{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A6BSPEHMZXEAPDD24TTVCRUJUW","short_pith_number":"pith:A6BSPEHM","canonical_record":{"source":{"id":"1611.06629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T01:42:55Z","cross_cats_sorted":[],"title_canon_sha256":"ba0fe40d8f26ffbdcff40955f696be9e2dc23cb18d838a17271161b5ae27bf47","abstract_canon_sha256":"046846d725c94bf360b560bfd548db5fd5bcd65cc8c4eacffcae8cdbc252d79f"},"schema_version":"1.0"},"canonical_sha256":"07832790eccdc8078c7ae4e7514689a5956d62e337a8faf38bc475e5d4d453e9","source":{"kind":"arxiv","id":"1611.06629","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06629","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06629v1","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06629","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"A6BSPEHMZXEA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A6BSPEHMZXEAPDD2","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A6BSPEHM","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A6BSPEHMZXEAPDD24TTVCRUJUW","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T01:42:55Z","cross_cats_sorted":[],"title_canon_sha256":"ba0fe40d8f26ffbdcff40955f696be9e2dc23cb18d838a17271161b5ae27bf47","abstract_canon_sha256":"046846d725c94bf360b560bfd548db5fd5bcd65cc8c4eacffcae8cdbc252d79f"},"schema_version":"1.0"},"canonical_sha256":"07832790eccdc8078c7ae4e7514689a5956d62e337a8faf38bc475e5d4d453e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:33.324179Z","signature_b64":"7ruZ9ZIj2KUTHoU9sVWTu22Yr+5sUMGpytZcspF0LtSdg0s2OsP55F9OJqecsjsNDKoB9yMYaiNyzXMYHeCpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07832790eccdc8078c7ae4e7514689a5956d62e337a8faf38bc475e5d4d453e9","last_reissued_at":"2026-05-18T00:57:33.323769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:33.323769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06629","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":"2026-05-18T00:57:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ozmIR02pp+dJP3Rx0FCDYt1KYHubFtlfq3Bt/MYoQax3w9MUqXc6SCVTpRaiTXvpWeIL6/uRoQDP+rzw4UKtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:41:06.415003Z"},"content_sha256":"a79caf989cde40564c08fb5c3b4d0e0279cd364d660712c8fd1d222992abfd0b","schema_version":"1.0","event_id":"sha256:a79caf989cde40564c08fb5c3b4d0e0279cd364d660712c8fd1d222992abfd0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A6BSPEHMZXEAPDD24TTVCRUJUW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremal hypergraphs for matching number and domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Liying Kang, Shan Li, Yanxia Dong","submitted_at":"2016-11-21T01:42:55Z","abstract_excerpt":"A matching in a hypergraph $\\mathcal{H}$ is a set of pairwise disjoint hyperedges. The matching number $\\nu(\\mathcal{H})$ of $\\mathcal{H}$ is the size of a maximum matching in $\\mathcal{H}$. A subset $D$ of vertices of $\\mathcal{H}$ is a dominating set of $\\mathcal{H}$ if for every $v\\in V\\setminus D$ there exists $u\\in D$ such that $u$ and $v$ lie in an hyperedge of $\\mathcal{H}$. The cardinality of a minimum dominating set of $\\mathcal{H}$ is the domination number of $\\mathcal{H}$, denoted by $\\gamma(\\mathcal{H})$. It was proved that $\\gamma(\\mathcal{H})\\leq (r-1)\\nu(\\mathcal{H})$ for $r$-un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06629","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":"2026-05-18T00:57:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HpY2ucYmgGbOATk70qP7er+TDZmcxbK7l0cSGuR8GQJFilIOwMN1BrFmNrVxf5N3YDeChBzDa3dejgnYW2dNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:41:06.415681Z"},"content_sha256":"c73d492979aa6a07ede4e1f65842d78e689a960c5ecb3f9469ac3e2cf2dd61e1","schema_version":"1.0","event_id":"sha256:c73d492979aa6a07ede4e1f65842d78e689a960c5ecb3f9469ac3e2cf2dd61e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A6BSPEHMZXEAPDD24TTVCRUJUW/bundle.json","state_url":"https://pith.science/pith/A6BSPEHMZXEAPDD24TTVCRUJUW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A6BSPEHMZXEAPDD24TTVCRUJUW/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":"2026-05-27T05:41:06Z","links":{"resolver":"https://pith.science/pith/A6BSPEHMZXEAPDD24TTVCRUJUW","bundle":"https://pith.science/pith/A6BSPEHMZXEAPDD24TTVCRUJUW/bundle.json","state":"https://pith.science/pith/A6BSPEHMZXEAPDD24TTVCRUJUW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A6BSPEHMZXEAPDD24TTVCRUJUW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A6BSPEHMZXEAPDD24TTVCRUJUW","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":"046846d725c94bf360b560bfd548db5fd5bcd65cc8c4eacffcae8cdbc252d79f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T01:42:55Z","title_canon_sha256":"ba0fe40d8f26ffbdcff40955f696be9e2dc23cb18d838a17271161b5ae27bf47"},"schema_version":"1.0","source":{"id":"1611.06629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06629","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06629v1","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06629","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"A6BSPEHMZXEA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A6BSPEHMZXEAPDD2","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A6BSPEHM","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:c73d492979aa6a07ede4e1f65842d78e689a960c5ecb3f9469ac3e2cf2dd61e1","target":"graph","created_at":"2026-05-18T00:57:33Z","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":"A matching in a hypergraph $\\mathcal{H}$ is a set of pairwise disjoint hyperedges. The matching number $\\nu(\\mathcal{H})$ of $\\mathcal{H}$ is the size of a maximum matching in $\\mathcal{H}$. A subset $D$ of vertices of $\\mathcal{H}$ is a dominating set of $\\mathcal{H}$ if for every $v\\in V\\setminus D$ there exists $u\\in D$ such that $u$ and $v$ lie in an hyperedge of $\\mathcal{H}$. The cardinality of a minimum dominating set of $\\mathcal{H}$ is the domination number of $\\mathcal{H}$, denoted by $\\gamma(\\mathcal{H})$. It was proved that $\\gamma(\\mathcal{H})\\leq (r-1)\\nu(\\mathcal{H})$ for $r$-un","authors_text":"Erfang Shan, Liying Kang, Shan Li, Yanxia Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T01:42:55Z","title":"Extremal hypergraphs for matching number and domination number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06629","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:a79caf989cde40564c08fb5c3b4d0e0279cd364d660712c8fd1d222992abfd0b","target":"record","created_at":"2026-05-18T00:57:33Z","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":"046846d725c94bf360b560bfd548db5fd5bcd65cc8c4eacffcae8cdbc252d79f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T01:42:55Z","title_canon_sha256":"ba0fe40d8f26ffbdcff40955f696be9e2dc23cb18d838a17271161b5ae27bf47"},"schema_version":"1.0","source":{"id":"1611.06629","kind":"arxiv","version":1}},"canonical_sha256":"07832790eccdc8078c7ae4e7514689a5956d62e337a8faf38bc475e5d4d453e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07832790eccdc8078c7ae4e7514689a5956d62e337a8faf38bc475e5d4d453e9","first_computed_at":"2026-05-18T00:57:33.323769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:33.323769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ruZ9ZIj2KUTHoU9sVWTu22Yr+5sUMGpytZcspF0LtSdg0s2OsP55F9OJqecsjsNDKoB9yMYaiNyzXMYHeCpDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:33.324179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a79caf989cde40564c08fb5c3b4d0e0279cd364d660712c8fd1d222992abfd0b","sha256:c73d492979aa6a07ede4e1f65842d78e689a960c5ecb3f9469ac3e2cf2dd61e1"],"state_sha256":"fdf5e43eda05be63120e30e015a237a283cea09c40c24da0681871d3e0d8ce49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wnCq5BLoYAOhEHp6Nn/xs1ySHCjvc64GQPkUK1edMd9rbV/JZ/dTJ9vIlYgJgYHO7hmQPm/qd+j6pODLO8FhAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:41:06.419389Z","bundle_sha256":"423f1552b2da254f2b8029d358cc014eda505aff24feace58b31082673667e4f"}}