{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L7WM5DGRILAWMNWHRZMMUFJZZG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fd0d454dc1441d38b48a5a67d4ea04ab0d110fe3b52fa0c69e7d1c36d272b918","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-26T16:12:18Z","title_canon_sha256":"e5956d5f89d05594e942cafc28a281081654c08ba1181087ee622c3ca03fe598"},"schema_version":"1.0","source":{"id":"1409.7613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7613","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7613v1","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7613","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"pith_short_12","alias_value":"L7WM5DGRILAW","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L7WM5DGRILAWMNWH","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L7WM5DGR","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:d77e13ae9382ac4673c8f786eadfa7df0a547c38c58175b9712bbca425f3e903","target":"graph","created_at":"2026-05-18T01:19:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We endow the set of isomorphic classes of matroids with a new Hopf algebra structure, in which the coproduct is implemented via the combinatorial operations of restriction and deletion. We also initiate the investigation of dendriform coalgebra structures on matroids and introduce a monomial invariant which satisfy a convolution identity with respect to restriction and deletion.","authors_text":"A. Tanasa, C. Tollu, N. Hoang-Nghia","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-26T16:12:18Z","title":"Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7613","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a90113b208269918f1cd583c3edf6f412a409c084c58e3927ca6b763525afecd","target":"record","created_at":"2026-05-18T01:19:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fd0d454dc1441d38b48a5a67d4ea04ab0d110fe3b52fa0c69e7d1c36d272b918","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-26T16:12:18Z","title_canon_sha256":"e5956d5f89d05594e942cafc28a281081654c08ba1181087ee622c3ca03fe598"},"schema_version":"1.0","source":{"id":"1409.7613","kind":"arxiv","version":1}},"canonical_sha256":"5fecce8cd142c16636c78e58ca1539c9af5c7848f25c409685d8e8333a023fb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fecce8cd142c16636c78e58ca1539c9af5c7848f25c409685d8e8333a023fb6","first_computed_at":"2026-05-18T01:19:57.597337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:57.597337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nkRy9YdItzQ6pwyQHRdm3wOEB4Sgtsl3ynTShRTZEPsKgsudk0t/CbKww6pyHyAzuwbV2tL1XJSgjVrLhpl3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:57.597982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a90113b208269918f1cd583c3edf6f412a409c084c58e3927ca6b763525afecd","sha256:d77e13ae9382ac4673c8f786eadfa7df0a547c38c58175b9712bbca425f3e903"],"state_sha256":"502cc5ae2fb27a65d4e3b4f9d50eb8b482f97916171e875dcf386de17c571d7a"}