{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TZ3BZ3M6AHXSOIUDWPONZCW3KG","short_pith_number":"pith:TZ3BZ3M6","canonical_record":{"source":{"id":"2402.02303","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-04T00:00:00Z","cross_cats_sorted":["cs.GT","econ.EM","stat.AP","stat.TH"],"title_canon_sha256":"648e76d3f23c717efd45f0a97f42fcb4b71eedf22aa865c2837a55433d556061","abstract_canon_sha256":"d1b765c9248a03a1ed1043152776417d7d271a0ca71ea59ddb1d50532d023caf"},"schema_version":"1.0"},"canonical_sha256":"9e761ced9e01ef272283b3dcdc8adb51b79672ffc4baa6ca7fcee151293328b9","source":{"kind":"arxiv","id":"2402.02303","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.02303","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"2402.02303v6","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.02303","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"TZ3BZ3M6AHXS","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"pith_short_16","alias_value":"TZ3BZ3M6AHXSOIUD","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"pith_short_8","alias_value":"TZ3BZ3M6","created_at":"2026-07-05T10:27:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TZ3BZ3M6AHXSOIUDWPONZCW3KG","target":"record","payload":{"canonical_record":{"source":{"id":"2402.02303","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-04T00:00:00Z","cross_cats_sorted":["cs.GT","econ.EM","stat.AP","stat.TH"],"title_canon_sha256":"648e76d3f23c717efd45f0a97f42fcb4b71eedf22aa865c2837a55433d556061","abstract_canon_sha256":"d1b765c9248a03a1ed1043152776417d7d271a0ca71ea59ddb1d50532d023caf"},"schema_version":"1.0"},"canonical_sha256":"9e761ced9e01ef272283b3dcdc8adb51b79672ffc4baa6ca7fcee151293328b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:27:07.204679Z","signature_b64":"8TeVtPD5oJecWwmcpiUTgJDZlrtpKjYUFV7YcIF1gfLkBZ6/1H61YlouVRpdJgBv3yPM+dCIbfp8ZweW7jN4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e761ced9e01ef272283b3dcdc8adb51b79672ffc4baa6ca7fcee151293328b9","last_reissued_at":"2026-07-05T10:27:07.204159Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:27:07.204159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.02303","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lg88xT3fkTMQOZBt1TE98C//roK9btfYzErBmyP58OAFi+woj8rXV4MBYpvIt0FGDZLHbAsNyhaH0KjCU+P9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T11:07:06.412659Z"},"content_sha256":"0477dad37e198726a3a646aea085686595904efa8e16830d39cf1dc7fc7cb713","schema_version":"1.0","event_id":"sha256:0477dad37e198726a3a646aea085686595904efa8e16830d39cf1dc7fc7cb713"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TZ3BZ3M6AHXSOIUDWPONZCW3KG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.GT","econ.EM","stat.AP","stat.TH"],"primary_cat":"math.ST","authors_text":"Christian Kroer, Luofeng Liao","submitted_at":"2024-02-04T00:00:00Z","abstract_excerpt":"The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in first-price auctions. In certain practical settings such as advertising auctions, there is an interest in performing statistical inference over these models. A popular methodology for general statistical inference is the bootstrap procedure. Yet, for LFM and FPPE there is no existing theory for the valid application of bootstrap procedures. In this paper, we i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.02303","kind":"arxiv","version":6},"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/2402.02303/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hk3ungo1Pv4ONadiMCLc6lfwY0hJtA7ZIHON3Fw8q6WTO2Rps+tTP910AAqP2vs2C4ez0ywDkMMsz/nnaCezAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T11:07:06.412986Z"},"content_sha256":"cad1f0697535de52a93a6e69bc6763862782f1cfe3970934ac47543b15f8b6d9","schema_version":"1.0","event_id":"sha256:cad1f0697535de52a93a6e69bc6763862782f1cfe3970934ac47543b15f8b6d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TZ3BZ3M6AHXSOIUDWPONZCW3KG/bundle.json","state_url":"https://pith.science/pith/TZ3BZ3M6AHXSOIUDWPONZCW3KG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TZ3BZ3M6AHXSOIUDWPONZCW3KG/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":"2026-08-21T11:07:06Z","links":{"resolver":"https://pith.science/pith/TZ3BZ3M6AHXSOIUDWPONZCW3KG","bundle":"https://pith.science/pith/TZ3BZ3M6AHXSOIUDWPONZCW3KG/bundle.json","state":"https://pith.science/pith/TZ3BZ3M6AHXSOIUDWPONZCW3KG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TZ3BZ3M6AHXSOIUDWPONZCW3KG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TZ3BZ3M6AHXSOIUDWPONZCW3KG","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":"d1b765c9248a03a1ed1043152776417d7d271a0ca71ea59ddb1d50532d023caf","cross_cats_sorted":["cs.GT","econ.EM","stat.AP","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-04T00:00:00Z","title_canon_sha256":"648e76d3f23c717efd45f0a97f42fcb4b71eedf22aa865c2837a55433d556061"},"schema_version":"1.0","source":{"id":"2402.02303","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.02303","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"2402.02303v6","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.02303","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"TZ3BZ3M6AHXS","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"pith_short_16","alias_value":"TZ3BZ3M6AHXSOIUD","created_at":"2026-07-05T10:27:07Z"},{"alias_kind":"pith_short_8","alias_value":"TZ3BZ3M6","created_at":"2026-07-05T10:27:07Z"}],"graph_snapshots":[{"event_id":"sha256:cad1f0697535de52a93a6e69bc6763862782f1cfe3970934ac47543b15f8b6d9","target":"graph","created_at":"2026-07-05T10:27:07Z","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/2402.02303/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in first-price auctions. In certain practical settings such as advertising auctions, there is an interest in performing statistical inference over these models. A popular methodology for general statistical inference is the bootstrap procedure. Yet, for LFM and FPPE there is no existing theory for the valid application of bootstrap procedures. In this paper, we i","authors_text":"Christian Kroer, Luofeng Liao","cross_cats":["cs.GT","econ.EM","stat.AP","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-04T00:00:00Z","title":"Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.02303","kind":"arxiv","version":6},"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":"sha256:0477dad37e198726a3a646aea085686595904efa8e16830d39cf1dc7fc7cb713","target":"record","created_at":"2026-07-05T10:27:07Z","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":"d1b765c9248a03a1ed1043152776417d7d271a0ca71ea59ddb1d50532d023caf","cross_cats_sorted":["cs.GT","econ.EM","stat.AP","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-04T00:00:00Z","title_canon_sha256":"648e76d3f23c717efd45f0a97f42fcb4b71eedf22aa865c2837a55433d556061"},"schema_version":"1.0","source":{"id":"2402.02303","kind":"arxiv","version":6}},"canonical_sha256":"9e761ced9e01ef272283b3dcdc8adb51b79672ffc4baa6ca7fcee151293328b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e761ced9e01ef272283b3dcdc8adb51b79672ffc4baa6ca7fcee151293328b9","first_computed_at":"2026-07-05T10:27:07.204159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:27:07.204159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8TeVtPD5oJecWwmcpiUTgJDZlrtpKjYUFV7YcIF1gfLkBZ6/1H61YlouVRpdJgBv3yPM+dCIbfp8ZweW7jN4DA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:27:07.204679Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.02303","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0477dad37e198726a3a646aea085686595904efa8e16830d39cf1dc7fc7cb713","sha256:cad1f0697535de52a93a6e69bc6763862782f1cfe3970934ac47543b15f8b6d9"],"state_sha256":"8d77449e20adc79dc5723fc7c2fc98fc14c5204e305640747ec2118be7f0423d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROsPi+Rahji5RoVjcPEyT7AsQiOrm60pdfSzgZH6/aDz5Ku/vGdsx3GfS3lSsNoXFRtVbiBKT7VRJq1IlcG5BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T11:07:06.415986Z","bundle_sha256":"93d9b87771fb5af1ec3f1d64ffe6082055c8ab490470a27d71431b1065a93cb6"}}