{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TU73A4WM2AP5TU7DGZ2XL24QAE","short_pith_number":"pith:TU73A4WM","canonical_record":{"source":{"id":"1507.07381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T12:05:37Z","cross_cats_sorted":[],"title_canon_sha256":"5a3239f19abe0b3d79485bcb38caf8092bb353271c5270691c85fb926a5429f2","abstract_canon_sha256":"0fafe83b783a7c67504e75c2de4291b744f7abb85b0219dddde49af02e1dfa30"},"schema_version":"1.0"},"canonical_sha256":"9d3fb072ccd01fd9d3e3367575eb900117f3417adabc3a40fd760cf04837f38b","source":{"kind":"arxiv","id":"1507.07381","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07381","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07381v1","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07381","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"TU73A4WM2AP5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TU73A4WM2AP5TU7D","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TU73A4WM","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TU73A4WM2AP5TU7DGZ2XL24QAE","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T12:05:37Z","cross_cats_sorted":[],"title_canon_sha256":"5a3239f19abe0b3d79485bcb38caf8092bb353271c5270691c85fb926a5429f2","abstract_canon_sha256":"0fafe83b783a7c67504e75c2de4291b744f7abb85b0219dddde49af02e1dfa30"},"schema_version":"1.0"},"canonical_sha256":"9d3fb072ccd01fd9d3e3367575eb900117f3417adabc3a40fd760cf04837f38b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:39.081725Z","signature_b64":"bENKhEZpTPc31ItxB/haZki15FTvAFQWNpKnFTKLL0Up0IPI9RyM2Gxa3uy+WxoEd3mbj8b6E5yAdTwBlsUvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d3fb072ccd01fd9d3e3367575eb900117f3417adabc3a40fd760cf04837f38b","last_reissued_at":"2026-05-18T00:44:39.081340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:39.081340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07381","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":"2026-05-18T00:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mc3FyG2KDsE+agG9+0acKg2zIhPSq1pXkP28NAA3mE8f1CuRtkZlSOotkrZI1t66TeIY3WPtuszJJEIIzzMdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:23:35.429932Z"},"content_sha256":"199ba686cac92f180cf84f3af800a45977a4d238c45d95da60baf8168e82c538","schema_version":"1.0","event_id":"sha256:199ba686cac92f180cf84f3af800a45977a4d238c45d95da60baf8168e82c538"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TU73A4WM2AP5TU7DGZ2XL24QAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On degree anti-Ramsey numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Hefetz, Shoni Gilboa","submitted_at":"2015-07-27T12:05:37Z","abstract_excerpt":"The degree anti-Ramsey number $AR_d(H)$ of a graph $H$ is the smallest integer $k$ for which there exists a graph $G$ with maximum degree at most $k$ such that any proper edge colouring of $G$ yields a rainbow copy of $H$. In this paper we prove a general upper bound on degree anti-Ramsey numbers, determine the precise value of the degree anti-Ramsey number of any forest, and prove an upper bound on the degree anti-Ramsey numbers of cycles of any length which is best possible up to a multiplicative factor of $2$. Our proofs involve a variety of tools, including a classical result of Bollob\\'as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07381","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":"2026-05-18T00:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kVSINdEGlx4/cKq7ObCjVov/qN+uZM8QCQJstC5ZZI9SPWOSCsYxvm1QhFi5SeC90B2c7hQ/UZfh785fWLV8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:23:35.430270Z"},"content_sha256":"bbb11b7e82718129c01065eb619391a3aa1177fec5b5b0daf105b55aab863481","schema_version":"1.0","event_id":"sha256:bbb11b7e82718129c01065eb619391a3aa1177fec5b5b0daf105b55aab863481"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TU73A4WM2AP5TU7DGZ2XL24QAE/bundle.json","state_url":"https://pith.science/pith/TU73A4WM2AP5TU7DGZ2XL24QAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TU73A4WM2AP5TU7DGZ2XL24QAE/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":"2026-06-02T14:23:35Z","links":{"resolver":"https://pith.science/pith/TU73A4WM2AP5TU7DGZ2XL24QAE","bundle":"https://pith.science/pith/TU73A4WM2AP5TU7DGZ2XL24QAE/bundle.json","state":"https://pith.science/pith/TU73A4WM2AP5TU7DGZ2XL24QAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TU73A4WM2AP5TU7DGZ2XL24QAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TU73A4WM2AP5TU7DGZ2XL24QAE","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":"0fafe83b783a7c67504e75c2de4291b744f7abb85b0219dddde49af02e1dfa30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T12:05:37Z","title_canon_sha256":"5a3239f19abe0b3d79485bcb38caf8092bb353271c5270691c85fb926a5429f2"},"schema_version":"1.0","source":{"id":"1507.07381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07381","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07381v1","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07381","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"TU73A4WM2AP5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TU73A4WM2AP5TU7D","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TU73A4WM","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:bbb11b7e82718129c01065eb619391a3aa1177fec5b5b0daf105b55aab863481","target":"graph","created_at":"2026-05-18T00:44:39Z","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 degree anti-Ramsey number $AR_d(H)$ of a graph $H$ is the smallest integer $k$ for which there exists a graph $G$ with maximum degree at most $k$ such that any proper edge colouring of $G$ yields a rainbow copy of $H$. In this paper we prove a general upper bound on degree anti-Ramsey numbers, determine the precise value of the degree anti-Ramsey number of any forest, and prove an upper bound on the degree anti-Ramsey numbers of cycles of any length which is best possible up to a multiplicative factor of $2$. Our proofs involve a variety of tools, including a classical result of Bollob\\'as","authors_text":"Dan Hefetz, Shoni Gilboa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T12:05:37Z","title":"On degree anti-Ramsey numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07381","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":"sha256:199ba686cac92f180cf84f3af800a45977a4d238c45d95da60baf8168e82c538","target":"record","created_at":"2026-05-18T00:44:39Z","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":"0fafe83b783a7c67504e75c2de4291b744f7abb85b0219dddde49af02e1dfa30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T12:05:37Z","title_canon_sha256":"5a3239f19abe0b3d79485bcb38caf8092bb353271c5270691c85fb926a5429f2"},"schema_version":"1.0","source":{"id":"1507.07381","kind":"arxiv","version":1}},"canonical_sha256":"9d3fb072ccd01fd9d3e3367575eb900117f3417adabc3a40fd760cf04837f38b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d3fb072ccd01fd9d3e3367575eb900117f3417adabc3a40fd760cf04837f38b","first_computed_at":"2026-05-18T00:44:39.081340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:39.081340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bENKhEZpTPc31ItxB/haZki15FTvAFQWNpKnFTKLL0Up0IPI9RyM2Gxa3uy+WxoEd3mbj8b6E5yAdTwBlsUvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:39.081725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:199ba686cac92f180cf84f3af800a45977a4d238c45d95da60baf8168e82c538","sha256:bbb11b7e82718129c01065eb619391a3aa1177fec5b5b0daf105b55aab863481"],"state_sha256":"c1bf6369fca6f7b90c6168d3cbecfa1217962dfddba5177debbddd4514712c76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Ms+G9ORFg/GLvuxqacpb3hiUrO2yxDk556u+U2hLX+iiOc8R8kIJDUX518t7c3ZFtrQVeDxX7uVL7JGMOklBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:23:35.432383Z","bundle_sha256":"d08923ba24b1913b459763db9b14bb8a3877d54cadb45d750a6b9e642907c4ab"}}