{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:DTXYBKX4TR5MD3TH4PXX3NEJNO","short_pith_number":"pith:DTXYBKX4","canonical_record":{"source":{"id":"2504.16973","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-23T16:11:48Z","cross_cats_sorted":[],"title_canon_sha256":"6f2cfea12dcf093281e74120f9fd29a9b08553d56d4be32c43a84def404436ae","abstract_canon_sha256":"0ebe800b4159cb2ee6381a36999c58e38936eb48b8b4954357fa53f6483b182b"},"schema_version":"1.0"},"canonical_sha256":"1cef80aafc9c7ac1ee67e3ef7db4896ba9347a8ae2ecc2d079ede8d1dc566912","source":{"kind":"arxiv","id":"2504.16973","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16973","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16973v3","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16973","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"pith_short_12","alias_value":"DTXYBKX4TR5M","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"pith_short_16","alias_value":"DTXYBKX4TR5MD3TH","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"pith_short_8","alias_value":"DTXYBKX4","created_at":"2026-07-05T11:44:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:DTXYBKX4TR5MD3TH4PXX3NEJNO","target":"record","payload":{"canonical_record":{"source":{"id":"2504.16973","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-23T16:11:48Z","cross_cats_sorted":[],"title_canon_sha256":"6f2cfea12dcf093281e74120f9fd29a9b08553d56d4be32c43a84def404436ae","abstract_canon_sha256":"0ebe800b4159cb2ee6381a36999c58e38936eb48b8b4954357fa53f6483b182b"},"schema_version":"1.0"},"canonical_sha256":"1cef80aafc9c7ac1ee67e3ef7db4896ba9347a8ae2ecc2d079ede8d1dc566912","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:04.596882Z","signature_b64":"t2PILDvunn5L9LO93y0TInXacmmwu/0dTmVt5K8fGLJ/jgaQVHCl5OrvFkSnEh0Ko5vBKDoxT6xgi1h/mq75DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cef80aafc9c7ac1ee67e3ef7db4896ba9347a8ae2ecc2d079ede8d1dc566912","last_reissued_at":"2026-07-05T11:44:04.596329Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:04.596329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.16973","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:44:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2sZ4qPKRJh5ry95ncm9hTr+cgavooXN7M/pPY2r1KwVVM2Th6dy+tEjhVNeXQWpjFxuIuWgjbnxAI70/YrhWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T04:38:28.956833Z"},"content_sha256":"4328422c7af95f72b5c7ee463b42c7f9b959d223e68ddfe77573b98219921989","schema_version":"1.0","event_id":"sha256:4328422c7af95f72b5c7ee463b42c7f9b959d223e68ddfe77573b98219921989"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:DTXYBKX4TR5MD3TH4PXX3NEJNO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Tur\\'an number of the $G_{3\\times 3}$ in linear hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jozsef Solymosi","submitted_at":"2025-04-23T16:11:48Z","abstract_excerpt":"We show a construction for dense 3-uniform linear hypergraphs without $3\\times 3$ grids, improving the lower bound on its Tur\\'an number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16973","kind":"arxiv","version":3},"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/2504.16973/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":"2026-07-05T11:44:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0pjApPVW0xgyzxFcBC+hZ8zViLgsQH/g2b9iKC8IsA7H2CFByGfQgK0pNXmoV5XTdnf9sKL6Xs0cKmv9h6uzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T04:38:28.957184Z"},"content_sha256":"4535ecb05ccbab56cfe74c5871e8507711f76f32f83a158ae2515cda69b264e4","schema_version":"1.0","event_id":"sha256:4535ecb05ccbab56cfe74c5871e8507711f76f32f83a158ae2515cda69b264e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTXYBKX4TR5MD3TH4PXX3NEJNO/bundle.json","state_url":"https://pith.science/pith/DTXYBKX4TR5MD3TH4PXX3NEJNO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTXYBKX4TR5MD3TH4PXX3NEJNO/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":"2026-07-24T04:38:28Z","links":{"resolver":"https://pith.science/pith/DTXYBKX4TR5MD3TH4PXX3NEJNO","bundle":"https://pith.science/pith/DTXYBKX4TR5MD3TH4PXX3NEJNO/bundle.json","state":"https://pith.science/pith/DTXYBKX4TR5MD3TH4PXX3NEJNO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTXYBKX4TR5MD3TH4PXX3NEJNO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DTXYBKX4TR5MD3TH4PXX3NEJNO","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":"0ebe800b4159cb2ee6381a36999c58e38936eb48b8b4954357fa53f6483b182b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-23T16:11:48Z","title_canon_sha256":"6f2cfea12dcf093281e74120f9fd29a9b08553d56d4be32c43a84def404436ae"},"schema_version":"1.0","source":{"id":"2504.16973","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16973","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16973v3","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16973","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"pith_short_12","alias_value":"DTXYBKX4TR5M","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"pith_short_16","alias_value":"DTXYBKX4TR5MD3TH","created_at":"2026-07-05T11:44:04Z"},{"alias_kind":"pith_short_8","alias_value":"DTXYBKX4","created_at":"2026-07-05T11:44:04Z"}],"graph_snapshots":[{"event_id":"sha256:4535ecb05ccbab56cfe74c5871e8507711f76f32f83a158ae2515cda69b264e4","target":"graph","created_at":"2026-07-05T11:44:04Z","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/2504.16973/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show a construction for dense 3-uniform linear hypergraphs without $3\\times 3$ grids, improving the lower bound on its Tur\\'an number.","authors_text":"Jozsef Solymosi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-23T16:11:48Z","title":"On the Tur\\'an number of the $G_{3\\times 3}$ in linear hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16973","kind":"arxiv","version":3},"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":"sha256:4328422c7af95f72b5c7ee463b42c7f9b959d223e68ddfe77573b98219921989","target":"record","created_at":"2026-07-05T11:44:04Z","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":"0ebe800b4159cb2ee6381a36999c58e38936eb48b8b4954357fa53f6483b182b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-23T16:11:48Z","title_canon_sha256":"6f2cfea12dcf093281e74120f9fd29a9b08553d56d4be32c43a84def404436ae"},"schema_version":"1.0","source":{"id":"2504.16973","kind":"arxiv","version":3}},"canonical_sha256":"1cef80aafc9c7ac1ee67e3ef7db4896ba9347a8ae2ecc2d079ede8d1dc566912","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cef80aafc9c7ac1ee67e3ef7db4896ba9347a8ae2ecc2d079ede8d1dc566912","first_computed_at":"2026-07-05T11:44:04.596329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:44:04.596329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t2PILDvunn5L9LO93y0TInXacmmwu/0dTmVt5K8fGLJ/jgaQVHCl5OrvFkSnEh0Ko5vBKDoxT6xgi1h/mq75DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:44:04.596882Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.16973","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4328422c7af95f72b5c7ee463b42c7f9b959d223e68ddfe77573b98219921989","sha256:4535ecb05ccbab56cfe74c5871e8507711f76f32f83a158ae2515cda69b264e4"],"state_sha256":"075366261ef82635ab7ac2e5ce4ad688b8ab9eb927673e93cdd23a0defe4975c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0JQVEweBSFvPYxSHaUCuAybTWj6r+od+4e27/sBg3+un6GwP8X3u26QzDFuRykccwYsS6rVfO3LpZ+nu55P5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-24T04:38:28.959219Z","bundle_sha256":"2eb09cecab6f7d5f72cba667b0300cc0575c18252460e178aaebabecb331ce1d"}}