{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QHFQIV3C7E42VQG3GTA7O6JL2I","short_pith_number":"pith:QHFQIV3C","canonical_record":{"source":{"id":"1601.02319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-11T04:36:19Z","cross_cats_sorted":[],"title_canon_sha256":"1c889eef4a81071cd423056a1718ad777e35a4ab628158950092381def674027","abstract_canon_sha256":"9d5919b1e2d44a9f10e549d56cd594c1b688c0a829e539c74a4cf34505046933"},"schema_version":"1.0"},"canonical_sha256":"81cb045762f939aac0db34c1f7792bd22b64f80ad62ebe725e7c7fad215f1e86","source":{"kind":"arxiv","id":"1601.02319","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02319","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02319v2","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02319","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"QHFQIV3C7E42","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHFQIV3C7E42VQG3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHFQIV3C","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QHFQIV3C7E42VQG3GTA7O6JL2I","target":"record","payload":{"canonical_record":{"source":{"id":"1601.02319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-11T04:36:19Z","cross_cats_sorted":[],"title_canon_sha256":"1c889eef4a81071cd423056a1718ad777e35a4ab628158950092381def674027","abstract_canon_sha256":"9d5919b1e2d44a9f10e549d56cd594c1b688c0a829e539c74a4cf34505046933"},"schema_version":"1.0"},"canonical_sha256":"81cb045762f939aac0db34c1f7792bd22b64f80ad62ebe725e7c7fad215f1e86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:53.135071Z","signature_b64":"ZrWmQCGQUyipnOp3ft8wEVBmkudyEu6aMitW1KWn1JjT9j1EzChRY4PGbFa7U6H5kJet/0ADCqpCNmtcO9cqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81cb045762f939aac0db34c1f7792bd22b64f80ad62ebe725e7c7fad215f1e86","last_reissued_at":"2026-05-18T01:19:53.134483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:53.134483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.02319","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0shG8mpi9ogT1Ts6IjqpaGLv/o7syElYxRCy8+/aO5hZqj9pQVh9m/EtLVLoZurG+AgkHOxNRypaOevEuhIvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:23:20.915896Z"},"content_sha256":"89e14c80122f8fb8e62e30b38b3a06b0f90f179f5f75bf1a870804252de933e3","schema_version":"1.0","event_id":"sha256:89e14c80122f8fb8e62e30b38b3a06b0f90f179f5f75bf1a870804252de933e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QHFQIV3C7E42VQG3GTA7O6JL2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic Pricing and Distributed Energy Management for Demand Response","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lang Tong, Liyan Jia","submitted_at":"2016-01-11T04:36:19Z","abstract_excerpt":"The problem of dynamic pricing of electricity in a retail market is considered. A Stackelberg game is used to model interactions between a retailer and its customers; the retailer sets the day-ahead hourly price of electricity and consumers adjust real-time consumptions to maximize individual consumer surplus.\n  For thermostatic demands, the optimal aggregated demand is shown to be an affine function of the day-ahead hourly price. A complete characterization of the trade-offs between consumer surplus and retail profit is obtained. The Pareto front of achievable trade-offs is shown to be concav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02319","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NCCJbyAFkIfl30ZaWzJUvDRtPAo00KhIx3Zba24eYZdMgaeoruc43o88MIpSANlf/fc91/VbMjldWiyHReB3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:23:20.916244Z"},"content_sha256":"781486c7c1bdf2d1214892840837444f705c517b6299c255767e94709dd9a5e6","schema_version":"1.0","event_id":"sha256:781486c7c1bdf2d1214892840837444f705c517b6299c255767e94709dd9a5e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHFQIV3C7E42VQG3GTA7O6JL2I/bundle.json","state_url":"https://pith.science/pith/QHFQIV3C7E42VQG3GTA7O6JL2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHFQIV3C7E42VQG3GTA7O6JL2I/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T10:23:20Z","links":{"resolver":"https://pith.science/pith/QHFQIV3C7E42VQG3GTA7O6JL2I","bundle":"https://pith.science/pith/QHFQIV3C7E42VQG3GTA7O6JL2I/bundle.json","state":"https://pith.science/pith/QHFQIV3C7E42VQG3GTA7O6JL2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHFQIV3C7E42VQG3GTA7O6JL2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QHFQIV3C7E42VQG3GTA7O6JL2I","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":"9d5919b1e2d44a9f10e549d56cd594c1b688c0a829e539c74a4cf34505046933","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-11T04:36:19Z","title_canon_sha256":"1c889eef4a81071cd423056a1718ad777e35a4ab628158950092381def674027"},"schema_version":"1.0","source":{"id":"1601.02319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02319","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02319v2","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02319","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"QHFQIV3C7E42","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHFQIV3C7E42VQG3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHFQIV3C","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:781486c7c1bdf2d1214892840837444f705c517b6299c255767e94709dd9a5e6","target":"graph","created_at":"2026-05-18T01:19:53Z","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":"The problem of dynamic pricing of electricity in a retail market is considered. A Stackelberg game is used to model interactions between a retailer and its customers; the retailer sets the day-ahead hourly price of electricity and consumers adjust real-time consumptions to maximize individual consumer surplus.\n  For thermostatic demands, the optimal aggregated demand is shown to be an affine function of the day-ahead hourly price. A complete characterization of the trade-offs between consumer surplus and retail profit is obtained. The Pareto front of achievable trade-offs is shown to be concav","authors_text":"Lang Tong, Liyan Jia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-11T04:36:19Z","title":"Dynamic Pricing and Distributed Energy Management for Demand Response"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02319","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":"sha256:89e14c80122f8fb8e62e30b38b3a06b0f90f179f5f75bf1a870804252de933e3","target":"record","created_at":"2026-05-18T01:19:53Z","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":"9d5919b1e2d44a9f10e549d56cd594c1b688c0a829e539c74a4cf34505046933","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-11T04:36:19Z","title_canon_sha256":"1c889eef4a81071cd423056a1718ad777e35a4ab628158950092381def674027"},"schema_version":"1.0","source":{"id":"1601.02319","kind":"arxiv","version":2}},"canonical_sha256":"81cb045762f939aac0db34c1f7792bd22b64f80ad62ebe725e7c7fad215f1e86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81cb045762f939aac0db34c1f7792bd22b64f80ad62ebe725e7c7fad215f1e86","first_computed_at":"2026-05-18T01:19:53.134483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:53.134483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZrWmQCGQUyipnOp3ft8wEVBmkudyEu6aMitW1KWn1JjT9j1EzChRY4PGbFa7U6H5kJet/0ADCqpCNmtcO9cqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:53.135071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89e14c80122f8fb8e62e30b38b3a06b0f90f179f5f75bf1a870804252de933e3","sha256:781486c7c1bdf2d1214892840837444f705c517b6299c255767e94709dd9a5e6"],"state_sha256":"3df2e964e614d8c25ca02f4d83d1960cc4b5c381216e814763108446a0356ce7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DKDPM1Zbvaumt8aYHShQXO5aP+hRmSqOGj7HGPUIQLMpq1CiTYeaepOqpWVsg2UImSu3rBEWjjEK2OdNInUOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:23:20.918161Z","bundle_sha256":"77a496bc646b9be37f1c1f39f342bbca003c53fdc9b28e05f1a90f7bec851f9e"}}