{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:H32WALVCZQ23QKNS7EVL3WC7MA","short_pith_number":"pith:H32WALVC","canonical_record":{"source":{"id":"1605.04441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-14T17:38:03Z","cross_cats_sorted":[],"title_canon_sha256":"f843aa93e109ca6afebc5e330a6cc74806adcd6ec8f11e5edac0fb2f447924a4","abstract_canon_sha256":"d255c6c1d4b7f3b01a50eb2558288e861b40934b033feb62497aa4e04c002df8"},"schema_version":"1.0"},"canonical_sha256":"3ef5602ea2cc35b829b2f92abdd85f602cec1327e9b301afd1b33f1d776d8d33","source":{"kind":"arxiv","id":"1605.04441","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04441","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04441v1","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04441","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"pith_short_12","alias_value":"H32WALVCZQ23","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H32WALVCZQ23QKNS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H32WALVC","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:H32WALVCZQ23QKNS7EVL3WC7MA","target":"record","payload":{"canonical_record":{"source":{"id":"1605.04441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-14T17:38:03Z","cross_cats_sorted":[],"title_canon_sha256":"f843aa93e109ca6afebc5e330a6cc74806adcd6ec8f11e5edac0fb2f447924a4","abstract_canon_sha256":"d255c6c1d4b7f3b01a50eb2558288e861b40934b033feb62497aa4e04c002df8"},"schema_version":"1.0"},"canonical_sha256":"3ef5602ea2cc35b829b2f92abdd85f602cec1327e9b301afd1b33f1d776d8d33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:47.196498Z","signature_b64":"1J2sWa4rzD4JVYRPHEAm4+9ipKRzbyDLvM/Lke72MymfboqWSuWffq9NLy276LJaamBg+mBcOkLeL8qccCPiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ef5602ea2cc35b829b2f92abdd85f602cec1327e9b301afd1b33f1d776d8d33","last_reissued_at":"2026-05-18T01:14:47.195835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:47.195835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.04441","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":"2026-05-18T01:14:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XnKrclPCGYzUYl/vk5aNHVDfKwHvCdhGo+8yfWXzbIldfbL83xj1dfYUEydqppo5LmlfoFAOy8Uerj8uJlosDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:27:07.045926Z"},"content_sha256":"7f9483556ae2bd9c7f2e6eebc3ec07f45c4ef76ff277bf5fd089bbfc1a79611e","schema_version":"1.0","event_id":"sha256:7f9483556ae2bd9c7f2e6eebc3ec07f45c4ef76ff277bf5fd089bbfc1a79611e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:H32WALVCZQ23QKNS7EVL3WC7MA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on $4$-colorings of Quadrangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arthur Hoffmann-Ostenhof, Atsuhiro Nakamoto","submitted_at":"2016-05-14T17:38:03Z","abstract_excerpt":"Let $G$ be a quadrangulation on an orientable surface and let $g$ be a proper vertex-$4$-coloring of $G$. A face $F$ of $G$ is said to be a rainbow-face if all four distinct colors appear on its boundary. A $(c_1,c_2,c_3,c_4)$-face in $G$ is a rainbow face with colors $c_i$, $i=1,2,3,4$ on the boundary in clockwise order. We show that the number of $(c_1,c_2,c_3,c_4)$-faces in $G$ equals the number of $(c_4,c_3,c_2,c_1)$-faces. This implies in particular that the number of rainbow-faces of $G$ is even."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04441","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":"2026-05-18T01:14:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mg1yO1oDPUBQt+Qed/LlBHDmc+9dl9F2NWdBmmMnqyhqTHd9Ul1iZ5xTFWCljjwiuskiDi41DVWpwurGg8/nAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:27:07.046560Z"},"content_sha256":"1cb239a753c42b96e69a734e2c7461d31dce6ed98064e7255bdaf868559f58d3","schema_version":"1.0","event_id":"sha256:1cb239a753c42b96e69a734e2c7461d31dce6ed98064e7255bdaf868559f58d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H32WALVCZQ23QKNS7EVL3WC7MA/bundle.json","state_url":"https://pith.science/pith/H32WALVCZQ23QKNS7EVL3WC7MA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H32WALVCZQ23QKNS7EVL3WC7MA/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":"2026-06-01T21:27:07Z","links":{"resolver":"https://pith.science/pith/H32WALVCZQ23QKNS7EVL3WC7MA","bundle":"https://pith.science/pith/H32WALVCZQ23QKNS7EVL3WC7MA/bundle.json","state":"https://pith.science/pith/H32WALVCZQ23QKNS7EVL3WC7MA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H32WALVCZQ23QKNS7EVL3WC7MA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H32WALVCZQ23QKNS7EVL3WC7MA","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":"d255c6c1d4b7f3b01a50eb2558288e861b40934b033feb62497aa4e04c002df8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-14T17:38:03Z","title_canon_sha256":"f843aa93e109ca6afebc5e330a6cc74806adcd6ec8f11e5edac0fb2f447924a4"},"schema_version":"1.0","source":{"id":"1605.04441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04441","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04441v1","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04441","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"pith_short_12","alias_value":"H32WALVCZQ23","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H32WALVCZQ23QKNS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H32WALVC","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:1cb239a753c42b96e69a734e2c7461d31dce6ed98064e7255bdaf868559f58d3","target":"graph","created_at":"2026-05-18T01:14:47Z","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":"Let $G$ be a quadrangulation on an orientable surface and let $g$ be a proper vertex-$4$-coloring of $G$. A face $F$ of $G$ is said to be a rainbow-face if all four distinct colors appear on its boundary. A $(c_1,c_2,c_3,c_4)$-face in $G$ is a rainbow face with colors $c_i$, $i=1,2,3,4$ on the boundary in clockwise order. We show that the number of $(c_1,c_2,c_3,c_4)$-faces in $G$ equals the number of $(c_4,c_3,c_2,c_1)$-faces. This implies in particular that the number of rainbow-faces of $G$ is even.","authors_text":"Arthur Hoffmann-Ostenhof, Atsuhiro Nakamoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-14T17:38:03Z","title":"A Note on $4$-colorings of Quadrangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04441","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":"sha256:7f9483556ae2bd9c7f2e6eebc3ec07f45c4ef76ff277bf5fd089bbfc1a79611e","target":"record","created_at":"2026-05-18T01:14:47Z","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":"d255c6c1d4b7f3b01a50eb2558288e861b40934b033feb62497aa4e04c002df8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-14T17:38:03Z","title_canon_sha256":"f843aa93e109ca6afebc5e330a6cc74806adcd6ec8f11e5edac0fb2f447924a4"},"schema_version":"1.0","source":{"id":"1605.04441","kind":"arxiv","version":1}},"canonical_sha256":"3ef5602ea2cc35b829b2f92abdd85f602cec1327e9b301afd1b33f1d776d8d33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ef5602ea2cc35b829b2f92abdd85f602cec1327e9b301afd1b33f1d776d8d33","first_computed_at":"2026-05-18T01:14:47.195835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:47.195835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1J2sWa4rzD4JVYRPHEAm4+9ipKRzbyDLvM/Lke72MymfboqWSuWffq9NLy276LJaamBg+mBcOkLeL8qccCPiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:47.196498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f9483556ae2bd9c7f2e6eebc3ec07f45c4ef76ff277bf5fd089bbfc1a79611e","sha256:1cb239a753c42b96e69a734e2c7461d31dce6ed98064e7255bdaf868559f58d3"],"state_sha256":"e6d026141566b252d8ecf6f5af5c126808822dcbe4c276ffd46afe43b0446123"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ogviAykXEfgk42kzYc/ai/AohQBDPtfSPvzLcl9AZt+GXJTIWI37rrKy97dfreBRBSC7nertG2Bf5wMi9u0uCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:27:07.049550Z","bundle_sha256":"95ebc86012e1521753c628bc252411402d417c3e40fbc67fd3baa25614189e29"}}