{"id":"W4414533853","doi":"10.5539/jmr.v17n3p1","title":"On the Palindromic Complexity of Words by Substitution of Letter Power in Modulo-recurrent Words","year":2025,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Palindrome; Word (group theory); Substitution (logic); Integer (computer science); Power (physics); Word length; Combinatorics on words","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"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":[0.0007670929,0.0005180543,0.0005512625,0.001587248,0.0009364162,0.001965521,0.0006692462,0.0006476093,0.003904506],"category_scores_gemma":[0.004211507,0.0003134939,0.0007755181,0.001034283,0.002296987,0.003758835,0.001175829,0.001030928,0.0004663163],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001296944,"about_ca_system_score_gemma":0.0004282734,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006920795,"about_ca_topic_score_gemma":0.0006129278,"domain_scores_codex":[0.9992895,0.000166687,0.00004786067,0.0001390894,0.0002177955,0.000139084],"domain_scores_gemma":[0.997243,0.001709802,0.0003877447,0.0002064513,0.0002628462,0.0001900464],"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":[0.000110623,0.00003381077,0.001237852,0.0001012154,0.00001538397,0.0002559065,0.0009352845,0.008606641,0.007818355,0.9686458,0.0004657687,0.01177333],"study_design_scores_gemma":[0.00002372167,0.0001127407,0.001767318,0.00002819614,0.00002273062,0.0003444405,0.0001844281,0.03982626,0.005295846,0.9491557,0.003193033,0.00004570775],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8594317,0.0008348252,0.1143509,0.0004188872,0.00005240025,0.00004679355,0.0001434194,0.0001212668,0.02459994],"genre_scores_gemma":[0.9805775,0.0003990054,0.01439639,0.00006474362,0.000134033,0.00006430678,0.0001189841,0.00004949426,0.004195405],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003904506,"threshold_uncertainty_score":0.01306182,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08914577765917518,"score_gpt":0.3731454157720771,"score_spread":0.2839996381129019,"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."}}