{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AT3ZTM4KDWCTYANK63CZD65CAO","short_pith_number":"pith:AT3ZTM4K","schema_version":"1.0","canonical_sha256":"04f799b38a1d853c01aaf6c591fba203bd8a707b1332eb14746e1acbf47922a2","source":{"kind":"arxiv","id":"1212.0529","version":3},"attestation_state":"computed","paper":{"title":"Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Bertrand Duplantier (IPHT), R\\'emi Rhodes (CEREMADE), Scott Sheffield (MIT), Vincent Vargas (CEREMADE)","submitted_at":"2012-12-03T20:30:17Z","abstract_excerpt":"Gaussian Multiplicative Chaos is a way to produce a measure on $\\R^d$ (or subdomain of $\\R^d$) of the form $e^{\\gamma X(x)} dx$, where $X$ is a log-correlated Gaussian field and $\\gamma \\in [0,\\sqrt{2d})$ is a fixed constant. A renormalization procedure is needed to make this precise, since $X$ oscillates between $-\\infty$ and $\\infty$ and is not a function in the usual sense. This procedure yields the zero measure when $\\gamma=\\sqrt{2d}$.\n  Two methods have been proposed to produce a non-trivial measure when $\\gamma=\\sqrt{2d}$. The first involves taking a derivative at $\\gamma=\\sqrt{2d}$ (and"},"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":"1212.0529","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-03T20:30:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"364e64443f098325014a1c086b3fde16391bff38bcef915ee9e8fcb7a56841df","abstract_canon_sha256":"c4eaf47aa9a81e7b04fac049643d186ffc3d686d4dc71492f4157a0fd70bdd83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:22.444485Z","signature_b64":"+SBCEga0LANH6O/zBwDG+l6F5wo4apwYhNsizY+xsBfXRG96cw1DPuSgADm0qDg3bW9RrBfLeHldGYEiKYXiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04f799b38a1d853c01aaf6c591fba203bd8a707b1332eb14746e1acbf47922a2","last_reissued_at":"2026-05-18T03:12:22.443808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:22.443808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Bertrand Duplantier (IPHT), R\\'emi Rhodes (CEREMADE), Scott Sheffield (MIT), Vincent Vargas (CEREMADE)","submitted_at":"2012-12-03T20:30:17Z","abstract_excerpt":"Gaussian Multiplicative Chaos is a way to produce a measure on $\\R^d$ (or subdomain of $\\R^d$) of the form $e^{\\gamma X(x)} dx$, where $X$ is a log-correlated Gaussian field and $\\gamma \\in [0,\\sqrt{2d})$ is a fixed constant. A renormalization procedure is needed to make this precise, since $X$ oscillates between $-\\infty$ and $\\infty$ and is not a function in the usual sense. This procedure yields the zero measure when $\\gamma=\\sqrt{2d}$.\n  Two methods have been proposed to produce a non-trivial measure when $\\gamma=\\sqrt{2d}$. The first involves taking a derivative at $\\gamma=\\sqrt{2d}$ (and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0529","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":""},"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":"1212.0529","created_at":"2026-05-18T03:12:22.443909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0529v3","created_at":"2026-05-18T03:12:22.443909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0529","created_at":"2026-05-18T03:12:22.443909+00:00"},{"alias_kind":"pith_short_12","alias_value":"AT3ZTM4KDWCT","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AT3ZTM4KDWCTYANK","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AT3ZTM4K","created_at":"2026-05-18T12:26:58.693483+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/AT3ZTM4KDWCTYANK63CZD65CAO","json":"https://pith.science/pith/AT3ZTM4KDWCTYANK63CZD65CAO.json","graph_json":"https://pith.science/api/pith-number/AT3ZTM4KDWCTYANK63CZD65CAO/graph.json","events_json":"https://pith.science/api/pith-number/AT3ZTM4KDWCTYANK63CZD65CAO/events.json","paper":"https://pith.science/paper/AT3ZTM4K"},"agent_actions":{"view_html":"https://pith.science/pith/AT3ZTM4KDWCTYANK63CZD65CAO","download_json":"https://pith.science/pith/AT3ZTM4KDWCTYANK63CZD65CAO.json","view_paper":"https://pith.science/paper/AT3ZTM4K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0529&json=true","fetch_graph":"https://pith.science/api/pith-number/AT3ZTM4KDWCTYANK63CZD65CAO/graph.json","fetch_events":"https://pith.science/api/pith-number/AT3ZTM4KDWCTYANK63CZD65CAO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AT3ZTM4KDWCTYANK63CZD65CAO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AT3ZTM4KDWCTYANK63CZD65CAO/action/storage_attestation","attest_author":"https://pith.science/pith/AT3ZTM4KDWCTYANK63CZD65CAO/action/author_attestation","sign_citation":"https://pith.science/pith/AT3ZTM4KDWCTYANK63CZD65CAO/action/citation_signature","submit_replication":"https://pith.science/pith/AT3ZTM4KDWCTYANK63CZD65CAO/action/replication_record"}},"created_at":"2026-05-18T03:12:22.443909+00:00","updated_at":"2026-05-18T03:12:22.443909+00:00"}