{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B3DAXBWBFVV44AQZFD5LGKHGYS","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":"f8c7017f506329ae435bad15bf2066b761300e9b9a66bdccbb6a3134483d37ae","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-06T11:01:36Z","title_canon_sha256":"bed74154588114aec92a28a54752f88ca4b2ea3199c250a57f3ffbd5765a6b46"},"schema_version":"1.0","source":{"id":"1207.1582","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1582","created_at":"2026-05-18T01:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1582v2","created_at":"2026-05-18T01:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1582","created_at":"2026-05-18T01:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"B3DAXBWBFVV4","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B3DAXBWBFVV44AQZ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B3DAXBWB","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:5271f8a34d338bda66b0052e1f50de8416731bb6b41ead52f9327957619c5652","target":"graph","created_at":"2026-05-18T01:56:33Z","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":"Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.","authors_text":"Laurent Chevillard (Phys-ENS), R\\'emi Rhodes (CEREMADE), Vincent Vargas (CEREMADE)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-06T11:01:36Z","title":"Gaussian multiplicative Chaos for symmetric isotropic matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1582","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:b961ff115609c78b2282d87007fa29398d4ca6de5ff285cd6e849166f56c3e55","target":"record","created_at":"2026-05-18T01:56:33Z","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":"f8c7017f506329ae435bad15bf2066b761300e9b9a66bdccbb6a3134483d37ae","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-06T11:01:36Z","title_canon_sha256":"bed74154588114aec92a28a54752f88ca4b2ea3199c250a57f3ffbd5765a6b46"},"schema_version":"1.0","source":{"id":"1207.1582","kind":"arxiv","version":2}},"canonical_sha256":"0ec60b86c12d6bce021928fab328e6c4a4906c91264a62921859617a68d78568","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ec60b86c12d6bce021928fab328e6c4a4906c91264a62921859617a68d78568","first_computed_at":"2026-05-18T01:56:33.808907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:33.808907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wzYNz7lcMILuy1L8M9T8FImUWTCxHi8nmQK2II8N6dn38fHD4E41YYGi+z0LXUvl8SeSexnEmBnfMukeYOLpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:33.809457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1582","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b961ff115609c78b2282d87007fa29398d4ca6de5ff285cd6e849166f56c3e55","sha256:5271f8a34d338bda66b0052e1f50de8416731bb6b41ead52f9327957619c5652"],"state_sha256":"1cae51a217b62543f84afdd32aa81925c78f8971166ef234bb6ddcac19a9fe9f"}