{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RUU66QB4DKT5SAINVS35MOES6W","short_pith_number":"pith:RUU66QB4","canonical_record":{"source":{"id":"1112.5524","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-23T07:05:15Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"fc81395b1cf5804687f49510203ae993013e5cdfac4b338fd892c872cdf224cb","abstract_canon_sha256":"8f6ae9adf8bcb9fc63455548ac4074aafb47969a048c0cd90b0cf0100ea6cbbc"},"schema_version":"1.0"},"canonical_sha256":"8d29ef403c1aa7d9010dacb7d63892f59c18f19f72ac6f9963df4677343f2c21","source":{"kind":"arxiv","id":"1112.5524","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5524","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5524v4","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5524","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"RUU66QB4DKT5","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RUU66QB4DKT5SAIN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RUU66QB4","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RUU66QB4DKT5SAINVS35MOES6W","target":"record","payload":{"canonical_record":{"source":{"id":"1112.5524","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-23T07:05:15Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"fc81395b1cf5804687f49510203ae993013e5cdfac4b338fd892c872cdf224cb","abstract_canon_sha256":"8f6ae9adf8bcb9fc63455548ac4074aafb47969a048c0cd90b0cf0100ea6cbbc"},"schema_version":"1.0"},"canonical_sha256":"8d29ef403c1aa7d9010dacb7d63892f59c18f19f72ac6f9963df4677343f2c21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:18.027443Z","signature_b64":"YgUF2ojNSY+OgiA12oG0zAHtKkoxljkH/KOmBIvTxf8b4l0K6l3uAd3uRpRqIFK3OCNhra8lw7XRmLL0emCcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d29ef403c1aa7d9010dacb7d63892f59c18f19f72ac6f9963df4677343f2c21","last_reissued_at":"2026-05-18T00:52:18.026850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:18.026850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.5524","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fwsTDNijjQoZQk+/IgLQkJ4ndmU8QOaEgIO2pQVUmLi76pSK+pIxQLxfb0uLr7FRd+j7ZuXJcjDMB7WdVvBnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:09:25.178585Z"},"content_sha256":"1475a789a6e9ea41c2b63e6e0fe834f156f1bb4e6ddfc9259fa1b0287ca505b9","schema_version":"1.0","event_id":"sha256:1475a789a6e9ea41c2b63e6e0fe834f156f1bb4e6ddfc9259fa1b0287ca505b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RUU66QB4DKT5SAINVS35MOES6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonrepetitive Colouring via Entropy Compression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"David R. Wood, Gwena\\\"el Joret, Jakub Kozik, Vida Dujmovi\\'c","submitted_at":"2011-12-23T07:05:15Z","abstract_excerpt":"A vertex colouring of a graph is \\emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\\Delta$ is $c\\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5524","kind":"arxiv","version":4},"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":"2026-05-18T00:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SfyCczWQHXGwy9xAcjuKnC6Gn56AqlTRDRpS+YqO8thE1O6yy5gEGDE/JINjqZxg+s/NkVYJLrrhW3nLKZc3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:09:25.179256Z"},"content_sha256":"f3aaded23c66f9d6b8d32d5480f1e1e8033e920194ecf89a80dfe725e5bb80f8","schema_version":"1.0","event_id":"sha256:f3aaded23c66f9d6b8d32d5480f1e1e8033e920194ecf89a80dfe725e5bb80f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUU66QB4DKT5SAINVS35MOES6W/bundle.json","state_url":"https://pith.science/pith/RUU66QB4DKT5SAINVS35MOES6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUU66QB4DKT5SAINVS35MOES6W/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":"2026-05-26T04:09:25Z","links":{"resolver":"https://pith.science/pith/RUU66QB4DKT5SAINVS35MOES6W","bundle":"https://pith.science/pith/RUU66QB4DKT5SAINVS35MOES6W/bundle.json","state":"https://pith.science/pith/RUU66QB4DKT5SAINVS35MOES6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUU66QB4DKT5SAINVS35MOES6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RUU66QB4DKT5SAINVS35MOES6W","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":"8f6ae9adf8bcb9fc63455548ac4074aafb47969a048c0cd90b0cf0100ea6cbbc","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-23T07:05:15Z","title_canon_sha256":"fc81395b1cf5804687f49510203ae993013e5cdfac4b338fd892c872cdf224cb"},"schema_version":"1.0","source":{"id":"1112.5524","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5524","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5524v4","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5524","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"RUU66QB4DKT5","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RUU66QB4DKT5SAIN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RUU66QB4","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:f3aaded23c66f9d6b8d32d5480f1e1e8033e920194ecf89a80dfe725e5bb80f8","target":"graph","created_at":"2026-05-18T00:52:18Z","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 vertex colouring of a graph is \\emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\\Delta$ is $c\\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge ","authors_text":"David R. Wood, Gwena\\\"el Joret, Jakub Kozik, Vida Dujmovi\\'c","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-23T07:05:15Z","title":"Nonrepetitive Colouring via Entropy Compression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5524","kind":"arxiv","version":4},"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":"sha256:1475a789a6e9ea41c2b63e6e0fe834f156f1bb4e6ddfc9259fa1b0287ca505b9","target":"record","created_at":"2026-05-18T00:52:18Z","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":"8f6ae9adf8bcb9fc63455548ac4074aafb47969a048c0cd90b0cf0100ea6cbbc","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-23T07:05:15Z","title_canon_sha256":"fc81395b1cf5804687f49510203ae993013e5cdfac4b338fd892c872cdf224cb"},"schema_version":"1.0","source":{"id":"1112.5524","kind":"arxiv","version":4}},"canonical_sha256":"8d29ef403c1aa7d9010dacb7d63892f59c18f19f72ac6f9963df4677343f2c21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d29ef403c1aa7d9010dacb7d63892f59c18f19f72ac6f9963df4677343f2c21","first_computed_at":"2026-05-18T00:52:18.026850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:18.026850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YgUF2ojNSY+OgiA12oG0zAHtKkoxljkH/KOmBIvTxf8b4l0K6l3uAd3uRpRqIFK3OCNhra8lw7XRmLL0emCcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:18.027443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5524","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1475a789a6e9ea41c2b63e6e0fe834f156f1bb4e6ddfc9259fa1b0287ca505b9","sha256:f3aaded23c66f9d6b8d32d5480f1e1e8033e920194ecf89a80dfe725e5bb80f8"],"state_sha256":"09f741b557b5277b95c8c80e01ee970d57316f92039ef78f6c0ce4a4bb75a622"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETQCCSxMytZKjK4XoU1yrzCZybzhSUcgdnAQBPuDAa5gCDaQN/+V9i7Gs8W5CB4qSKdovnQ1VMghuLhJThfPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:09:25.184720Z","bundle_sha256":"409bd25fbe74495e5e36baa50c4d4d8a59954014b2531273c5317ff88a2785e0"}}