{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4HJR45ZCL3YJH5Y5GIKY7YFP3T","short_pith_number":"pith:4HJR45ZC","schema_version":"1.0","canonical_sha256":"e1d31e77225ef093f71d32158fe0afdcf9ca0c16aad836899d5615329b506833","source":{"kind":"arxiv","id":"1302.4098","version":1},"attestation_state":"computed","paper":{"title":"Mathematics for some classes of networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. A. Zamyatin, V. A. Malyshev","submitted_at":"2013-02-17T18:11:58Z","abstract_excerpt":"Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of networks which interested the authors for some time. In section 4 we consider in detail a new class of networks, related to markets with many agents."},"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":"1302.4098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-17T18:11:58Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0fb421dec2b83c30c56e0137c13c9808d337e4f4aae0a84362b0472477837500","abstract_canon_sha256":"af0c5d66b098fc97025758b1dd432f7a3f3968ee10a2e2d098cffdb6471a862f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:24.137690Z","signature_b64":"3dSEdkBYKQ6ITlZ6N/qNincvVmnZHCKeYr1NA8Yt3ORc4V9bw+FDOIWoqlUF+E8zKuCt6TwEt3syYCwMap7KAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1d31e77225ef093f71d32158fe0afdcf9ca0c16aad836899d5615329b506833","last_reissued_at":"2026-05-18T03:33:24.136991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:24.136991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mathematics for some classes of networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. A. Zamyatin, V. A. Malyshev","submitted_at":"2013-02-17T18:11:58Z","abstract_excerpt":"Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of networks which interested the authors for some time. In section 4 we consider in detail a new class of networks, related to markets with many agents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4098","kind":"arxiv","version":1},"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":"1302.4098","created_at":"2026-05-18T03:33:24.137104+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.4098v1","created_at":"2026-05-18T03:33:24.137104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4098","created_at":"2026-05-18T03:33:24.137104+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HJR45ZCL3YJ","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HJR45ZCL3YJH5Y5","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HJR45ZC","created_at":"2026-05-18T12:27:34.582898+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/4HJR45ZCL3YJH5Y5GIKY7YFP3T","json":"https://pith.science/pith/4HJR45ZCL3YJH5Y5GIKY7YFP3T.json","graph_json":"https://pith.science/api/pith-number/4HJR45ZCL3YJH5Y5GIKY7YFP3T/graph.json","events_json":"https://pith.science/api/pith-number/4HJR45ZCL3YJH5Y5GIKY7YFP3T/events.json","paper":"https://pith.science/paper/4HJR45ZC"},"agent_actions":{"view_html":"https://pith.science/pith/4HJR45ZCL3YJH5Y5GIKY7YFP3T","download_json":"https://pith.science/pith/4HJR45ZCL3YJH5Y5GIKY7YFP3T.json","view_paper":"https://pith.science/paper/4HJR45ZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.4098&json=true","fetch_graph":"https://pith.science/api/pith-number/4HJR45ZCL3YJH5Y5GIKY7YFP3T/graph.json","fetch_events":"https://pith.science/api/pith-number/4HJR45ZCL3YJH5Y5GIKY7YFP3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HJR45ZCL3YJH5Y5GIKY7YFP3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HJR45ZCL3YJH5Y5GIKY7YFP3T/action/storage_attestation","attest_author":"https://pith.science/pith/4HJR45ZCL3YJH5Y5GIKY7YFP3T/action/author_attestation","sign_citation":"https://pith.science/pith/4HJR45ZCL3YJH5Y5GIKY7YFP3T/action/citation_signature","submit_replication":"https://pith.science/pith/4HJR45ZCL3YJH5Y5GIKY7YFP3T/action/replication_record"}},"created_at":"2026-05-18T03:33:24.137104+00:00","updated_at":"2026-05-18T03:33:24.137104+00:00"}