{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:I4ZBTYY4DBWZVRK5U6XJFIC4JH","short_pith_number":"pith:I4ZBTYY4","schema_version":"1.0","canonical_sha256":"473219e31c186d9ac55da7ae92a05c49d80c5e43e023b92a86490b010d54f83a","source":{"kind":"arxiv","id":"1407.1604","version":1},"attestation_state":"computed","paper":{"title":"Dual Garside structure of braids and free cumulants of products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Patrick Dehornoy (LMNO), Philippe Biane (LIGM)","submitted_at":"2014-07-07T07:05:44Z","abstract_excerpt":"We count the n-strand braids whose normal decomposition has length at most two in the dual braid monoid B_n+* by reducing the question to a computation of free cumulants for a product of independent variables, for which we establish a general formula."},"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":"1407.1604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-07T07:05:44Z","cross_cats_sorted":[],"title_canon_sha256":"528a8f887b5f748fd7f5b3a156138a33c6824b88971853e33cd4943aa3209b18","abstract_canon_sha256":"be9f75d487df5eefd4deb587aa6cbe15ebe8d3b8cb0f1c166cb7fcac7241ed51"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:10.934196Z","signature_b64":"z/CQrFqhexy461xwCFE2X/hgwN3cqos9uzjCtpw2j5qghZWE5Osah2P2H9VCOQIrr0Le0ZULyMBtYWIfaQ5JBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"473219e31c186d9ac55da7ae92a05c49d80c5e43e023b92a86490b010d54f83a","last_reissued_at":"2026-05-18T02:48:10.933474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:10.933474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dual Garside structure of braids and free cumulants of products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Patrick Dehornoy (LMNO), Philippe Biane (LIGM)","submitted_at":"2014-07-07T07:05:44Z","abstract_excerpt":"We count the n-strand braids whose normal decomposition has length at most two in the dual braid monoid B_n+* by reducing the question to a computation of free cumulants for a product of independent variables, for which we establish a general formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1604","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":""},"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":"1407.1604","created_at":"2026-05-18T02:48:10.933589+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1604v1","created_at":"2026-05-18T02:48:10.933589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1604","created_at":"2026-05-18T02:48:10.933589+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4ZBTYY4DBWZ","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4ZBTYY4DBWZVRK5","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4ZBTYY4","created_at":"2026-05-18T12:28:33.132498+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/I4ZBTYY4DBWZVRK5U6XJFIC4JH","json":"https://pith.science/pith/I4ZBTYY4DBWZVRK5U6XJFIC4JH.json","graph_json":"https://pith.science/api/pith-number/I4ZBTYY4DBWZVRK5U6XJFIC4JH/graph.json","events_json":"https://pith.science/api/pith-number/I4ZBTYY4DBWZVRK5U6XJFIC4JH/events.json","paper":"https://pith.science/paper/I4ZBTYY4"},"agent_actions":{"view_html":"https://pith.science/pith/I4ZBTYY4DBWZVRK5U6XJFIC4JH","download_json":"https://pith.science/pith/I4ZBTYY4DBWZVRK5U6XJFIC4JH.json","view_paper":"https://pith.science/paper/I4ZBTYY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1604&json=true","fetch_graph":"https://pith.science/api/pith-number/I4ZBTYY4DBWZVRK5U6XJFIC4JH/graph.json","fetch_events":"https://pith.science/api/pith-number/I4ZBTYY4DBWZVRK5U6XJFIC4JH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4ZBTYY4DBWZVRK5U6XJFIC4JH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4ZBTYY4DBWZVRK5U6XJFIC4JH/action/storage_attestation","attest_author":"https://pith.science/pith/I4ZBTYY4DBWZVRK5U6XJFIC4JH/action/author_attestation","sign_citation":"https://pith.science/pith/I4ZBTYY4DBWZVRK5U6XJFIC4JH/action/citation_signature","submit_replication":"https://pith.science/pith/I4ZBTYY4DBWZVRK5U6XJFIC4JH/action/replication_record"}},"created_at":"2026-05-18T02:48:10.933589+00:00","updated_at":"2026-05-18T02:48:10.933589+00:00"}