{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GWQKLTWTO2FBE3TPCMDTIENP2E","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":"039730c22a1a8343264fcf8d058b91d41e8c2254e8a8227bf4e2e10a521bee5e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-23T14:20:02Z","title_canon_sha256":"d5b01ee726968cfb8020d73029d31e9d36df46160d88684f1e82c5a61bf7bba1"},"schema_version":"1.0","source":{"id":"1708.07015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07015","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07015v1","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07015","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"GWQKLTWTO2FB","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GWQKLTWTO2FBE3TP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GWQKLTWT","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:e9af013f35f456cfe8cdda35e44c6f578ce61d81ec9579599e62b4bf24524529","target":"graph","created_at":"2026-05-18T00:36:48Z","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":"We consider the ensemble of random Gaussian Laplace eigenfunctions on $\\mathbb{T}^3=\\mathbb{R}^3/\\mathbb{Z}^3$ (`$3d$ arithmetic random waves'), and study the distribution of their nodal surface area. The expected area is proportional to the square root of the eigenvalue, or `energy', of the eigenfunction. We show that the nodal area variance obeys an asymptotic law. The resulting asymptotic formula is closely related to the angular distribution and correlations of lattice points lying on spheres.","authors_text":"Jacques Benatar, Riccardo W. Maffucci","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-23T14:20:02Z","title":"Random waves on $\\mathbb{T}^3$: nodal area variance and lattice point correlations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07015","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:a05c28bb279bd83e0ad2116d7e0aadb938a8dd3a6e74c1559c95be4573ede610","target":"record","created_at":"2026-05-18T00:36:48Z","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":"039730c22a1a8343264fcf8d058b91d41e8c2254e8a8227bf4e2e10a521bee5e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-23T14:20:02Z","title_canon_sha256":"d5b01ee726968cfb8020d73029d31e9d36df46160d88684f1e82c5a61bf7bba1"},"schema_version":"1.0","source":{"id":"1708.07015","kind":"arxiv","version":1}},"canonical_sha256":"35a0a5ced3768a126e6f13073411afd12754cc4246dfb5b7acc36b9af667b3bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35a0a5ced3768a126e6f13073411afd12754cc4246dfb5b7acc36b9af667b3bc","first_computed_at":"2026-05-18T00:36:48.624380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:48.624380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BuUnnKB29l3keyH0OOxP1L33Mvdb7JvFm2SWe/E6/SpM5dc3+nKv/XraD6yb5qyfjXCN2e+mb4qCeIqHkeYhAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:48.624871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a05c28bb279bd83e0ad2116d7e0aadb938a8dd3a6e74c1559c95be4573ede610","sha256:e9af013f35f456cfe8cdda35e44c6f578ce61d81ec9579599e62b4bf24524529"],"state_sha256":"a17467c9b4ac5133fd2c4f04aba0f229319b9c6575402b66b384b65835888ac5"}