamily := EncodingFamily.fourSymbolBlock,
  symbolReliability := CodingQ.mk (Q0_64.ofRatio 90 100),        -- 0.90
  pairConstraintStrength := CodingQ.mk (Q0_64.ofRatio 50 100),   -- 0.50
  stabilityScore := CodingQ.mk (Q0_64.ofRatio 99 100),            -- 0.99
  copyFidelity := CodingQ.mk (Q0_64.ofRatio 95 100),             -- 0.95
  decodingEfficiency := CodingQ.mk (Q0_64.ofRatio 85 100)        -- 0.85
}

-- ═══════════════════════════════════════════════════════════════════════════
-- §6  CODE EXPANSION (Block Length Extension)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Non-standard symbol for expanded codes -/
structure ExtendedSymbol where
  symbolId : String
  properties : List String
  blockAssignment : Option String
  deriving Repr, Inhabited

/-- Code expansion strategy -/
inductive ExpansionStrategy where
  | reservedBlockRecoding : String → ExpansionStrategy
  | blockLengthExtension : ExpansionStrategy
  | senseBlockReassignment : String → ExpansionStrategy
  deriving Repr

/-- Code system definition (pure combinatorics, no translation) -/
structure CodeSystem where
  name : String
  alphabetSize : Nat
  blockLength : Nat
  totalBlocks : Nat
  senseBlocks : Nat
  stopBlocks : Nat
  extendedSymbols : List ExtendedSymbol
  orthogonalDecoder : Bool
  deriving Repr, Inhabited

/-- Standard 64-block system (4^3) -/
def standardCodeSystem : CodeSystem := {
  name := "Standard 64-Block",
  alphabetSize := 4,
  blockLength := 3,
  totalBlocks := 64,
  senseBlocks := 61,
  stopBlocks := 3,
  extendedSymbols := [],
  orthogonalDecoder := false
}

/-- Extended 320-block system (4^4 with overlap) -/
def extendedCodeSystem : CodeSystem := {
  name := "Extended 320-Block",
  alphabetSize := 4,
  blockLength := 4,
  totalBlocks := 320,
  senseBlocks := 300,
  stopBlocks := 20,
  extendedSymbols := [
    { symbolId := "AzF", properties := ["click-chemistry", "photocrosslinker"], blockAssignment := some "AGGA" },
    { symbolId := "AcF", properties := ["ketone-reactive"], blockAssignment := some "AGGG" }
  ],
  orthogonalDecoder := true
}

/-- 512-block system (8^3) -/
def expanded512CodeSystem : CodeSystem := {
  name := "Expanded 512-Block",
  alphabetSize := 8,
  blockLength := 3,
  totalBlocks := 512,
  senseBlocks := 480,
  stopBlocks := 32,
  extendedSymbols := [],
  orthogonalDecoder := false
}

-- ═══════════════════════════════════════════════════════════════════════════
-- §7  COMPRESSION FUNCTIONS (Information Theory — All CodingQ)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Compute compression potential of a symbol sequence.
    Returns CodingQ [0, 1]. Higher info density → lower redundancy → higher compression. -/
def compressionPotential
    (alphabetSize : Nat)
    (_sequenceLength : Nat)
    (redundancyFactor : CodingQ) : CodingQ :=
  let infoContent := (normalizedCapacity alphabetSize).value
  let oneMinusRedundancy := Q0_64.sub one redundancyFactor.value
  CodingQ.mk (Q0_64.mul infoContent oneMinusRedundancy)

/-- Channel stability score: combines reliability and stability -/
def channelStabilityScore (ch : ChannelParameters) : CodingQ :=
  let r1 := Q0_64.mul ch.symbolReliability.value (Q0_64.ofRatio 3 10)   -- weight 0.3
  let r2 := Q0_64.mul ch.stabilityScore.value (Q0_64.ofRatio 4 10)      -- weight 0.4
  let r3 := Q0_64.mul ch.copyFidelity.value (Q0_64.ofRatio 3 10)       -- weight 0.3
  CodingQ.mk (Q0_64.add (Q0_64.add r1 r2) r3)

/-- Block optimization score: penalize low-efficiency codes -/
def blockOptimizationScore
    (blockUsageTable : Array CodingQ)
    (desiredBlock : Nat)
    (rareBlockThreshold : CodingQ) : CodingQ :=
  if desiredBlock >= blockUsageTable.size then CodingQ.mk zero
  else
    let frequency := blockUsageTable[desiredBlock]!.value
    if frequency < rareBlockThreshold.value
    then CodingQ.mk (Q0_64.ofRatio 5 10)  -- penalize: 0.5
    else CodingQ.mk one

-- ═══════════════════════════════════════════════════════════════════════════
-- §8  GCL SURFACE BIND FUNCTIONS (All return CodingQ)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Information-theoretic bind: measures coding efficiency -/
def informationalBind (code : CodeSystem) : CodingQ :=
  let capacity := (normalizedCapacity code.alphabetSize).value
  let efficiency := Q0_64.ofRatio code.senseBlocks code.totalBlocks
  CodingQ.mk (Q0_64.mul capacity efficiency)

/-- Stability bind: noise resilience as CodingQ -/
def stabilityBind (ch : ChannelParameters) : CodingQ :=
  channelStabilityScore ch

/-- Control bind: decoder orthogonality and expansion capability -/
def controlBind (code : CodeSystem) : CodingQ :=
  if code.orthogonalDecoder then CodingQ.mk (Q0_64.ofRatio 8 10)  -- 0.8
  else CodingQ.mk (Q0_64.ofRatio 4 10)                             -- 0.4

-- ═══════════════════════════════════════════════════════════════════════════
-- §9  DELTA-PHI-GAMMA-LAMBDA AUDIT GRAMMAR (v3 Delta Definitions)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Delta (Δ): Residual change — what was lost, distorted, or left over.
    Magnitude is CodingQ [0, 1]: normalized residual. -/
structure DeltaResidual where
  changeDescription : String
  magnitude : CodingQ
  receipt : Option String
  deriving Repr, Inhabited

/-- Phi (φ): Invariant structure — what must survive transformation -/
structure PhiInvariant where
  invariantDescription : String
  preserved : Bool
  proofReceipt : Option String
  deriving Repr, Inhabited

/-- Gamma (γ): Compression pressure — force toward collapse/abstraction.
    Normalized pressure level [0, 1] in CodingQ. -/
structure GammaPressure where
  pressureLevel : CodingQ
  description : String
  deriving Repr, Inhabited

/-- Lambda (λ): Scale band — resolution of comparison -/
structure LambdaScale where
  scaleDescription : String
  byteSpan : Option Nat
  temporalWindow : Option Nat
  deriving Repr, Inhabited

/-- Complete Delta-Phi-Gamma-Lambda audit record.
    All dimensionless quantities are CodingQ (Q0_64). -/
structure DeltaPhiGammaLambdaAudit where
  delta : DeltaResidual
  phi : PhiInvariant
  gamma : GammaPressure
  lambda : LambdaScale
  auditPassed : Bool
  deriving Repr, Inhabited

/-- Audit check: Did phi survive within bounded delta under gamma at lambda? -/
def dpglAuditCheck (audit : DeltaPhiGammaLambdaAudit) : Bool :=
  audit.phi.preserved &&
  audit.delta.magnitude.value < Q0_64.ofRatio 1 10 &&  -- threshold 0.1
  audit.auditPassed

-- ═══════════════════════════════════════════════════════════════════════════
-- §10  AUTHORITY STATES (v3 Delta Definitions)
-- ═══════════════════════════════════════════════════════════════════════════

/-- GCL separates existence from authority. Objects exist but must earn authority. -/
inductive AuthorityState where
  | U_scope     -- Unscoped: exploratory, no authority
  | HOLD        -- Important but unresolved; preserve but do not promote
  | V_scope     -- Valid under declared local scope only
  | REVIEWED    -- Review or audit receipts exist
  | CANONICAL_LEAN  -- Formal artifact builds without hidden gaps
  | QUARANTINE  -- Unsafe, misleading, or category-confused
  deriving BEq, DecidableEq, Repr, Inhabited

/-- Check if authority state permits promotion -/
def canPromote (auth : AuthorityState) : Bool :=
  match auth with
  | AuthorityState.CANONICAL_LEAN => true
  | AuthorityState.REVIEWED => true
  | _ => false

-- ═══════════════════════════════════════════════════════════════════════════
-- §11  COMBINED GCL CODING OBJECT (v3 Delta Definitions)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Combined GCL Coding Object for unified inspection across regimes.
    All coding values are CodingQ. Raw measurements use BioCodingProjection. -/
structure CombinedGCLCodingObject where
  gclId : String
  preferredName : String
  aliases : List String
  codingVariant : String
  kind : String
  claimState : String
  authorityScope : AuthorityState
  definition : String
  genotype : String
  expression : String
  expansionSlots : List String
  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
