{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V6RNSRMI5S6L2OVPLCIYNJEOGQ","short_pith_number":"pith:V6RNSRMI","canonical_record":{"source":{"id":"1712.00831","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-03T20:15:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"85c5d97a2eb230f7758434ea93b54a51578a49ed6aa310c1d19201ef73cc044e","abstract_canon_sha256":"c29a11066063ac5c06b91055fb05293d840a4acc349d9375777e17a383b0ac65"},"schema_version":"1.0"},"canonical_sha256":"afa2d94588ecbcbd3aaf589186a48e34194ff8030dfe91f1b93e69653b20f9ce","source":{"kind":"arxiv","id":"1712.00831","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00831","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00831v1","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00831","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"pith_short_12","alias_value":"V6RNSRMI5S6L","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V6RNSRMI5S6L2OVP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V6RNSRMI","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V6RNSRMI5S6L2OVPLCIYNJEOGQ","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00831","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-03T20:15:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"85c5d97a2eb230f7758434ea93b54a51578a49ed6aa310c1d19201ef73cc044e","abstract_canon_sha256":"c29a11066063ac5c06b91055fb05293d840a4acc349d9375777e17a383b0ac65"},"schema_version":"1.0"},"canonical_sha256":"afa2d94588ecbcbd3aaf589186a48e34194ff8030dfe91f1b93e69653b20f9ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:00.288197Z","signature_b64":"gknkRBeYLdEmeYkHNi2+nFBFo0jJuDhNze07NWrc6zsRS/c4eGQFBpdc4BLCjGmL/5YpjF2wFNQo85U0j7QBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afa2d94588ecbcbd3aaf589186a48e34194ff8030dfe91f1b93e69653b20f9ce","last_reissued_at":"2026-05-18T00:29:00.287681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:00.287681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00831","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":"2026-05-18T00:29:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"32TUedGXYka2C8wiB0HSGpx+2tbyElQusOCcs0ctm+SY7Ci8et2FaMgkdkFIwzLdJ4vZ+vQ8hP3NYdYrrtMhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:04:43.814540Z"},"content_sha256":"c9d4cca1b64d2296e059ba4f50104d6b233afd0d55c38d57f98834498fac0031","schema_version":"1.0","event_id":"sha256:c9d4cca1b64d2296e059ba4f50104d6b233afd0d55c38d57f98834498fac0031"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V6RNSRMI5S6L2OVPLCIYNJEOGQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Generalized Tur\\'an Problem and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Asaf Shapira, Lior Gishboliner","submitted_at":"2017-12-03T20:15:43Z","abstract_excerpt":"The investigation of conditions guaranteeing the appearance of cycles of certain lengths is one of the most well-studied topics in graph theory. In this paper we consider a problem of this type which asks, for fixed integers ${\\ell}$ and $k$, how many copies of the $k$-cycle guarantee the appearance of an $\\ell$-cycle? Extending previous results of Bollob\\'as--Gy\\H{o}ri--Li and Alon--Shikhelman, we fully resolve this problem by giving tight (or nearly tight) bounds for all values of $\\ell$ and $k$.\n  We also present a somewhat surprising application of the above mentioned estimates to the stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00831","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":"2026-05-18T00:29:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dts9ifvIk7p5LFxB48rAWf1kjgM4oTS5+DMaPDSvzxHZmF8yd4cUe7drF1IujOBCw1eG7roP4d4PxLEkMbwCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:04:43.814901Z"},"content_sha256":"39b952369dac3e66a333a939c96a172076e2e1cf64ee8182d8b792f1e83c4345","schema_version":"1.0","event_id":"sha256:39b952369dac3e66a333a939c96a172076e2e1cf64ee8182d8b792f1e83c4345"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6RNSRMI5S6L2OVPLCIYNJEOGQ/bundle.json","state_url":"https://pith.science/pith/V6RNSRMI5S6L2OVPLCIYNJEOGQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6RNSRMI5S6L2OVPLCIYNJEOGQ/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":"2026-06-03T19:04:43Z","links":{"resolver":"https://pith.science/pith/V6RNSRMI5S6L2OVPLCIYNJEOGQ","bundle":"https://pith.science/pith/V6RNSRMI5S6L2OVPLCIYNJEOGQ/bundle.json","state":"https://pith.science/pith/V6RNSRMI5S6L2OVPLCIYNJEOGQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6RNSRMI5S6L2OVPLCIYNJEOGQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V6RNSRMI5S6L2OVPLCIYNJEOGQ","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":"c29a11066063ac5c06b91055fb05293d840a4acc349d9375777e17a383b0ac65","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-03T20:15:43Z","title_canon_sha256":"85c5d97a2eb230f7758434ea93b54a51578a49ed6aa310c1d19201ef73cc044e"},"schema_version":"1.0","source":{"id":"1712.00831","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00831","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00831v1","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00831","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"pith_short_12","alias_value":"V6RNSRMI5S6L","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V6RNSRMI5S6L2OVP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V6RNSRMI","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:39b952369dac3e66a333a939c96a172076e2e1cf64ee8182d8b792f1e83c4345","target":"graph","created_at":"2026-05-18T00:29:00Z","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":"The investigation of conditions guaranteeing the appearance of cycles of certain lengths is one of the most well-studied topics in graph theory. In this paper we consider a problem of this type which asks, for fixed integers ${\\ell}$ and $k$, how many copies of the $k$-cycle guarantee the appearance of an $\\ell$-cycle? Extending previous results of Bollob\\'as--Gy\\H{o}ri--Li and Alon--Shikhelman, we fully resolve this problem by giving tight (or nearly tight) bounds for all values of $\\ell$ and $k$.\n  We also present a somewhat surprising application of the above mentioned estimates to the stud","authors_text":"Asaf Shapira, Lior Gishboliner","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-03T20:15:43Z","title":"A Generalized Tur\\'an Problem and its Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00831","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:c9d4cca1b64d2296e059ba4f50104d6b233afd0d55c38d57f98834498fac0031","target":"record","created_at":"2026-05-18T00:29:00Z","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":"c29a11066063ac5c06b91055fb05293d840a4acc349d9375777e17a383b0ac65","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-03T20:15:43Z","title_canon_sha256":"85c5d97a2eb230f7758434ea93b54a51578a49ed6aa310c1d19201ef73cc044e"},"schema_version":"1.0","source":{"id":"1712.00831","kind":"arxiv","version":1}},"canonical_sha256":"afa2d94588ecbcbd3aaf589186a48e34194ff8030dfe91f1b93e69653b20f9ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afa2d94588ecbcbd3aaf589186a48e34194ff8030dfe91f1b93e69653b20f9ce","first_computed_at":"2026-05-18T00:29:00.287681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:00.287681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gknkRBeYLdEmeYkHNi2+nFBFo0jJuDhNze07NWrc6zsRS/c4eGQFBpdc4BLCjGmL/5YpjF2wFNQo85U0j7QBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:00.288197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00831","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9d4cca1b64d2296e059ba4f50104d6b233afd0d55c38d57f98834498fac0031","sha256:39b952369dac3e66a333a939c96a172076e2e1cf64ee8182d8b792f1e83c4345"],"state_sha256":"e155aa6dbb847a7547bcec595c8fee4aa01a64d2de6a0a44e7d8d8ad955d6fd2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xvKI+O3wM3/CUFThUcxkrT9j3WplUZbvK302VvWNUhuSzAHq5AkmvjVzN1RCWThWETMsJjpjLBnD2FvE3c3PCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:04:43.817447Z","bundle_sha256":"b299ff8c337ac3dcd1409e0491e2db090bf4e0e2539ecc468f193bb82d9ef2ea"}}