{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:45XUDCMPYOFGAL3WL2TYIFXM6I","short_pith_number":"pith:45XUDCMP","canonical_record":{"source":{"id":"1306.3797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-17T10:12:27Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"06f4e4e8f8b336e230f7fd5814e8ffa2b0a272554cbd2a54a091f70b2de8bbcc","abstract_canon_sha256":"29330bf57bd31fa25bce9e8fd87df25872f9ca9bf7548059e8383ae49e91a279"},"schema_version":"1.0"},"canonical_sha256":"e76f41898fc38a602f765ea78416ecf215c2f03a5229296409a5bf2c049b97e9","source":{"kind":"arxiv","id":"1306.3797","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3797","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3797v1","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3797","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"45XUDCMPYOFG","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"45XUDCMPYOFGAL3W","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"45XUDCMP","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:45XUDCMPYOFGAL3WL2TYIFXM6I","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-17T10:12:27Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"06f4e4e8f8b336e230f7fd5814e8ffa2b0a272554cbd2a54a091f70b2de8bbcc","abstract_canon_sha256":"29330bf57bd31fa25bce9e8fd87df25872f9ca9bf7548059e8383ae49e91a279"},"schema_version":"1.0"},"canonical_sha256":"e76f41898fc38a602f765ea78416ecf215c2f03a5229296409a5bf2c049b97e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:46.407197Z","signature_b64":"fVl9K/8qvDR2IDwz55oNjRE5P03HQ8giqmF4BVIIKX6siD0t1IfnQMWUyET6rM5nMaEWYfBbD7PakmiOLaniDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e76f41898fc38a602f765ea78416ecf215c2f03a5229296409a5bf2c049b97e9","last_reissued_at":"2026-05-18T03:20:46.406363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:46.406363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3797","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vGEaU8BmnFs+FdewMfGy3S+Zd5vmlBZsDnfu3/1n1+1rGTnCz6iDtSgP9Zw1WkyeaamN6d+g2dOvr5K2GID1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:37:07.001909Z"},"content_sha256":"833f5bd1e5e4fee5b820fa5e262cb084daa278ed2996f1b1ca40d6d211c52556","schema_version":"1.0","event_id":"sha256:833f5bd1e5e4fee5b820fa5e262cb084daa278ed2996f1b1ca40d6d211c52556"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:45XUDCMPYOFGAL3WL2TYIFXM6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greedy algorithms and poset matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Luca Ferrari","submitted_at":"2013-06-17T10:12:27Z","abstract_excerpt":"We generalize the matroid-theoretic approach to greedy algorithms to the setting of poset matroids, in the sense of Barnabei, Nicoletti and Pezzoli (1998) [BNP]. We illustrate our result by providing a generalization of Kruskal algorithm (which finds a minimum spanning subtree of a weighted graph) to abstract simplicial complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3797","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QMzpnNfW4fgv3DyYVACEkjrSVHgnzHGIGoQze9wvTbMebLunyPGQpCNe3iZkn0hXO+VfCvNA9tOXkVOYgwd9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:37:07.002250Z"},"content_sha256":"8142ed8aacac0060717aa545af453c3fa508dde26c70faea8596507d8153b958","schema_version":"1.0","event_id":"sha256:8142ed8aacac0060717aa545af453c3fa508dde26c70faea8596507d8153b958"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/45XUDCMPYOFGAL3WL2TYIFXM6I/bundle.json","state_url":"https://pith.science/pith/45XUDCMPYOFGAL3WL2TYIFXM6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/45XUDCMPYOFGAL3WL2TYIFXM6I/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T09:37:07Z","links":{"resolver":"https://pith.science/pith/45XUDCMPYOFGAL3WL2TYIFXM6I","bundle":"https://pith.science/pith/45XUDCMPYOFGAL3WL2TYIFXM6I/bundle.json","state":"https://pith.science/pith/45XUDCMPYOFGAL3WL2TYIFXM6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/45XUDCMPYOFGAL3WL2TYIFXM6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:45XUDCMPYOFGAL3WL2TYIFXM6I","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":"29330bf57bd31fa25bce9e8fd87df25872f9ca9bf7548059e8383ae49e91a279","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-17T10:12:27Z","title_canon_sha256":"06f4e4e8f8b336e230f7fd5814e8ffa2b0a272554cbd2a54a091f70b2de8bbcc"},"schema_version":"1.0","source":{"id":"1306.3797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3797","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3797v1","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3797","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"45XUDCMPYOFG","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"45XUDCMPYOFGAL3W","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"45XUDCMP","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:8142ed8aacac0060717aa545af453c3fa508dde26c70faea8596507d8153b958","target":"graph","created_at":"2026-05-18T03:20:46Z","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 generalize the matroid-theoretic approach to greedy algorithms to the setting of poset matroids, in the sense of Barnabei, Nicoletti and Pezzoli (1998) [BNP]. We illustrate our result by providing a generalization of Kruskal algorithm (which finds a minimum spanning subtree of a weighted graph) to abstract simplicial complexes.","authors_text":"Luca Ferrari","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-17T10:12:27Z","title":"Greedy algorithms and poset matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3797","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":"sha256:833f5bd1e5e4fee5b820fa5e262cb084daa278ed2996f1b1ca40d6d211c52556","target":"record","created_at":"2026-05-18T03:20:46Z","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":"29330bf57bd31fa25bce9e8fd87df25872f9ca9bf7548059e8383ae49e91a279","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-17T10:12:27Z","title_canon_sha256":"06f4e4e8f8b336e230f7fd5814e8ffa2b0a272554cbd2a54a091f70b2de8bbcc"},"schema_version":"1.0","source":{"id":"1306.3797","kind":"arxiv","version":1}},"canonical_sha256":"e76f41898fc38a602f765ea78416ecf215c2f03a5229296409a5bf2c049b97e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e76f41898fc38a602f765ea78416ecf215c2f03a5229296409a5bf2c049b97e9","first_computed_at":"2026-05-18T03:20:46.406363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:46.406363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fVl9K/8qvDR2IDwz55oNjRE5P03HQ8giqmF4BVIIKX6siD0t1IfnQMWUyET6rM5nMaEWYfBbD7PakmiOLaniDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:46.407197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:833f5bd1e5e4fee5b820fa5e262cb084daa278ed2996f1b1ca40d6d211c52556","sha256:8142ed8aacac0060717aa545af453c3fa508dde26c70faea8596507d8153b958"],"state_sha256":"e422f477c6fc73ac8a820fedfa40a90348ab07f1613dbe6450bfbe9e973a088d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MvzvIl5IsSXkV4/A+xne/1ERBV0IUdAcUDwf4BgDb9I9XDp7Z/7zoqoYKsd9ZYIHetPoZPk1/RNsrioLVflzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:37:07.004175Z","bundle_sha256":"25f28b6f9406ad9dca00a77423ed67707ab427296e1a7fc6a56a3971ac5509e2"}}