{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3HOVDBRROP6X7BYDKQ7KSCNLSN","short_pith_number":"pith:3HOVDBRR","canonical_record":{"source":{"id":"1908.05694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-08-15T18:07:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7fb583131cb6a58419f656e4442bbc873c5e1f16a1b8bfd1b2708c839ff631e1","abstract_canon_sha256":"611175fd869a6319da2a7d5ca268547ac6887dbeca49bf4cfc6517f637c769bf"},"schema_version":"1.0"},"canonical_sha256":"d9dd51863173fd7f8703543ea909ab9365d38a32bb5a7aa400e7468949022ff2","source":{"kind":"arxiv","id":"1908.05694","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05694","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05694v1","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05694","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"3HOVDBRROP6X","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"pith_short_16","alias_value":"3HOVDBRROP6X7BYD","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"pith_short_8","alias_value":"3HOVDBRR","created_at":"2026-07-04T23:57:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3HOVDBRROP6X7BYDKQ7KSCNLSN","target":"record","payload":{"canonical_record":{"source":{"id":"1908.05694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-08-15T18:07:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7fb583131cb6a58419f656e4442bbc873c5e1f16a1b8bfd1b2708c839ff631e1","abstract_canon_sha256":"611175fd869a6319da2a7d5ca268547ac6887dbeca49bf4cfc6517f637c769bf"},"schema_version":"1.0"},"canonical_sha256":"d9dd51863173fd7f8703543ea909ab9365d38a32bb5a7aa400e7468949022ff2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:57:52.465987Z","signature_b64":"p7kdp/HQDIZQ+LUuR6yndQcWu2pcGyx1zUDea2yDDKBCzwHl5X99gYAhggwxEXUnpmL1DUHkStuuA+yZVQ2RBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9dd51863173fd7f8703543ea909ab9365d38a32bb5a7aa400e7468949022ff2","last_reissued_at":"2026-07-04T23:57:52.465515Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:57:52.465515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.05694","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":"2026-07-04T23:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2UrVoLbwIqcQPQqg/ifCUHo6nKxmAZCfYCKH/VMn6HT3o0usoE8qAcQNXnj4u+i6tDibuDzWdNbWskU+g+E9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:11:57.116012Z"},"content_sha256":"221d23d32146362d4df186e4f899447acf00c8b0b97c22fb499ba3a318828575","schema_version":"1.0","event_id":"sha256:221d23d32146362d4df186e4f899447acf00c8b0b97c22fb499ba3a318828575"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3HOVDBRROP6X7BYDKQ7KSCNLSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How many ways to color the map of America?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.HO","authors_text":"Jasbir S. Chahal, Jennifer Canizales, Rebekah Bassett, Thomas Fackrell, Vanessa Rico","submitted_at":"2019-08-15T18:07:17Z","abstract_excerpt":"Although the Four Color Conjecture originated in cartography, surprisingly, there is nothing in the literature on the number of ways to color an actual geographic map with four or fewer colors. In this paper, we compute these numbers, with exponentially increasing order of difficulty, for the maps of Canada, France, and the USA. Our attempts to compute the latter two lead to some new results on the chromatic polynomial of graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05694","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05694/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UsI14SoBjQ/gAmKXWoyYfcKFYjyKf93o0oGqlk1QMMoaxOtYgXzu5bYHzSmAFSakXvuS0xxXpN6aE/qFZ1xbDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:11:57.116536Z"},"content_sha256":"c24f90b89a696566f4f1b992b9cba330cb612ad02957464b7154446891578fb7","schema_version":"1.0","event_id":"sha256:c24f90b89a696566f4f1b992b9cba330cb612ad02957464b7154446891578fb7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HOVDBRROP6X7BYDKQ7KSCNLSN/bundle.json","state_url":"https://pith.science/pith/3HOVDBRROP6X7BYDKQ7KSCNLSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HOVDBRROP6X7BYDKQ7KSCNLSN/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":"2026-08-16T10:11:57Z","links":{"resolver":"https://pith.science/pith/3HOVDBRROP6X7BYDKQ7KSCNLSN","bundle":"https://pith.science/pith/3HOVDBRROP6X7BYDKQ7KSCNLSN/bundle.json","state":"https://pith.science/pith/3HOVDBRROP6X7BYDKQ7KSCNLSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HOVDBRROP6X7BYDKQ7KSCNLSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3HOVDBRROP6X7BYDKQ7KSCNLSN","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":"611175fd869a6319da2a7d5ca268547ac6887dbeca49bf4cfc6517f637c769bf","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-08-15T18:07:17Z","title_canon_sha256":"7fb583131cb6a58419f656e4442bbc873c5e1f16a1b8bfd1b2708c839ff631e1"},"schema_version":"1.0","source":{"id":"1908.05694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05694","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05694v1","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05694","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"3HOVDBRROP6X","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"pith_short_16","alias_value":"3HOVDBRROP6X7BYD","created_at":"2026-07-04T23:57:52Z"},{"alias_kind":"pith_short_8","alias_value":"3HOVDBRR","created_at":"2026-07-04T23:57:52Z"}],"graph_snapshots":[{"event_id":"sha256:c24f90b89a696566f4f1b992b9cba330cb612ad02957464b7154446891578fb7","target":"graph","created_at":"2026-07-04T23:57:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.05694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Although the Four Color Conjecture originated in cartography, surprisingly, there is nothing in the literature on the number of ways to color an actual geographic map with four or fewer colors. In this paper, we compute these numbers, with exponentially increasing order of difficulty, for the maps of Canada, France, and the USA. Our attempts to compute the latter two lead to some new results on the chromatic polynomial of graphs.","authors_text":"Jasbir S. Chahal, Jennifer Canizales, Rebekah Bassett, Thomas Fackrell, Vanessa Rico","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-08-15T18:07:17Z","title":"How many ways to color the map of America?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05694","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":"sha256:221d23d32146362d4df186e4f899447acf00c8b0b97c22fb499ba3a318828575","target":"record","created_at":"2026-07-04T23:57:52Z","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":"611175fd869a6319da2a7d5ca268547ac6887dbeca49bf4cfc6517f637c769bf","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-08-15T18:07:17Z","title_canon_sha256":"7fb583131cb6a58419f656e4442bbc873c5e1f16a1b8bfd1b2708c839ff631e1"},"schema_version":"1.0","source":{"id":"1908.05694","kind":"arxiv","version":1}},"canonical_sha256":"d9dd51863173fd7f8703543ea909ab9365d38a32bb5a7aa400e7468949022ff2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9dd51863173fd7f8703543ea909ab9365d38a32bb5a7aa400e7468949022ff2","first_computed_at":"2026-07-04T23:57:52.465515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:57:52.465515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p7kdp/HQDIZQ+LUuR6yndQcWu2pcGyx1zUDea2yDDKBCzwHl5X99gYAhggwxEXUnpmL1DUHkStuuA+yZVQ2RBw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:57:52.465987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:221d23d32146362d4df186e4f899447acf00c8b0b97c22fb499ba3a318828575","sha256:c24f90b89a696566f4f1b992b9cba330cb612ad02957464b7154446891578fb7"],"state_sha256":"b2e5475ab821305f71974d2e5301579b4bf6014e7dbd3b4a68f6539364ad2c4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"58lhWY7PaT2ysr5iysFsZJRZY1my6GJ8v90/mn8mILJrhaSAdjneaw6BCgLXC6TqrSZ7n9XV4+M61Mg3F6XHAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:11:57.120743Z","bundle_sha256":"0a9e1795c3d0e5022f4f284a76b197ec02885a744523bb321d91c177c1962ee1"}}