{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DJZTW3MTBGMMUY4SB3O2WPBX3Z","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":"7094a8cdd24288828282d3b85f10033b6800eab9ab7ff0848572124d30d2d653","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-03-16T21:35:40Z","title_canon_sha256":"34a35fbafe35d3f4c8c13fda3a8a3a28df81f7ba3746d2a31599bf9dd0d84efa"},"schema_version":"1.0","source":{"id":"1103.3301","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3301","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3301v2","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3301","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"DJZTW3MTBGMM","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DJZTW3MTBGMMUY4S","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DJZTW3MT","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:3d9219a3baf8856d57ec46538a98dbb453cd0477f9c31b48648d1ebabfb4def5","target":"graph","created_at":"2026-05-18T04:05:05Z","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 p-median problem is a common model for optimal facility location. The task is to place p facilities (e.g., warehouses or schools) in a heterogeneously populated space such that the average distance from a person's home to the nearest facility is minimized. Here we study the special case where the population lives along a line (e.g., a road or a river). If facilities are optimally placed, the length of the line segment served by a facility is inversely proportional to the square root of the population density. This scaling law is derived analytically and confirmed for concrete numerical exa","authors_text":"Michael T. Gastner","cross_cats":["cond-mat.stat-mech","cs.SI","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-03-16T21:35:40Z","title":"Scaling and entropy in p-median facility location along a line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3301","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:bc4638a1b1248367910a60734a68ac839e3fdf7c3a303c097fbd4ddad4f20df8","target":"record","created_at":"2026-05-18T04:05:05Z","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":"7094a8cdd24288828282d3b85f10033b6800eab9ab7ff0848572124d30d2d653","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-03-16T21:35:40Z","title_canon_sha256":"34a35fbafe35d3f4c8c13fda3a8a3a28df81f7ba3746d2a31599bf9dd0d84efa"},"schema_version":"1.0","source":{"id":"1103.3301","kind":"arxiv","version":2}},"canonical_sha256":"1a733b6d930998ca63920eddab3c37de7faf0b0552971215be284e52912d37c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a733b6d930998ca63920eddab3c37de7faf0b0552971215be284e52912d37c5","first_computed_at":"2026-05-18T04:05:05.345078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:05.345078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lWaLedHUbqjoQ1quDPvujQ5ZYVGhWnnw1ysrqP0FoZxZaVuJmsZ7pccSWDEw0bOmsu5NPQPx91QgMwLuNrhCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:05.345635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3301","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc4638a1b1248367910a60734a68ac839e3fdf7c3a303c097fbd4ddad4f20df8","sha256:3d9219a3baf8856d57ec46538a98dbb453cd0477f9c31b48648d1ebabfb4def5"],"state_sha256":"acf727da64446254407ba94cec169b26bce4d477832ac7170a4b27e75511a2e5"}