{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6ZKRSJLEFNFZDMPKHU7YLF2OVO","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":"702d5575ab1ef8a759f918e7a96719237d67ce312c2fcf0c9d23ea9399c3c2db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-18T22:16:10Z","title_canon_sha256":"09520133a92816595291948db5cf71ff7db3dd385215f8003204b5929be49f1f"},"schema_version":"1.0","source":{"id":"1310.5175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5175","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5175v1","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5175","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"6ZKRSJLEFNFZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6ZKRSJLEFNFZDMPK","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6ZKRSJLE","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:85c48d14e7f18727f086196fe536bb1fbf8a363e08516a0e06c50b5fcd9a9882","target":"graph","created_at":"2026-05-18T03:09:47Z","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":"In this short note, we present a theorem concerning certain \"additive structure\" for the level sets of non-degenerate Gaussian fields, which yields the multiple valley phenomenon for extremal fields with exponentially many valleys.","authors_text":"Amir Dembo, Jian Ding, Sourav Chatterjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-18T22:16:10Z","title":"On level sets of Gaussian fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5175","kind":"arxiv","version":1},"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:ee30b250bfe30e47e96f0763c3de99bac2af50570e9b721a43bdbb2429f46abb","target":"record","created_at":"2026-05-18T03:09:47Z","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":"702d5575ab1ef8a759f918e7a96719237d67ce312c2fcf0c9d23ea9399c3c2db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-18T22:16:10Z","title_canon_sha256":"09520133a92816595291948db5cf71ff7db3dd385215f8003204b5929be49f1f"},"schema_version":"1.0","source":{"id":"1310.5175","kind":"arxiv","version":1}},"canonical_sha256":"f6551925642b4b91b1ea3d3f85974eaba01c56c1c860cf59ce065e1a7db7252f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6551925642b4b91b1ea3d3f85974eaba01c56c1c860cf59ce065e1a7db7252f","first_computed_at":"2026-05-18T03:09:47.071746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:47.071746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6gn0DEBkYUX1TMgT1djQMKUXI88ngOWhQXG+u/tP8RbRAsf3f8Gm+iMFZw1b+DeHn7lo/RphMCYe2e8Af5vIAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:47.072610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee30b250bfe30e47e96f0763c3de99bac2af50570e9b721a43bdbb2429f46abb","sha256:85c48d14e7f18727f086196fe536bb1fbf8a363e08516a0e06c50b5fcd9a9882"],"state_sha256":"771f9fd84b9cd8832a06a12f67d5f99d3b8e0e74a5f1e97b80e992a0b7115b85"}