{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QCPUOKA5G22WHPNBPB7NSGT2EE","short_pith_number":"pith:QCPUOKA5","schema_version":"1.0","canonical_sha256":"809f47281d36b563bda1787ed91a7a213998db1b48daaa0057b9aef1581c1ebf","source":{"kind":"arxiv","id":"1412.5310","version":1},"attestation_state":"computed","paper":{"title":"Reduction and Fixed Points of Boolean Networks and Linear Network Coding Solvability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.DS","math.IT"],"primary_cat":"cs.IT","authors_text":"Adrien Richard, Eric Fanchon, Maximilien Gadouleau","submitted_at":"2014-12-17T09:56:53Z","abstract_excerpt":"Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the destinations can be simultaneously satisfied by using linear network coding. The guessing number approach converts this problem to determining the number of fixed points of coding functions $f:A^n\\to A^n$ over a finite alphabet $A$ (usually referred to as Boolean networks if $A = \\{0,1\\}$) with a given interaction graph, that describes which local functions d"},"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":"1412.5310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-12-17T09:56:53Z","cross_cats_sorted":["cs.DM","math.DS","math.IT"],"title_canon_sha256":"8331f9aa701fe1349c5b0d43370ec068439c659f1aa770a2b494faa61ba8883f","abstract_canon_sha256":"78f4ba889e839036fad37fcbe6bd870f6a37c97a559f536bf2944300b65548b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:03.273560Z","signature_b64":"kHDcuhNEgAvZ4Ktcmfm3iBoBe1JRxg7I3p4YHnXyrzsmeYyvxcji9bvrCLEVnM6FBv4WSoTxdON30d/PFnXaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"809f47281d36b563bda1787ed91a7a213998db1b48daaa0057b9aef1581c1ebf","last_reissued_at":"2026-05-18T02:31:03.273081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:03.273081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reduction and Fixed Points of Boolean Networks and Linear Network Coding Solvability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.DS","math.IT"],"primary_cat":"cs.IT","authors_text":"Adrien Richard, Eric Fanchon, Maximilien Gadouleau","submitted_at":"2014-12-17T09:56:53Z","abstract_excerpt":"Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the destinations can be simultaneously satisfied by using linear network coding. The guessing number approach converts this problem to determining the number of fixed points of coding functions $f:A^n\\to A^n$ over a finite alphabet $A$ (usually referred to as Boolean networks if $A = \\{0,1\\}$) with a given interaction graph, that describes which local functions d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5310","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":"1412.5310","created_at":"2026-05-18T02:31:03.273155+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5310v1","created_at":"2026-05-18T02:31:03.273155+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5310","created_at":"2026-05-18T02:31:03.273155+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCPUOKA5G22W","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCPUOKA5G22WHPNB","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCPUOKA5","created_at":"2026-05-18T12:28:43.426989+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/QCPUOKA5G22WHPNBPB7NSGT2EE","json":"https://pith.science/pith/QCPUOKA5G22WHPNBPB7NSGT2EE.json","graph_json":"https://pith.science/api/pith-number/QCPUOKA5G22WHPNBPB7NSGT2EE/graph.json","events_json":"https://pith.science/api/pith-number/QCPUOKA5G22WHPNBPB7NSGT2EE/events.json","paper":"https://pith.science/paper/QCPUOKA5"},"agent_actions":{"view_html":"https://pith.science/pith/QCPUOKA5G22WHPNBPB7NSGT2EE","download_json":"https://pith.science/pith/QCPUOKA5G22WHPNBPB7NSGT2EE.json","view_paper":"https://pith.science/paper/QCPUOKA5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5310&json=true","fetch_graph":"https://pith.science/api/pith-number/QCPUOKA5G22WHPNBPB7NSGT2EE/graph.json","fetch_events":"https://pith.science/api/pith-number/QCPUOKA5G22WHPNBPB7NSGT2EE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCPUOKA5G22WHPNBPB7NSGT2EE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCPUOKA5G22WHPNBPB7NSGT2EE/action/storage_attestation","attest_author":"https://pith.science/pith/QCPUOKA5G22WHPNBPB7NSGT2EE/action/author_attestation","sign_citation":"https://pith.science/pith/QCPUOKA5G22WHPNBPB7NSGT2EE/action/citation_signature","submit_replication":"https://pith.science/pith/QCPUOKA5G22WHPNBPB7NSGT2EE/action/replication_record"}},"created_at":"2026-05-18T02:31:03.273155+00:00","updated_at":"2026-05-18T02:31:03.273155+00:00"}