{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AUPTCWPISY2RBIETW5LOGQMEW4","short_pith_number":"pith:AUPTCWPI","canonical_record":{"source":{"id":"1810.00731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-10-01T14:44:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a14103ccd67611b0d9fdf32e4c564e547dc18be7074f7175cfde3b795a79aebe","abstract_canon_sha256":"f05f01a752cfa4685aea9bd6d8567e7bc50be1a25f8288fe299b4027c666d507"},"schema_version":"1.0"},"canonical_sha256":"051f3159e8963510a093b756e34184b716009dbc2fd0bbe7ad7c324086e188db","source":{"kind":"arxiv","id":"1810.00731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00731","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00731v1","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00731","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"AUPTCWPISY2R","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AUPTCWPISY2RBIET","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AUPTCWPI","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AUPTCWPISY2RBIETW5LOGQMEW4","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-10-01T14:44:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a14103ccd67611b0d9fdf32e4c564e547dc18be7074f7175cfde3b795a79aebe","abstract_canon_sha256":"f05f01a752cfa4685aea9bd6d8567e7bc50be1a25f8288fe299b4027c666d507"},"schema_version":"1.0"},"canonical_sha256":"051f3159e8963510a093b756e34184b716009dbc2fd0bbe7ad7c324086e188db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:24.975439Z","signature_b64":"U/3i+YmCJdfgbtURHhd4jka3gwD2XzJ6cB1GRmA3rsDv0lxcQH/45fCw4/0CgN2A6t35sOz3L2mukGJy8Ir0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"051f3159e8963510a093b756e34184b716009dbc2fd0bbe7ad7c324086e188db","last_reissued_at":"2026-05-18T00:04:24.974855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:24.974855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00731","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":"2026-05-18T00:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pNfkfBPI7aB6EA6brXUiRvaRU+hZmo8VegWs1kKVIU4jGhTe1CShwgwDARdj9sF0QWEdVw8HQoE3nE2jwvQ2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:02:05.195676Z"},"content_sha256":"ea41f6765fc4488dc4fcf8e2081833f85dfbbeb1aa1fb0882895dbf3695698ce","schema_version":"1.0","event_id":"sha256:ea41f6765fc4488dc4fcf8e2081833f85dfbbeb1aa1fb0882895dbf3695698ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AUPTCWPISY2RBIETW5LOGQMEW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Cereceda's conjecture for planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Carl Feghali, Eduard Eiben","submitted_at":"2018-10-01T14:44:08Z","abstract_excerpt":"The reconfiguration graph $R_k(G)$ of the $k$-colourings of a graph $G$ has as vertex set the set of all possible $k$-colourings of $G$ and two colourings are adjacent if they differ on the colour of exactly one vertex. Cereceda conjectured ten years ago that, for every $k$-degenerate graph $G$ on $n$ vertices, $R_{k+2}(G)$ has diameter $\\mathcal{O}({n^2})$. The conjecture is wide open, with a best known bound of $\\mathcal{O}({k^n})$, even for planar graphs. We improve this bound for planar graphs to $2^{\\mathcal{O}({\\sqrt{n}})}$. Our proof can be transformed into an algorithm that runs in $2^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00731","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":"2026-05-18T00:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q33R9MajvZavtxHcoXC79ltZwg908k1k5/q/rr8yN64JMaWhoQbWyqXsfs2YyrQkdJ7LWpq6tgfyduL6Q5dFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:02:05.196395Z"},"content_sha256":"bdbe303b7f65a576b7295b15287add92bca12145fc5fb381fe093526a4d5fa44","schema_version":"1.0","event_id":"sha256:bdbe303b7f65a576b7295b15287add92bca12145fc5fb381fe093526a4d5fa44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AUPTCWPISY2RBIETW5LOGQMEW4/bundle.json","state_url":"https://pith.science/pith/AUPTCWPISY2RBIETW5LOGQMEW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AUPTCWPISY2RBIETW5LOGQMEW4/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":"2026-05-25T12:02:05Z","links":{"resolver":"https://pith.science/pith/AUPTCWPISY2RBIETW5LOGQMEW4","bundle":"https://pith.science/pith/AUPTCWPISY2RBIETW5LOGQMEW4/bundle.json","state":"https://pith.science/pith/AUPTCWPISY2RBIETW5LOGQMEW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AUPTCWPISY2RBIETW5LOGQMEW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AUPTCWPISY2RBIETW5LOGQMEW4","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":"f05f01a752cfa4685aea9bd6d8567e7bc50be1a25f8288fe299b4027c666d507","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-10-01T14:44:08Z","title_canon_sha256":"a14103ccd67611b0d9fdf32e4c564e547dc18be7074f7175cfde3b795a79aebe"},"schema_version":"1.0","source":{"id":"1810.00731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00731","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00731v1","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00731","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"AUPTCWPISY2R","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AUPTCWPISY2RBIET","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AUPTCWPI","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:bdbe303b7f65a576b7295b15287add92bca12145fc5fb381fe093526a4d5fa44","target":"graph","created_at":"2026-05-18T00:04:24Z","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 reconfiguration graph $R_k(G)$ of the $k$-colourings of a graph $G$ has as vertex set the set of all possible $k$-colourings of $G$ and two colourings are adjacent if they differ on the colour of exactly one vertex. Cereceda conjectured ten years ago that, for every $k$-degenerate graph $G$ on $n$ vertices, $R_{k+2}(G)$ has diameter $\\mathcal{O}({n^2})$. The conjecture is wide open, with a best known bound of $\\mathcal{O}({k^n})$, even for planar graphs. We improve this bound for planar graphs to $2^{\\mathcal{O}({\\sqrt{n}})}$. Our proof can be transformed into an algorithm that runs in $2^","authors_text":"Carl Feghali, Eduard Eiben","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-10-01T14:44:08Z","title":"Towards Cereceda's conjecture for planar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00731","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:ea41f6765fc4488dc4fcf8e2081833f85dfbbeb1aa1fb0882895dbf3695698ce","target":"record","created_at":"2026-05-18T00:04:24Z","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":"f05f01a752cfa4685aea9bd6d8567e7bc50be1a25f8288fe299b4027c666d507","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-10-01T14:44:08Z","title_canon_sha256":"a14103ccd67611b0d9fdf32e4c564e547dc18be7074f7175cfde3b795a79aebe"},"schema_version":"1.0","source":{"id":"1810.00731","kind":"arxiv","version":1}},"canonical_sha256":"051f3159e8963510a093b756e34184b716009dbc2fd0bbe7ad7c324086e188db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"051f3159e8963510a093b756e34184b716009dbc2fd0bbe7ad7c324086e188db","first_computed_at":"2026-05-18T00:04:24.974855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:24.974855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U/3i+YmCJdfgbtURHhd4jka3gwD2XzJ6cB1GRmA3rsDv0lxcQH/45fCw4/0CgN2A6t35sOz3L2mukGJy8Ir0DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:24.975439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea41f6765fc4488dc4fcf8e2081833f85dfbbeb1aa1fb0882895dbf3695698ce","sha256:bdbe303b7f65a576b7295b15287add92bca12145fc5fb381fe093526a4d5fa44"],"state_sha256":"4ca67b88b86a53ef94dad37dae7230e6ef8c03ec6e98b720bc725a9b8de8ddcb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GiXZPxHHIRFBbOr70YfIqnb5lmPTnhpWHD6AY0m0x01fpgEldkEkoAE+juIIntyDOIcTBUg1/W4rb6Uc7XbUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:02:05.200495Z","bundle_sha256":"35b885ec6f521199a5d709f8fb26e2b1f464ef2cd8ffb9db764c8c96fdcf90db"}}