{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:MZ7WW55DGT2CYXC72SYIJZYXNS","short_pith_number":"pith:MZ7WW55D","canonical_record":{"source":{"id":"2107.14713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-07-30T15:35:39Z","cross_cats_sorted":[],"title_canon_sha256":"ab9f1c0231cbc7b1a4f5f8ab8670a147fb992eedb37a72e8249a74358e4c64df","abstract_canon_sha256":"d2102903880da5868f3c2ddba97f7ad47e083c537c13847107abbf04085bec41"},"schema_version":"1.0"},"canonical_sha256":"667f6b77a334f42c5c5fd4b084e7176cad020bf8222d83b0906e6acb35c7e192","source":{"kind":"arxiv","id":"2107.14713","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.14713","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"2107.14713v1","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.14713","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"MZ7WW55DGT2C","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"pith_short_16","alias_value":"MZ7WW55DGT2CYXC7","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"pith_short_8","alias_value":"MZ7WW55D","created_at":"2026-07-05T03:02:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:MZ7WW55DGT2CYXC72SYIJZYXNS","target":"record","payload":{"canonical_record":{"source":{"id":"2107.14713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-07-30T15:35:39Z","cross_cats_sorted":[],"title_canon_sha256":"ab9f1c0231cbc7b1a4f5f8ab8670a147fb992eedb37a72e8249a74358e4c64df","abstract_canon_sha256":"d2102903880da5868f3c2ddba97f7ad47e083c537c13847107abbf04085bec41"},"schema_version":"1.0"},"canonical_sha256":"667f6b77a334f42c5c5fd4b084e7176cad020bf8222d83b0906e6acb35c7e192","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:02:03.748916Z","signature_b64":"PZJK69K9cehHUbrxy7ckkBTC6ZEBAtXUcg76Uh7Bhu139xL4ZFEb3gxjHVjOaLJn5t9m/FP3L/Ui6k+p6XX7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"667f6b77a334f42c5c5fd4b084e7176cad020bf8222d83b0906e6acb35c7e192","last_reissued_at":"2026-07-05T03:02:03.748080Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:02:03.748080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.14713","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":"2026-07-05T03:02:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfCJX9rG5e7/U/xccvTLducOgtJ+b1EFBqH9jLVLirghHK7b2ffqY8kkKWibtdLwivUn3YlUexFCpk7WiiwBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:30:32.506205Z"},"content_sha256":"c88e0a96444373675acaac59a17874fefa93831f9188562421caa7471c5f894c","schema_version":"1.0","event_id":"sha256:c88e0a96444373675acaac59a17874fefa93831f9188562421caa7471c5f894c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:MZ7WW55DGT2CYXC72SYIJZYXNS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Crowns in linear $3$-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alvaro Carbonero, Andr\\'as Gy\\'arf\\'as, Jing Guo, Rona Wang, Shiyu Yan, Willem Fletcher","submitted_at":"2021-07-30T15:35:39Z","abstract_excerpt":"A \\textit{linear $3$-graph}, $H = (V, E)$, is a set, $V$, of vertices together with a set, $E$, of $3$-element subsets of $V$, called edges, so that any two distinct edges intersect in at most one vertex. The linear Tur\\'an number, ${\\rm ex}(n,F)$, is the maximum number of edges in a linear $3$-graph $H$ with $n$ vertices containing no copy of $F$.\n  We focus here on the \\textit{crown}, $C$, which consists of three pairwise disjoint edges (jewels) and a fourth edge (base) which intersects all of the jewels. Our main result is that every linear $3$-graph with minimum degree at least $4$ contain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.14713","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.14713/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:02:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9H9a++L+cdq6xKvWEwwmJGNvOfPu3INxL80a4jD98ocyDBsAkgkEJZfppA+3LvPIGhXnDYtX+hoQlpMNwv7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:30:32.506805Z"},"content_sha256":"8b534e49a066b68a6393fb36043129277bde950511009774e5336bfb877efc2c","schema_version":"1.0","event_id":"sha256:8b534e49a066b68a6393fb36043129277bde950511009774e5336bfb877efc2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZ7WW55DGT2CYXC72SYIJZYXNS/bundle.json","state_url":"https://pith.science/pith/MZ7WW55DGT2CYXC72SYIJZYXNS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZ7WW55DGT2CYXC72SYIJZYXNS/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":"2026-08-06T11:30:32Z","links":{"resolver":"https://pith.science/pith/MZ7WW55DGT2CYXC72SYIJZYXNS","bundle":"https://pith.science/pith/MZ7WW55DGT2CYXC72SYIJZYXNS/bundle.json","state":"https://pith.science/pith/MZ7WW55DGT2CYXC72SYIJZYXNS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZ7WW55DGT2CYXC72SYIJZYXNS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MZ7WW55DGT2CYXC72SYIJZYXNS","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":"d2102903880da5868f3c2ddba97f7ad47e083c537c13847107abbf04085bec41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-07-30T15:35:39Z","title_canon_sha256":"ab9f1c0231cbc7b1a4f5f8ab8670a147fb992eedb37a72e8249a74358e4c64df"},"schema_version":"1.0","source":{"id":"2107.14713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.14713","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"2107.14713v1","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.14713","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"MZ7WW55DGT2C","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"pith_short_16","alias_value":"MZ7WW55DGT2CYXC7","created_at":"2026-07-05T03:02:03Z"},{"alias_kind":"pith_short_8","alias_value":"MZ7WW55D","created_at":"2026-07-05T03:02:03Z"}],"graph_snapshots":[{"event_id":"sha256:8b534e49a066b68a6393fb36043129277bde950511009774e5336bfb877efc2c","target":"graph","created_at":"2026-07-05T03:02:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.14713/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A \\textit{linear $3$-graph}, $H = (V, E)$, is a set, $V$, of vertices together with a set, $E$, of $3$-element subsets of $V$, called edges, so that any two distinct edges intersect in at most one vertex. The linear Tur\\'an number, ${\\rm ex}(n,F)$, is the maximum number of edges in a linear $3$-graph $H$ with $n$ vertices containing no copy of $F$.\n  We focus here on the \\textit{crown}, $C$, which consists of three pairwise disjoint edges (jewels) and a fourth edge (base) which intersects all of the jewels. Our main result is that every linear $3$-graph with minimum degree at least $4$ contain","authors_text":"Alvaro Carbonero, Andr\\'as Gy\\'arf\\'as, Jing Guo, Rona Wang, Shiyu Yan, Willem Fletcher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-07-30T15:35:39Z","title":"Crowns in linear $3$-graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.14713","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:c88e0a96444373675acaac59a17874fefa93831f9188562421caa7471c5f894c","target":"record","created_at":"2026-07-05T03:02:03Z","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":"d2102903880da5868f3c2ddba97f7ad47e083c537c13847107abbf04085bec41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-07-30T15:35:39Z","title_canon_sha256":"ab9f1c0231cbc7b1a4f5f8ab8670a147fb992eedb37a72e8249a74358e4c64df"},"schema_version":"1.0","source":{"id":"2107.14713","kind":"arxiv","version":1}},"canonical_sha256":"667f6b77a334f42c5c5fd4b084e7176cad020bf8222d83b0906e6acb35c7e192","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"667f6b77a334f42c5c5fd4b084e7176cad020bf8222d83b0906e6acb35c7e192","first_computed_at":"2026-07-05T03:02:03.748080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:02:03.748080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZJK69K9cehHUbrxy7ckkBTC6ZEBAtXUcg76Uh7Bhu139xL4ZFEb3gxjHVjOaLJn5t9m/FP3L/Ui6k+p6XX7Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:02:03.748916Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.14713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c88e0a96444373675acaac59a17874fefa93831f9188562421caa7471c5f894c","sha256:8b534e49a066b68a6393fb36043129277bde950511009774e5336bfb877efc2c"],"state_sha256":"192795010642b3e81f5fdbaaa6993207d5408b92de77c8de01d8d5d860b7753b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhciDuw1lC9WiqNIjchXcLDWYQgDd/rs2DiF2UjaYu4W4b6qyzE0xKpaq8eKO0y5/IlU7iEmynjnhJsb7cu5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T11:30:32.510684Z","bundle_sha256":"990b2dfdee82c289cd8c85d5d5357a2d5ec4ce0a2afc8af23ca2905df30beb18"}}