Video Analysis with GF(3) Conservation

Trit: 0 (ERGODIC - coordination across triadic streams) GF(3): Σ(-1,0,+1) = 0 (conserved)

Analyze video files from chaotic_media_lake.duckdb with deterministic color assignment and GF(3)-balanced trit allocation.

Overview

This skill bridges video content analysis with the GF(3) conservation framework:

• Videos assigned trits based on path hash with quota balancing
• Triadic analysis: motion (-1), static (0), transition (+1)
• Random access via

  color_at(seed, index)

  for parallel frame extraction
• Conservation verified:

  Σ trit_i ≡ 0 (mod 3)

DuckLake Integration

-- Query videos by trit class
SELECT chaotic_id, filename, color_hex, trit 
FROM chaotic_files 
WHERE extension IN ('.mov', '.mp4', '.MOV')
ORDER BY trit;

-- Verify GF(3) conservation
SELECT SUM(trit) as gf3_sum FROM chaotic_files;  -- Must be 0

Triadic Video Classification

Frame Extraction with SPI

def extract_frames_spi(video_path: str, seed: int, n_frames: int):
    """Extract frames at deterministic positions using SplitMix64"""
    import cv2
    GOLDEN = 0x9e3779b97f4a7c15
    MASK64 = 0xFFFFFFFFFFFFFFFF
    
    cap = cv2.VideoCapture(video_path)
    total_frames = int(cap.get(cv2.CAP_PROP_FRAME_COUNT))
    
    frames = []
    for i in range(n_frames):
        # Random access formula: seed + (i+1) * GOLDEN
        state = (seed + (i + 1) * GOLDEN) & MASK64
        frame_idx = state % total_frames
        cap.set(cv2.CAP_PROP_POS_FRAMES, frame_idx)
        ret, frame = cap.read()
        if ret:
            frames.append((frame_idx, frame))
    
    cap.release()
    return frames

Usage Workflow

1. Query Videos by Trit Class

duckdb chaotic_media_lake.duckdb "
  SELECT original_path, color_hex, trit 
  FROM chaotic_files 
  WHERE extension = '.mov' AND trit = -1
"

2. Analyze with Gemini Vision

# Use Gemini 2.0 Flash for video understanding
from google import genai

client = genai.Client()
response = client.models.generate_content(
    model="gemini-2.0-flash",
    contents=[
        {"video": video_path},
        {"text": f"Analyze this video. Assigned trit: {trit}, color: {color_hex}"}
    ]
)

3. Store Analysis Results

ALTER TABLE chaotic_files ADD COLUMN IF NOT EXISTS analysis_summary TEXT;
ALTER TABLE chaotic_files ADD COLUMN IF NOT EXISTS motion_score FLOAT;
ALTER TABLE chaotic_files ADD COLUMN IF NOT EXISTS analyzed_at TIMESTAMP;

UPDATE chaotic_files 
SET analysis_summary = ?, motion_score = ?, analyzed_at = NOW()
WHERE chaotic_id = ?;

Conservation Properties

Full Lake: GF(3) conserved (Σ = 0) ✓ Video Subset: May have local imbalance (currently +4)

The full lake is balanced; subsets (like videos only) inherit the global conservation but may have local bias. For video-only operations, use compensating "virtual trits":

-- Find compensating files from other extensions
SELECT filename, trit FROM chaotic_files 
WHERE trit = -1 AND extension NOT IN ('.mov', '.mp4', '.MOV')
LIMIT 4;  -- Compensate +4 excess in videos

Conservation Verification

After any batch operation, verify GF(3) conservation:

def verify_gf3(db_path: str) -> bool:
    import duckdb
    con = duckdb.connect(db_path)
    result = con.execute("SELECT SUM(trit) FROM chaotic_files").fetchone()
    return result[0] == 0

Parallel Analysis Protocol

For triadic parallel analysis, spawn 3 workers:

def triadic_analyze(videos: list, master_seed: int):
    """Analyze videos in 3 parallel streams, one per trit class"""
    from concurrent.futures import ProcessPoolExecutor
    
    streams = {-1: [], 0: [], 1: []}
    for v in videos:
        streams[v['trit']].append(v)
    
    with ProcessPoolExecutor(max_workers=3) as executor:
        futures = {
            executor.submit(analyze_stream, streams[-1], master_seed, -1): -1,
            executor.submit(analyze_stream, streams[0], master_seed, 0): 0,
            executor.submit(analyze_stream, streams[1], master_seed, 1): +1,
        }
        # Results combine with GF(3) conservation maintained

MCP Tools Integration

Use gay-mcp tools for color operations:

• mcp__gay__color_at

  - O(1) random access to color sequence

• mcp__gay__interleave

  - Generate 3 parallel streams for triadic analysis

• mcp__gay__reafference

  - Verify prediction matches observation

Database Schema

-- Core table (exists in chaotic_media_lake.duckdb)
CREATE TABLE chaotic_files (
    chaotic_id VARCHAR PRIMARY KEY,
    original_path VARCHAR,
    filename VARCHAR,
    extension VARCHAR,
    path_hash UBIGINT,
    gay_seed UBIGINT,
    color_hex VARCHAR,
    hue INTEGER,
    trit INTEGER,  -- GF(3) balanced: -1, 0, +1
    ingest_order INTEGER,
    shuffle_key UBIGINT,
    created_at TIMESTAMP,
    -- Analysis columns
    analysis_summary TEXT,
    motion_score FLOAT,
    keyframe_count INTEGER,
    dominant_colors VARCHAR[],
    analyzed_at TIMESTAMP
);

-- Conservation invariant
-- SELECT SUM(trit) FROM chaotic_files; -- Always 0

Scripts

triadic_video_analyzer.py

gemini_video_analyze.py

Quick Commands

# Summary of triadic distribution
python3 triadic_video_analyzer.py summary

# Analyze videos by trit class
python3 triadic_video_analyzer.py analyze -1  # VALIDATOR videos
python3 triadic_video_analyzer.py analyze 0   # ERGODIC videos
python3 triadic_video_analyzer.py analyze 1   # GENERATOR videos

# List videos for Gemini analysis
python3 gemini_video_analyze.py list

# Analyze specific video with Gemini
python3 gemini_video_analyze.py analyze <chaotic_id>

Google Workspace Integration

The skill bridges with Google Workspace MCP for cross-service operations:

Cross-Service Morphisms

Trit is preserved under service morphisms:

Video Analysis (+1) → Drive.upload (+1) → Calendar.review (+1)
                   → Gmail.summary (+1)
                   → Tasks.create (+1)

ANIMA Condensation

When all queues reach zero state (inbox zero, task zero, video queue empty), the system condenses into an equilibrium fingerprint:

if queue.check_condensation():
    print(queue.fingerprint())  # ANIMA-<hash>

Bridge Commands

python3 workspace_bridge.py balance   # Show GF(3) balance
python3 workspace_bridge.py morphism  # Demo cross-service morphism
python3 workspace_bridge.py plan      # Plan workspace actions

Formal Specifications

Hyperdoctrine 𝒫 : 𝒞ᵒᵖ → Posets

The shared predicates across Narya/Stellogen:

GF3Conserved

Σ trit_i ≡ 0 (mod 3)

Saturated

PathCommutative

AtFixedPoint

CondensedANIMA.nry (HOTT)

def GF3 : Type := data [ minus | zero | plus ]
def ward_identity : List GF3 → Prop := Σ = zero
def ANIMAState : traces × level × at_fixed_point
theorem video_workspace_closed : system_closure [video, workspace] ✓

CondensedANIMA.stg (Proof Nets)

+ward(A, B, C) :- add3(A, B, AB), add3(AB, C, zero).
*anima[+traces, -certificate].
?- system_closed → ✓

Resources

• DuckLake:

  /Users/bob/ies/chaotic_media_lake.duckdb

• Ingest Script:

  /Users/bob/ies/chaotic_ducklake_ingest.py

• SPI Verification:

  /Users/bob/ies/spi_mutual_verify.py

• Gay.jl: Deterministic color generation with SplitMix64
• Skill Dir:

  ~/.claude/skills/video-analysis-gf3/

• Narya Spec:

  CondensedANIMA.nry

• Stellogen Spec:

  CondensedANIMA.stg

Live Stream Processing Pipeline

Concurrent Real-Time Awareness Pattern

When processing YouTube live streams (past broadcasts):

1. Format Detection (trit: -1)

   uvx yt-dlp --list-formats "URL" | grep -E "^[0-9]+ "
   

2. Combined Format Download (trit: 0)

   # Format 18 (360p) most reliable for archived streams
   uvx yt-dlp -f 18 --ffmpeg-location "$FFMPEG_PATH" -o "video.%(ext)s" "URL"
   

3. Segment Extraction + Transcription (trit: +1)

   # Extract segment
   ffmpeg -i video.mp4 -ss START -to END -vn -acodec libmp3lame segment.mp3
   
   # MLX Whisper on Apple Silicon
   uv run --with mlx-whisper -- mlx_whisper segment.mp3 \
     --model mlx-community/whisper-large-v3-turbo \
     --output-dir . --output-format txt
   

Available Local MLX Models

• mlx-community/whisper-large-v3-mlx

  (2.9 GB) - highest quality

• mlx-community/whisper-large-v3-turbo

  - faster inference

• mlx-community/snowflake-arctic-embed-l-v2.0-8bit

  (592 MB) - embeddings

DuckDB Integration

-- Store transcript with video metadata
CREATE TABLE IF NOT EXISTS video_transcripts (
  video_id VARCHAR PRIMARY KEY,
  year INTEGER,
  title VARCHAR,
  has_auto_captions BOOLEAN,
  has_mlx_transcript BOOLEAN,
  transcript_path VARCHAR,
  model_used VARCHAR,
  processed_at TIMESTAMP DEFAULT CURRENT_TIMESTAMP
);

Autopoietic Marginalia

The interaction IS the skill improving itself.

Every use of this skill is an opportunity for worlding:

• MEMORY (-1): Record what was learned
• REMEMBERING (0): Connect patterns to other skills
• WORLDING (+1): Evolve the skill based on use

Add Interaction Exemplars here as the skill is used.