{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:N4L42DZ46QNA3BC5G7H72Y5CSX","short_pith_number":"pith:N4L42DZ4","schema_version":"1.0","canonical_sha256":"6f17cd0f3cf41a0d845d37cffd63a295e1dc16f02471bd2fef8d9b0a7e065a6d","source":{"kind":"arxiv","id":"1704.06058","version":3},"attestation_state":"computed","paper":{"title":"Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ellen Powell","submitted_at":"2017-04-20T09:04:29Z","abstract_excerpt":"We show that, for general convolution approximations to a large class of log-correlated fields, including the 2d Gaussian free field, the critical chaos measures with derivative normalisation converge to a limiting measure {\\mu}'. This limiting measure does not depend on the choice of approximation. Moreover, it is equal to the measure obtained using the Seneta--Heyde renormalisation at criticality, or using a white-noise approximation to the field."},"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":"1704.06058","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-20T09:04:29Z","cross_cats_sorted":[],"title_canon_sha256":"b282fe28237ef4d474e38b89fbb54b6911b1669b12ec64a45a264b2205e44199","abstract_canon_sha256":"d314bb0d09e9f787081eb49ea1e512b19796bae6dcb431a3880d5cb78491da30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:18:42.014650Z","signature_b64":"/zLstcDn/UckAtsZGg+trO2Mj5itzJYPwqM+/kWNsOBGicQr4PSHyCgTp4XoKuUYLSkoe9kFdY1XZ9Af53TRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f17cd0f3cf41a0d845d37cffd63a295e1dc16f02471bd2fef8d9b0a7e065a6d","last_reissued_at":"2026-07-05T05:18:42.014235Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:18:42.014235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ellen Powell","submitted_at":"2017-04-20T09:04:29Z","abstract_excerpt":"We show that, for general convolution approximations to a large class of log-correlated fields, including the 2d Gaussian free field, the critical chaos measures with derivative normalisation converge to a limiting measure {\\mu}'. This limiting measure does not depend on the choice of approximation. Moreover, it is equal to the measure obtained using the Seneta--Heyde renormalisation at criticality, or using a white-noise approximation to the field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06058","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/1704.06058/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":"1704.06058","created_at":"2026-07-05T05:18:42.014294+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.06058v3","created_at":"2026-07-05T05:18:42.014294+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06058","created_at":"2026-07-05T05:18:42.014294+00:00"},{"alias_kind":"pith_short_12","alias_value":"N4L42DZ46QNA","created_at":"2026-07-05T05:18:42.014294+00:00"},{"alias_kind":"pith_short_16","alias_value":"N4L42DZ46QNA3BC5","created_at":"2026-07-05T05:18:42.014294+00:00"},{"alias_kind":"pith_short_8","alias_value":"N4L42DZ4","created_at":"2026-07-05T05:18:42.014294+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/N4L42DZ46QNA3BC5G7H72Y5CSX","json":"https://pith.science/pith/N4L42DZ46QNA3BC5G7H72Y5CSX.json","graph_json":"https://pith.science/api/pith-number/N4L42DZ46QNA3BC5G7H72Y5CSX/graph.json","events_json":"https://pith.science/api/pith-number/N4L42DZ46QNA3BC5G7H72Y5CSX/events.json","paper":"https://pith.science/paper/N4L42DZ4"},"agent_actions":{"view_html":"https://pith.science/pith/N4L42DZ46QNA3BC5G7H72Y5CSX","download_json":"https://pith.science/pith/N4L42DZ46QNA3BC5G7H72Y5CSX.json","view_paper":"https://pith.science/paper/N4L42DZ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.06058&json=true","fetch_graph":"https://pith.science/api/pith-number/N4L42DZ46QNA3BC5G7H72Y5CSX/graph.json","fetch_events":"https://pith.science/api/pith-number/N4L42DZ46QNA3BC5G7H72Y5CSX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N4L42DZ46QNA3BC5G7H72Y5CSX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N4L42DZ46QNA3BC5G7H72Y5CSX/action/storage_attestation","attest_author":"https://pith.science/pith/N4L42DZ46QNA3BC5G7H72Y5CSX/action/author_attestation","sign_citation":"https://pith.science/pith/N4L42DZ46QNA3BC5G7H72Y5CSX/action/citation_signature","submit_replication":"https://pith.science/pith/N4L42DZ46QNA3BC5G7H72Y5CSX/action/replication_record"}},"created_at":"2026-07-05T05:18:42.014294+00:00","updated_at":"2026-07-05T05:18:42.014294+00:00"}