{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JAUDEOJL2TIIKXU2XKLZDFWNRW","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":"b0459195ab26050a53792477f332116917a923d1082bdf9ad4f5ff7c4dd98322","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2024-10-31T01:56:13Z","title_canon_sha256":"15af9309a77149176df9e67564fc918a526d05b74c92cf6f5f2121aaf0e1b256"},"schema_version":"1.0","source":{"id":"2410.23559","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.23559","created_at":"2026-07-05T09:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"2410.23559v2","created_at":"2026-07-05T09:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23559","created_at":"2026-07-05T09:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"JAUDEOJL2TII","created_at":"2026-07-05T09:41:43Z"},{"alias_kind":"pith_short_16","alias_value":"JAUDEOJL2TIIKXU2","created_at":"2026-07-05T09:41:43Z"},{"alias_kind":"pith_short_8","alias_value":"JAUDEOJL","created_at":"2026-07-05T09:41:43Z"}],"graph_snapshots":[{"event_id":"sha256:ec1c2e0ffb5c230add1244d3e6e99480333af3ea155bbea8b468eaf041533b50","target":"graph","created_at":"2026-07-05T09:41:43Z","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/2410.23559/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where geographic principles are succinctly expressed within a defined metric space. However, common spatial representations, including map-based or network-based approaches, fall short by incompletely or inaccurately defining this metric space. Here we show, by introducing an inverse friction factor that captures the spatial constraints in spatial networks, that a homoge","authors_text":"Hezhishi Jiang, Hongmou Zhang, Jintong Tang, Liyan Xu, Tianshu Li, Yu Liu, Yuxuan Wang, Zekun Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2024-10-31T01:56:13Z","title":"Geographic Space as Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23559","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":"sha256:99cdd6eff1551981fbe211db4566c2f30fbffcf79f52b9cdbd7ffc2f64a8d0b6","target":"record","created_at":"2026-07-05T09:41:43Z","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":"b0459195ab26050a53792477f332116917a923d1082bdf9ad4f5ff7c4dd98322","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2024-10-31T01:56:13Z","title_canon_sha256":"15af9309a77149176df9e67564fc918a526d05b74c92cf6f5f2121aaf0e1b256"},"schema_version":"1.0","source":{"id":"2410.23559","kind":"arxiv","version":2}},"canonical_sha256":"482832392bd4d0855e9aba979196cd8da8c0c9a83aa1c04f7264afcafe509caf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"482832392bd4d0855e9aba979196cd8da8c0c9a83aa1c04f7264afcafe509caf","first_computed_at":"2026-07-05T09:41:43.930268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:43.930268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rq3sHQ5EWs4hhTWr03/guNeCV/l65/Nf5dGdmyajSDFs3MGwg1tToK8og3HGZ080BelHAD1tI3Nb9ehYAbB5Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:43.930744Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.23559","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99cdd6eff1551981fbe211db4566c2f30fbffcf79f52b9cdbd7ffc2f64a8d0b6","sha256:ec1c2e0ffb5c230add1244d3e6e99480333af3ea155bbea8b468eaf041533b50"],"state_sha256":"4feacf5259d320931e936f5701e8ef6f58904b56e7d913861a4bb54dd68deac4"}