{"id":"W4414899341","doi":"10.48550/arxiv.2506.03108","title":"Higher Order Rigidity and Energy","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Thermodynamics and Statistical Mechanics","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Rigidity (electromagnetism); Order (exchange); Derivative (finance); Third order; Second derivative; Function (biology)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001412228,0.0006758696,0.0006622602,0.001938683,0.001625231,0.002178947,0.001005116,0.001320398,0.006660878],"category_scores_gemma":[0.005215663,0.0003408478,0.0009623634,0.001000486,0.006386151,0.005583859,0.002768879,0.00258125,0.0006099618],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001546844,"about_ca_system_score_gemma":0.0006499868,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001240269,"about_ca_topic_score_gemma":0.001092431,"domain_scores_codex":[0.9982504,0.0003739604,0.000080751,0.0002903424,0.0006787545,0.0003257032],"domain_scores_gemma":[0.9952146,0.002056732,0.0007345918,0.0008188983,0.0006055896,0.0005695994],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000009635296,0.000006827159,0.0003253729,0.00002015666,0.000003741984,0.0000391051,0.00007556821,0.002082807,0.0005556177,0.9946622,0.0001555869,0.002063346],"study_design_scores_gemma":[0.000003701466,0.00003414834,0.001173026,0.00001667757,0.000003920287,0.0001669611,0.00008540126,0.0126597,0.0008164198,0.9814958,0.003521199,0.00002308991],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4453012,0.002322738,0.4204891,0.00253297,0.0003241325,0.00006265557,0.0003567713,0.0003522615,0.1282581],"genre_scores_gemma":[0.9736258,0.0003529352,0.01869105,0.0001960746,0.0001571861,0.00003330285,0.0001428178,0.0001142746,0.00668655],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006660878,"threshold_uncertainty_score":0.02228284,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01933339330015212,"score_gpt":0.270811613104993,"score_spread":0.2514782198048409,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}