{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GTRD6JX4J4B2ZLX32QQ7QETWEC","short_pith_number":"pith:GTRD6JX4","canonical_record":{"source":{"id":"2602.04402","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-04T10:32:03Z","cross_cats_sorted":["cs.AI","cs.CY","cs.LG","math.ST","stat.TH"],"title_canon_sha256":"567b64287d632e219ed33c3568ecf42926c087afbc2874b4464f7bb5cff5884c","abstract_canon_sha256":"06c66898232a1970fce7e85b4628a2c9f85621e1e9fca3d9712f438996bb1928"},"schema_version":"1.0"},"canonical_sha256":"34e23f26fc4f03acaefbd421f8127620a883c7e341868713a11a54f670d9ec3e","source":{"kind":"arxiv","id":"2602.04402","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.04402","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"2602.04402v3","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04402","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"GTRD6JX4J4B2","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"pith_short_16","alias_value":"GTRD6JX4J4B2ZLX3","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"pith_short_8","alias_value":"GTRD6JX4","created_at":"2026-06-09T02:08:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GTRD6JX4J4B2ZLX32QQ7QETWEC","target":"record","payload":{"canonical_record":{"source":{"id":"2602.04402","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-04T10:32:03Z","cross_cats_sorted":["cs.AI","cs.CY","cs.LG","math.ST","stat.TH"],"title_canon_sha256":"567b64287d632e219ed33c3568ecf42926c087afbc2874b4464f7bb5cff5884c","abstract_canon_sha256":"06c66898232a1970fce7e85b4628a2c9f85621e1e9fca3d9712f438996bb1928"},"schema_version":"1.0"},"canonical_sha256":"34e23f26fc4f03acaefbd421f8127620a883c7e341868713a11a54f670d9ec3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:38.440647Z","signature_b64":"FZnba0BKOSrHpZucppIf8/vfky99cxSSizYAQhens4aYqI/sUJlYp/R69bc9x/W0iNOlyZ8U5V/0Jy9USiz4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34e23f26fc4f03acaefbd421f8127620a883c7e341868713a11a54f670d9ec3e","last_reissued_at":"2026-06-09T02:08:38.439674Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:38.439674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.04402","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T02:08:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gvKI/O8UEGQXtT26UcHcyiMsibBN4B08/4rNlWD5VNC5PYXFW5jNDi/0oQnFNBQS2A11pcDSekKfAh7ZfBx1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T23:24:54.696857Z"},"content_sha256":"9d82ec0be67e41fa1694e6bd97470c9f21e8964c5277aafd17b36803a57283e8","schema_version":"1.0","event_id":"sha256:9d82ec0be67e41fa1694e6bd97470c9f21e8964c5277aafd17b36803a57283e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GTRD6JX4J4B2ZLX32QQ7QETWEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Performative Learning Theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.CY","cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"James Bailie, Julian Rodemann, Krikamol Muandet, Unai Fischer-Abaigar","submitted_at":"2026-02-04T10:32:03Z","abstract_excerpt":"Performative predictions influence the very outcomes they aim to forecast. We study performative predictions that affect a sample (e.g., only existing users of an app) and/or the whole population (e.g., all potential app users). This raises the question of how well models generalize under performativity. For example, how well can we draw insights about new app users based on existing users when both of them react to the app's predictions? We address this question by embedding performative predictions into statistical learning theory. We prove generalization bounds under performative effects on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04402","kind":"arxiv","version":3},"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/2602.04402/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":"2026-06-09T02:08:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QQ1eLxrQ0GjgDypmB/UnJPD6vU7UjA8dH/Uw7Ila1pD6J64IjMa9eReX+zP4yrSSxlxMcXcjt27Q+Q4sZPNTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T23:24:54.697235Z"},"content_sha256":"c4da3861a87a46e8552b5a5741d00b338d6be2abba736bf897750cf58d9e452a","schema_version":"1.0","event_id":"sha256:c4da3861a87a46e8552b5a5741d00b338d6be2abba736bf897750cf58d9e452a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTRD6JX4J4B2ZLX32QQ7QETWEC/bundle.json","state_url":"https://pith.science/pith/GTRD6JX4J4B2ZLX32QQ7QETWEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTRD6JX4J4B2ZLX32QQ7QETWEC/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":"2026-06-28T23:24:54Z","links":{"resolver":"https://pith.science/pith/GTRD6JX4J4B2ZLX32QQ7QETWEC","bundle":"https://pith.science/pith/GTRD6JX4J4B2ZLX32QQ7QETWEC/bundle.json","state":"https://pith.science/pith/GTRD6JX4J4B2ZLX32QQ7QETWEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTRD6JX4J4B2ZLX32QQ7QETWEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GTRD6JX4J4B2ZLX32QQ7QETWEC","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":"06c66898232a1970fce7e85b4628a2c9f85621e1e9fca3d9712f438996bb1928","cross_cats_sorted":["cs.AI","cs.CY","cs.LG","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-04T10:32:03Z","title_canon_sha256":"567b64287d632e219ed33c3568ecf42926c087afbc2874b4464f7bb5cff5884c"},"schema_version":"1.0","source":{"id":"2602.04402","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.04402","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"2602.04402v3","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04402","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"GTRD6JX4J4B2","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"pith_short_16","alias_value":"GTRD6JX4J4B2ZLX3","created_at":"2026-06-09T02:08:38Z"},{"alias_kind":"pith_short_8","alias_value":"GTRD6JX4","created_at":"2026-06-09T02:08:38Z"}],"graph_snapshots":[{"event_id":"sha256:c4da3861a87a46e8552b5a5741d00b338d6be2abba736bf897750cf58d9e452a","target":"graph","created_at":"2026-06-09T02:08:38Z","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/2602.04402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Performative predictions influence the very outcomes they aim to forecast. We study performative predictions that affect a sample (e.g., only existing users of an app) and/or the whole population (e.g., all potential app users). This raises the question of how well models generalize under performativity. For example, how well can we draw insights about new app users based on existing users when both of them react to the app's predictions? We address this question by embedding performative predictions into statistical learning theory. We prove generalization bounds under performative effects on","authors_text":"James Bailie, Julian Rodemann, Krikamol Muandet, Unai Fischer-Abaigar","cross_cats":["cs.AI","cs.CY","cs.LG","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-04T10:32:03Z","title":"Performative Learning Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04402","kind":"arxiv","version":3},"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":"sha256:9d82ec0be67e41fa1694e6bd97470c9f21e8964c5277aafd17b36803a57283e8","target":"record","created_at":"2026-06-09T02:08:38Z","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":"06c66898232a1970fce7e85b4628a2c9f85621e1e9fca3d9712f438996bb1928","cross_cats_sorted":["cs.AI","cs.CY","cs.LG","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-04T10:32:03Z","title_canon_sha256":"567b64287d632e219ed33c3568ecf42926c087afbc2874b4464f7bb5cff5884c"},"schema_version":"1.0","source":{"id":"2602.04402","kind":"arxiv","version":3}},"canonical_sha256":"34e23f26fc4f03acaefbd421f8127620a883c7e341868713a11a54f670d9ec3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34e23f26fc4f03acaefbd421f8127620a883c7e341868713a11a54f670d9ec3e","first_computed_at":"2026-06-09T02:08:38.439674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:38.439674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FZnba0BKOSrHpZucppIf8/vfky99cxSSizYAQhens4aYqI/sUJlYp/R69bc9x/W0iNOlyZ8U5V/0Jy9USiz4DA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:38.440647Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.04402","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d82ec0be67e41fa1694e6bd97470c9f21e8964c5277aafd17b36803a57283e8","sha256:c4da3861a87a46e8552b5a5741d00b338d6be2abba736bf897750cf58d9e452a"],"state_sha256":"51492fe6918ae7c411c365d948869f5fe4e3f890b70dffb35e64b0ebb69d4f59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ARvEYtTe1UpveSTVxXhcK+8RTo+xGdN+MWU/ulBtOTI7vfhkxbhE92DYjr3YMOMJOy93cyRZkVGXOSCmFxleBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T23:24:54.699179Z","bundle_sha256":"f23a6df22424feacc156453cbf2bcbdd0c01c4948dbc4bb0ac31b6401feb090b"}}