{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OZD7G4DSIFIVDOCEHBU7ZQW643","short_pith_number":"pith:OZD7G4DS","canonical_record":{"source":{"id":"1609.01884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-07T08:47:58Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9f244b0379d23d8cb243a9f3fca2dca362b25730de43fda6bafab2a29ffab880","abstract_canon_sha256":"0848c015c08816344ad2c02f4df7d9e77d6b51e0d6702f0e98d7c980abdef16e"},"schema_version":"1.0"},"canonical_sha256":"7647f37072415151b8443869fcc2dee6dcea6f8495c09e88ad1579ff2ebada51","source":{"kind":"arxiv","id":"1609.01884","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01884","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01884v2","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01884","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"OZD7G4DSIFIV","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OZD7G4DSIFIVDOCE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OZD7G4DS","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OZD7G4DSIFIVDOCEHBU7ZQW643","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-07T08:47:58Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9f244b0379d23d8cb243a9f3fca2dca362b25730de43fda6bafab2a29ffab880","abstract_canon_sha256":"0848c015c08816344ad2c02f4df7d9e77d6b51e0d6702f0e98d7c980abdef16e"},"schema_version":"1.0"},"canonical_sha256":"7647f37072415151b8443869fcc2dee6dcea6f8495c09e88ad1579ff2ebada51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:32.736695Z","signature_b64":"cZ1jveCkag4CAMre89/jAIbGOLrB/heOM4HZqdwEZHn7o//pmbehe0Njj2bh7W21rNosk28q/futY3JdtdQ3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7647f37072415151b8443869fcc2dee6dcea6f8495c09e88ad1579ff2ebada51","last_reissued_at":"2026-05-18T00:03:32.736154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:32.736154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01884","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":"2026-05-18T00:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61jB+mQ7j59d0uBEUuju8Y+1Qa4SJlY2QUNYJz16SzT601Dh5iTdvTqCefSzdL11Ag1vF/k0IEWQ/TjVWVL8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:39:06.199859Z"},"content_sha256":"9851233a8ea7e4554caf94e360c8bbac831bca6c5bf0f116c69530a46f73c9c9","schema_version":"1.0","event_id":"sha256:9851233a8ea7e4554caf94e360c8bbac831bca6c5bf0f116c69530a46f73c9c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OZD7G4DSIFIVDOCEHBU7ZQW643","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on Large H-Intersecting Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Nathan Keller, Noam Lifshitz","submitted_at":"2016-09-07T08:47:58Z","abstract_excerpt":"A family $F$ of graphs on a fixed set of $n$ vertices is called triangle-intersecting if for any $G_1,G_2 \\in F$, the intersection $G_1 \\cap G_2$ contains a triangle. More generally, for a fixed graph $H$, a family $F$ is $H$-intersecting if the intersection of any two graphs in $F$ contains a sub-graph isomorphic to $H$.\n  In [D. Ellis, Y. Filmus, and E. Friedgut, Triangle-intersecting families of graphs, J. Eur. Math. Soc. 14 (2012), pp. 841--885], Ellis, Filmus and Friedgut proved a 36-year old conjecture of Simonovits and S\\'{o}s stating that the maximal size of a triangle-intersecting fam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01884","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":"2026-05-18T00:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuNCZ4pjJe8n7fuXt4CBqLbg5NG4McgjWsZrBsfNEEBC4vMnV8kittsq+0wZSxyJqG4ilmYRYcjcrW0n9Sk5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:39:06.200204Z"},"content_sha256":"582221c326551930a89606bb380823f6c5e2b9b8f9b152051c623cb7d2bec578","schema_version":"1.0","event_id":"sha256:582221c326551930a89606bb380823f6c5e2b9b8f9b152051c623cb7d2bec578"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZD7G4DSIFIVDOCEHBU7ZQW643/bundle.json","state_url":"https://pith.science/pith/OZD7G4DSIFIVDOCEHBU7ZQW643/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZD7G4DSIFIVDOCEHBU7ZQW643/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":"2026-06-25T22:39:06Z","links":{"resolver":"https://pith.science/pith/OZD7G4DSIFIVDOCEHBU7ZQW643","bundle":"https://pith.science/pith/OZD7G4DSIFIVDOCEHBU7ZQW643/bundle.json","state":"https://pith.science/pith/OZD7G4DSIFIVDOCEHBU7ZQW643/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZD7G4DSIFIVDOCEHBU7ZQW643/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OZD7G4DSIFIVDOCEHBU7ZQW643","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":"0848c015c08816344ad2c02f4df7d9e77d6b51e0d6702f0e98d7c980abdef16e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-07T08:47:58Z","title_canon_sha256":"9f244b0379d23d8cb243a9f3fca2dca362b25730de43fda6bafab2a29ffab880"},"schema_version":"1.0","source":{"id":"1609.01884","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01884","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01884v2","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01884","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"OZD7G4DSIFIV","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OZD7G4DSIFIVDOCE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OZD7G4DS","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:582221c326551930a89606bb380823f6c5e2b9b8f9b152051c623cb7d2bec578","target":"graph","created_at":"2026-05-18T00:03:32Z","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 family $F$ of graphs on a fixed set of $n$ vertices is called triangle-intersecting if for any $G_1,G_2 \\in F$, the intersection $G_1 \\cap G_2$ contains a triangle. More generally, for a fixed graph $H$, a family $F$ is $H$-intersecting if the intersection of any two graphs in $F$ contains a sub-graph isomorphic to $H$.\n  In [D. Ellis, Y. Filmus, and E. Friedgut, Triangle-intersecting families of graphs, J. Eur. Math. Soc. 14 (2012), pp. 841--885], Ellis, Filmus and Friedgut proved a 36-year old conjecture of Simonovits and S\\'{o}s stating that the maximal size of a triangle-intersecting fam","authors_text":"Nathan Keller, Noam Lifshitz","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-07T08:47:58Z","title":"A Note on Large H-Intersecting Families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01884","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":"sha256:9851233a8ea7e4554caf94e360c8bbac831bca6c5bf0f116c69530a46f73c9c9","target":"record","created_at":"2026-05-18T00:03:32Z","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":"0848c015c08816344ad2c02f4df7d9e77d6b51e0d6702f0e98d7c980abdef16e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-07T08:47:58Z","title_canon_sha256":"9f244b0379d23d8cb243a9f3fca2dca362b25730de43fda6bafab2a29ffab880"},"schema_version":"1.0","source":{"id":"1609.01884","kind":"arxiv","version":2}},"canonical_sha256":"7647f37072415151b8443869fcc2dee6dcea6f8495c09e88ad1579ff2ebada51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7647f37072415151b8443869fcc2dee6dcea6f8495c09e88ad1579ff2ebada51","first_computed_at":"2026-05-18T00:03:32.736154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:32.736154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cZ1jveCkag4CAMre89/jAIbGOLrB/heOM4HZqdwEZHn7o//pmbehe0Njj2bh7W21rNosk28q/futY3JdtdQ3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:32.736695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01884","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9851233a8ea7e4554caf94e360c8bbac831bca6c5bf0f116c69530a46f73c9c9","sha256:582221c326551930a89606bb380823f6c5e2b9b8f9b152051c623cb7d2bec578"],"state_sha256":"c9c466fbd71a19b260782f3efee2f9548cb73bc4d02cf309baf7597f7f74073d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jT4fGOkbdihdcg/9IaZ33nCVggsy+hcyAWQipMyI61Rg5+AEu+3QMxpcvixoycVa3JodCY6VFx+NP0ajlZu3AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:39:06.202257Z","bundle_sha256":"deb7451bf42a4832e2baa0986daae9f0110aa02f46c87d76e0f04e5f7d689b9e"}}