{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3RD23HZEAIFZTRC2XQ47G2QPDL","short_pith_number":"pith:3RD23HZE","canonical_record":{"source":{"id":"1502.06238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-22T15:39:27Z","cross_cats_sorted":[],"title_canon_sha256":"bb0b6e308687d782956b0853cfc91f6ae7abeeb486dbf495ebc9833e3016e688","abstract_canon_sha256":"532c003126a2b4d077a8ed3b2a75fa3afc98e6818bc02af004f7b0089a611847"},"schema_version":"1.0"},"canonical_sha256":"dc47ad9f24020b99c45abc39f36a0f1ae747b8a3f12afbbfdd794da331ad13ac","source":{"kind":"arxiv","id":"1502.06238","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06238","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06238v2","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06238","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"3RD23HZEAIFZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3RD23HZEAIFZTRC2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3RD23HZE","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3RD23HZEAIFZTRC2XQ47G2QPDL","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-22T15:39:27Z","cross_cats_sorted":[],"title_canon_sha256":"bb0b6e308687d782956b0853cfc91f6ae7abeeb486dbf495ebc9833e3016e688","abstract_canon_sha256":"532c003126a2b4d077a8ed3b2a75fa3afc98e6818bc02af004f7b0089a611847"},"schema_version":"1.0"},"canonical_sha256":"dc47ad9f24020b99c45abc39f36a0f1ae747b8a3f12afbbfdd794da331ad13ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:39.434794Z","signature_b64":"pu8fADvk6pv2kDz7FCH54E518wiWY/HYLmoGmCtZw9GbMwt0qKYD7mOCPcI4hNyHywegjBNrvhXmgG2JMMwYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc47ad9f24020b99c45abc39f36a0f1ae747b8a3f12afbbfdd794da331ad13ac","last_reissued_at":"2026-05-18T01:25:39.434228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:39.434228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06238","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a/yZgNdHQZ2jglurBzZ6U3Q/RzfSoiXsxHRBaAUYLJPUBTWlnWfnh4xbBRw69ntIu0jwDkyRW4KSqEQ4Q/+nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:35:31.796297Z"},"content_sha256":"6d96fe4e5f4eddcd347f15dfca8baf1cd93f2c445d34643769be3892b0215f83","schema_version":"1.0","event_id":"sha256:6d96fe4e5f4eddcd347f15dfca8baf1cd93f2c445d34643769be3892b0215f83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3RD23HZEAIFZTRC2XQ47G2QPDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Matra\\'s, Artur Siemaszko","submitted_at":"2015-02-22T15:39:27Z","abstract_excerpt":"The distant graph $G = G(\\mathbb{P}(Z),\\triangle)$ of the projective line over the ring of integers is considered. The shortest path problem in this graph is solved by use of Klein's geometric interpretation of Euclidean continued fractions. In case the minimal path is non-unique, all the possible splitting are described which allows us to give necessary and sufficient conditions for existence of a unique shortest path."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06238","kind":"arxiv","version":2},"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":"2026-05-18T01:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUG+0wWPm8zRGDxKrFbYz1DETwq0+zXHi4JyNoavfC3kLlrHjNG1LZjROX09yIwy7uqkoOE+D3usANPI0ZymCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:35:31.796664Z"},"content_sha256":"efcba6efc4706705d77e63f2de37960d0cde4f3166358e77f8368ef9a5b0ba48","schema_version":"1.0","event_id":"sha256:efcba6efc4706705d77e63f2de37960d0cde4f3166358e77f8368ef9a5b0ba48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RD23HZEAIFZTRC2XQ47G2QPDL/bundle.json","state_url":"https://pith.science/pith/3RD23HZEAIFZTRC2XQ47G2QPDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RD23HZEAIFZTRC2XQ47G2QPDL/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":"2026-06-09T12:35:31Z","links":{"resolver":"https://pith.science/pith/3RD23HZEAIFZTRC2XQ47G2QPDL","bundle":"https://pith.science/pith/3RD23HZEAIFZTRC2XQ47G2QPDL/bundle.json","state":"https://pith.science/pith/3RD23HZEAIFZTRC2XQ47G2QPDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RD23HZEAIFZTRC2XQ47G2QPDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3RD23HZEAIFZTRC2XQ47G2QPDL","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":"532c003126a2b4d077a8ed3b2a75fa3afc98e6818bc02af004f7b0089a611847","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-22T15:39:27Z","title_canon_sha256":"bb0b6e308687d782956b0853cfc91f6ae7abeeb486dbf495ebc9833e3016e688"},"schema_version":"1.0","source":{"id":"1502.06238","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06238","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06238v2","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06238","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"3RD23HZEAIFZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3RD23HZEAIFZTRC2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3RD23HZE","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:efcba6efc4706705d77e63f2de37960d0cde4f3166358e77f8368ef9a5b0ba48","target":"graph","created_at":"2026-05-18T01:25:39Z","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 distant graph $G = G(\\mathbb{P}(Z),\\triangle)$ of the projective line over the ring of integers is considered. The shortest path problem in this graph is solved by use of Klein's geometric interpretation of Euclidean continued fractions. In case the minimal path is non-unique, all the possible splitting are described which allows us to give necessary and sufficient conditions for existence of a unique shortest path.","authors_text":"Andrzej Matra\\'s, Artur Siemaszko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-22T15:39:27Z","title":"The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06238","kind":"arxiv","version":2},"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":"sha256:6d96fe4e5f4eddcd347f15dfca8baf1cd93f2c445d34643769be3892b0215f83","target":"record","created_at":"2026-05-18T01:25:39Z","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":"532c003126a2b4d077a8ed3b2a75fa3afc98e6818bc02af004f7b0089a611847","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-22T15:39:27Z","title_canon_sha256":"bb0b6e308687d782956b0853cfc91f6ae7abeeb486dbf495ebc9833e3016e688"},"schema_version":"1.0","source":{"id":"1502.06238","kind":"arxiv","version":2}},"canonical_sha256":"dc47ad9f24020b99c45abc39f36a0f1ae747b8a3f12afbbfdd794da331ad13ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc47ad9f24020b99c45abc39f36a0f1ae747b8a3f12afbbfdd794da331ad13ac","first_computed_at":"2026-05-18T01:25:39.434228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:39.434228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pu8fADvk6pv2kDz7FCH54E518wiWY/HYLmoGmCtZw9GbMwt0qKYD7mOCPcI4hNyHywegjBNrvhXmgG2JMMwYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:39.434794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06238","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d96fe4e5f4eddcd347f15dfca8baf1cd93f2c445d34643769be3892b0215f83","sha256:efcba6efc4706705d77e63f2de37960d0cde4f3166358e77f8368ef9a5b0ba48"],"state_sha256":"7df9c2d05240b8ffa74827a11f4770f709e484e50095d1ac22482387551c4a75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZExFq7LeiNZNOHl8Zjp/TMtyHBqv1JWV3lxBwbgxcaJo5XmkKe8MR7ooEFCrnJ4Zxa5vxFG6TiWX7RNgAD6Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:35:31.798540Z","bundle_sha256":"d992deb66f746479bb889835066016f2293f18c59337419a849d274586a95390"}}