{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4WPPLDTZEKTJP2WFPTC7R6GVPW","short_pith_number":"pith:4WPPLDTZ","canonical_record":{"source":{"id":"1108.2769","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-13T06:57:36Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"decc631d2d0e95ef585d3264b089d3e97bf4e1927d5998e550087f4dc8fe8a86","abstract_canon_sha256":"e18efdf258f2325477ab27cffc4e33f87d0275fe381f538fd40815cace36d5b0"},"schema_version":"1.0"},"canonical_sha256":"e59ef58e7922a697eac57cc5f8f8d57d95935369c244ef7fa46371a6665dd546","source":{"kind":"arxiv","id":"1108.2769","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2769","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2769v2","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2769","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"4WPPLDTZEKTJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WPPLDTZEKTJP2WF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WPPLDTZ","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4WPPLDTZEKTJP2WFPTC7R6GVPW","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2769","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-13T06:57:36Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"decc631d2d0e95ef585d3264b089d3e97bf4e1927d5998e550087f4dc8fe8a86","abstract_canon_sha256":"e18efdf258f2325477ab27cffc4e33f87d0275fe381f538fd40815cace36d5b0"},"schema_version":"1.0"},"canonical_sha256":"e59ef58e7922a697eac57cc5f8f8d57d95935369c244ef7fa46371a6665dd546","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:34.022501Z","signature_b64":"1eu1NG4/nOsTjOOtYgCuNhY6qRtm5oU/fBtuOeAcQwpUVKFMu3pZ4XUYGKJQM7TAhsJF5EYc0YmwTV7AhUfTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e59ef58e7922a697eac57cc5f8f8d57d95935369c244ef7fa46371a6665dd546","last_reissued_at":"2026-05-18T03:56:34.022079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:34.022079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2769","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9tNrE0/5or02C0hAuOoX3y3QhOhdIOhmoqB6wS/KqorQJZ5il1oXlVbJmSt1nlMwZl7aRj+BOD7XdoFkKU1nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:14:35.380517Z"},"content_sha256":"7561f88157b8b9295ec17b83c47f954b7c456c7faa59161d8a2c98badde2bee6","schema_version":"1.0","event_id":"sha256:7561f88157b8b9295ec17b83c47f954b7c456c7faa59161d8a2c98badde2bee6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4WPPLDTZEKTJP2WFPTC7R6GVPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Locally identifying colourings for graphs with given maximum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Aline Parreau (IF), Florent Foucaud (LaBRI), Guillem Perarnau (UPC), Iiro Honkala, Tero Laihonen","submitted_at":"2011-08-13T06:57:36Z","abstract_excerpt":"A proper vertex-colouring of a graph G is said to be locally identifying if for any pair u,v of adjacent vertices with distinct closed neighbourhoods, the sets of colours in the closed neighbourhoods of u and v are different. We show that any graph G has a locally identifying colouring with $2\\Delta^2-3\\Delta+3$ colours, where $\\Delta$ is the maximum degree of G, answering in a positive way a question asked by Esperet et al. We also provide similar results for locally identifying colourings which have the property that the colours in the neighbourhood of each vertex are all different and apply"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2769","kind":"arxiv","version":2},"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":"2026-05-18T03:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gDGJrebA7RYOBPHLZCwzrGNcLUTBq5R0PqarZnlQWYOdxbDYgggXK5jgo+jAc3HogI/FGZl4mngmilOsVcU1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:14:35.380880Z"},"content_sha256":"98c64bd5522a0e341c7566effd998a67da21e744ed6ca9e8838864c72008e592","schema_version":"1.0","event_id":"sha256:98c64bd5522a0e341c7566effd998a67da21e744ed6ca9e8838864c72008e592"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WPPLDTZEKTJP2WFPTC7R6GVPW/bundle.json","state_url":"https://pith.science/pith/4WPPLDTZEKTJP2WFPTC7R6GVPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WPPLDTZEKTJP2WFPTC7R6GVPW/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":"2026-06-23T13:14:35Z","links":{"resolver":"https://pith.science/pith/4WPPLDTZEKTJP2WFPTC7R6GVPW","bundle":"https://pith.science/pith/4WPPLDTZEKTJP2WFPTC7R6GVPW/bundle.json","state":"https://pith.science/pith/4WPPLDTZEKTJP2WFPTC7R6GVPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WPPLDTZEKTJP2WFPTC7R6GVPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4WPPLDTZEKTJP2WFPTC7R6GVPW","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":"e18efdf258f2325477ab27cffc4e33f87d0275fe381f538fd40815cace36d5b0","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-13T06:57:36Z","title_canon_sha256":"decc631d2d0e95ef585d3264b089d3e97bf4e1927d5998e550087f4dc8fe8a86"},"schema_version":"1.0","source":{"id":"1108.2769","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2769","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2769v2","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2769","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"4WPPLDTZEKTJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WPPLDTZEKTJP2WF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WPPLDTZ","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:98c64bd5522a0e341c7566effd998a67da21e744ed6ca9e8838864c72008e592","target":"graph","created_at":"2026-05-18T03:56:34Z","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":"A proper vertex-colouring of a graph G is said to be locally identifying if for any pair u,v of adjacent vertices with distinct closed neighbourhoods, the sets of colours in the closed neighbourhoods of u and v are different. We show that any graph G has a locally identifying colouring with $2\\Delta^2-3\\Delta+3$ colours, where $\\Delta$ is the maximum degree of G, answering in a positive way a question asked by Esperet et al. We also provide similar results for locally identifying colourings which have the property that the colours in the neighbourhood of each vertex are all different and apply","authors_text":"Aline Parreau (IF), Florent Foucaud (LaBRI), Guillem Perarnau (UPC), Iiro Honkala, Tero Laihonen","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-13T06:57:36Z","title":"Locally identifying colourings for graphs with given maximum degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2769","kind":"arxiv","version":2},"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":"sha256:7561f88157b8b9295ec17b83c47f954b7c456c7faa59161d8a2c98badde2bee6","target":"record","created_at":"2026-05-18T03:56:34Z","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":"e18efdf258f2325477ab27cffc4e33f87d0275fe381f538fd40815cace36d5b0","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-13T06:57:36Z","title_canon_sha256":"decc631d2d0e95ef585d3264b089d3e97bf4e1927d5998e550087f4dc8fe8a86"},"schema_version":"1.0","source":{"id":"1108.2769","kind":"arxiv","version":2}},"canonical_sha256":"e59ef58e7922a697eac57cc5f8f8d57d95935369c244ef7fa46371a6665dd546","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e59ef58e7922a697eac57cc5f8f8d57d95935369c244ef7fa46371a6665dd546","first_computed_at":"2026-05-18T03:56:34.022079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:34.022079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1eu1NG4/nOsTjOOtYgCuNhY6qRtm5oU/fBtuOeAcQwpUVKFMu3pZ4XUYGKJQM7TAhsJF5EYc0YmwTV7AhUfTDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:34.022501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2769","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7561f88157b8b9295ec17b83c47f954b7c456c7faa59161d8a2c98badde2bee6","sha256:98c64bd5522a0e341c7566effd998a67da21e744ed6ca9e8838864c72008e592"],"state_sha256":"ae519a8a37108ba307c51c31e718037130b19d6b7fa00a167766fa1214cab5ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4NhuNugeRi1eyRA8nzl17ZiL1PG0uer//Q+RB2FRJdOUl3wIh4asgtH3sg6Qt85CcE33BRl3wpCG4U7oC/SlBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:14:35.382916Z","bundle_sha256":"82f5f8702f3aff45e0a52beff3ed716248d721e73dc7fcca8cce38cd401a8471"}}