TIDAR Thread Probe Skill

Tree-structured Iterative Decomposition And Recombination for cross-system thread pattern discovery across AMP, Claude, Codex, and Warp.

Capability

Analyzes threads across multiple AI agent interaction surfaces using ordered locale site semantics:

1. Shared Patterns: Fields/behaviors present in ALL systems
2. Pairwise Patterns: Fields shared by exactly 2 systems
3. Unique Patterns: System-specific fields and behaviors
4. Perplexing Patterns: Anomalies, contradictions, mysteries

Ordered Locale vs Ordered Locale Sites

• Ordered Locale: Complete Heyting algebra (frame) L with compatible preorder ≤ satisfying open cone condition. Each thread lives in an ordered locale (its workspace/project).

• Ordered Locale Site: Grothendieck site on ordered locale with coverage relation J. Cross-system observation uses ordered locale sites where sheaves model behavioral coalgebra.

Thread Counts (as of 2025-12-26)

Source	Threads	Sessions	Messages
AMP	616	-	2,535 tool calls
Claude	-	236	36,057 messages
Codex	-	36+	~400 records
Total	888 canonical threads

Canonical Universal Schema

ATOMIC FIELDS (required):
  thread_id   : string  - unique session/thread identifier
  timestamp   : int64   - Unix ms (or ISO-8601 converted)
  workspace   : string  - absolute path to project/cwd
  role        : enum    - user|assistant|system|tool
  content     : string  - message text content

OPTIONAL ATOMIC:
  model       : string  - model identifier
  originator  : string  - source tool (amp, claude, codex)

DERIVED FIELDS:
  message_count    : COUNT(messages in thread)
  tool_call_count  : COUNT(tool invocations)
  acceptance_rate  : 1 - (reverted / total)
  trit             : GF(3) from hash(thread_id) mod 3 - 1
  role_semantic    : trit → {validator, coordinator, generator}

GF(3) Conservation Status

Current cross-system trit distribution:

• MINUS (-1): 284 threads
• ERGODIC (0): 288 threads
• PLUS (+1): 316 threads
• Σ trits = 32 (mod 3 = 2) → NOT CONSERVED

Need 1 more MINUS thread or 2 more ERGODIC threads to balance.

Usage

# Run TIDAR analysis
python3 src/universal_thread_schema.py

# Query specific source
duckdb trit_stream.duckdb -c "SELECT * FROM amp_threads LIMIT 10"
jq -s '.' ~/.claude/history.jsonl | head

Perplexing Patterns

1. AMP

   .org

   files have 45% revert rate vs 0% for .clj/.jl/.bb
2. AMP threads with 40+ hour durations but only 5-9 tool calls
3. Codex uses

   danger-full-access

   sandbox policy in production
4. Claude longest session: 841 messages in 182 seconds (4.6 msg/sec)
5. AMP bimodal acceptance: threads cluster at 0% or 100%
6. Codex embeds ~50KB instructions per session (redundant)
7. Claude

   pastedContents

   used in only 0.5% of entries

Source-Specific Mappings

AMP → Canonical

• thread_id → thread_id
• first_ts/last_ts → timestamp range
• uri → workspace (extracted)
• tool_id → tool invocation
• reverted → acceptance tracking

Claude → Canonical

• sessionId → thread_id
• timestamp → timestamp (already Unix ms)
• project → workspace
• display → content

Codex → Canonical

• payload.id → thread_id
• timestamp → timestamp (ISO-8601 → Unix ms)
• cwd → workspace
• message/content → content

Integration with Gay-MCP Colors

Each thread's trit determines its Gay-MCP hue:

• MINUS (-1): Cold hues (180-300°) - Blue/Violet spectrum
• ERGODIC (0): Neutral hues (60-180°) - Green/Cyan spectrum
• PLUS (+1): Warm hues (0-60°, 300-360°) - Red/Yellow spectrum

Visualization:

scripts/gay_stream.py --threads

Dependencies

• duckdb

  for AMP queries

• jq

  for Claude JSONL parsing
• Python 3.10+ with dataclasses

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 10. Adventure Game Example

Concepts: autonomous agent, game, synthesis

GF(3) Balanced Triad

tidar-thread-probe (+) + SDF.Ch10 (+) + [balancer] (+) = 0

Skill Trit: 1 (PLUS - generation)

Secondary Chapters

• Ch3: Variations on an Arithmetic Theme
• Ch4: Pattern Matching
• Ch8: Degeneracy

Connection Pattern

Adventure games synthesize techniques. This skill integrates multiple patterns.