{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2YF6C536VUHBYQ7ADFQCHGNQNS","short_pith_number":"pith:2YF6C536","schema_version":"1.0","canonical_sha256":"d60be1777ead0e1c43e019602399b06cb70f8c273bc91caf17fe7ee305106432","source":{"kind":"arxiv","id":"1401.3941","version":1},"attestation_state":"computed","paper":{"title":"Network Coding for $3$s$/n$t Sum-Networks","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chau Yuen, Kai Cai, Rongquan Feng, Wentu Song","submitted_at":"2014-01-16T09:05:29Z","abstract_excerpt":"A sum-network is a directed acyclic network where each source independently generates one symbol from a given field $\\mathbb F$ and each terminal wants to receive the sum $($over $\\mathbb F)$ of the source symbols. For sum-networks with two sources or two terminals, the solvability is characterized by the connection condition of each source-terminal pair [3]. A necessary and sufficient condition for the solvability of the $3$-source $3$-terminal $(3$s$/3$t$)$ sum-networks was given by Shenvi and Dey [6]. However, the general case of arbitrary sources/sinks is still open. In this paper, we inve"},"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":"1401.3941","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2014-01-16T09:05:29Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"b0ea299dc1cfc2c2cbb326d9827deb9dc3c3b92e89926ef2b5ed37980faf6c03","abstract_canon_sha256":"84f239f9307ee3dc19e84651674af925077e9fe043e4dbca276b44026158ed9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:57.700808Z","signature_b64":"H7DqwNlsan4jmUPUznwtPCHhYWh+TtLMNvabHIW9t8PNp4wQ4Qyx0x1NVtEMqC9RhEMtZZu39TcwnPd7ILukDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d60be1777ead0e1c43e019602399b06cb70f8c273bc91caf17fe7ee305106432","last_reissued_at":"2026-05-18T03:01:57.700034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:57.700034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Network Coding for $3$s$/n$t Sum-Networks","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chau Yuen, Kai Cai, Rongquan Feng, Wentu Song","submitted_at":"2014-01-16T09:05:29Z","abstract_excerpt":"A sum-network is a directed acyclic network where each source independently generates one symbol from a given field $\\mathbb F$ and each terminal wants to receive the sum $($over $\\mathbb F)$ of the source symbols. For sum-networks with two sources or two terminals, the solvability is characterized by the connection condition of each source-terminal pair [3]. A necessary and sufficient condition for the solvability of the $3$-source $3$-terminal $(3$s$/3$t$)$ sum-networks was given by Shenvi and Dey [6]. However, the general case of arbitrary sources/sinks is still open. In this paper, we inve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3941","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":"1401.3941","created_at":"2026-05-18T03:01:57.700170+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.3941v1","created_at":"2026-05-18T03:01:57.700170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3941","created_at":"2026-05-18T03:01:57.700170+00:00"},{"alias_kind":"pith_short_12","alias_value":"2YF6C536VUHB","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2YF6C536VUHBYQ7A","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2YF6C536","created_at":"2026-05-18T12:28:11.866339+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/2YF6C536VUHBYQ7ADFQCHGNQNS","json":"https://pith.science/pith/2YF6C536VUHBYQ7ADFQCHGNQNS.json","graph_json":"https://pith.science/api/pith-number/2YF6C536VUHBYQ7ADFQCHGNQNS/graph.json","events_json":"https://pith.science/api/pith-number/2YF6C536VUHBYQ7ADFQCHGNQNS/events.json","paper":"https://pith.science/paper/2YF6C536"},"agent_actions":{"view_html":"https://pith.science/pith/2YF6C536VUHBYQ7ADFQCHGNQNS","download_json":"https://pith.science/pith/2YF6C536VUHBYQ7ADFQCHGNQNS.json","view_paper":"https://pith.science/paper/2YF6C536","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.3941&json=true","fetch_graph":"https://pith.science/api/pith-number/2YF6C536VUHBYQ7ADFQCHGNQNS/graph.json","fetch_events":"https://pith.science/api/pith-number/2YF6C536VUHBYQ7ADFQCHGNQNS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2YF6C536VUHBYQ7ADFQCHGNQNS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2YF6C536VUHBYQ7ADFQCHGNQNS/action/storage_attestation","attest_author":"https://pith.science/pith/2YF6C536VUHBYQ7ADFQCHGNQNS/action/author_attestation","sign_citation":"https://pith.science/pith/2YF6C536VUHBYQ7ADFQCHGNQNS/action/citation_signature","submit_replication":"https://pith.science/pith/2YF6C536VUHBYQ7ADFQCHGNQNS/action/replication_record"}},"created_at":"2026-05-18T03:01:57.700170+00:00","updated_at":"2026-05-18T03:01:57.700170+00:00"}