HIDEKI-SQ/cot-backfire: v1.1.A2: Cue-Conditional Length Effects (A2 Main)

v1.1.A2: Cue-Conditional Length Effects (A2 Main) What's New Paper A2: Cue-Conditional Length Effects (Main) HIDEKI. "Length Effects in Chain-of-Thought Are Conditional on Explicit Answer-Cue Availability." Preprint (2026). DOI: 10.5281/zenodo.18144101 This release adds the complete experimental code, data, and figures for the main A2 paper, which establishes a cue-conditional length law and proposes a dual-path processing model for how language models consume reasoning traces. Paper A2-preliminary: Cue-Dominant Extraction (Archived) HIDEKI. "Cue-Dominant Extraction Explains Length Effects in Corrupted Reasoning Traces." Preprint (2025). DOI: 10.5281/zenodo.18132430 The previous A2 experiments (E1-E5) are now archived as A2-preliminary, representing the exploratory work that led to the main findings. Key Findings (A2 Main) Cue-Conditional Length Law: Length effects exist only when answer cues are absent; with cues present, accuracy saturates regardless of trace length (∆L ≈ 0 pp even at c=0.8) Dual-Path Processing Model: Cue-preferential extraction (fast path) with fallback computation (slow path) when cues are unavailable or unreliable Corruption Sensitivity: Models differ not in extraction ability but in threshold for abandoning extraction—Claude tolerates more corruption (99.5%) than GPT-4o (75.9%) Cross-Model Validation: Key patterns replicate across Claude Sonnet 4 and GPT-4o, with model-specific sensitivity thresholds explaining divergent length effects Design Implication: Cue integrity and corruption sensitivity calibration—not trace length—should be primary design targets Added Files Notebooks (7 new experiments) L5_L20_trace_generation.ipynb — Trace generation at L ∈ {5, 10, 15, 20} E6_conflicting_cue_v2_FIXED.ipynb — Conflicting-cue (Claude) A2_GPT4o_E6_v2_FIXED.ipynb — Conflicting-cue (GPT-4o) E7_trace_only_v2_FIXED.ipynb — Trace-only extraction (Claude) A2_GPT4o_E7_trace_only.ipynb — Trace-only extraction (GPT-4o) E8_length_cue_v2_FIXED.ipynb — Length × Cue × Corruption factorial (Claude) E8prime_GPT4o_v2_FIXED.ipynb — Cross-model replication (GPT-4o) Data (7 new directories) trace_generation_L5_L20_20260103/ E6_conflicting_cue_v2_20260103/ A2_GPT4o_E6_v2_20260103/ E7_trace_only_v2_20260103/ A2_GPT4o_E7_trace_only_20260103/ E8_length_cue_v2_20260103/ E8prime_GPT4o_v2_20260103/ Figures (new directory structure) A2/ (Main — PDF + PNG) fig1_e8_main_result.pdf/.png fig2_e7_trace_only.pdf/.png fig3_e6_conflicting_cue.pdf/.png fig4_corruption_sensitivity.pdf/.png fig5_dual_path_model.pdf/.png A2_Preliminary/ (Archived — PDF only) fig1_experimental_design.pdf fig2_main_results.pdf fig3_order_vs_position.pdf fig4_mechanistic_model.pdf Experimental Summary (A2 Main) Experiment Design Models Key Result E6 Conflicting-cue Claude, GPT-4o Wrong cue rejected (1.5-6.0% follow rate) E7 Trace-only (no problem) Claude, GPT-4o 98.5-99.5% accuracy; problem effect ≈ 0 E8 L × Cue × Corruption Claude ∆L ≈ 0 (cue+), ∆L = +14-16 pp (cue−) E8' L × Cue × Corruption GPT-4o ∆L = +13.8 pp (cue+), higher sensitivity Total new inferences: ~6,000+ (E6-E8 across both models) Cross-Model Comparison Metric Claude Sonnet 4 GPT-4o E6-B: Correct cue + corrupted 99.5% 75.9% E7-A: Trace-only + cue 98.5% 99.5% E8: ∆L (cue+, c=0.8) 0.0 pp +13.8 pp Corruption sensitivity Low High Citation A2 Main (use this) @article{hideki2026cue, title={Length Effects in Chain-of-Thought Are Conditional on Explicit Answer-Cue Availability}, author={HIDEKI}, journal={Preprint}, year={2026}, doi={10.5281/zenodo.18144101} } A2-preliminary (archived) @article{hideki2025extraction, title={Cue-Dominant Extraction Explains Length Effects in Corrupted Reasoning Traces}, author={HIDEKI}, journal={Preprint}, year={2025}, doi={10.5281/zenodo.18132430} } Full Changelog v1.0.A2 → v1.1.A2 Added A2 main experiments (E6, E7, E8, E8') Added trace generation for L ∈ {5, 10, 15, 20} Added cross-model validation (GPT-4o) Added A2 main figures (PDF + PNG) Reorganized figures: A2/ (main) and A2_Preliminary/ (archived) Updated README with A2 main documentation Archived previous A2 as "A2-preliminary" Updated paper title to "Length Effects in Chain-of-Thought Are Conditional on Explicit Answer-Cue Availability" New DOI: 10.5281/zenodo.18144101