{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P6HSB3ZVCYU3R23V4T5CSR4ZVE","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":"9bd34a99aac11d996f78ec66477d7ccc1504ae1d0b3ce2fe442116e681808222","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-01T20:56:55Z","title_canon_sha256":"519eb2e185699acb6414cf7a317ffe0e75dab45f8ecc4a809afd6816af887f50"},"schema_version":"1.0","source":{"id":"1507.00335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00335","created_at":"2026-05-18T01:37:26Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00335v1","created_at":"2026-05-18T01:37:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00335","created_at":"2026-05-18T01:37:26Z"},{"alias_kind":"pith_short_12","alias_value":"P6HSB3ZVCYU3","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P6HSB3ZVCYU3R23V","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P6HSB3ZV","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:c838383f7bd4c945e891198d2c7cfa2f825da3f0b21d75bbad56db7ddc0bea74","target":"graph","created_at":"2026-05-18T01:37:26Z","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":"Inspired by the question of whether one can create a visually informative map in which distances reflect travel-times rather than physical proximity, we examine whether it is possible to construct a meaningful travel time function between points in a region. We argue that such a function should constitute a mathematical metric, and we offer a reasonable candidate using a max-min approach.","authors_text":"Kenneth Halpern","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-01T20:56:55Z","title":"A Travel-Time Metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00335","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:c45f2ccd0a780f12a088c9a81f29c5220101edc726182745d6cd37f5dede0c12","target":"record","created_at":"2026-05-18T01:37:26Z","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":"9bd34a99aac11d996f78ec66477d7ccc1504ae1d0b3ce2fe442116e681808222","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-01T20:56:55Z","title_canon_sha256":"519eb2e185699acb6414cf7a317ffe0e75dab45f8ecc4a809afd6816af887f50"},"schema_version":"1.0","source":{"id":"1507.00335","kind":"arxiv","version":1}},"canonical_sha256":"7f8f20ef351629b8eb75e4fa294799a92deb8f78a768652fefa6b784d4c56938","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f8f20ef351629b8eb75e4fa294799a92deb8f78a768652fefa6b784d4c56938","first_computed_at":"2026-05-18T01:37:26.858091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:26.858091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9D+mwFYkgSPOl6T1Ue2lthk3DKZ6M1YmirLD9NhDCrITNuz5Xm9z5w6LTmtqOSgx+XK75u5/PoBsnYNcr1xeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:26.858729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c45f2ccd0a780f12a088c9a81f29c5220101edc726182745d6cd37f5dede0c12","sha256:c838383f7bd4c945e891198d2c7cfa2f825da3f0b21d75bbad56db7ddc0bea74"],"state_sha256":"5930503c1f0ea0ce7bd6d0e950c9b130b1d115903e68f7ede4971095aee70a93"}