{"id":"W2072726992","doi":"10.1016/j.aim.2012.04.003","title":"A geometric deletion–restriction formula","year":2012,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"","keywords":"Mathematics; Hyperplane; Ideal (ethics); Logarithm; Pure mathematics; Polynomial; Euler's formula; Variety (cybernetics); Equivalence (formal languages); Discrete mathematics; Combinatorics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008865783,0.0007558726,0.001019743,0.001296196,0.001918741,0.002136379,0.002019285,0.001421254,0.0145025],"category_scores_gemma":[0.002841186,0.0004764389,0.0008470389,0.001639397,0.004244216,0.008209321,0.0042494,0.005195285,0.002469057],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009559937,"about_ca_system_score_gemma":0.0005398721,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005159793,"about_ca_topic_score_gemma":0.0002869227,"domain_scores_codex":[0.9991881,0.0001821578,0.00003723313,0.0001885253,0.0002715598,0.0001323636],"domain_scores_gemma":[0.9988824,0.0005293766,0.0000771975,0.0002123453,0.000178763,0.0001200397],"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":[0.00001742678,0.000008644772,0.00006263352,0.00001734976,0.000002037696,0.00007002076,0.00007623163,0.000109138,0.0004136472,0.9931232,0.001665474,0.004434233],"study_design_scores_gemma":[0.00001761705,0.00001044873,0.0001175435,0.000007166059,0.00000989401,0.0002965513,0.0000574022,0.0009828317,0.0005409517,0.9897236,0.008226132,0.000009869922],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1841361,0.001514465,0.2782197,0.01102271,0.001870211,0.00007365378,0.000441012,0.0007586461,0.5219634],"genre_scores_gemma":[0.8517664,0.001188444,0.05119714,0.00245883,0.001473745,0.0001105286,0.0006930754,0.0005402857,0.09057149],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0145025,"threshold_uncertainty_score":0.04851568,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02649843879962792,"score_gpt":0.317139636080277,"score_spread":0.290641197280649,"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."}}