{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YAZFHGQHG2ZPTXP2IW5PEKARGV","short_pith_number":"pith:YAZFHGQH","canonical_record":{"source":{"id":"1109.3390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-15T15:41:59Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"a75f262426a7d556c9eb182cc24d0f9fb2167056af79cc4df208739e7cd311bf","abstract_canon_sha256":"8088c40d0d341863a329c0b55a85cb708848db134e6b99c92c316e0d7f1dc679"},"schema_version":"1.0"},"canonical_sha256":"c032539a0736b2f9ddfa45baf22811354d205afd0f898f39211c16f2c5779c6c","source":{"kind":"arxiv","id":"1109.3390","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3390","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3390v1","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3390","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"YAZFHGQHG2ZP","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YAZFHGQHG2ZPTXP2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YAZFHGQH","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YAZFHGQHG2ZPTXP2IW5PEKARGV","target":"record","payload":{"canonical_record":{"source":{"id":"1109.3390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-15T15:41:59Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"a75f262426a7d556c9eb182cc24d0f9fb2167056af79cc4df208739e7cd311bf","abstract_canon_sha256":"8088c40d0d341863a329c0b55a85cb708848db134e6b99c92c316e0d7f1dc679"},"schema_version":"1.0"},"canonical_sha256":"c032539a0736b2f9ddfa45baf22811354d205afd0f898f39211c16f2c5779c6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:56.837813Z","signature_b64":"TtnlQpXduGYh5xJaKRbpkVVNxvc3mgcjWGE3Z3hg45lcazrcRWXmDAurRirLrTt7Qrjc/YvjthyJ0xMdFKaiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c032539a0736b2f9ddfa45baf22811354d205afd0f898f39211c16f2c5779c6c","last_reissued_at":"2026-05-18T04:12:56.837434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:56.837434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.3390","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":"2026-05-18T04:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ahCjQV07eWex0ngPtGskdItB/CfPhX6peLxxIywkwW9Ng6JV0VSvvh5pQYwHN5UvmpuN4Mw/Mm2uHEuvYL3aAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:48:22.786876Z"},"content_sha256":"b727754fe1b4d496dd0d8eec5027a6da1c0cde6d8a1f188e664a292a297425f0","schema_version":"1.0","event_id":"sha256:b727754fe1b4d496dd0d8eec5027a6da1c0cde6d8a1f188e664a292a297425f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YAZFHGQHG2ZPTXP2IW5PEKARGV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Not All Saturated 3-Forests Are Tight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anna Gundert, Heidi Gebauer, Robin A. Moser, Yoshio Okamoto","submitted_at":"2011-09-15T15:41:59Z","abstract_excerpt":"A basic statement in graph theory is that every inclusion-maximal forest is connected, i.e. a tree. Using a definiton for higher dimensional forests by Graham and Lovasz and the connectivity-related notion of tightness for hypergraphs introduced by Arocha, Bracho and Neumann-Lara in, we provide an example of a saturated, i.e. inclusion-maximal 3-forest that is not tight. This resolves an open problem posed by Strausz."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3390","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":"2026-05-18T04:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rnmukHr5kQ92SkT+DsFCjM6r0hYUvqEmEVxY4HDIxBoPTRKZie6Lne/DyLhqYLgj2UYje3e4w1QOXFwlIih0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:48:22.787585Z"},"content_sha256":"83c9dbcd6273da2fb84d39ed2d7c851b68146a53a996a85bd4843fab6861a32d","schema_version":"1.0","event_id":"sha256:83c9dbcd6273da2fb84d39ed2d7c851b68146a53a996a85bd4843fab6861a32d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAZFHGQHG2ZPTXP2IW5PEKARGV/bundle.json","state_url":"https://pith.science/pith/YAZFHGQHG2ZPTXP2IW5PEKARGV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAZFHGQHG2ZPTXP2IW5PEKARGV/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":"2026-05-28T21:48:22Z","links":{"resolver":"https://pith.science/pith/YAZFHGQHG2ZPTXP2IW5PEKARGV","bundle":"https://pith.science/pith/YAZFHGQHG2ZPTXP2IW5PEKARGV/bundle.json","state":"https://pith.science/pith/YAZFHGQHG2ZPTXP2IW5PEKARGV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAZFHGQHG2ZPTXP2IW5PEKARGV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YAZFHGQHG2ZPTXP2IW5PEKARGV","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":"8088c40d0d341863a329c0b55a85cb708848db134e6b99c92c316e0d7f1dc679","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-15T15:41:59Z","title_canon_sha256":"a75f262426a7d556c9eb182cc24d0f9fb2167056af79cc4df208739e7cd311bf"},"schema_version":"1.0","source":{"id":"1109.3390","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3390","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3390v1","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3390","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"YAZFHGQHG2ZP","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YAZFHGQHG2ZPTXP2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YAZFHGQH","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:83c9dbcd6273da2fb84d39ed2d7c851b68146a53a996a85bd4843fab6861a32d","target":"graph","created_at":"2026-05-18T04:12:56Z","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 basic statement in graph theory is that every inclusion-maximal forest is connected, i.e. a tree. Using a definiton for higher dimensional forests by Graham and Lovasz and the connectivity-related notion of tightness for hypergraphs introduced by Arocha, Bracho and Neumann-Lara in, we provide an example of a saturated, i.e. inclusion-maximal 3-forest that is not tight. This resolves an open problem posed by Strausz.","authors_text":"Anna Gundert, Heidi Gebauer, Robin A. Moser, Yoshio Okamoto","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-15T15:41:59Z","title":"Not All Saturated 3-Forests Are Tight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3390","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:b727754fe1b4d496dd0d8eec5027a6da1c0cde6d8a1f188e664a292a297425f0","target":"record","created_at":"2026-05-18T04:12:56Z","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":"8088c40d0d341863a329c0b55a85cb708848db134e6b99c92c316e0d7f1dc679","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-15T15:41:59Z","title_canon_sha256":"a75f262426a7d556c9eb182cc24d0f9fb2167056af79cc4df208739e7cd311bf"},"schema_version":"1.0","source":{"id":"1109.3390","kind":"arxiv","version":1}},"canonical_sha256":"c032539a0736b2f9ddfa45baf22811354d205afd0f898f39211c16f2c5779c6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c032539a0736b2f9ddfa45baf22811354d205afd0f898f39211c16f2c5779c6c","first_computed_at":"2026-05-18T04:12:56.837434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:56.837434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TtnlQpXduGYh5xJaKRbpkVVNxvc3mgcjWGE3Z3hg45lcazrcRWXmDAurRirLrTt7Qrjc/YvjthyJ0xMdFKaiAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:56.837813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3390","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b727754fe1b4d496dd0d8eec5027a6da1c0cde6d8a1f188e664a292a297425f0","sha256:83c9dbcd6273da2fb84d39ed2d7c851b68146a53a996a85bd4843fab6861a32d"],"state_sha256":"ba4d3695026f3d3d19a874a7e4de1367a4330ddd1ba72577f70b9f72915ea689"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8qAu45wb5Uqc3cx3gHrRm3qKCsBV7tPPczwGozrndXJ8Ac0CAom/ASTbk/RxOfWRvJyDBlWxYD0Pug4+BegDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:48:22.791159Z","bundle_sha256":"883f39e303fa42096de78cb0c5476b0a8efd2ca2cb2e5770d44e3bca7c8d2e94"}}