{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:Y4BFCOH5SFJHF3ZFULVKTT6ZUZ","short_pith_number":"pith:Y4BFCOH5","schema_version":"1.0","canonical_sha256":"c7025138fd915272ef25a2eaa9cfd9a67fb9f447522d83fb9cfbf5233768c423","source":{"kind":"arxiv","id":"2605.25274","version":1},"attestation_state":"computed","paper":{"title":"Pal's permanent conjecture: proof for block uniform matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.CO","authors_text":"Andrea Ottolini, Shannon Starr","submitted_at":"2026-05-24T22:02:13Z","abstract_excerpt":"Consider a symmetric function $\\mathcal{C}(x,y)$ on $[0,1]\\times[0,1]$ which is twice continuously differentiable up to the boundary, and which satisfies $ \\mathcal{C}(x,y)=\\mathcal{C}(1-x,1-y)$. Let $A^{(n)} = \\big(a^{(n)}_{i,j}\\, :\\, i,j \\in [n]\\big)$ be the matrix with entries $a^{(n)}_{i,j}\\, =\\, \\exp(-\\mathcal{C}(i/n,j/n))$. Soumik Pal conjectured the asymptotics $$\\operatorname{perm}\\big(A^{(n)}\\big)/n!\\sim \\exp\\big(n \\Lambda[\\mathcal{C}]\\big)/ \\sqrt{\\mathcal{D}[\\mathcal{C}]}$$ as $n \\to \\infty$ for known functionals that arise naturally in the context of entropy regularized optimal tran"},"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":"2605.25274","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-24T22:02:13Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"6a3919718e76685b9428bc71e0ac631dfe5360de031261c2bdd3eee7a474ea97","abstract_canon_sha256":"1f35dbf6ed9dd4972ebec4ae545dc1e1caf0ad7f628ff7e3bd7d9885b755c0e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:26.839416Z","signature_b64":"nWDXXpkRF/gsNO/dZOBNCWwTvnkDdgGunOsmXQyZySQtxSvRldwbqcm4lMSs6Ajat3Df1KPBv8m8LLus8JTTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7025138fd915272ef25a2eaa9cfd9a67fb9f447522d83fb9cfbf5233768c423","last_reissued_at":"2026-05-26T02:04:26.838705Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:26.838705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pal's permanent conjecture: proof for block uniform matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.CO","authors_text":"Andrea Ottolini, Shannon Starr","submitted_at":"2026-05-24T22:02:13Z","abstract_excerpt":"Consider a symmetric function $\\mathcal{C}(x,y)$ on $[0,1]\\times[0,1]$ which is twice continuously differentiable up to the boundary, and which satisfies $ \\mathcal{C}(x,y)=\\mathcal{C}(1-x,1-y)$. Let $A^{(n)} = \\big(a^{(n)}_{i,j}\\, :\\, i,j \\in [n]\\big)$ be the matrix with entries $a^{(n)}_{i,j}\\, =\\, \\exp(-\\mathcal{C}(i/n,j/n))$. Soumik Pal conjectured the asymptotics $$\\operatorname{perm}\\big(A^{(n)}\\big)/n!\\sim \\exp\\big(n \\Lambda[\\mathcal{C}]\\big)/ \\sqrt{\\mathcal{D}[\\mathcal{C}]}$$ as $n \\to \\infty$ for known functionals that arise naturally in the context of entropy regularized optimal tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25274","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/2605.25274/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":"2605.25274","created_at":"2026-05-26T02:04:26.838814+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25274v1","created_at":"2026-05-26T02:04:26.838814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25274","created_at":"2026-05-26T02:04:26.838814+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y4BFCOH5SFJH","created_at":"2026-05-26T02:04:26.838814+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y4BFCOH5SFJHF3ZF","created_at":"2026-05-26T02:04:26.838814+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y4BFCOH5","created_at":"2026-05-26T02:04:26.838814+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/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ","json":"https://pith.science/pith/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ.json","graph_json":"https://pith.science/api/pith-number/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/graph.json","events_json":"https://pith.science/api/pith-number/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/events.json","paper":"https://pith.science/paper/Y4BFCOH5"},"agent_actions":{"view_html":"https://pith.science/pith/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ","download_json":"https://pith.science/pith/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ.json","view_paper":"https://pith.science/paper/Y4BFCOH5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25274&json=true","fetch_graph":"https://pith.science/api/pith-number/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/action/storage_attestation","attest_author":"https://pith.science/pith/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/action/author_attestation","sign_citation":"https://pith.science/pith/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/action/citation_signature","submit_replication":"https://pith.science/pith/Y4BFCOH5SFJHF3ZFULVKTT6ZUZ/action/replication_record"}},"created_at":"2026-05-26T02:04:26.838814+00:00","updated_at":"2026-05-26T02:04:26.838814+00:00"}