{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:S5XPQACFQOXPOCQIENHW4RJMEA","short_pith_number":"pith:S5XPQACF","canonical_record":{"source":{"id":"1809.08148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-09-21T14:38:06Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"35575a865970e0703ddfb94ec6b3aeb03f6b279f60750d46dba5fffcf8b2f9c6","abstract_canon_sha256":"61d7311275afc76242e79d17d3d94b2ecff6f49da28b3dfa193913bfabd44797"},"schema_version":"1.0"},"canonical_sha256":"976ef8004583aef70a08234f6e452c2022da73688bda2e14979db789c6d53194","source":{"kind":"arxiv","id":"1809.08148","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08148","created_at":"2026-05-17T23:58:37Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08148v1","created_at":"2026-05-17T23:58:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08148","created_at":"2026-05-17T23:58:37Z"},{"alias_kind":"pith_short_12","alias_value":"S5XPQACFQOXP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S5XPQACFQOXPOCQI","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S5XPQACF","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:S5XPQACFQOXPOCQIENHW4RJMEA","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-09-21T14:38:06Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"35575a865970e0703ddfb94ec6b3aeb03f6b279f60750d46dba5fffcf8b2f9c6","abstract_canon_sha256":"61d7311275afc76242e79d17d3d94b2ecff6f49da28b3dfa193913bfabd44797"},"schema_version":"1.0"},"canonical_sha256":"976ef8004583aef70a08234f6e452c2022da73688bda2e14979db789c6d53194","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:37.594859Z","signature_b64":"N3ywa8C20Jdw67KGkE9QG1iFEZL4QhKeRBPvo8jOHYXnXsixGg6krS5hRP47KPXtjuMSZXFiIxk+bWXN1zDVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"976ef8004583aef70a08234f6e452c2022da73688bda2e14979db789c6d53194","last_reissued_at":"2026-05-17T23:58:37.594175Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:37.594175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08148","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":"2026-05-17T23:58:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wmr3L2KJ65G5EfNBiynlUAwhNXaoLZL/2w0AGzS23EFOwFHObYI76LAPbuclpAOgow3anUDSraV36QCi2xTFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:23:11.270798Z"},"content_sha256":"90ebdaeebd35e002d49e01873ed1ad2d9978d826d12f5d077e69694c75aa2b9f","schema_version":"1.0","event_id":"sha256:90ebdaeebd35e002d49e01873ed1ad2d9978d826d12f5d077e69694c75aa2b9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:S5XPQACFQOXPOCQIENHW4RJMEA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a classification of planar maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexandre Diet, Marc Barthelemy","submitted_at":"2018-09-21T14:38:06Z","abstract_excerpt":"Planar graphs and their spatial embedding -- planar maps -- are used in many different fields due to their ubiquity in the real world (leaf veins in biology, street patterns in urban studies, etc.) and are also fundamental objects in mathematics and combinatorics. These graphs have been well described in the literature, but we do not have so far a clear way to cluster them in different families. A typology of planar maps would be very useful and would allow to monitor their changes, to compare them with each other, or to correlate their structure with other properties. Using an algorithm which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08148","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":"2026-05-17T23:58:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//jI/vr8v0hFDwspDfK3vt4qP6TDc308QTDWnpHv5BAcc9okw84EkpWE52b5CROvcm0g/kQyoJS6zOzIQc9cDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:23:11.271443Z"},"content_sha256":"0f51d5ba3fa3d5c0886bdb4ac67a4ee2023898c0a9ca4d06781aa3c3d28728d2","schema_version":"1.0","event_id":"sha256:0f51d5ba3fa3d5c0886bdb4ac67a4ee2023898c0a9ca4d06781aa3c3d28728d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5XPQACFQOXPOCQIENHW4RJMEA/bundle.json","state_url":"https://pith.science/pith/S5XPQACFQOXPOCQIENHW4RJMEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5XPQACFQOXPOCQIENHW4RJMEA/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":"2026-06-01T22:23:11Z","links":{"resolver":"https://pith.science/pith/S5XPQACFQOXPOCQIENHW4RJMEA","bundle":"https://pith.science/pith/S5XPQACFQOXPOCQIENHW4RJMEA/bundle.json","state":"https://pith.science/pith/S5XPQACFQOXPOCQIENHW4RJMEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5XPQACFQOXPOCQIENHW4RJMEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S5XPQACFQOXPOCQIENHW4RJMEA","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":"61d7311275afc76242e79d17d3d94b2ecff6f49da28b3dfa193913bfabd44797","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-09-21T14:38:06Z","title_canon_sha256":"35575a865970e0703ddfb94ec6b3aeb03f6b279f60750d46dba5fffcf8b2f9c6"},"schema_version":"1.0","source":{"id":"1809.08148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08148","created_at":"2026-05-17T23:58:37Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08148v1","created_at":"2026-05-17T23:58:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08148","created_at":"2026-05-17T23:58:37Z"},{"alias_kind":"pith_short_12","alias_value":"S5XPQACFQOXP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S5XPQACFQOXPOCQI","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S5XPQACF","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:0f51d5ba3fa3d5c0886bdb4ac67a4ee2023898c0a9ca4d06781aa3c3d28728d2","target":"graph","created_at":"2026-05-17T23:58:37Z","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":"Planar graphs and their spatial embedding -- planar maps -- are used in many different fields due to their ubiquity in the real world (leaf veins in biology, street patterns in urban studies, etc.) and are also fundamental objects in mathematics and combinatorics. These graphs have been well described in the literature, but we do not have so far a clear way to cluster them in different families. A typology of planar maps would be very useful and would allow to monitor their changes, to compare them with each other, or to correlate their structure with other properties. Using an algorithm which","authors_text":"Alexandre Diet, Marc Barthelemy","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-09-21T14:38:06Z","title":"Towards a classification of planar maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08148","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":"sha256:90ebdaeebd35e002d49e01873ed1ad2d9978d826d12f5d077e69694c75aa2b9f","target":"record","created_at":"2026-05-17T23:58:37Z","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":"61d7311275afc76242e79d17d3d94b2ecff6f49da28b3dfa193913bfabd44797","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-09-21T14:38:06Z","title_canon_sha256":"35575a865970e0703ddfb94ec6b3aeb03f6b279f60750d46dba5fffcf8b2f9c6"},"schema_version":"1.0","source":{"id":"1809.08148","kind":"arxiv","version":1}},"canonical_sha256":"976ef8004583aef70a08234f6e452c2022da73688bda2e14979db789c6d53194","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"976ef8004583aef70a08234f6e452c2022da73688bda2e14979db789c6d53194","first_computed_at":"2026-05-17T23:58:37.594175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:37.594175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N3ywa8C20Jdw67KGkE9QG1iFEZL4QhKeRBPvo8jOHYXnXsixGg6krS5hRP47KPXtjuMSZXFiIxk+bWXN1zDVBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:37.594859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90ebdaeebd35e002d49e01873ed1ad2d9978d826d12f5d077e69694c75aa2b9f","sha256:0f51d5ba3fa3d5c0886bdb4ac67a4ee2023898c0a9ca4d06781aa3c3d28728d2"],"state_sha256":"9ff49951467d39722d783746a7eee5c1f07ea380a21a0b6669c0e77527cbc10a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVRGtfjjeGXXJ15+ja+QdBpdz7299GixnIf0Ki9u+O3dIiM09HTMRnS+e+JYdQjqRYsYooKq1lFKwvMyQHiPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:23:11.274638Z","bundle_sha256":"68f0c76ed8e5509ff5366defb580c490af50d8e8bfa0c44cca81d8c475e2401e"}}