{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QMNNWXV6CA2JV7KQ7QSACQK6E3","short_pith_number":"pith:QMNNWXV6","canonical_record":{"source":{"id":"1708.07679","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-25T10:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"40569b848d97d9caf15e605d691ffa3173dac160c07fb4f69f31eb8a7185ab32","abstract_canon_sha256":"b9e94a0e7559810b5b9e9813b99b5f2e9f4fd1b640a896a40563330a3ccb5f67"},"schema_version":"1.0"},"canonical_sha256":"831adb5ebe10349afd50fc2401415e26fdcbecd20ba51c0891da9a4dc02addfc","source":{"kind":"arxiv","id":"1708.07679","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07679","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07679v1","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07679","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"QMNNWXV6CA2J","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QMNNWXV6CA2JV7KQ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QMNNWXV6","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QMNNWXV6CA2JV7KQ7QSACQK6E3","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07679","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-25T10:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"40569b848d97d9caf15e605d691ffa3173dac160c07fb4f69f31eb8a7185ab32","abstract_canon_sha256":"b9e94a0e7559810b5b9e9813b99b5f2e9f4fd1b640a896a40563330a3ccb5f67"},"schema_version":"1.0"},"canonical_sha256":"831adb5ebe10349afd50fc2401415e26fdcbecd20ba51c0891da9a4dc02addfc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:42.387110Z","signature_b64":"FgipXdyxxrBVv0aiMw9vwdSd7vgPgrjLO386hEEnYHOIOCJKJPz78ApJ/cMqKFqFX0z+PTqHXWwB3YWJYps8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"831adb5ebe10349afd50fc2401415e26fdcbecd20ba51c0891da9a4dc02addfc","last_reissued_at":"2026-05-18T00:36:42.386415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:42.386415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07679","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EEF6m/6SY+xamXi1Etkdl/8EucQhZDoymkGviwTwx9MT4ACPS31Gi0P8r5qz/d56zIa2gKiGAH1P1ufIW/KyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:50:20.007797Z"},"content_sha256":"b23a13f4bc06c816ea00f9d9c4fb7f9a27d213de39ef38d9d793fce77c4a980a","schema_version":"1.0","event_id":"sha256:b23a13f4bc06c816ea00f9d9c4fb7f9a27d213de39ef38d9d793fce77c4a980a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QMNNWXV6CA2JV7KQ7QSACQK6E3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nodal area distribution for arithmetic random waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Valentina Cammarota","submitted_at":"2017-08-25T10:19:17Z","abstract_excerpt":"We obtain the limiting distribution of the nodal area of random Gaussian Laplace eigenfunctions on $\\mathbb{T}^3= \\mathbb{R}^3/ \\mathbb{Z}^3$ ($3$-dimensional 'arithmetic random waves'). We prove that, as the multiplicity of the eigenspace goes to infinity, the nodal area converges to a universal, non-Gaussian, distribution. Universality follows from the equidistribution of lattice points on the sphere. Our arguments rely on the Wiener chaos expansion of the nodal area: we show that, analogous to (Marinucci, Peccati, Rossi and Wigman, 2016), the fluctuations are dominated by the fourth-order c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07679","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Poy+1WGiu8Yg6t6BnZ2mAeT1Q9Cyh5UcDIvq+G2/bRNk5BGCHMucAxbxS7q8eKmgp5lorxZupbPFfUz2klIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:50:20.008125Z"},"content_sha256":"f5e042feae495a44b56e906f17e58701e8f62dcebadb131505022f775ef8bcfd","schema_version":"1.0","event_id":"sha256:f5e042feae495a44b56e906f17e58701e8f62dcebadb131505022f775ef8bcfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QMNNWXV6CA2JV7KQ7QSACQK6E3/bundle.json","state_url":"https://pith.science/pith/QMNNWXV6CA2JV7KQ7QSACQK6E3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QMNNWXV6CA2JV7KQ7QSACQK6E3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T10:50:20Z","links":{"resolver":"https://pith.science/pith/QMNNWXV6CA2JV7KQ7QSACQK6E3","bundle":"https://pith.science/pith/QMNNWXV6CA2JV7KQ7QSACQK6E3/bundle.json","state":"https://pith.science/pith/QMNNWXV6CA2JV7KQ7QSACQK6E3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QMNNWXV6CA2JV7KQ7QSACQK6E3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QMNNWXV6CA2JV7KQ7QSACQK6E3","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":"b9e94a0e7559810b5b9e9813b99b5f2e9f4fd1b640a896a40563330a3ccb5f67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-25T10:19:17Z","title_canon_sha256":"40569b848d97d9caf15e605d691ffa3173dac160c07fb4f69f31eb8a7185ab32"},"schema_version":"1.0","source":{"id":"1708.07679","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07679","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07679v1","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07679","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"QMNNWXV6CA2J","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QMNNWXV6CA2JV7KQ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QMNNWXV6","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:f5e042feae495a44b56e906f17e58701e8f62dcebadb131505022f775ef8bcfd","target":"graph","created_at":"2026-05-18T00:36:42Z","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 obtain the limiting distribution of the nodal area of random Gaussian Laplace eigenfunctions on $\\mathbb{T}^3= \\mathbb{R}^3/ \\mathbb{Z}^3$ ($3$-dimensional 'arithmetic random waves'). We prove that, as the multiplicity of the eigenspace goes to infinity, the nodal area converges to a universal, non-Gaussian, distribution. Universality follows from the equidistribution of lattice points on the sphere. Our arguments rely on the Wiener chaos expansion of the nodal area: we show that, analogous to (Marinucci, Peccati, Rossi and Wigman, 2016), the fluctuations are dominated by the fourth-order c","authors_text":"Valentina Cammarota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-25T10:19:17Z","title":"Nodal area distribution for arithmetic random waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07679","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:b23a13f4bc06c816ea00f9d9c4fb7f9a27d213de39ef38d9d793fce77c4a980a","target":"record","created_at":"2026-05-18T00:36:42Z","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":"b9e94a0e7559810b5b9e9813b99b5f2e9f4fd1b640a896a40563330a3ccb5f67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-25T10:19:17Z","title_canon_sha256":"40569b848d97d9caf15e605d691ffa3173dac160c07fb4f69f31eb8a7185ab32"},"schema_version":"1.0","source":{"id":"1708.07679","kind":"arxiv","version":1}},"canonical_sha256":"831adb5ebe10349afd50fc2401415e26fdcbecd20ba51c0891da9a4dc02addfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"831adb5ebe10349afd50fc2401415e26fdcbecd20ba51c0891da9a4dc02addfc","first_computed_at":"2026-05-18T00:36:42.386415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:42.386415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FgipXdyxxrBVv0aiMw9vwdSd7vgPgrjLO386hEEnYHOIOCJKJPz78ApJ/cMqKFqFX0z+PTqHXWwB3YWJYps8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:42.387110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b23a13f4bc06c816ea00f9d9c4fb7f9a27d213de39ef38d9d793fce77c4a980a","sha256:f5e042feae495a44b56e906f17e58701e8f62dcebadb131505022f775ef8bcfd"],"state_sha256":"0aca040a602aecc41dcd5b36a300682cea6457f39fa31550e62bf915151e18e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VWGbAP0Rhwv/1AD/IhFEubP/FecMhF4Ihhcx5hWlhS7vXiGTLRo9MK+Mv7X+ZNAgyaJDFKu7eeJZKsIH0CcVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:50:20.010017Z","bundle_sha256":"2c46b7a555bfb257e7eba2e693d460a11615c999f81bf604556730259044bed4"}}