{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IDKFDB76AOVTLME2I5CAQRPWD2","short_pith_number":"pith:IDKFDB76","schema_version":"1.0","canonical_sha256":"40d45187fe03ab35b09a47440845f61ebea1d57b39834bd31e64e5cab5dba602","source":{"kind":"arxiv","id":"2605.25028","version":1},"attestation_state":"computed","paper":{"title":"A note on the complexity of two-stage stochastic linear optimization with small second stage","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christoph Buchheim","submitted_at":"2026-05-24T12:09:14Z","abstract_excerpt":"Two-stage stochastic linear optimization is known to be #P-hard when all involved random variables are independently and uniformly distributed over intervals, even with fixed recourse. We show that this problem is actually #P-hard in the strong sense. More surprisingly, this hardness persists when the random vector is one-dimensional, i.e., uniformly distributed over a single interval. To obtain this result, we show that computing the area of a two-dimensional polytope given by a compact extended formulation is strongly #P-hard. Furthermore, we obtain the same complexity result in case the num"},"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":"2605.25028","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-24T12:09:14Z","cross_cats_sorted":[],"title_canon_sha256":"1e3439f6a4847a4f23017d534c90ee19810e786a6ac68021a033b636771c548a","abstract_canon_sha256":"61561453c6198ff319dabf859ce58412e32d0705006acb3d518f3cfeca81ec24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:04:11.162258Z","signature_b64":"9INNg4gXHlHB5PMP2gwHyWLufdQIW15K3NdRPJArvx38UoMYru+wY2IXcynngMhlTrq8Kmb7ArBWKY6nm37WCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40d45187fe03ab35b09a47440845f61ebea1d57b39834bd31e64e5cab5dba602","last_reissued_at":"2026-05-26T01:04:11.161715Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:04:11.161715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the complexity of two-stage stochastic linear optimization with small second stage","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christoph Buchheim","submitted_at":"2026-05-24T12:09:14Z","abstract_excerpt":"Two-stage stochastic linear optimization is known to be #P-hard when all involved random variables are independently and uniformly distributed over intervals, even with fixed recourse. We show that this problem is actually #P-hard in the strong sense. More surprisingly, this hardness persists when the random vector is one-dimensional, i.e., uniformly distributed over a single interval. To obtain this result, we show that computing the area of a two-dimensional polytope given by a compact extended formulation is strongly #P-hard. Furthermore, we obtain the same complexity result in case the num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25028","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25028/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.25028","created_at":"2026-05-26T01:04:11.161795+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25028v1","created_at":"2026-05-26T01:04:11.161795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25028","created_at":"2026-05-26T01:04:11.161795+00:00"},{"alias_kind":"pith_short_12","alias_value":"IDKFDB76AOVT","created_at":"2026-05-26T01:04:11.161795+00:00"},{"alias_kind":"pith_short_16","alias_value":"IDKFDB76AOVTLME2","created_at":"2026-05-26T01:04:11.161795+00:00"},{"alias_kind":"pith_short_8","alias_value":"IDKFDB76","created_at":"2026-05-26T01:04:11.161795+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/IDKFDB76AOVTLME2I5CAQRPWD2","json":"https://pith.science/pith/IDKFDB76AOVTLME2I5CAQRPWD2.json","graph_json":"https://pith.science/api/pith-number/IDKFDB76AOVTLME2I5CAQRPWD2/graph.json","events_json":"https://pith.science/api/pith-number/IDKFDB76AOVTLME2I5CAQRPWD2/events.json","paper":"https://pith.science/paper/IDKFDB76"},"agent_actions":{"view_html":"https://pith.science/pith/IDKFDB76AOVTLME2I5CAQRPWD2","download_json":"https://pith.science/pith/IDKFDB76AOVTLME2I5CAQRPWD2.json","view_paper":"https://pith.science/paper/IDKFDB76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25028&json=true","fetch_graph":"https://pith.science/api/pith-number/IDKFDB76AOVTLME2I5CAQRPWD2/graph.json","fetch_events":"https://pith.science/api/pith-number/IDKFDB76AOVTLME2I5CAQRPWD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IDKFDB76AOVTLME2I5CAQRPWD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IDKFDB76AOVTLME2I5CAQRPWD2/action/storage_attestation","attest_author":"https://pith.science/pith/IDKFDB76AOVTLME2I5CAQRPWD2/action/author_attestation","sign_citation":"https://pith.science/pith/IDKFDB76AOVTLME2I5CAQRPWD2/action/citation_signature","submit_replication":"https://pith.science/pith/IDKFDB76AOVTLME2I5CAQRPWD2/action/replication_record"}},"created_at":"2026-05-26T01:04:11.161795+00:00","updated_at":"2026-05-26T01:04:11.161795+00:00"}