{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NSYVXMBML3SIDCEPXTUOS23NX7","short_pith_number":"pith:NSYVXMBM","canonical_record":{"source":{"id":"1205.6847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-30T22:16:23Z","cross_cats_sorted":[],"title_canon_sha256":"46f9adabfadbee942d656acd72725d2aa78df43772c7ed3c2ffded154712cb59","abstract_canon_sha256":"bf9e56eb435bccd9e331e132ab95c180e16f05f032dd5b475bcc69c77a418ff9"},"schema_version":"1.0"},"canonical_sha256":"6cb15bb02c5ee481888fbce8e96b6dbfd63e0e575bd057788b5cfcea4e0ff872","source":{"kind":"arxiv","id":"1205.6847","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6847","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6847v1","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6847","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"NSYVXMBML3SI","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NSYVXMBML3SIDCEP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NSYVXMBM","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NSYVXMBML3SIDCEPXTUOS23NX7","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-30T22:16:23Z","cross_cats_sorted":[],"title_canon_sha256":"46f9adabfadbee942d656acd72725d2aa78df43772c7ed3c2ffded154712cb59","abstract_canon_sha256":"bf9e56eb435bccd9e331e132ab95c180e16f05f032dd5b475bcc69c77a418ff9"},"schema_version":"1.0"},"canonical_sha256":"6cb15bb02c5ee481888fbce8e96b6dbfd63e0e575bd057788b5cfcea4e0ff872","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:36.736449Z","signature_b64":"Xy8LJurE+BL8YvFDizjodJP9BKZiphQkK4aHvdM47ErRMKW7qvPCEj7Zc04om9iakBpHJQuG8URU9CWvx+bAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cb15bb02c5ee481888fbce8e96b6dbfd63e0e575bd057788b5cfcea4e0ff872","last_reissued_at":"2026-05-18T03:54:36.735761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:36.735761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6847","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":"2026-05-18T03:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4dq3o377zcwHTsPmqwKKlJqa50sMqOra01ImxnLqXJCnfRGa/G4TEzUx39CwdLC4dK7pYFUeWUV44CQpi0TWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:40:34.009893Z"},"content_sha256":"fdd94744f5db298e8ae4c820339cc33ced6cc36fa284f2776c841c580c1bd409","schema_version":"1.0","event_id":"sha256:fdd94744f5db298e8ae4c820339cc33ced6cc36fa284f2776c841c580c1bd409"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NSYVXMBML3SIDCEPXTUOS23NX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Maximum Number of Edges in a Hypergraph with Given Matching Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Frankl","submitted_at":"2012-05-30T22:16:23Z","abstract_excerpt":"The aim of the present paper is to prove that the maximum number of edges in a 3-uniform hypergraph on n vertices and matching number s is max{\\binom(3s+2,3), \\binom(n,3) - \\binom(n-s,3)} for all n,s, n >= 3s+2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6847","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":"2026-05-18T03:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rTmR1zOhZBRV33OQBO4hcbQDdDKJtcTSaCVOj/8Ux/fDrvkGTBZ/CTp4QUDUSllecE+CW4kZqOJaGKM8YzbXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:40:34.010241Z"},"content_sha256":"d7ef8f1140b8776d8f7f0759a4ef285f44f63a8218a1d5edad5449bfbadda7c5","schema_version":"1.0","event_id":"sha256:d7ef8f1140b8776d8f7f0759a4ef285f44f63a8218a1d5edad5449bfbadda7c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSYVXMBML3SIDCEPXTUOS23NX7/bundle.json","state_url":"https://pith.science/pith/NSYVXMBML3SIDCEPXTUOS23NX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSYVXMBML3SIDCEPXTUOS23NX7/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":"2026-06-03T14:40:34Z","links":{"resolver":"https://pith.science/pith/NSYVXMBML3SIDCEPXTUOS23NX7","bundle":"https://pith.science/pith/NSYVXMBML3SIDCEPXTUOS23NX7/bundle.json","state":"https://pith.science/pith/NSYVXMBML3SIDCEPXTUOS23NX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSYVXMBML3SIDCEPXTUOS23NX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NSYVXMBML3SIDCEPXTUOS23NX7","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":"bf9e56eb435bccd9e331e132ab95c180e16f05f032dd5b475bcc69c77a418ff9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-30T22:16:23Z","title_canon_sha256":"46f9adabfadbee942d656acd72725d2aa78df43772c7ed3c2ffded154712cb59"},"schema_version":"1.0","source":{"id":"1205.6847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6847","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6847v1","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6847","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"NSYVXMBML3SI","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NSYVXMBML3SIDCEP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NSYVXMBM","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:d7ef8f1140b8776d8f7f0759a4ef285f44f63a8218a1d5edad5449bfbadda7c5","target":"graph","created_at":"2026-05-18T03:54:36Z","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":"The aim of the present paper is to prove that the maximum number of edges in a 3-uniform hypergraph on n vertices and matching number s is max{\\binom(3s+2,3), \\binom(n,3) - \\binom(n-s,3)} for all n,s, n >= 3s+2.","authors_text":"Peter Frankl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-30T22:16:23Z","title":"On the Maximum Number of Edges in a Hypergraph with Given Matching Number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6847","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:fdd94744f5db298e8ae4c820339cc33ced6cc36fa284f2776c841c580c1bd409","target":"record","created_at":"2026-05-18T03:54:36Z","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":"bf9e56eb435bccd9e331e132ab95c180e16f05f032dd5b475bcc69c77a418ff9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-30T22:16:23Z","title_canon_sha256":"46f9adabfadbee942d656acd72725d2aa78df43772c7ed3c2ffded154712cb59"},"schema_version":"1.0","source":{"id":"1205.6847","kind":"arxiv","version":1}},"canonical_sha256":"6cb15bb02c5ee481888fbce8e96b6dbfd63e0e575bd057788b5cfcea4e0ff872","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cb15bb02c5ee481888fbce8e96b6dbfd63e0e575bd057788b5cfcea4e0ff872","first_computed_at":"2026-05-18T03:54:36.735761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:36.735761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xy8LJurE+BL8YvFDizjodJP9BKZiphQkK4aHvdM47ErRMKW7qvPCEj7Zc04om9iakBpHJQuG8URU9CWvx+bAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:36.736449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdd94744f5db298e8ae4c820339cc33ced6cc36fa284f2776c841c580c1bd409","sha256:d7ef8f1140b8776d8f7f0759a4ef285f44f63a8218a1d5edad5449bfbadda7c5"],"state_sha256":"f5fa38d055326a3d03d0bb2f19df3c8379241163cbc7a445efea7712118f7408"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dFUmX4GuJMuINupp7HweeA3pBHJK6EXaZMtx8BiQ7ui+zWbZdGwAkPaPKWflOQWWXHiymQteMAE3BMGrhjztBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:40:34.012261Z","bundle_sha256":"8ad2b8028eddc99b47a80afe628dde06c44b87d86564fe79b5bddd9c04ecdd14"}}