{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OYDO4N5AS5Q6GTFKQWBENDVLPE","short_pith_number":"pith:OYDO4N5A","canonical_record":{"source":{"id":"1608.05730","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:45Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b748a320d6f23b410ffd3e03b9bdfe9a2da4ff8a43bade5a5cea197a945820c4","abstract_canon_sha256":"a372a7748898859d4e97b022a23c1328a4fa4e3e704bc076922fc185c789c353"},"schema_version":"1.0"},"canonical_sha256":"7606ee37a09761e34caa8582468eab79295c3b9d1a4d4318f724808c905060f5","source":{"kind":"arxiv","id":"1608.05730","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05730","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05730v2","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05730","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"OYDO4N5AS5Q6","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OYDO4N5AS5Q6GTFK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OYDO4N5A","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OYDO4N5AS5Q6GTFKQWBENDVLPE","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05730","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:45Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b748a320d6f23b410ffd3e03b9bdfe9a2da4ff8a43bade5a5cea197a945820c4","abstract_canon_sha256":"a372a7748898859d4e97b022a23c1328a4fa4e3e704bc076922fc185c789c353"},"schema_version":"1.0"},"canonical_sha256":"7606ee37a09761e34caa8582468eab79295c3b9d1a4d4318f724808c905060f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:09.628935Z","signature_b64":"GJRaaMwyBpH9hpeU+KMKvlyI8bQ8/d682m/pqIEqXG/5ga1mOj4FNNZlcq6k3ahaeqxw3ZohgK7ZpYD6ntWfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7606ee37a09761e34caa8582468eab79295c3b9d1a4d4318f724808c905060f5","last_reissued_at":"2026-05-18T00:36:09.628366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:09.628366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05730","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JqPp0XCKhS4TboPb3/GnviG/5KKqeiLsR3n0aN6ImdYUJNMMwJvetrvQ3n+yhJyEYLerVMgucAvnJUCwh3NsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:57:23.540142Z"},"content_sha256":"ed7fdb39931c79d0129e485de451a6363844f46597cf6cf8d983648d65a89464","schema_version":"1.0","event_id":"sha256:ed7fdb39931c79d0129e485de451a6363844f46597cf6cf8d983648d65a89464"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OYDO4N5AS5Q6GTFKQWBENDVLPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supermodularity in Unweighted Graph Optimization II: Matroidal Term Rank Augmentation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andr\\'as Frank, Krist\\'of B\\'erczi","submitted_at":"2016-08-19T20:21:45Z","abstract_excerpt":"Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\\ell$. In a previous paper by the authors, a generalization was developed for the case when the degrees are constrained by upper and lower bounds. Here two other extensions of Ryser's theorem are discussed. The first one is a matroidal model, while the second one settles the augmentation version. In fact, the two directions shall be integrated into one single framework."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05730","kind":"arxiv","version":2},"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":"2026-05-18T00:36:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxiP4A0XSfaJt2ZXIkhqF94u/eOnBiCKL0WUrBTLm+ynj/R4amvSTKR1iLW3HhW0sNqmHnrBoFVq9cPKg5zWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:57:23.540492Z"},"content_sha256":"98e680c96cf3b16cd2268d8e45117da98468687f8880c9bddccecbb7e07709a1","schema_version":"1.0","event_id":"sha256:98e680c96cf3b16cd2268d8e45117da98468687f8880c9bddccecbb7e07709a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYDO4N5AS5Q6GTFKQWBENDVLPE/bundle.json","state_url":"https://pith.science/pith/OYDO4N5AS5Q6GTFKQWBENDVLPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYDO4N5AS5Q6GTFKQWBENDVLPE/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":"2026-06-27T16:57:23Z","links":{"resolver":"https://pith.science/pith/OYDO4N5AS5Q6GTFKQWBENDVLPE","bundle":"https://pith.science/pith/OYDO4N5AS5Q6GTFKQWBENDVLPE/bundle.json","state":"https://pith.science/pith/OYDO4N5AS5Q6GTFKQWBENDVLPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYDO4N5AS5Q6GTFKQWBENDVLPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OYDO4N5AS5Q6GTFKQWBENDVLPE","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":"a372a7748898859d4e97b022a23c1328a4fa4e3e704bc076922fc185c789c353","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:45Z","title_canon_sha256":"b748a320d6f23b410ffd3e03b9bdfe9a2da4ff8a43bade5a5cea197a945820c4"},"schema_version":"1.0","source":{"id":"1608.05730","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05730","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05730v2","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05730","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"OYDO4N5AS5Q6","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OYDO4N5AS5Q6GTFK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OYDO4N5A","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:98e680c96cf3b16cd2268d8e45117da98468687f8880c9bddccecbb7e07709a1","target":"graph","created_at":"2026-05-18T00:36:09Z","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":"Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\\ell$. In a previous paper by the authors, a generalization was developed for the case when the degrees are constrained by upper and lower bounds. Here two other extensions of Ryser's theorem are discussed. The first one is a matroidal model, while the second one settles the augmentation version. In fact, the two directions shall be integrated into one single framework.","authors_text":"Andr\\'as Frank, Krist\\'of B\\'erczi","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:45Z","title":"Supermodularity in Unweighted Graph Optimization II: Matroidal Term Rank Augmentation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05730","kind":"arxiv","version":2},"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:ed7fdb39931c79d0129e485de451a6363844f46597cf6cf8d983648d65a89464","target":"record","created_at":"2026-05-18T00:36:09Z","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":"a372a7748898859d4e97b022a23c1328a4fa4e3e704bc076922fc185c789c353","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:45Z","title_canon_sha256":"b748a320d6f23b410ffd3e03b9bdfe9a2da4ff8a43bade5a5cea197a945820c4"},"schema_version":"1.0","source":{"id":"1608.05730","kind":"arxiv","version":2}},"canonical_sha256":"7606ee37a09761e34caa8582468eab79295c3b9d1a4d4318f724808c905060f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7606ee37a09761e34caa8582468eab79295c3b9d1a4d4318f724808c905060f5","first_computed_at":"2026-05-18T00:36:09.628366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:09.628366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GJRaaMwyBpH9hpeU+KMKvlyI8bQ8/d682m/pqIEqXG/5ga1mOj4FNNZlcq6k3ahaeqxw3ZohgK7ZpYD6ntWfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:09.628935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05730","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed7fdb39931c79d0129e485de451a6363844f46597cf6cf8d983648d65a89464","sha256:98e680c96cf3b16cd2268d8e45117da98468687f8880c9bddccecbb7e07709a1"],"state_sha256":"dc14cc9511dd2fae2297ae4f0c632efec6d671a07be216685998d36cf5e2f988"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Gv/VRGNPeqW7AdB+5wxVM5cMKS1+mmXt9kHZUOZLfhg6aNFGS3bbvao8sl4BMh9DfoNsIcLeoqKJuGwfEptBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:57:23.542359Z","bundle_sha256":"90c94fd3f492348d6b1b444c92a8b32661899d300f0ab4fc5594030bab956237"}}