craigdsouza/pegs-and-threads

Dataset Card for Pegs & Threads (v2)

Dataset Summary

Pegs & Threads is a synthetic benchmark designed to evaluate spatial reasoning, 3D state tracking, and topological mechanics in Large Language Models (LLMs) and Vision-Language Models (VLMs).

Unlike standard spatial benchmarks that rely on static visual perception, Pegs & Threads forces models to perform a mental physical execution over continuous 3D strand trajectories, discrete elevation crossings ($Z$-stacks), boundary pinches, and friction-driven capstan binding vs. Reidemeister Type I unspooling.

Frontier models struggle with this benchmark because token-prediction engines lack an internal 3D physics emulator or persistent topological state machine.

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Benchmark Statistics

• Total Episodes: ~1,000,000 unique, seed-locked instances across varying trajectory depths.
• Complexity Ranks: Stratified across 6 difficulty tiers (3, 4, 5, 6, 7, and 8 wrapping steps) with ~162k–169k balanced samples per step count.
• Class Balance: Exactly 50% Bound Knots (is_knot=True) vs. 50% Unknots (is_knot=False) across all complexity ranks.
• Outcome Distribution: 16 discrete ground-truth classes across []L, []R, [...]L, and [...]R

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Dataset Fields

• episode_id (int64): Unique integer identifier for each episode (ranging from 0 to 99,999).
• prompt (string): Step-by-step puzzle description in standardized DSL (character length ranges from 352 to 378).
• ground_truth (string / class): Target output string formatted as [PEGS]END across 16 discrete canonical topological classes (e.g., [B,C]L, []R, [A,B,C]R).
• is_knot (bool): Binary classification flag (true if pulling forms a persistent bound knot; false if it unspools into an unknot).
• num_pegs_enclosed (int64): Count of pegs remaining inside the bound loop after the pull operation (ranges from 0 to 3).
• pulled_strand (string / class): The strand end tucked and pulled ("L" or "R").
• complexity_rank (int64): Trajectory depth / total number of sequential wrapping steps executed in the episode (values: 3, 4, 5, 6, 7, 8).

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Usage & Evaluation

To evaluate models on pegs-and-threads, use the following system prompt to provide domain context and enforce strict output formatting ([PEGS]END).

Benchmark System Prompt

You are a deterministic spatial reasoning engine specializing in 3D knot topology and mechanical string kinematics.

ENVIRONMENT & PHYSICS RULES:
1. ANCHOR & STRANDS: String is anchored at Peg B, splitting into Left (L) and Right (R) free ends.
2. 3D ELEVATION (OVER/UNDER): Each newly moved or tucked strand segment passes OVER all pre-existing strands already on the board.
3. BOUNDARY PINCHES: Pegs listed in "Pinch:" are firmly clamped. String segments CANNOT slide past or unspool from pinched pegs.
4. KNOT MECHANICS:
   - REIDEMEISTER I (UNSPOOLING): If a pulled strand wraps with opposing directions or has no boundary lock, tension pulls it straight, resulting in an unknot ([]).
   - CAPSTAN BINDING (KNOT): If a pulled strand tucks into its own loop against an anchored/pinched boundary, friction locks it into a knot around those peg(s).

INPUT FORMAT:
Sequences of 3D wrapping operations followed by pinch constraints and a final tuck/pull action.

OUTPUT FORMAT CONSTRAINTS (STRICT):
- Identify the set of pegs enclosed by the resulting loop inside square brackets `[...]` in ALPHABETICAL ORDER, followed immediately by the pulled strand (`L` or `R`).
- Examples: `[A]L`, `[A,B]R`, `[B,C]L`, `[]L`, `[]R`
- Output ONLY the formatted string. Do NOT output any markdown, thinking, preamble, or explanations.