{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:L3YRUSQU4R7ZTZOVVJDNS4UEXU","short_pith_number":"pith:L3YRUSQU","canonical_record":{"source":{"id":"1609.08645","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-27T20:12:49Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dba87900ec86a19454f9383d014c1293350751d4231ac11c3c7f0a3fd01f362d","abstract_canon_sha256":"38251d16f182be836f491e57076b5296f8b2e936841c273949c41795bd9ea72d"},"schema_version":"1.0"},"canonical_sha256":"5ef11a4a14e47f99e5d5aa46d97284bd1ea8b6432a61b39f7d90e5e7edd6b6af","source":{"kind":"arxiv","id":"1609.08645","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08645","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08645v3","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08645","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"pith_short_12","alias_value":"L3YRUSQU4R7Z","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L3YRUSQU4R7ZTZOV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L3YRUSQU","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:L3YRUSQU4R7ZTZOVVJDNS4UEXU","target":"record","payload":{"canonical_record":{"source":{"id":"1609.08645","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-27T20:12:49Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dba87900ec86a19454f9383d014c1293350751d4231ac11c3c7f0a3fd01f362d","abstract_canon_sha256":"38251d16f182be836f491e57076b5296f8b2e936841c273949c41795bd9ea72d"},"schema_version":"1.0"},"canonical_sha256":"5ef11a4a14e47f99e5d5aa46d97284bd1ea8b6432a61b39f7d90e5e7edd6b6af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:07.976603Z","signature_b64":"HODchgJzU/LJg6WqQC61bVpWWB9uIpRhMQZCWSXBF6fpt5jvCaN8ZD+oRE6x62hRZCxWcPJiftUwsCbnH4bYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ef11a4a14e47f99e5d5aa46d97284bd1ea8b6432a61b39f7d90e5e7edd6b6af","last_reissued_at":"2026-05-18T00:40:07.976141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:07.976141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.08645","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":"2026-05-18T00:40:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yeQDnJzx1Tmoq9nxrQhMe2tm5TKuXlTU5UYyUN/OtpWfFPPoyWr+5et+PRU/mg84ZitPTtTXFtHOz55R0H4ZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:07:28.183224Z"},"content_sha256":"415ac7eb7b6e9cb4a27582bbbeeb76dda4df8b51c9377cfc70cc4217cf257482","schema_version":"1.0","event_id":"sha256:415ac7eb7b6e9cb4a27582bbbeeb76dda4df8b51c9377cfc70cc4217cf257482"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:L3YRUSQU4R7ZTZOVVJDNS4UEXU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Colouring squares of claw-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Lucas Pastor, R\\'emi de Joannis de Verclos, Ross J. Kang","submitted_at":"2016-09-27T20:12:49Z","abstract_excerpt":"Is there some absolute $\\varepsilon > 0$ such that for any claw-free graph $G$, the chromatic number of the square of $G$ satisfies $\\chi(G^2) \\le (2-\\varepsilon) \\omega(G)^2$, where $\\omega(G)$ is the clique number of $G$? Erd\\H{o}s and Ne\\v{s}et\\v{r}il asked this question for the specific case of $G$ the line graph of a simple graph and this was answered in the affirmative by Molloy and Reed. We show that the answer to the more general question is also yes, and moreover that it essentially reduces to the original question of Erd\\H{o}s and Ne\\v{s}et\\v{r}il."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08645","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":""},"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":"2026-05-18T00:40:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RG/J84UOcpznISzg3O41ZyBasqlr8a3y6Z29O5BMSz8UnyxVnk3IXQS+DjDjBBNw9UAiOvCQWZtbW8ZO2UjwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:07:28.183652Z"},"content_sha256":"8c8ebe1346a5c86772b9c6e63008a6bbf17a87d154c8d11cf4bc1c58132761c8","schema_version":"1.0","event_id":"sha256:8c8ebe1346a5c86772b9c6e63008a6bbf17a87d154c8d11cf4bc1c58132761c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3YRUSQU4R7ZTZOVVJDNS4UEXU/bundle.json","state_url":"https://pith.science/pith/L3YRUSQU4R7ZTZOVVJDNS4UEXU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3YRUSQU4R7ZTZOVVJDNS4UEXU/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":"2026-06-05T14:07:28Z","links":{"resolver":"https://pith.science/pith/L3YRUSQU4R7ZTZOVVJDNS4UEXU","bundle":"https://pith.science/pith/L3YRUSQU4R7ZTZOVVJDNS4UEXU/bundle.json","state":"https://pith.science/pith/L3YRUSQU4R7ZTZOVVJDNS4UEXU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3YRUSQU4R7ZTZOVVJDNS4UEXU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:L3YRUSQU4R7ZTZOVVJDNS4UEXU","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":"38251d16f182be836f491e57076b5296f8b2e936841c273949c41795bd9ea72d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-27T20:12:49Z","title_canon_sha256":"dba87900ec86a19454f9383d014c1293350751d4231ac11c3c7f0a3fd01f362d"},"schema_version":"1.0","source":{"id":"1609.08645","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08645","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08645v3","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08645","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"pith_short_12","alias_value":"L3YRUSQU4R7Z","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L3YRUSQU4R7ZTZOV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L3YRUSQU","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:8c8ebe1346a5c86772b9c6e63008a6bbf17a87d154c8d11cf4bc1c58132761c8","target":"graph","created_at":"2026-05-18T00:40:07Z","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":"Is there some absolute $\\varepsilon > 0$ such that for any claw-free graph $G$, the chromatic number of the square of $G$ satisfies $\\chi(G^2) \\le (2-\\varepsilon) \\omega(G)^2$, where $\\omega(G)$ is the clique number of $G$? Erd\\H{o}s and Ne\\v{s}et\\v{r}il asked this question for the specific case of $G$ the line graph of a simple graph and this was answered in the affirmative by Molloy and Reed. We show that the answer to the more general question is also yes, and moreover that it essentially reduces to the original question of Erd\\H{o}s and Ne\\v{s}et\\v{r}il.","authors_text":"Lucas Pastor, R\\'emi de Joannis de Verclos, Ross J. Kang","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-27T20:12:49Z","title":"Colouring squares of claw-free graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08645","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":"sha256:415ac7eb7b6e9cb4a27582bbbeeb76dda4df8b51c9377cfc70cc4217cf257482","target":"record","created_at":"2026-05-18T00:40:07Z","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":"38251d16f182be836f491e57076b5296f8b2e936841c273949c41795bd9ea72d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-27T20:12:49Z","title_canon_sha256":"dba87900ec86a19454f9383d014c1293350751d4231ac11c3c7f0a3fd01f362d"},"schema_version":"1.0","source":{"id":"1609.08645","kind":"arxiv","version":3}},"canonical_sha256":"5ef11a4a14e47f99e5d5aa46d97284bd1ea8b6432a61b39f7d90e5e7edd6b6af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ef11a4a14e47f99e5d5aa46d97284bd1ea8b6432a61b39f7d90e5e7edd6b6af","first_computed_at":"2026-05-18T00:40:07.976141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:07.976141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HODchgJzU/LJg6WqQC61bVpWWB9uIpRhMQZCWSXBF6fpt5jvCaN8ZD+oRE6x62hRZCxWcPJiftUwsCbnH4bYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:07.976603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08645","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:415ac7eb7b6e9cb4a27582bbbeeb76dda4df8b51c9377cfc70cc4217cf257482","sha256:8c8ebe1346a5c86772b9c6e63008a6bbf17a87d154c8d11cf4bc1c58132761c8"],"state_sha256":"f8a6042787d0fba85fe9ae1e162ef480e90f124c954edfea3f7d0f4e1fb74af4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j0ZlSP3f2aNDFmdNAUdT9BXHy3WPbHLHFpaAKq/FMfp6qCyysznRd02ltrDoiLLtie7yHHbfk/JV+gpqMo+1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:07:28.185698Z","bundle_sha256":"d3320c68ce3b22d9d1fab918e55059af6aff7588b25eba2f18d66e50621b31b0"}}