{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:IW3TL6VFE2KSKXH62SBSZ54MDS","short_pith_number":"pith:IW3TL6VF","schema_version":"1.0","canonical_sha256":"45b735faa52695255cfed4832cf78c1c97876572debf35311998ef2ad63b8b32","source":{"kind":"arxiv","id":"0812.4866","version":1},"attestation_state":"computed","paper":{"title":"The optimal assignment problem for a countable state space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Marianne Akian, Stephane Gaubert, Vassili Kolokoltsov","submitted_at":"2008-12-30T09:43:59Z","abstract_excerpt":"Given a square matrix B=(b_{ij}) with real entries, the optimal assignment problem is to find a bijection s between the rows and the columns maximising the sum of the b_{is(i)}. In discrete optimal control and in the theory of discrete event systems, one often encounters the problem of solving the equation Bf=g for a given vector g, where the same symbol B denotes the corresponding max-plus linear operator, (Bf)_i:=max_j (b_{ij}+f_j). The matrix B is said to be strongly regular when there exists a vector g such that the equation Bf=g has a unique solution f. A result of Butkovic and Hevery sho"},"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":"0812.4866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-30T09:43:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cffbd018de9e55072c62344074662a1a09d8ed1df4df1397bf4239aa8edb1407","abstract_canon_sha256":"ae57f2f6559bda5c8c4b0e280c7e14cee007cefbc5847e21dcb19f37ccdffd6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:35.344849Z","signature_b64":"qcVO6FhPV3GadtOLdSrM077/SRIvfAUWLHEKUJqXPRTjYykPeMGOJRrSS+S/3gwjN2p1t1g5eESy+OU9xyI4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45b735faa52695255cfed4832cf78c1c97876572debf35311998ef2ad63b8b32","last_reissued_at":"2026-05-18T04:32:35.344302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:35.344302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The optimal assignment problem for a countable state space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Marianne Akian, Stephane Gaubert, Vassili Kolokoltsov","submitted_at":"2008-12-30T09:43:59Z","abstract_excerpt":"Given a square matrix B=(b_{ij}) with real entries, the optimal assignment problem is to find a bijection s between the rows and the columns maximising the sum of the b_{is(i)}. In discrete optimal control and in the theory of discrete event systems, one often encounters the problem of solving the equation Bf=g for a given vector g, where the same symbol B denotes the corresponding max-plus linear operator, (Bf)_i:=max_j (b_{ij}+f_j). The matrix B is said to be strongly regular when there exists a vector g such that the equation Bf=g has a unique solution f. A result of Butkovic and Hevery sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4866","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":"0812.4866","created_at":"2026-05-18T04:32:35.344377+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.4866v1","created_at":"2026-05-18T04:32:35.344377+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4866","created_at":"2026-05-18T04:32:35.344377+00:00"},{"alias_kind":"pith_short_12","alias_value":"IW3TL6VFE2KS","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"IW3TL6VFE2KSKXH6","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"IW3TL6VF","created_at":"2026-05-18T12:25:57.157939+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/IW3TL6VFE2KSKXH62SBSZ54MDS","json":"https://pith.science/pith/IW3TL6VFE2KSKXH62SBSZ54MDS.json","graph_json":"https://pith.science/api/pith-number/IW3TL6VFE2KSKXH62SBSZ54MDS/graph.json","events_json":"https://pith.science/api/pith-number/IW3TL6VFE2KSKXH62SBSZ54MDS/events.json","paper":"https://pith.science/paper/IW3TL6VF"},"agent_actions":{"view_html":"https://pith.science/pith/IW3TL6VFE2KSKXH62SBSZ54MDS","download_json":"https://pith.science/pith/IW3TL6VFE2KSKXH62SBSZ54MDS.json","view_paper":"https://pith.science/paper/IW3TL6VF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.4866&json=true","fetch_graph":"https://pith.science/api/pith-number/IW3TL6VFE2KSKXH62SBSZ54MDS/graph.json","fetch_events":"https://pith.science/api/pith-number/IW3TL6VFE2KSKXH62SBSZ54MDS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IW3TL6VFE2KSKXH62SBSZ54MDS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IW3TL6VFE2KSKXH62SBSZ54MDS/action/storage_attestation","attest_author":"https://pith.science/pith/IW3TL6VFE2KSKXH62SBSZ54MDS/action/author_attestation","sign_citation":"https://pith.science/pith/IW3TL6VFE2KSKXH62SBSZ54MDS/action/citation_signature","submit_replication":"https://pith.science/pith/IW3TL6VFE2KSKXH62SBSZ54MDS/action/replication_record"}},"created_at":"2026-05-18T04:32:35.344377+00:00","updated_at":"2026-05-18T04:32:35.344377+00:00"}