{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4Q5EYYQWVYPXCVEW6BS6XDDTVO","short_pith_number":"pith:4Q5EYYQW","schema_version":"1.0","canonical_sha256":"e43a4c6216ae1f715496f065eb8c73abbfde702d27384c92ab4c9767fb4dfabe","source":{"kind":"arxiv","id":"2501.01345","version":1},"attestation_state":"computed","paper":{"title":"Maximum Likelihood, permutohedra and Associativity Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"No\\'emie C. Combe","submitted_at":"2025-01-02T16:53:35Z","abstract_excerpt":"We consider the cone of concentration matrices related to linear concentration models and Wishart laws. We prove that this cone is a Monge--Amp\\`ere domain and that the log-likelihood function generates its potential function at the identity. The tangent sheaf carries the structure of a pre-Lie algebra. We also show that the moduli space of diagonal matrices parameterizing the polyhedral spectrahedron satisfies the Associativity Equations, a notion central in mirror symmetry, and that its compactification is a toric variety associated to a permutohedron, reminiscent to Losev--Manin spaces. Fin"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.01345","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T16:53:35Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"5dea77a7c5776590b8ad6d9feee5a36a45ff89659cbfc6131376c3506b44fd9b","abstract_canon_sha256":"2153450624aec5db91490547fcd98eca472e3abf5f788fb307e31a6150f63cb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:18.435777Z","signature_b64":"6ejIYxFoxA9HeJjF5fQ9qfKPkyCbAnk7M05t/s68wQo+4gNsdasuS6gRrpQJhIrpR4tEbhUCrs208MPiwSZ/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e43a4c6216ae1f715496f065eb8c73abbfde702d27384c92ab4c9767fb4dfabe","last_reissued_at":"2026-07-05T09:56:18.435304Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:18.435304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum Likelihood, permutohedra and Associativity Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"No\\'emie C. Combe","submitted_at":"2025-01-02T16:53:35Z","abstract_excerpt":"We consider the cone of concentration matrices related to linear concentration models and Wishart laws. We prove that this cone is a Monge--Amp\\`ere domain and that the log-likelihood function generates its potential function at the identity. The tangent sheaf carries the structure of a pre-Lie algebra. We also show that the moduli space of diagonal matrices parameterizing the polyhedral spectrahedron satisfies the Associativity Equations, a notion central in mirror symmetry, and that its compactification is a toric variety associated to a permutohedron, reminiscent to Losev--Manin spaces. Fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01345","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.01345/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.01345","created_at":"2026-07-05T09:56:18.435375+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.01345v1","created_at":"2026-07-05T09:56:18.435375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01345","created_at":"2026-07-05T09:56:18.435375+00:00"},{"alias_kind":"pith_short_12","alias_value":"4Q5EYYQWVYPX","created_at":"2026-07-05T09:56:18.435375+00:00"},{"alias_kind":"pith_short_16","alias_value":"4Q5EYYQWVYPXCVEW","created_at":"2026-07-05T09:56:18.435375+00:00"},{"alias_kind":"pith_short_8","alias_value":"4Q5EYYQW","created_at":"2026-07-05T09:56:18.435375+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO","json":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO.json","graph_json":"https://pith.science/api/pith-number/4Q5EYYQWVYPXCVEW6BS6XDDTVO/graph.json","events_json":"https://pith.science/api/pith-number/4Q5EYYQWVYPXCVEW6BS6XDDTVO/events.json","paper":"https://pith.science/paper/4Q5EYYQW"},"agent_actions":{"view_html":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO","download_json":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO.json","view_paper":"https://pith.science/paper/4Q5EYYQW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.01345&json=true","fetch_graph":"https://pith.science/api/pith-number/4Q5EYYQWVYPXCVEW6BS6XDDTVO/graph.json","fetch_events":"https://pith.science/api/pith-number/4Q5EYYQWVYPXCVEW6BS6XDDTVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO/action/storage_attestation","attest_author":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO/action/author_attestation","sign_citation":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO/action/citation_signature","submit_replication":"https://pith.science/pith/4Q5EYYQWVYPXCVEW6BS6XDDTVO/action/replication_record"}},"created_at":"2026-07-05T09:56:18.435375+00:00","updated_at":"2026-07-05T09:56:18.435375+00:00"}