# Metaprobe Approach for GCL Diff Technology

**Version:** 1.0  
**Date:** 2026-04-29  
**Status:** Domain-Gated Verification Standard

---

## Core Philosophy

The GCL (Genetic Compression Layer) diff metaprobe approach formalizes delta compression algorithms with Lean theorem verification, hardware-native fixed-point arithmetic, and domain-appropriate evidence standards. The approach prioritizes:

1. **Formal correctness** via Lean theorem verification for compression algorithms
2. **Hardware compatibility** via Q16_16 fixed-point arithmetic for delta calculations
3. **Domain-gated validation** per claim type (compression → SI ratios, not sigma)
4. **Three-layer compression stack** with multiplicative optimization
5. **Evidence standards** aligned with skepticism gradient gate

---

## GCL Diff Three-Layer Compression Stack

```
┌─────────────────────────────────────┐
│   Variable-Length GCL Encoding      │  ← Top layer (codon optimization)
├─────────────────────────────────────┤
│   PTOS Field Dictionary Compression  │  ← Middle layer (value mapping)
├─────────────────────────────────────┤
│   Delta Encoding                    │  ← Bottom layer (change detection)
└─────────────────────────────────────┘
```

### Data Flow

```
Input Manifest
    ↓
[Delta Encoder] → Detect changes from previous state
    ↓
[PTOS Dictionary] → Map common values to indices
    ↓
[Variable-Length GCL] → Optimize frequent codons
    ↓
Output: Delta GCL Sequence (9-15 chars)
```

---

## Layer 1: Delta Encoding Metaprobe

### Concept

For sequential data (messages, metrics, heartbeats), store only what changed between consecutive states rather than full state snapshots.

### Lean Formalization

```lean
structure DeltaEncoding where
  has_delta : Bool
  changed_fields : List String
  delta_values : HashMap String Q16_16

def computeDelta (current previous : GCLManifest) : DeltaEncoding :=
  if previous == none then
    { has_delta := false, changed_fields := [], delta_values := HashMap.empty }
  else
    let prev := previous.get!
    let changedFields := (["layer", "domain", "tier", "condition"]).filter λ f =>
      current.get f ≠ prev.get f
    let deltaValues := changedFields.foldl (λ acc f =>
      acc.insert f (current.get f)) HashMap.empty
    {
      has_delta := changedFields.length > 0,
      changed_fields := changedFields,
      delta_values := deltaValues
    }
```

### Theorems

```lean
/-- Theorem: Delta encoding with identical states has no delta -/
theorem deltaNoChange (m : GCLManifest) :
    (computeDelta m m).has_delta = false := by
  simp [computeDelta]

/-- Theorem: Delta encoding preserves changed field values -/
theorem deltaPreservesValues (current previous : GCLManifest) (field : String) :
    field ∈ (computeDelta current previous).changed_fields →
    (computeDelta current previous).delta_values.get? field = current.get? field := by
  sorry  -- Proof requires field membership reasoning
```

---

## Layer 2: PTOS Dictionary Metaprobe

### Concept

Map common field values to single-byte indices (0x00-0xFF). Unknown values use 0xFF marker.

### Lean Formalization

```lean
structure PTOSDictionary where
  layer_map : HashMap String UInt8
  domain_map : HashMap String UInt8
  tier_map : HashMap String UInt8
  condition_map : HashMap String UInt8

def defaultPTOSDictionary : PTOSDictionary :=
  {
    layer_map := HashMap.ofList [
      ("CORE", 0x00), ("CARRY", 0x01), ("RULE", 0x02), ("STORE", 0x03)
    ],
    domain_map := HashMap.ofList [
      ("COMPUTE", 0x00), ("TOKEN", 0x01), ("RULE", 0x02), ("STORE", 0x03)
    ],
    tier_map := HashMap.ofList [
      ("SINGULARITY", 0x00), ("PLASMA", 0x01), ("CRYSTALLINE", 0x02), ("FOAM", 0x03)
    ],
    condition_map := HashMap.ofList [
      ("STABLE", 0x00), ("EXPERIMENTAL", 0x01), ("EXTREME", 0x02)
    ]
  }

def applyPTOSDictionary (dict : PTOSDictionary) (manifest : GCLManifest) : ByteArray :=
  let layerByte := dict.layer_map.get? (manifest.get "layer") |>.getD 0xFF
  let domainByte := dict.domain_map.get? (manifest.get "domain") |>.getD 0xFF
  let tierByte := dict.tier_map.get? (manifest.get "tier") |>.getD 0xFF
  let conditionByte := dict.condition_map.get? (manifest.get "condition") |>.getD 0xFF
  #[layerByte, domainByte, tierByte, conditionByte]
```

### Theorems

```lean
/-- Theorem: PTOS dictionary encoding is deterministic -/
theorem ptosDeterministic (dict : PTOSDictionary) (manifest : GCLManifest) :
    applyPTOSDictionary dict manifest = applyPTOSDictionary dict manifest := by
  rfl

/-- Theorem: Known values map to non-0xFF bytes -/
theorem ptosKnownValues (dict : PTOSDictionary) (field value : String) :
    dict.layer_map.get? field = some value →
    value ≠ 0xFF := by
  sorry  -- Proof requires dictionary invariant verification
```

---

## Layer 3: Variable-Length GCL Metaprobe

### Concept

Frequent codons (patterns) use shorter encoding (1-2 characters instead of 3). Similar to Huffman coding but for genetic codons.

### Lean Formalization

```lean
structure ShortCodonMap where
  start_codon : String  -- "ATG" → "A"
  stop_codon : String   -- "TAA" → "T"
  store_codon : String  -- "CTU" → "C"
  foam_codon : String   -- "GCU" → "G"

def defaultShortCodonMap : ShortCodonMap :=
  { start_codon := "A", stop_codon := "T", store_codon := "C", foam_codon := "G" }

def encodeCodon (map : ShortCodonMap) (codon : String) : String :=
  if codon = "ATG" then map.start_codon
  else if codon = "TAA" then map.stop_codon
  else if codon = "CTU" then map.store_codon
  else if codon = "GCU" then map.foam_codon
  else codon  -- Standard 3-char encoding
```

### Theorems

```lean
/-- Theorem: Short codon encoding reduces length -/
theorem shortCodonReducesLength (map : ShortCodonMap) (codon : String) :
    (encodeCodon map codon).length ≤ codon.length := by
  sorry  -- Proof requires case analysis on codon patterns

/-- Theorem: Encoding is injective for known codons -/
theorem encodingInjective (map : ShortCodonMap) (c1 c2 : String) :
    encodeCodon map c1 = encodeCodon map c2 →
    c1 ∈ ["ATG", "TAA", "CTU", "GCU"] →
    c2 ∈ ["ATG", "TAA", "CTU", "GCU"] →
    c1 = c2 := by
  sorry  -- Proof requires injectivity verification
```

---

## Combined Delta GCL Metaprobe

### Full Algorithm

```lean
def encodeToDeltaGCL (manifest : GCLManifest) (previous : Option GCLManifest) : String :=
  let delta := computeDelta manifest previous
  let ptosBytes := applyPTOSDictionary defaultPTOSDictionary manifest
  let ptosHex := ByteArray.toHex ptosBytes
  let deltaMarker := if delta.has_delta then "D" else "F"
  let fieldCodes := if delta.has_delta
    then delta.changed_fields.map (λ f => String.hash f % 8 |> toString) |> String.join ""
    else ""
  deltaMarker ++ ptosHex ++ fieldCodes

def decodeFromDeltaGCL (sequence : String) (previous : Option GCLManifest) : GCLManifest :=
  let deltaMarker := sequence.get 0
  let isDelta := deltaMarker = 'D'
  let ptosHex := sequence.substring 1 8
  let ptosBytes := ByteArray.fromHex ptosHex
  let manifest := decodePTOSDictionary defaultPTOSDictionary ptosBytes
  if isDelta then
    let fieldCodes := sequence.substring 9 sequence.length
    applyDelta manifest previous fieldCodes
  else
    manifest
```

### Theorems

```lean
/-- Theorem: Round-trip encoding preserves manifest -/
theorem roundTripPreserves (manifest : GCLManifest) (previous : Option GCLManifest) :
    decodeFromDeltaGCL (encodeToDeltaGCL manifest previous) previous = manifest := by
  sorry  -- Proof requires verification of all three layers

/-- Theorem: Delta encoding reduces size for similar states -/
theorem deltaReducesSize (current previous : GCLManifest) :
    (computeDelta current previous).has_delta →
    (encodeToDeltaGCL current previous).length < (encodeToDeltaGCL current none).length := by
  sorry  -- Proof requires length comparison analysis
```

---

## Domain-Gated Verification for GCL Diff

### Claim Type Classification

| Domain | Validator | Evidence Required |
|--------|-----------|------------------|
| **Compression ratio claims** | SI compression ratio (original/compressed), corpus provenance, baseline against standard codecs | Named corpus, file sizes, compression times |
| **Round-trip correctness** | Lean theorem proof, `#eval` witnesses | Theorem statement, proof term, lake build evidence |
| **Algorithmic complexity** | Complexity argument, benchmark against named baseline | Named workload, timing measurements |
| **Hardware extraction** | Verilog synthesis evidence, FPGA timing closure | Synthesis report, timing analysis |

### Critical Boundary

**Sigma does NOT apply to compression claims.**

- **DO use:** SI compression ratio (original/compressed bytes), baseline comparison against zlib/gzip/brotli/zstd, corpus provenance, file sizes, compression times
- **DO NOT use:** Sigma thresholds for compression ratio claims (sigma is for statistical detection/model selection only)

### Example Evidence Requirements

**Compression Claim:**
```
[BEAUTIFUL_PROVISIONAL - 92% reduction from 117 bases to 9 characters - requires baseline comparison evidence with corpus provenance and SI standard compression ratio]

Current State: Theoretical calculation from Lean #eval witnesses (compressionRatio 117 9 = 13.0, reductionPercent 117 9 = 0.923).
Corpus Provenance: 581 Lean files, 4,914,200 bytes total (measured with bash: find . -name "*.lean" -exec du -b {} +)
Theoretical Compressed Size: 4,914,200 / 13 = 378,015 bytes (92.3% reduction)
Missing: Baseline comparison against zlib/gzip/brotli/zstd on real corpus with file sizes and compression times.
```

**Round-Trip Claim:**
```
[REVIEWED - Round-trip encoding preserves manifest - requires Lean theorem verification evidence]

Current State: Theorems in DeltaGCLBenchmark.lean prove constant size functions (deltaGCLSize = 9, baselineGCLSize = 117).
Missing: Theorem proving round-trip encoding/decoding preserves manifest semantics.
```

**Hardware Claim:**
```
[CALIBRATED_ENGINEERING_DELTA - Delta encoder synthesizes to 45 LUTs on Xilinx 7-series - requires Verilog synthesis evidence with corpus provenance]
```

---

## Performance Characteristics

### Compression Ratios (Theoretical)

**Note:** These are theoretical calculations from Lean #eval witnesses. Actual compression ratios on real corpus data require baseline comparison evidence.

| Data Type | Baseline | Delta GCL | Reduction | Evidence Status |
|-----------|----------|----------|-----------|----------------|
| Sequential messages | 117 bases | 9 chars | 92% | Theoretical, awaiting baseline comparison |
| Lean metadata | 4.1MB | 4KB | 99.9% | Theoretical, awaiting baseline comparison |
| WebRTC actions (10K) | 50MB | 90KB | 99.8% | Theoretical, awaiting baseline comparison |
| Resource metrics | Variable | 9 chars | 92% | Theoretical, awaiting baseline comparison |

### Time Complexity

- **Encoding:** O(n) where n = number of fields
- **Decoding:** O(n) where n = number of fields
- **Delta computation:** O(n) where n = number of fields
- **Dictionary lookup:** O(1) using hash map

### Space Complexity

- **Encoder state:** O(k) where k = dictionary size (~100 entries)
- **Previous state:** O(n) where n = number of fields
- **Compressed output:** O(1) constant (9-15 chars)

---

## Integration Patterns

### Message Queue Integration

```lean
-- Producer side
def encodeMessageStream (messages : List GCLManifest) : List String :=
  let encoder := defaultDeltaGCLEncoder
  messages.foldl (λ acc m =>
    let previous := acc.getLast?
    let gcl := encodeToDeltaGCL m previous
    acc ++ [gcl]) []

-- Consumer side
def decodeMessageStream (gclSequences : List String) : List GCLManifest :=
  let decoder := defaultDeltaGCLEncoder
  gclSequences.foldl (λ acc g =>
    let previous := acc.getLast?
    let manifest := decodeFromDeltaGCL g previous
    acc ++ [manifest]) []
```

### Database Integration

```lean
-- Store compressed metadata
def storeCompressedMetadata (records : List DatabaseRecord) : Unit :=
  records.forall λ r =>
    let manifest := extractManifest r
    let gcl := encodeToDeltaGCL manifest none
    database.insert r.id gcl

-- Retrieve and decompress
def retrieveCompressedMetadata (ids : List RecordId) : List GCLManifest :=
  ids.map λ id =>
    let gcl := database.get id
    decodeFromDeltaGCL gcl none
```

---

## Verification Standards

### Per-Claim Evidence Requirements

**Compression Claims:**
- [ ] SI compression ratio (original/compressed bytes)
- [ ] Baseline against standard codecs (zlib/gzip/brotli/zstd)
- [ ] Corpus provenance (file sizes, compression times)
- [ ] Reproducibility package

**Round-Trip Correctness:**
- [ ] Lean theorem statement with proof term
- [ ] `lake build` passes with zero warnings
- [ ] No `sorry` in committed code (or documented TODO)
- [ ] `#eval` witness for encoding/decoding

**Hardware Extraction:**
- [ ] Verilog synthesis evidence
- [ ] FPGA timing closure report
- [ ] LUT/FF utilization metrics
- [ ] Hardware provenance documented

---

## Current GCL Diff Metaprobe Modules

### Core Compression
- `DeltaGCLCompression.lean` — Delta GCL compression algorithms
- `GCLFieldEquationsMetaprobe.lean` — GCL field equations

### Related Modules
- `QuantizationMetaprobe.lean` — Quantization analysis for compression
- `InfoThermodynamicsMetaprobe.lean` — Information thermodynamics

---

## Success Criteria

### Correctness Metrics
- **Lean Compilation:** 100% success rate
- **Theorem Proving:** All theorems prove without `sorry` in main path
- **Round-Trip:** 100% manifest preservation
- **Verification:** Domain-appropriate evidence for all claims

### Performance Metrics
- **Compression Ratio:** ≥90% reduction for sequential data
- **Encoding Time:** O(n) complexity with small constant factor
- **Decoding Time:** O(n) complexity with small constant factor
- **Memory:** O(k) encoder state (k = dictionary size)

### Integration Metrics
- **Code Coverage:** ≥90% for compression algorithms
- **Feature Flags:** All layers independently controllable
- **Rollback:** Original code paths retained for 3 months
- **Testing:** Unit tests + integration tests + benchmarks

---

## References

- **AGENTS.md v2.1** — Anti-Drift Evidence Standards
- **DELTA_GCL_COMPRESSION_LANGUAGE_AGNOSTIC.md** — Complete specification
- **DeltaGCLCompression.lean** — Lean source of truth (specification and implementation)
- **scripts/delta_gcl_encoder.py** — Python extraction shim (I/O harness against the Lean spec)

---

**End of Document**