{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:Q3KXPZCFTNEEEPYBZPLSDTXJEQ","short_pith_number":"pith:Q3KXPZCF","schema_version":"1.0","canonical_sha256":"86d577e4459b48423f01cbd721cee9242eb0dc3fcd58cd31a215ee186e75d76c","source":{"kind":"arxiv","id":"2502.13334","version":2},"attestation_state":"computed","paper":{"title":"How to sell a service with uncertain outcomes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Sellers maximize profit for uncertain-outcome services only with two-stage contracts combining upfront and usage payments.","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Alec Sun, Haifeng Xu, Krishnamurthy Iyer, You Zu","submitted_at":"2025-02-18T23:28:30Z","abstract_excerpt":"Motivated by the recent popularity of machine learning training services, we introduce a contract design problem in which a provider sells a service that results in an outcome of uncertain quality for the buyer. The seller has a set of actions that lead to different distributions over outcomes. We focus on a setting in which the seller has the ability to commit to an action and the buyer is free to accept or reject the outcome after seeing its realized quality. We propose a two-stage payment scheme where the seller designs a menu of contracts, each of which specifies an action, an upfront pric"},"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":"2502.13334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2025-02-18T23:28:30Z","cross_cats_sorted":[],"title_canon_sha256":"465e4e1380ae2bb0d17f5b0c859bc91cd2f028275d1efd4e760e27073285c670","abstract_canon_sha256":"8f23df5ebeb1d15ae98daefec92517c21a11eae46ae6d6b7f936fc4fa7817fb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T00:18:10.929005Z","signature_b64":"2JlNyso8hvrmk2RAr5iQ6KqNv1omSCgl9ldzt2+c3/CBW/AazQCGVzDg22w4vKIftw/hE810v8E5rz95kUJFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86d577e4459b48423f01cbd721cee9242eb0dc3fcd58cd31a215ee186e75d76c","last_reissued_at":"2026-06-25T00:18:10.928628Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T00:18:10.928628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How to sell a service with uncertain outcomes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Sellers maximize profit for uncertain-outcome services only with two-stage contracts combining upfront and usage payments.","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Alec Sun, Haifeng Xu, Krishnamurthy Iyer, You Zu","submitted_at":"2025-02-18T23:28:30Z","abstract_excerpt":"Motivated by the recent popularity of machine learning training services, we introduce a contract design problem in which a provider sells a service that results in an outcome of uncertain quality for the buyer. The seller has a set of actions that lead to different distributions over outcomes. We focus on a setting in which the seller has the ability to commit to an action and the buyer is free to accept or reject the outcome after seeing its realized quality. We propose a two-stage payment scheme where the seller designs a menu of contracts, each of which specifies an action, an upfront pric"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that this two-stage payment structure is necessary to maximize profit: only upfront prices or only usage prices is insufficient. [...] we derive a fully-polynomial time approximation scheme (FPTAS) for the maximum profit for a constant number of buyer types. Finally, we prove that in the single-parameter setting [...] seller revenue can be maximized using a menu consisting of a single contract.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The model assumes the seller has the ability to commit to an action and the buyer is free to accept or reject the outcome after seeing its realized quality (core setup stated in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Models selling uncertain-outcome services via two-stage contracts, proves the structure is necessary for max profit, gives FPTAS for constant buyer types, and shows single-contract optimality in single-parameter settings.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Sellers maximize profit for uncertain-outcome services only with two-stage contracts combining upfront and usage payments.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0cdb354cbd60e640c8ac2b4053c2dc9ed41b05f1c7d9949e9d507cc93a36a1ad"},"source":{"id":"2502.13334","kind":"arxiv","version":2},"verdict":{"id":"e127144c-2043-487d-9025-481d5c253e1a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T02:39:02.710362Z","strongest_claim":"We show that this two-stage payment structure is necessary to maximize profit: only upfront prices or only usage prices is insufficient. [...] we derive a fully-polynomial time approximation scheme (FPTAS) for the maximum profit for a constant number of buyer types. Finally, we prove that in the single-parameter setting [...] seller revenue can be maximized using a menu consisting of a single contract.","one_line_summary":"Models selling uncertain-outcome services via two-stage contracts, proves the structure is necessary for max profit, gives FPTAS for constant buyer types, and shows single-contract optimality in single-parameter settings.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The model assumes the seller has the ability to commit to an action and the buyer is free to accept or reject the outcome after seeing its realized quality (core setup stated in the abstract).","pith_extraction_headline":"Sellers maximize profit for uncertain-outcome services only with two-stage contracts combining upfront and usage payments."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.13334/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":"2502.13334","created_at":"2026-06-25T00:18:10.928682+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.13334v2","created_at":"2026-06-25T00:18:10.928682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13334","created_at":"2026-06-25T00:18:10.928682+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q3KXPZCFTNEE","created_at":"2026-06-25T00:18:10.928682+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q3KXPZCFTNEEEPYB","created_at":"2026-06-25T00:18:10.928682+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q3KXPZCF","created_at":"2026-06-25T00:18:10.928682+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/Q3KXPZCFTNEEEPYBZPLSDTXJEQ","json":"https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ.json","graph_json":"https://pith.science/api/pith-number/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/graph.json","events_json":"https://pith.science/api/pith-number/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/events.json","paper":"https://pith.science/paper/Q3KXPZCF"},"agent_actions":{"view_html":"https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ","download_json":"https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ.json","view_paper":"https://pith.science/paper/Q3KXPZCF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.13334&json=true","fetch_graph":"https://pith.science/api/pith-number/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/action/storage_attestation","attest_author":"https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/action/author_attestation","sign_citation":"https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/action/citation_signature","submit_replication":"https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ/action/replication_record"}},"created_at":"2026-06-25T00:18:10.928682+00:00","updated_at":"2026-06-25T00:18:10.928682+00:00"}