{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4SWO2W4LLWCSCNEQE527RPEAFC","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":"f77d155d9ea24e52941986874fb7ea0f05be6b8a89e35bb6d7d4407a7e567519","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-05-27T09:49:52Z","title_canon_sha256":"d9c6ba77751c7b899dd1f3a89d65ddfea63fa4123b9129bb8dc0f39a70d56aa4"},"schema_version":"1.0","source":{"id":"1905.11084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11084","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11084v1","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11084","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"4SWO2W4LLWCS","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4SWO2W4LLWCSCNEQ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4SWO2W4L","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:d795026ac0dbd6d40a2113c2a2e92f2c3d8d0af37e1a283a6ac1e8fd0441fbdf","target":"graph","created_at":"2026-05-17T23:45:02Z","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"},"paper":{"abstract_excerpt":"This paper studies a setting in which multiple suppliers compete for a buyer's procurement business. The buyer faces uncertain demand and there is a requirement to reserve capacity in advance of knowing the demand. Each supplier has costs that are two dimensional, with some costs incurred before demand is realized in order to reserve capacity and some costs incurred after demand is realized at the time of delivery. A distinctive feature of our model is that the marginal costs may not be constants, and this naturally leads us to a supply function competition framework in which each supplier off","authors_text":"Bo Chen, Edward Anderson, Lusheng Shao","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-05-27T09:49:52Z","title":"Capacity Games with Supply Function Competition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11084","kind":"arxiv","version":1},"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:e9cb8b15d8e6cbbf624bd73395810a12baf985d1c455bd1fb286becacf044a8d","target":"record","created_at":"2026-05-17T23:45:02Z","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":"f77d155d9ea24e52941986874fb7ea0f05be6b8a89e35bb6d7d4407a7e567519","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-05-27T09:49:52Z","title_canon_sha256":"d9c6ba77751c7b899dd1f3a89d65ddfea63fa4123b9129bb8dc0f39a70d56aa4"},"schema_version":"1.0","source":{"id":"1905.11084","kind":"arxiv","version":1}},"canonical_sha256":"e4aced5b8b5d852134902775f8bc8028bd7957c08d317e5bbbe63549b0dac19e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4aced5b8b5d852134902775f8bc8028bd7957c08d317e5bbbe63549b0dac19e","first_computed_at":"2026-05-17T23:45:02.973252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:02.973252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1I27fdPbY6QTFGzBKRHOb/fXwkcTzRbeNvZ71imqpLa3fu0B3zMG1S51JX0H1yLq378zk++0zkNW+O5c77bNDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:02.973837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.11084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9cb8b15d8e6cbbf624bd73395810a12baf985d1c455bd1fb286becacf044a8d","sha256:d795026ac0dbd6d40a2113c2a2e92f2c3d8d0af37e1a283a6ac1e8fd0441fbdf"],"state_sha256":"2795aa2a23d2990650be9cae83af7890761c35f3ee706ac7185a0933dd7e4eb2"}