{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BRTVG4PY3VJDUU2FONUFGJBB52","short_pith_number":"pith:BRTVG4PY","canonical_record":{"source":{"id":"1510.06057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-20T20:53:04Z","cross_cats_sorted":[],"title_canon_sha256":"25e3ad4a1292d756103c363fce08ce287ae398826a4e60a24d1009779e35f735","abstract_canon_sha256":"5feee7b762e3974ea32739df123e5bb323210a83a8e50cba4dd3a660324fecf6"},"schema_version":"1.0"},"canonical_sha256":"0c675371f8dd523a53457368532421eea7ad621d2d2648031043837f56ddc6da","source":{"kind":"arxiv","id":"1510.06057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06057","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06057v1","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06057","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"BRTVG4PY3VJD","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BRTVG4PY3VJDUU2F","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BRTVG4PY","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BRTVG4PY3VJDUU2FONUFGJBB52","target":"record","payload":{"canonical_record":{"source":{"id":"1510.06057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-20T20:53:04Z","cross_cats_sorted":[],"title_canon_sha256":"25e3ad4a1292d756103c363fce08ce287ae398826a4e60a24d1009779e35f735","abstract_canon_sha256":"5feee7b762e3974ea32739df123e5bb323210a83a8e50cba4dd3a660324fecf6"},"schema_version":"1.0"},"canonical_sha256":"0c675371f8dd523a53457368532421eea7ad621d2d2648031043837f56ddc6da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:38.788053Z","signature_b64":"SJaf9q72613pNBeNM0ME83D76w1T9UEuUrLJ468ebTjT70+knRCv8SmfvKDt9fchQDa45IreLHyqs/wPaarABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c675371f8dd523a53457368532421eea7ad621d2d2648031043837f56ddc6da","last_reissued_at":"2026-05-18T01:29:38.787333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:38.787333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.06057","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":"2026-05-18T01:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k5v/eSRLymznpDglpBBVeWJelqNRVEw8xWDq7j+doLzapO9grPtTN93MVOdP/0nFiJCkruUFN/e0cHseFwf+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:19:39.021712Z"},"content_sha256":"0a5770f2847f2e44f2a3476a8c620e6c86037a6d4f1588e8b696daf04a5415c3","schema_version":"1.0","event_id":"sha256:0a5770f2847f2e44f2a3476a8c620e6c86037a6d4f1588e8b696daf04a5415c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BRTVG4PY3VJDUU2FONUFGJBB52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refined Tur\\'an numbers and Ramsey numbers for the loose 3-uniform path of length three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Ruci\\'nski, Joanna Polcyn","submitted_at":"2015-10-20T20:53:04Z","abstract_excerpt":"Let $P$ denote a 3-uniform hypergraph consisting of 7 vertices $a,b,c,d,e,f,g$ and 3 edges $\\{a,b,c\\}, \\{c,d,e\\},$ and $\\{e,f,g\\}$. It is known that the $r$-color Ramsey number for $P$ is $R(P;r)=r+6$ for $r\\le 7$. The proof of this result relies on a careful analysis of the Tur\\'an numbers for $P$. In this paper, we refine this analysis further and compute, for all $n$, the third and fourth order Tur\\'an numbers for $P$. With the help of the former, we confirm the formula $R(P;r)=r+6$ for $r\\in\\{8,9\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06057","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":"2026-05-18T01:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dDc98M7SX8bDff99uNoyARWNJIbLt73VGupMKvzfF/PpCboeMjw3lGZVhkpWahZTfKss9Wz2UJJyboRI+WAJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:19:39.022055Z"},"content_sha256":"b6b67c28bce03206055323825bd5a1e03d47742caa3ab609d681bed86b08b1b7","schema_version":"1.0","event_id":"sha256:b6b67c28bce03206055323825bd5a1e03d47742caa3ab609d681bed86b08b1b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRTVG4PY3VJDUU2FONUFGJBB52/bundle.json","state_url":"https://pith.science/pith/BRTVG4PY3VJDUU2FONUFGJBB52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRTVG4PY3VJDUU2FONUFGJBB52/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":"2026-06-08T13:19:39Z","links":{"resolver":"https://pith.science/pith/BRTVG4PY3VJDUU2FONUFGJBB52","bundle":"https://pith.science/pith/BRTVG4PY3VJDUU2FONUFGJBB52/bundle.json","state":"https://pith.science/pith/BRTVG4PY3VJDUU2FONUFGJBB52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRTVG4PY3VJDUU2FONUFGJBB52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BRTVG4PY3VJDUU2FONUFGJBB52","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":"5feee7b762e3974ea32739df123e5bb323210a83a8e50cba4dd3a660324fecf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-20T20:53:04Z","title_canon_sha256":"25e3ad4a1292d756103c363fce08ce287ae398826a4e60a24d1009779e35f735"},"schema_version":"1.0","source":{"id":"1510.06057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06057","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06057v1","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06057","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"BRTVG4PY3VJD","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BRTVG4PY3VJDUU2F","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BRTVG4PY","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:b6b67c28bce03206055323825bd5a1e03d47742caa3ab609d681bed86b08b1b7","target":"graph","created_at":"2026-05-18T01:29:38Z","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":"Let $P$ denote a 3-uniform hypergraph consisting of 7 vertices $a,b,c,d,e,f,g$ and 3 edges $\\{a,b,c\\}, \\{c,d,e\\},$ and $\\{e,f,g\\}$. It is known that the $r$-color Ramsey number for $P$ is $R(P;r)=r+6$ for $r\\le 7$. The proof of this result relies on a careful analysis of the Tur\\'an numbers for $P$. In this paper, we refine this analysis further and compute, for all $n$, the third and fourth order Tur\\'an numbers for $P$. With the help of the former, we confirm the formula $R(P;r)=r+6$ for $r\\in\\{8,9\\}$.","authors_text":"Andrzej Ruci\\'nski, Joanna Polcyn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-20T20:53:04Z","title":"Refined Tur\\'an numbers and Ramsey numbers for the loose 3-uniform path of length three"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06057","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":"sha256:0a5770f2847f2e44f2a3476a8c620e6c86037a6d4f1588e8b696daf04a5415c3","target":"record","created_at":"2026-05-18T01:29:38Z","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":"5feee7b762e3974ea32739df123e5bb323210a83a8e50cba4dd3a660324fecf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-20T20:53:04Z","title_canon_sha256":"25e3ad4a1292d756103c363fce08ce287ae398826a4e60a24d1009779e35f735"},"schema_version":"1.0","source":{"id":"1510.06057","kind":"arxiv","version":1}},"canonical_sha256":"0c675371f8dd523a53457368532421eea7ad621d2d2648031043837f56ddc6da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c675371f8dd523a53457368532421eea7ad621d2d2648031043837f56ddc6da","first_computed_at":"2026-05-18T01:29:38.787333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:38.787333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SJaf9q72613pNBeNM0ME83D76w1T9UEuUrLJ468ebTjT70+knRCv8SmfvKDt9fchQDa45IreLHyqs/wPaarABQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:38.788053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a5770f2847f2e44f2a3476a8c620e6c86037a6d4f1588e8b696daf04a5415c3","sha256:b6b67c28bce03206055323825bd5a1e03d47742caa3ab609d681bed86b08b1b7"],"state_sha256":"56528d76d551862289ab922f4c3c66ced7d5d0f8d42dfe5ce6b10f570cf0d993"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMH7kXI7Vq5VJKI4wCzz6m1UGNK0gEIhq8BZEXA/dSzvLh5D5DNUM54h6bivFdbHkXFIRe2S381A/d49DcvBAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:19:39.023986Z","bundle_sha256":"16d6dac90d8c987e1cbe1c36dda37a5464184d17237d825b17c8290874cf05d1"}}