{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UGGI2YLOTUQUZPUT2EWLHDCTSC","short_pith_number":"pith:UGGI2YLO","canonical_record":{"source":{"id":"2405.16452","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-05-26T06:47:33Z","cross_cats_sorted":[],"title_canon_sha256":"5536746b20e30b6605d03fa4ca453eb6c6008bca1cbf9b8a858ded487631096f","abstract_canon_sha256":"ee4ecf5531a798fd3c7dd44ed778178b7f4b12d321d2edd1279bc4b172dba595"},"schema_version":"1.0"},"canonical_sha256":"a18c8d616e9d214cbe93d12cb38c53909d4fba94dc6747afb7a60b7247dee7f5","source":{"kind":"arxiv","id":"2405.16452","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16452","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16452v1","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16452","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_12","alias_value":"UGGI2YLOTUQU","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_16","alias_value":"UGGI2YLOTUQUZPUT","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_8","alias_value":"UGGI2YLO","created_at":"2026-07-05T08:23:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UGGI2YLOTUQUZPUT2EWLHDCTSC","target":"record","payload":{"canonical_record":{"source":{"id":"2405.16452","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-05-26T06:47:33Z","cross_cats_sorted":[],"title_canon_sha256":"5536746b20e30b6605d03fa4ca453eb6c6008bca1cbf9b8a858ded487631096f","abstract_canon_sha256":"ee4ecf5531a798fd3c7dd44ed778178b7f4b12d321d2edd1279bc4b172dba595"},"schema_version":"1.0"},"canonical_sha256":"a18c8d616e9d214cbe93d12cb38c53909d4fba94dc6747afb7a60b7247dee7f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:23:30.577837Z","signature_b64":"4cH1UfiOaGgcdzIFuKI2V4W6RmEHVVfL15KHKCS2kKeMJ7iaRbcaSBEhJR89gKOkmuy4uZQB9e6kJYxRxSSFDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a18c8d616e9d214cbe93d12cb38c53909d4fba94dc6747afb7a60b7247dee7f5","last_reissued_at":"2026-07-05T08:23:30.577321Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:23:30.577321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.16452","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":"2026-07-05T08:23:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"08wK1nrJWdgQ+K5XCQmV53FXP7zTyuWI5QSeg0s9kbMq/2thuCREMuRjcVMENEMYgkcHoWU8NMqByn3ZhhLbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T02:42:09.881298Z"},"content_sha256":"91681804812a1359a2446c7ea71aaa45d1cd9b2e34a4d0ca2e3a75378d35bd14","schema_version":"1.0","event_id":"sha256:91681804812a1359a2446c7ea71aaa45d1cd9b2e34a4d0ca2e3a75378d35bd14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UGGI2YLOTUQUZPUT2EWLHDCTSC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangle-free triple systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G\\'abor Simonyi, Ido Goorevitch, Peter Frankl, Ron Holzman, Zolt\\'an F\\\"uredi","submitted_at":"2024-05-26T06:47:33Z","abstract_excerpt":"There are four non-isomorphic configurations of triples that can form a triangle in a $3$-uniform hypergraph. Forbidding different combinations of these four configurations, fifteen extremal problems can be defined, several of which already appeared in the literature in some different context. Here we systematically study all of these problems solving the new cases exactly or asymptotically. In many cases we also characterize the extremal constructions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16452","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/2405.16452/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":"2026-07-05T08:23:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xf0uk6ZfhcCAFAmDW5e/MpKnHoiFhq+TNFnE6awRh1fG/aGJQPJ2SrVgG06WlSWm6zlsAbJ7XQRNK6ceO5VaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T02:42:09.881695Z"},"content_sha256":"c44da8e9da0c238612ae817236d7af4292c542321fb28d26bfbafb6a2502c671","schema_version":"1.0","event_id":"sha256:c44da8e9da0c238612ae817236d7af4292c542321fb28d26bfbafb6a2502c671"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UGGI2YLOTUQUZPUT2EWLHDCTSC/bundle.json","state_url":"https://pith.science/pith/UGGI2YLOTUQUZPUT2EWLHDCTSC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UGGI2YLOTUQUZPUT2EWLHDCTSC/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":"2026-07-09T02:42:09Z","links":{"resolver":"https://pith.science/pith/UGGI2YLOTUQUZPUT2EWLHDCTSC","bundle":"https://pith.science/pith/UGGI2YLOTUQUZPUT2EWLHDCTSC/bundle.json","state":"https://pith.science/pith/UGGI2YLOTUQUZPUT2EWLHDCTSC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UGGI2YLOTUQUZPUT2EWLHDCTSC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UGGI2YLOTUQUZPUT2EWLHDCTSC","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":"ee4ecf5531a798fd3c7dd44ed778178b7f4b12d321d2edd1279bc4b172dba595","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-05-26T06:47:33Z","title_canon_sha256":"5536746b20e30b6605d03fa4ca453eb6c6008bca1cbf9b8a858ded487631096f"},"schema_version":"1.0","source":{"id":"2405.16452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16452","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16452v1","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16452","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_12","alias_value":"UGGI2YLOTUQU","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_16","alias_value":"UGGI2YLOTUQUZPUT","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_8","alias_value":"UGGI2YLO","created_at":"2026-07-05T08:23:30Z"}],"graph_snapshots":[{"event_id":"sha256:c44da8e9da0c238612ae817236d7af4292c542321fb28d26bfbafb6a2502c671","target":"graph","created_at":"2026-07-05T08:23:30Z","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/2405.16452/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There are four non-isomorphic configurations of triples that can form a triangle in a $3$-uniform hypergraph. Forbidding different combinations of these four configurations, fifteen extremal problems can be defined, several of which already appeared in the literature in some different context. Here we systematically study all of these problems solving the new cases exactly or asymptotically. In many cases we also characterize the extremal constructions.","authors_text":"G\\'abor Simonyi, Ido Goorevitch, Peter Frankl, Ron Holzman, Zolt\\'an F\\\"uredi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-05-26T06:47:33Z","title":"Triangle-free triple systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16452","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":"sha256:91681804812a1359a2446c7ea71aaa45d1cd9b2e34a4d0ca2e3a75378d35bd14","target":"record","created_at":"2026-07-05T08:23:30Z","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":"ee4ecf5531a798fd3c7dd44ed778178b7f4b12d321d2edd1279bc4b172dba595","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-05-26T06:47:33Z","title_canon_sha256":"5536746b20e30b6605d03fa4ca453eb6c6008bca1cbf9b8a858ded487631096f"},"schema_version":"1.0","source":{"id":"2405.16452","kind":"arxiv","version":1}},"canonical_sha256":"a18c8d616e9d214cbe93d12cb38c53909d4fba94dc6747afb7a60b7247dee7f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a18c8d616e9d214cbe93d12cb38c53909d4fba94dc6747afb7a60b7247dee7f5","first_computed_at":"2026-07-05T08:23:30.577321Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:23:30.577321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4cH1UfiOaGgcdzIFuKI2V4W6RmEHVVfL15KHKCS2kKeMJ7iaRbcaSBEhJR89gKOkmuy4uZQB9e6kJYxRxSSFDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:23:30.577837Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.16452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91681804812a1359a2446c7ea71aaa45d1cd9b2e34a4d0ca2e3a75378d35bd14","sha256:c44da8e9da0c238612ae817236d7af4292c542321fb28d26bfbafb6a2502c671"],"state_sha256":"9f4db96a340b1cdbe81272065099f07762df649f5ee1eea1f8418b061379fd64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tZcUHt5DNr9kBPAlSolSVutnuzWkakHw/K7t61C6m8NkmQXoVKCbZe/v4gFSsD+8KctWrpDY5evnP6fDylwBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T02:42:09.883727Z","bundle_sha256":"c4d2b40ed0d9f78b0d0bcba477aae9f809e119987ce4876a4e1fa83ac2b9657d"}}