{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QIAN273IKQVNDVRI57OKP2TSGF","short_pith_number":"pith:QIAN273I","schema_version":"1.0","canonical_sha256":"8200dd7f68542ad1d628efdca7ea72315f81577d2fd4251d8c3cd53fc6d2ba81","source":{"kind":"arxiv","id":"1501.02866","version":2},"attestation_state":"computed","paper":{"title":"The Strategic Formation of Multi-Layer Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.GT","authors_text":"Ebrahim Moradi Shahrivar, Shreyas Sundaram","submitted_at":"2015-01-13T02:10:16Z","abstract_excerpt":"We study the strategic formation of multi-layer networks, where each layer represents a different type of relationship between the nodes in the network and is designed to maximize some utility that depends on the topology of that layer and those of the other layers. We start by generalizing distance-based network formation to the two-layer setting, where edges are constructed in one layer (with fixed cost per edge) to minimize distances between nodes that are neighbors in another layer. We show that designing an optimal network in this setting is NP-hard. Despite the underlying complexity of t"},"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":"1501.02866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-01-13T02:10:16Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"e5a9eb5bb1169819559c440d2ac49a2235d552ef3b0d49bf60691b5b21f28095","abstract_canon_sha256":"cc6143ddd5c3084e298cab848d25d4aa35f67ae996a2cffc2b68e48d8e590c4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:38.863290Z","signature_b64":"g5WTaxxjqTQtuh385BLoI7VQFN3og7DYqPsF+1AJ2+lZcUoDz4KmICyWu2urNiT1UhoiKNHrhuMfAWsxY/eTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8200dd7f68542ad1d628efdca7ea72315f81577d2fd4251d8c3cd53fc6d2ba81","last_reissued_at":"2026-05-18T01:28:38.862709Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:38.862709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Strategic Formation of Multi-Layer Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.GT","authors_text":"Ebrahim Moradi Shahrivar, Shreyas Sundaram","submitted_at":"2015-01-13T02:10:16Z","abstract_excerpt":"We study the strategic formation of multi-layer networks, where each layer represents a different type of relationship between the nodes in the network and is designed to maximize some utility that depends on the topology of that layer and those of the other layers. We start by generalizing distance-based network formation to the two-layer setting, where edges are constructed in one layer (with fixed cost per edge) to minimize distances between nodes that are neighbors in another layer. We show that designing an optimal network in this setting is NP-hard. Despite the underlying complexity of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02866","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":"1501.02866","created_at":"2026-05-18T01:28:38.862814+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.02866v2","created_at":"2026-05-18T01:28:38.862814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02866","created_at":"2026-05-18T01:28:38.862814+00:00"},{"alias_kind":"pith_short_12","alias_value":"QIAN273IKQVN","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QIAN273IKQVNDVRI","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QIAN273I","created_at":"2026-05-18T12:29:37.295048+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/QIAN273IKQVNDVRI57OKP2TSGF","json":"https://pith.science/pith/QIAN273IKQVNDVRI57OKP2TSGF.json","graph_json":"https://pith.science/api/pith-number/QIAN273IKQVNDVRI57OKP2TSGF/graph.json","events_json":"https://pith.science/api/pith-number/QIAN273IKQVNDVRI57OKP2TSGF/events.json","paper":"https://pith.science/paper/QIAN273I"},"agent_actions":{"view_html":"https://pith.science/pith/QIAN273IKQVNDVRI57OKP2TSGF","download_json":"https://pith.science/pith/QIAN273IKQVNDVRI57OKP2TSGF.json","view_paper":"https://pith.science/paper/QIAN273I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.02866&json=true","fetch_graph":"https://pith.science/api/pith-number/QIAN273IKQVNDVRI57OKP2TSGF/graph.json","fetch_events":"https://pith.science/api/pith-number/QIAN273IKQVNDVRI57OKP2TSGF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QIAN273IKQVNDVRI57OKP2TSGF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QIAN273IKQVNDVRI57OKP2TSGF/action/storage_attestation","attest_author":"https://pith.science/pith/QIAN273IKQVNDVRI57OKP2TSGF/action/author_attestation","sign_citation":"https://pith.science/pith/QIAN273IKQVNDVRI57OKP2TSGF/action/citation_signature","submit_replication":"https://pith.science/pith/QIAN273IKQVNDVRI57OKP2TSGF/action/replication_record"}},"created_at":"2026-05-18T01:28:38.862814+00:00","updated_at":"2026-05-18T01:28:38.862814+00:00"}