LAB / WMSI-EXP-075
Structural Path Compression / Representation-Induced Complexity.
Can a successful long reasoning/proof trajectory be compressed by recovering its true dependency structure?
01 / QUESTION
Representation Search and Specialized Intellectual Geometry
Can a successful long reasoning/proof trajectory be compressed by recovering its true dependency structure?
This is a protocol scaffold, not a completed experiment or a frozen execution plan. No measured effect or research conclusion is claimed here.
Hypothesis to test
The manipulation described below produces a reproducible, condition-specific change in the measured system behavior or internal state that is not explained by the ordinary controls.
Ordinary competing explanation
The observed pattern is explained by ordinary sampling variation, prompt/representation artifacts, surface lexical cues, evaluator bias, or the known product/runtime mechanics captured by the controls.
02 / PLANNED DESIGN
How we intend to test it
Take solved long trajectories, extract dependencies, search for acyclic same-grade structure/generators, and rebuild shorter proofs/workflows.
Controls
Original trajectory; naive summarization; independent verifier.
What we would measure
Deleted obligations, proof length, verification success, downstream equivalence.
Access and instruments
Limited access or proxy measurement. This describes access requirements, not verified readiness on our Spark.
Proof parsers; graph tools; theorem verifier where available.
Before a full run
Feasibility=PARTIAL; priority=P0. Before confirmatory execution, run a small pilot to estimate variance/cost, freeze the scoring rules, and assign a run-count target.
Model revisions, final prompts, sample sizes, cost limits, and scoring rules must be settled through the pilot and protocol-freeze process.
03 / INTERPRETATION
What could fool us
Different data quality, vocabulary leakage, compute mismatch, representation chosen after seeing answer.
What would weaken the idea
Any lost theorem obligation, illegal shortcut, or failure under independent verification kills the compression.
Observation, inference, speculation, unknowns, and apparatus errors will be labeled separately. One striking transcript cannot establish a general effect.
04 / RECORD
Evidence we plan to preserve
Base checkpoint, training corpus hash, recoding candidates, dependency graphs, solution traces.
Planned visual evidence
Before/after dependency graph; path-length reduction.
No research runs or raw datasets are published for this experiment. The September 26, 2026 registry and protocol compendium (version 1.0) are the sources for this planning record.
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