{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:S4NFJDX3R5TY5LFW7CH2D7GZ4W","short_pith_number":"pith:S4NFJDX3","schema_version":"1.0","canonical_sha256":"971a548efb8f678eacb6f88fa1fcd9e5a09d25b4a968d435afba46dfd25560d9","source":{"kind":"arxiv","id":"1712.02937","version":2},"attestation_state":"computed","paper":{"title":"On Metropolis Growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM"],"primary_cat":"physics.soc-ph","authors_text":"Syed Amaar Ahmad","submitted_at":"2017-12-08T04:46:30Z","abstract_excerpt":"We consider the scaling laws, second-order statistics and entropy of the consumed energy of metropolis cities which are hybrid complex systems comprising social networks, engineering systems, agricultural output, economic activity and energy components. We abstract a city in terms of two fundamental variables; $s$ resource cells (of unit area) that represent energy-consuming geographic or spatial zones (e.g. land, housing or infrastructure etc.) and a population comprising $n$ mobile units that can migrate between these cells. We show that with a constant metropolis area (fixed $s$), the varia"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.02937","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-12-08T04:46:30Z","cross_cats_sorted":["econ.EM"],"title_canon_sha256":"7aac18d54e93c50984172e88b51bc4dbc35b66b8395b0642d4e6f0fb39e4504c","abstract_canon_sha256":"3423467f7f16bccf3d539e2178296f71d9a4a8ef180597da68a1a79e12cd0b56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:56.721573Z","signature_b64":"v6Hr8yvXaCBI75n/SvXT6lLb3WXxS5omH2EXhjvD1BJ+bHkRGofQlGt1z/obGsxyiDSvMzVVIu2uFT1G3wQMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"971a548efb8f678eacb6f88fa1fcd9e5a09d25b4a968d435afba46dfd25560d9","last_reissued_at":"2026-05-18T00:27:56.720846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:56.720846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Metropolis Growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM"],"primary_cat":"physics.soc-ph","authors_text":"Syed Amaar Ahmad","submitted_at":"2017-12-08T04:46:30Z","abstract_excerpt":"We consider the scaling laws, second-order statistics and entropy of the consumed energy of metropolis cities which are hybrid complex systems comprising social networks, engineering systems, agricultural output, economic activity and energy components. We abstract a city in terms of two fundamental variables; $s$ resource cells (of unit area) that represent energy-consuming geographic or spatial zones (e.g. land, housing or infrastructure etc.) and a population comprising $n$ mobile units that can migrate between these cells. We show that with a constant metropolis area (fixed $s$), the varia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02937","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.02937","created_at":"2026-05-18T00:27:56.720962+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.02937v2","created_at":"2026-05-18T00:27:56.720962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02937","created_at":"2026-05-18T00:27:56.720962+00:00"},{"alias_kind":"pith_short_12","alias_value":"S4NFJDX3R5TY","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"S4NFJDX3R5TY5LFW","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"S4NFJDX3","created_at":"2026-05-18T12:31:43.269735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W","json":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W.json","graph_json":"https://pith.science/api/pith-number/S4NFJDX3R5TY5LFW7CH2D7GZ4W/graph.json","events_json":"https://pith.science/api/pith-number/S4NFJDX3R5TY5LFW7CH2D7GZ4W/events.json","paper":"https://pith.science/paper/S4NFJDX3"},"agent_actions":{"view_html":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W","download_json":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W.json","view_paper":"https://pith.science/paper/S4NFJDX3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.02937&json=true","fetch_graph":"https://pith.science/api/pith-number/S4NFJDX3R5TY5LFW7CH2D7GZ4W/graph.json","fetch_events":"https://pith.science/api/pith-number/S4NFJDX3R5TY5LFW7CH2D7GZ4W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W/action/storage_attestation","attest_author":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W/action/author_attestation","sign_citation":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W/action/citation_signature","submit_replication":"https://pith.science/pith/S4NFJDX3R5TY5LFW7CH2D7GZ4W/action/replication_record"}},"created_at":"2026-05-18T00:27:56.720962+00:00","updated_at":"2026-05-18T00:27:56.720962+00:00"}