{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QVTKR3VE3STWKTWVCIVQCFN6LQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dc6a7d9fe4022ee0c322855f72fcbaecdfd6d86087bb5b18f908345d0fb9aa6f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-28T13:00:49Z","title_canon_sha256":"5ba452f0f34043157daa84771dd369c85b3b3f5e71da5428642b5904f9651029"},"schema_version":"1.0","source":{"id":"2404.03767","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.03767","created_at":"2026-07-05T08:11:03Z"},{"alias_kind":"arxiv_version","alias_value":"2404.03767v2","created_at":"2026-07-05T08:11:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.03767","created_at":"2026-07-05T08:11:03Z"},{"alias_kind":"pith_short_12","alias_value":"QVTKR3VE3STW","created_at":"2026-07-05T08:11:03Z"},{"alias_kind":"pith_short_16","alias_value":"QVTKR3VE3STWKTWV","created_at":"2026-07-05T08:11:03Z"},{"alias_kind":"pith_short_8","alias_value":"QVTKR3VE","created_at":"2026-07-05T08:11:03Z"}],"graph_snapshots":[{"event_id":"sha256:43c20643273fae9c73f418376c42d11607e22bf0146dd82c2eab188d1c1d09b9","target":"graph","created_at":"2026-07-05T08:11:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.03767/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mathematical Program Networks (MPNs) are introduced in this work. An MPN is a collection of interdependent Mathematical Programs (MPs) which are to be solved simultaneously, while respecting the connectivity pattern of the network defining their relationships. The network structure of an MPN impacts which decision variables each constituent mathematical program can influence, either directly or indirectly via solution graph constraints representing optimal decisions for their decedents. Many existing problem formulations can be formulated as MPNs, including Nash Equilibrium problems, multileve","authors_text":"Forrest Laine","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-28T13:00:49Z","title":"Mathematical Program Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03767","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a0db64c149a44745e48b860d14a088d6c4f69554b815708de8fb0c1dc7b71100","target":"record","created_at":"2026-07-05T08:11:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dc6a7d9fe4022ee0c322855f72fcbaecdfd6d86087bb5b18f908345d0fb9aa6f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-28T13:00:49Z","title_canon_sha256":"5ba452f0f34043157daa84771dd369c85b3b3f5e71da5428642b5904f9651029"},"schema_version":"1.0","source":{"id":"2404.03767","kind":"arxiv","version":2}},"canonical_sha256":"8566a8eea4dca7654ed5122b0115be5c191fb305c3c078045ee9ff6d619ac5c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8566a8eea4dca7654ed5122b0115be5c191fb305c3c078045ee9ff6d619ac5c3","first_computed_at":"2026-07-05T08:11:03.048854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:11:03.048854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+wOTi1snU5MYMP38f3VxJN1BKgfMZR9hOScfGL/+bo1CU3bV6ikevqTsq9XcyAZJy3Uq87+U5BPuW/wPLZg+Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:11:03.049231Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.03767","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0db64c149a44745e48b860d14a088d6c4f69554b815708de8fb0c1dc7b71100","sha256:43c20643273fae9c73f418376c42d11607e22bf0146dd82c2eab188d1c1d09b9"],"state_sha256":"da656a853c6369c5155ae802b01d488e10a2806eb4f404aa693684fa2c1835ee"}