{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I6APIA2RF65OYH6CKJITZUK7VC","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":"09148cb9a7eb9bde6ffc3ee37b2ff64286c6ad550d7e156e406da25f8517dfe3","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-10T07:34:51Z","title_canon_sha256":"7710fa322d1cf3acc55fffb3c4079f2dea455f8ef0260b232cf59662830bda4c"},"schema_version":"1.0","source":{"id":"1503.02794","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02794","created_at":"2026-05-18T02:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02794v1","created_at":"2026-05-18T02:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02794","created_at":"2026-05-18T02:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"I6APIA2RF65O","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I6APIA2RF65OYH6C","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I6APIA2R","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:cb4d20609a00e52ee42aee8bc9700f65cbe22d8e415699470b884862d8343252","target":"graph","created_at":"2026-05-18T02:25:13Z","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 prove quantitative equidistribution properties for orthonormal bases of eigenfunctions of the Laplacian on the rational $d$-torus. We show that the rate of equidistribution of such eigenfunctions is of polynomial decay. We also prove that equidistribution of eigenfunctions holds for symbols supported in balls with a radius shrinking at a polynomial rate.","authors_text":"Gabriel Riviere, Hamid Hezari","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-10T07:34:51Z","title":"Quantitative equidistribution properties of toral eigenfunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02794","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:ffc7b92bc8d7fee07ffe10388f09b78d2ce9b780adf59c976d44d05d92d903f1","target":"record","created_at":"2026-05-18T02:25:13Z","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":"09148cb9a7eb9bde6ffc3ee37b2ff64286c6ad550d7e156e406da25f8517dfe3","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-10T07:34:51Z","title_canon_sha256":"7710fa322d1cf3acc55fffb3c4079f2dea455f8ef0260b232cf59662830bda4c"},"schema_version":"1.0","source":{"id":"1503.02794","kind":"arxiv","version":1}},"canonical_sha256":"4780f403512fbaec1fc252513cd15fa88f4589b74d3740734a1654849d07a5c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4780f403512fbaec1fc252513cd15fa88f4589b74d3740734a1654849d07a5c8","first_computed_at":"2026-05-18T02:25:13.079903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:13.079903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lVONGNaLMiLegdlRzORfCgt+jaRCvHT0ahaX4nQcz2PnuAl8F5yjqkmUSjgOW435+9AspoiohfWKP+SFfW4YBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:13.080401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02794","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffc7b92bc8d7fee07ffe10388f09b78d2ce9b780adf59c976d44d05d92d903f1","sha256:cb4d20609a00e52ee42aee8bc9700f65cbe22d8e415699470b884862d8343252"],"state_sha256":"585f74de277d216b9ca9c000c9a3b93e88c7ee2a73e17970b2a7bcae20d6d938"}