LLM entropy Grammar+Fisher study

This release updates the preprint and supporting outputs for the LLM entropy Grammar+Fisher study. What is included Updated manuscript PDF: LLMGrammarFisherPreprint. pdf Fisher summaries and aggregation outputs for: all 4 regimes (factual, creative, mathematical, philosophical) LLM seeds 42, 99, 7 controls shuffled, randomᵤniform grammar-seed sweep 0, 1, 2 at fixed LLM seed 42 Key update in this version Completed the full 36/36 regime × LLM-seed × control matrix. Added/standardized creative multi-seed 10k runs (seeds 99 and 7) to match the existing 10k protocol. Regenerated Fisher outputs and merged multi-seed summaries. Updated manuscript text for numerical consistency: signal-to-noise range reported as 2. 2× to 263× controls collapse to a common noise floor of approximately 52–53. Main empirical result Across all tested combinations, both control conditions (shuffled, randomᵤniform) converge to a common Fisher tail noise floor, while real-signal (none) conditions remain consistently above this baseline. The weakest observed separation is 2. 2×, and the strongest is 263× (philosophical, seed 7), with strongest and most consistent elevation in mathematical/philosophical regimes. Reproducibility notes The repository contains the scripts used for: entropy collection (collectₗlmₑntropyₛeries. py) Fisher pipeline (runₗlmₑntropygrammarfisher. py) grammar-seed and multi-seed aggregation (aggregateₗlmfishergrammarₛeedₛweep. py, mergeₗlmfisherₘultiseedₛummaries. py) All outputs in this release were generated with the same SAX→LSTM→Fisher workflow used in the related Sycamore studies.