Research-Stack/6-Documentation/docs/pist_gcl_compression_validation_plan.md

PIST-GCL Compression Algorithm Validation Plan

Version: 2.0
Date: 2026-05-31
File Under Validation: /home/allaun/Research Stack/5-Applications/pist-scripts/pist_gcl_compression.py

---

Executive Summary

This validation plan documents comprehensive testing procedures for the PIST-GCL (PIST Geometry + Cognitive Load) manifold compression algorithm. The algorithm implements a 4-layer architecture combining number-theoretic geometry (PIST), cognitive load routing, variable-length delta encoding with PTOS dictionary, and thermodynamic verification.

Key Claim: The algorithm achieves lossless roundtrip compression with thermodynamic compliance (dS/dt ≤ 0) across 12 diverse test cases.

---

1. Core Component Analysis

1.1 PIST Encoding Functions

Location: Lines 38-64

Function	Purpose	Formula
pist_encode(n: int) -> tuple	Encode byte → (shell, offset)	k = ⌊√n⌋, t = n - k²
pist_decode(k: int, t: int) -> int	Decode coordinates back to byte	n = k² + t
pist_mass(k: int, t: int) -> int	Compute PIST mass	mass = t·(2k+1-t)
pist_normalized_tension(k, t) -> float	Normalized phase indicator	ρ = t/(2k+1)
pist_phase(k, t) -> str	Phase classification	grounded if mass=0, else seismic

Validation Requirements:

1. Verify formula mass = t·(2k+1-t) for all 256 byte values (0-255)
2. Confirm grounded bytes (perfect squares: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225) have mass=0
3. Verify maximum mass occurs at shell midpoint (t ≈ k+0.5)
4. Confirm pist_mirror(k, t) = (k, 2k+1-t) preserves mass

---

1.2 Cognitive Load Functions

Location: Lines 73-131

Function	Purpose
intrinsic_load(data: bytes) -> float	Shannon entropy: L_I = -Σ p·log₂(p)
extraneous_load_bpb(data: bytes) -> float	BPB penalty: L_E = max(0, BPB - optimal)
germane_load(L_E, trust=0.5, S=10) -> float	Learning from experience
surprise_metric(mi_actual, mi_predicted) -> float	Triggers learning

HomeostaticCanal Class:

• Adaptive threshold: threshold = 0.3 + 2.0·pressure (0.3 to 20.3)
• Canal width: λ_t = λ₀·(σ + (1-σ)·e^{-ξ·p_t})
• Pressure update: p_{t+1} = 0.95·p_t + (0.6·surprise + 0.4·regret)

---

1.3 Dictionary and Entropy Coding

Location: Lines 139-248

PTOSDictionary Class:

• 8-entry initial dictionary + learned entries (up to 256)
• 4-byte code format: 0x41534D00 | i
• Methods: lookup(quad), learn(quad)

HuffmanCoder Class:

• Static Huffman tree from byte frequencies
• Methods: build(data), encode(data), decode(data)
• Stores padding count in last byte

---

1.4 Compression Pipeline

Location: Lines 362-835

PISTGCLCompressor Class Architecture:

Layer 0: PIST Remap
  └─ bytes → (shell, offset, mass, tension, phase)

Layer 1: Cognitive Route
  ├─ Compute L_I (intrinsic load)
  ├─ Compute L_E (extraneous load via BPB)
  ├─ Update canal pressure
  └─ Route/drop based on mass/tension

Layer 2a: Variable-Length Delta Encoding
  ├─ RLE for consecutive identical (shell, mass) pairs
  ├─ 1-byte: coarse deltas (5-bit shell + 3-bit mass)
  ├─ 2-byte: medium deltas (8-bit shell + 12-bit mass)
  └─ 3-byte: wide deltas (16-bit shell + 16-bit mass)

Layer 2b: PTOS + VLE + Huffman
  ├─ PTOS dictionary lookup on 4-byte quads
  ├─ VLE encoding (0xFE=multi, 0xFF=escape)
  └─ Huffman entropy coding

Layer 3: Thermodynamic Verify
  ├─ Compute dS = S_out - S_in
  ├─ Verify dS ≤ threshold (relaxed for small blocks)
  └─ Compute Landauer bound

Compression Header Format:

[orig_len:4 bytes][routed_count:2 bytes][dropped:2 bytes]

RLE Format:

0xFD + shell(1) + mass(1) + count(1)

---

2. Component-Level Validation Tests

2.1 PIST Encoding Validation

Test File: test_pist_encoding.py

def test_pist_mass_formula():
    """Verify mass = t·(2k+1-t) for all 256 byte values."""
    failures = []
    for n in range(256):
        k, t = pist_encode(n)
        expected_mass = t * (2 * k + 1 - t)
        actual_mass = pist_mass(k, t)
        if expected_mass != actual_mass:
            failures.append((n, k, t, expected_mass, actual_mass))
    
    assert len(failures) == 0, f"Mass formula failures: {failures}"
    
    # Verify grounded bytes (perfect squares)
    perfect_squares = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225]
    for n in perfect_squares:
        k, t = pist_encode(n)
        assert pist_mass(k, t) == 0, f"Grounded byte {n} has non-zero mass"
    
    # Verify mirror preserves mass
    for n in range(256):
        k, t = pist_encode(n)
        m1 = pist_mass(k, t)
        k2, t2 = pist_mirror(k, t)
        m2 = pist_mass(k2, t2)
        assert m1 == m2, f"Mirror fails for {n}: {m1} != {m2}"

Expected Results:

• All 256 bytes encode/decode correctly
• 16 grounded bytes (perfect squares) have mass=0
• Mirror involution preserves mass for all bytes

---

2.2 Delta Encoding Validation

Test File: test_delta_encoding.py

RLE Validation:

def test_rle_two_byte_run_field():
    """Verify 2-byte run field handles runs ≥256 correctly."""
    compressor = PISTGCLCompressor()
    
    # Create data with run > 255
    # Note: Current implementation uses 1-byte run field (max 255)
    # This is a known limitation that should be documented
    long_run_data = bytes([42] * 300)
    result = compressor.compress(long_run_data)
    
    # Verify compression works (may not hit RLE if routed bytes differ)
    decompressed = compressor.decompress(result['compressed'])
    assert decompressed == long_run_data, "RLE roundtrip failed"

Note: The current RLE implementation uses a 1-byte run field (max 255). For runs ≥256, the implementation will create multiple RLE markers.

---

2.3 Cognitive Routing Validation

Test File: test_cognitive_routing.py

def test_cognitive_route_routed_count():
    """Verify routing logic and routed count."""
    compressor = PISTGCLCompressor()
    
    # High entropy data should route more bytes
    random_data = bytes([i % 256 for i in range(256)])
    coords = compressor._pist_remap_block(random_data)
    routed, dropped, stats = compressor._cognitive_route(coords)
    assert stats['routed'] > 0, "No bytes routed for random data"
    assert stats['total'] == len(coords), "Total count mismatch"
    
    # Low entropy data may drop more (grounded/low-tension)
    zero_data = bytes(200)
    coords = compressor._pist_remap_block(zero_data)
    routed, dropped, stats = compressor._cognitive_route(coords)
    # Grounded bytes (all zeros) should be dropped
    assert dropped > 0, "No bytes dropped for zero data"

Thermodynamic Validation:

def test_thermodynamic_compliance():
    """Verify dS/dt ≤ 0 for real compression."""
    compressor = PISTGCLCompressor()
    
    # High entropy data should compress well
    random_data = bytes([i % 256 for i in range(1024)])
    result = compressor.compress(random_data)
    stats = result['stats']
    
    # dS/dt should be ≤ threshold (relaxed for small blocks)
    dS_dt = stats['dS/dt']
    if len(random_data) < 100:
        assert dS_dt <= 2.0, f"dS/dt exceeds threshold: {dS_dt}"
    else:
        assert dS_dt <= 1.0, f"dS/dt exceeds threshold: {dS_dt}"
    
    # Landauer bound should be positive
    assert stats['landauer_bound_J'] >= 0, "Negative Landauer bound"

---

2.4 PTOS Dictionary Validation

Test File: test_ptos_dictionary.py

def test_ptos_dictionary_lookup():
    """Verify PTOS dictionary lookup and learning."""
    ptos = PTOSDictionary()
    
    # Initial entries should be found
    initial_quad = b'\x00\x00\x00\x00'
    code = ptos.lookup(initial_quad)
    assert code != initial_quad, "Initial entry not found"
    
    # Learned entries should be added
    new_quad = b'\xAB\xCD\xEF\x12'
    ptos.learn(new_quad)
    code = ptos.lookup(new_quad)
    assert code != new_quad, "Learned entry not found"
    assert len(ptos.entries) <= 256, "Dictionary exceeds max size"

---

2.5 Huffman Coding Validation

Test File: test_huffman_coding.py

def test_huffman_roundtrip():
    """Verify Huffman encode/decode roundtrip."""
    coder = HuffmanCoder()
    
    test_data = bytes([0, 1, 2, 3, 4, 5, 6, 7] * 16)
    
    # Build and encode
    coder.build(test_data)
    encoded = coder.encode(test_data)
    
    # Decode
    decoded = coder.decode(encoded)
    
    assert decoded == test_data, "Huffman roundtrip failed"
    assert len(encoded) <= len(test_data), "Huffman expansion on compressible data"

---

3. Roundtrip Validation Tests (All 12 Test Cases)

Test File: test_roundtrip_all_cases.py

3.1 Test Case Specifications

#	Test Case	Size	Pattern	Expected Behavior
1	English text	356 bytes	ASCII text	Moderate compression, some routed bytes
2	Zero block	200 bytes	All \x00	High compression, all grounded
3	Uniform random	1024 bytes	0-255 repeat	Low compression, high entropy
4	Periodic AB	256 bytes	AB×128	High compression, low entropy
5	Periodic ABC	255 bytes	ABC×85	High compression, low entropy
6	Rising sawtooth	512 bytes	i%256	Moderate compression, sequential pattern
7	Low entropy ramp	128 bytes	0..127	Moderate compression, monotonic
8	Binary bitmask	256 bytes	0xFF if i%3==0	Moderate compression, sparse
9	Pattern 0x00-0x07	256 bytes	i%8	High compression, 3-bit pattern
10	All same byte	200 bytes	\x42×200	High compression, RLE ideal
11	Empty bytes	0 bytes	Edge case	Minimal header
12	Single byte	1 byte	Edge case	Minimal header + byte

3.2 Roundtrip Test Implementation

def test_roundtrip_all_cases():
    """Test roundtrip for all 12 cases."""
    compressor = PISTGCLCompressor()
    
    test_cases = [
        ("English text", b'Hello, World! This is a test of the PIST-GCL manifold compression algorithm. '
                         b'The algorithm uses PIST geometry (hyperbolic shell coordinates from number theory), '
                         b'cognitive load routing (BPB-aware adaptation via homeostatic control), '
                         b'and thermodynamic verification (Landauer limit, dS/dt <= 0). '
                         b'This demonstrates cross-domain compression on natural language.'),
        ("Zero block", b'\x00' * 200),
        ("Uniform random", bytes(range(256)) * 4),
        ("Periodic AB", b'AB' * 128),
        ("Periodic ABC", b'ABC' * 85),
        ("Rising sawtooth", bytes(i % 256 for i in range(512))),
        ("Low entropy ramp", bytes(i for i in range(128))),
        ("Binary bitmask", bytes(0xFF if i % 3 == 0 else 0x00 for i in range(256))),
        ("Pattern 0x00-0x07", bytes(i % 8 for i in range(256))),
        ("All same byte", b'\x42' * 200),
        ("Empty bytes", b''),
        ("Single byte", b'\x42'),
    ]
    
    results = []
    for name, data in test_cases:
        result = compressor.compress(data)
        decompressed = compressor.decompress(result['compressed'])
        
        stats = result['stats']
        
        # Verify roundtrip
        roundtrip_ok = (decompressed == data)
        
        # Verify compression ratio >= 1.0
        ratio_ok = stats.get('ratio', 0) >= 1.0
        
        # Verify thermodynamic compliance
        dS_dt = stats.get('dS/dt', 0)
        threshold = 2.0 if len(data) < 100 else 1.0
        thermodynamic_ok = dS_dt <= threshold
        
        # Verify routed count
        routed_count_ok = stats.get('routed_count', 0) >= 0
        
        # Verify verified flag
        verified_ok = result['verified'] in [True, False]
        
        results.append({
            'name': name,
            'original_size': len(data),
            'compressed_size': stats.get('compressed_size', 0),
            'ratio': stats.get('ratio', 0),
            'dS_dt': dS_dt,
            'routed_count': stats.get('routed_count', 0),
            'dropped': stats.get('dropped', 0),
            'roundtrip_ok': roundtrip_ok,
            'ratio_ok': ratio_ok,
            'thermodynamic_ok': thermodynamic_ok,
            'routed_count_ok': routed_count_ok,
            'verified_ok': verified_ok,
        })
        
        status = "PASS" if all([
            roundtrip_ok, ratio_ok, thermodynamic_ok, 
            routed_count_ok, verified_ok
        ]) else "FAIL"
        
        print(f"{status} {name:20s} orig={len(data):4d} cmp={stats.get('compressed_size', 0):4d} "
              f"ratio={stats.get('ratio', 0):5.2f}x dS={dS_dt:+6.3f} routed={stats.get('routed_count', 0):4d}")
    
    # Summary
    all_pass = all(r['roundtrip_ok'] and r['ratio_ok'] for r in results)
    print(f"\n{'ALL TESTS PASS' if all_pass else 'SOME TESTS FAILED'}")
    
    return results

---

4. Concurrent Compression Validation

Test File: test_concurrent_compression.py

4.1 Thread-Safety Requirements

The concurrent_compress() method (not yet implemented in the file) must:

1. Split data into chunks
2. Create fresh PTOSDictionary() and HuffmanCoder() per chunk (via copy.deepcopy(self))
3. Compress chunks in parallel
4. Merge results in order via as_completed

4.2 Implementation Template

import copy
import concurrent.futures

def concurrent_compress(self, data: bytes, num_workers: int = 4) -> dict:
    """
    Thread-safe concurrent compression.
    Each chunk gets fresh PTOSDictionary and HuffmanCoder via deepcopy.
    """
    if not data:
        return {'compressed': b'\x00\x00\x00\x00', 'stats': {}, 'verified': True}
    
    # Split data into chunks
    chunk_size = max(1, len(data) // num_workers)
    chunks = []
    for i in range(0, len(data), chunk_size):
        chunks.append(data[i:i + chunk_size])
    
    # Compress chunks in parallel
    results = []
    with concurrent.futures.ThreadPoolExecutor(max_workers=num_workers) as executor:
        futures = {}
        for i, chunk in enumerate(chunks):
            # Create fresh compressor instance per chunk
            fresh_compressor = copy.deepcopy(self)
            futures[executor.submit(fresh_compressor.compress, chunk)] = i
        
        # Collect results in order
        ordered_results = [None] * len(chunks)
        for future in concurrent.futures.as_completed(futures):
            idx = futures[future]
            ordered_results[idx] = future.result()
    
    # Merge compressed data
    merged_compressed = b''.join(r['compressed'] for r in ordered_results)
    
    # Merge stats (simplified: sum sizes, average ratios)
    merged_stats = {
        'original_size': len(data),
        'compressed_size': len(merged_compressed),
        'ratio': len(data) / max(1, len(merged_compressed)),
        'chunks': len(chunks),
    }
    
    # Verify all chunks verified
    verified = all(r['verified'] for r in ordered_results)
    
    return {'compressed': merged_compressed, 'stats': merged_stats, 'verified': verified}

4.3 Thread-Safety Tests

def test_concurrent_thread_safety():
    """Verify concurrent compression produces same result as sequential."""
    original_data = bytes(range(256)) * 4  # 1024 bytes
    num_workers = 4
    
    # Sequential compression
    seq_compressor = PISTGCLCompressor()
    seq_result = seq_compressor.compress(original_data)
    
    # Concurrent compression
    conc_compressor = PISTGCLCompressor()
    conc_result = conc_compressor.concurrent_compress(original_data, num_workers)
    
    # Decompress and verify
    seq_decompressed = seq_compressor.decompress(seq_result['compressed'])
    conc_decompressed = conc_compressor.decompress(conc_result['compressed'])
    
    assert seq_decompressed == original_data, "Sequential roundtrip failed"
    assert conc_decompressed == original_data, "Concurrent roundtrip failed"
    assert seq_decompressed == conc_decompressed, "Concurrent differs from sequential"
    
    print("PASS: Concurrent compression thread-safe")


def test_concurrent_fresh_instances():
    """Verify each chunk gets fresh PTOSDictionary and HuffmanCoder."""
    data = bytes(range(256)) * 2
    
    with concurrent.futures.ThreadPoolExecutor(max_workers=2) as executor:
        results = list(executor.map(
            lambda chunk: PISTGCLCompressor().compress(chunk),
            [data[:256], data[256:]]
        ))
    
    # Verify both chunks compress correctly
    for i, result in enumerate(results):
        compressor = PISTGCLCompressor()
        decompressed = compressor.decompress(result['compressed'])
        assert decompressed == data[i*256:(i+1)*256], f"Chunk {i} roundtrip failed"
    
    print("PASS: Fresh instances per chunk")

---

5. Adaptive Precision Validation

Test File: test_adaptive_precision.py

5.1 Precision Modes

Mode	Delta Encoding	RLE	Use Case
High	2-3 bytes/coord	Conservative	High-entropy data
Medium	1-2 bytes	Balanced	Mixed entropy
Low	Coarse deltas	Aggressive	Low-entropy data

5.2 Auto Mode Implementation

def compress_adaptive(self, data: bytes, mode: str = 'auto') -> dict:
    """
    Adaptive precision compression.
    
    Modes:
    - 'high': Fine-grained deltas (2-3 bytes/coord)
    - 'medium': Balanced (1-2 bytes)
    - 'low': Coarse deltas + aggressive RLE
    - 'auto': Measure distribution and pick best
    """
    if mode == 'auto':
        # Measure distribution
        byte_freq = Counter(data)
        entropy = intrinsic_load(data)
        
        # Simple heuristic: low entropy → low precision
        if entropy < 4.0:
            mode = 'low'
        elif entropy < 6.0:
            mode = 'medium'
        else:
            mode = 'high'
    
    # Store mode for delta encoding
    self._precision_mode = mode
    
    return self.compress(data)

5.3 Adaptive Tests

def test_adaptive_precision_modes():
    """Test all precision modes."""
    test_cases = [
        ("Low entropy ramp", bytes(i for i in range(128)), 'low'),
        ("Periodic AB", b'AB' * 128, 'low'),
        ("Uniform random", bytes(range(256)) * 4, 'high'),
        ("English text", b'Hello World! ' * 20, 'medium'),
    ]
    
    for name, data, expected_mode in test_cases:
        compressor = PISTGCLCompressor()
        
        # Test specific mode
        result = compressor.compress_adaptive(data, mode=expected_mode)
        decompressed = compressor.decompress(result['compressed'])
        
        assert decompressed == data, f"{name} {expected_mode} mode roundtrip failed"
        
        # Verify compression ratio
        ratio = result['stats']['ratio']
        assert ratio >= 1.0, f"{name} {expected_mode} mode ratio < 1.0"
        
        print(f"PASS: {name} {expected_mode} mode ratio={ratio:.2f}x")


def test_auto_precision_selection():
    """Test auto mode selects appropriate precision."""
    test_cases = [
        ("Very low entropy", bytes([0, 1, 2, 3] * 100), 'low'),
        ("Low entropy", bytes(range(64)) * 4, 'low'),
        ("Medium entropy", bytes(range(128)) * 2, 'medium'),
        ("High entropy", bytes([i % 256 for i in range(1024)]), 'high'),
    ]
    
    for name, data, expected_mode in test_cases:
        compressor = PISTGCLCompressor()
        
        # Auto mode
        result = compressor.compress_adaptive(data, mode='auto')
        
        # Verify compression works
        decompressed = compressor.decompress(result['compressed'])
        assert decompressed == data, f"{name} auto mode roundtrip failed"
        
        print(f"PASS: {name} auto mode selected")

---

6. Edge Case Validation

Test File: test_edge_cases.py

6.1 Edge Cases

Case	Input	Expected Behavior
Empty	b''	Header only, verified=True
Single byte	b'\x42'	Minimal header + data
All zeros	b'\x00' * 1024	All grounded, high compression
All same	b'\xFF' * 1024	Low entropy, good compression
Max values	bytes(range(256))	High entropy, poor compression

6.2 Edge Case Tests

def test_edge_cases():
    """Test edge cases."""
    compressor = PISTGCLCompressor()
    
    edge_cases = [
        ("Empty", b''),
        ("Single byte", b'\x42'),
        ("Two bytes", b'\x00\xFF'),
        ("All zeros 1KB", b'\x00' * 1024),
        ("All same 1KB", b'\xFF' * 1024),
        ("Max values", bytes(range(256))),
        ("Max values x4", bytes(range(256)) * 4),
    ]
    
    for name, data in edge_cases:
        result = compressor.compress(data)
        decompressed = compressor.decompress(result['compressed'])
        
        # Verify roundtrip
        assert decompressed == data, f"{name} roundtrip failed"
        
        # Verify stats
        stats = result['stats']
        assert stats['original_size'] == len(data), f"{name} size mismatch"
        assert stats['ratio'] >= 1.0, f"{name} ratio < 1.0"
        
        # Verify verified flag
        assert result['verified'] in [True, False], f"{name} invalid verified flag"
        
        print(f"PASS: {name} orig={len(data):4d} cmp={stats['compressed_size']:4d} ratio={stats['ratio']:.2f}x")

---

7. Performance and Scalability Validation

Test File: test_performance.py

7.1 Performance Metrics

Metric	Target	Notes
Roundtrip correctness	100%	All data must reconstruct
Compression ratio	≥1.0	No expansion on compressible data
dS/dt ≤ threshold	100%	Thermodynamic compliance
Memory usage	O(n)	Linear in input size
Thread safety	Verified	Concurrent produces same result

7.2 Performance Tests

def test_performance_scalability():
    """Test compression performance across sizes."""
    import time
    
    compressor = PISTGCLCompressor()
    
    sizes = [16, 64, 256, 1024, 4096, 16384, 65536]
    
    print(f"{'Size':>8} {'Time (ms)':>12} {'Ratio':>8} {'dS/dt':>8}")
    print("-" * 40)
    
    for size in sizes:
        data = bytes([i % 256 for i in range(size)])
        
        t0 = time.time()
        result = compressor.compress(data)
        t1 = time.time()
        
        decompressed = compressor.decompress(result['compressed'])
        t2 = time.time()
        
        assert decompressed == data, f"Roundtrip failed for size {size}"
        
        elapsed_compress = (t1 - t0) * 1000
        elapsed_decompress = (t2 - t1) * 1000
        ratio = result['stats']['ratio']
        dS_dt = result['stats']['dS/dt']
        
        print(f"{size:>8} {elapsed_compress:>10.2f} {ratio:>8.2f}x {dS_dt:>+7.3f}")
    
    print("\nPASS: Performance scalability verified")

---

8. Validation Checklist

8.1 Component Validation

• PIST mass formula verified for all 256 bytes
• PIST encoding/decoding roundtrip verified
• Mirror involution preserves mass
• Grounded bytes (perfect squares) have mass=0
• Cognitive load functions compute correctly
• Homeostatic canal state updates properly
• PTOS dictionary lookup/learn works
• Huffman encode/decode roundtrip works
• Delta encoding handles all three precision modes
• RLE handles runs up to 255
• VLE encoding/decoding works

8.2 Roundtrip Validation

• English text (356 bytes) roundtrip
• Zero block (200 bytes) roundtrip
• Uniform random (1024 bytes) roundtrip
• Periodic AB (256 bytes) roundtrip
• Periodic ABC (255 bytes) roundtrip
• Rising sawtooth (512 bytes) roundtrip
• Low entropy ramp (128 bytes) roundtrip
• Binary bitmask (256 bytes) roundtrip
• Pattern 0x00-0x07 (256 bytes) roundtrip
• All same byte (200 bytes) roundtrip
• Empty bytes edge case
• Single byte edge case

8.3 Thermodynamic Validation

• dS/dt ≤ threshold for all test cases
• Landauer bound computed correctly
• Compression ratio ≥ 1.0 for all cases

8.4 Concurrent Validation

• Thread-safe concurrent compression
• Fresh PTOSDictionary per chunk
• Fresh HuffmanCoder per chunk
• Results merge in order via as_completed

8.5 Adaptive Precision Validation

• High precision mode works
• Medium precision mode works
• Low precision mode works
• Auto mode selects appropriate precision

8.6 Edge Case Validation

• Empty input handled
• Single byte handled
• All zeros handled
• All same byte handled
• Max values handled

---

9. Expected Results Summary

9.1 Compression Ratios (Expected)

Test Case	Expected Ratio	Notes
English text	1.2-1.5x	Moderate compression
Zero block	10-20x	All grounded bytes dropped
Uniform random	0.8-1.0x	Near Shannon limit
Periodic AB	5-10x	High pattern redundancy
Periodic ABC	5-10x	High pattern redundancy
Rising sawtooth	1.5-2.0x	Sequential pattern
Low entropy ramp	2-3x	Monotonic pattern
Binary bitmask	2-3x	Sparse pattern
Pattern 0x00-0x07	3-5x	3-bit pattern
All same byte	10-20x	Ideal RLE case
Empty	1.0x	Edge case
Single byte	1.0x	Overhead dominates

9.2 Thermodynamic Compliance

All test cases should satisfy:

• dS/dt ≤ 2.0 for blocks < 100 bytes
• dS/dt ≤ 1.0 for blocks ≥ 100 bytes
• Landauer_bound_J ≥ 0

9.3 Verified Flag

All successful roundtrips should set verified=True. Small blocks may have relaxed thresholds.

---

10. Known Limitations

10.1 RLE Run Field

Issue: Current RLE uses 1-byte run field (max 255).

Impact: Runs ≥256 create multiple RLE markers.

Mitigation: Document limitation; consider 2-byte run field for future version.

10.2 Delta Decoding Approximation

Issue: Variable-length delta decoding may approximate values.

Impact: Small rounding errors possible for large deltas.

Mitigation: Verify roundtrip for all test cases; document if approximation occurs.

10.3 Concurrent Compression

Issue: concurrent_compress() method not yet implemented.

Impact: No parallel compression support.

Mitigation: Implement per Section 4.2; add thread-safety tests.

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11. Validation Execution Plan

Phase 1: Component Tests (1-2 hours)

• Run test_pist_encoding.py
• Run test_delta_encoding.py
• Run test_cognitive_routing.py
• Run test_ptos_dictionary.py
• Run test_huffman_coding.py

Phase 2: Roundtrip Tests (30 minutes)

• Run test_roundtrip_all_cases.py
• Verify all 12 test cases pass
• Document any failures

Phase 3: Thermodynamic Tests (30 minutes)

• Run thermodynamic compliance tests
• Verify dS/dt ≤ threshold
• Verify Landauer bounds

Phase 4: Concurrent Tests (1 hour)

• Implement concurrent_compress() per Section 4.2
• Run thread-safety tests
• Verify ordered results

Phase 5: Adaptive Tests (30 minutes)

• Run adaptive precision tests
• Verify auto mode selection

Phase 6: Edge Case Tests (30 minutes)

• Run edge case tests
• Verify all edge cases handled

Phase 7: Performance Tests (1 hour)

• Run scalability tests
• Measure compression/decompression speed
• Document performance characteristics

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12. Success Criteria

The PIST-GCL compression algorithm is validated when:

1. Roundtrip Correctness: All 12 test cases pass roundtrip verification
2. Compression Ratio: All ratios ≥ 1.0 (no expansion on compressible data)
3. Thermodynamic Compliance: dS/dt ≤ threshold for 100% of test cases
4. Thread Safety: Concurrent compression produces identical results to sequential
5. Edge Cases: All edge cases (empty, single byte, max values) handled correctly

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13. References

1. PIST Geometry: mass = t·(2k+1-t) — hyperbolic shell coordinate system
2. Cognitive Load: L_I = -Σ p·log₂(p), L_E = BPB - optimal
3. Homeostatic Canal: λ_t = λ₀·(σ + (1-σ)·e^{-ξ·p_t})
4. Thermodynamic: dS/dt ≤ 0, Landauer bound W ≥ N·k_B·T·ln(2)
5. PTOS Dictionary: 4-byte codec with learning
6. Huffman Coding: Static entropy coding backend

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Document Version: 1.0
Last Updated: 2026-05-31
Prepared By: Validation Planning System
Status: Ready for Execution