{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:B3UBE2W3Q6SNXGUV6KBUPNIBYX","short_pith_number":"pith:B3UBE2W3","canonical_record":{"source":{"id":"1606.02057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-07T08:26:28Z","cross_cats_sorted":["math.CA","math.DG","math.SP"],"title_canon_sha256":"e0aa93890e71d15ecbeedba382fe68872dbe742ee64f2651a771bf82f93c19b0","abstract_canon_sha256":"e7e09925fb89abb01241778f9cc6fdc7cb75b781a62df4b9c71acfc4bc7331b8"},"schema_version":"1.0"},"canonical_sha256":"0ee8126adb87a4db9a95f28347b501c5ed045ab83dbbdddf0349a7a4326ae375","source":{"kind":"arxiv","id":"1606.02057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02057","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02057v1","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02057","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"B3UBE2W3Q6SN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B3UBE2W3Q6SNXGUV","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B3UBE2W3","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:B3UBE2W3Q6SNXGUV6KBUPNIBYX","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-07T08:26:28Z","cross_cats_sorted":["math.CA","math.DG","math.SP"],"title_canon_sha256":"e0aa93890e71d15ecbeedba382fe68872dbe742ee64f2651a771bf82f93c19b0","abstract_canon_sha256":"e7e09925fb89abb01241778f9cc6fdc7cb75b781a62df4b9c71acfc4bc7331b8"},"schema_version":"1.0"},"canonical_sha256":"0ee8126adb87a4db9a95f28347b501c5ed045ab83dbbdddf0349a7a4326ae375","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:59.483099Z","signature_b64":"+obGVmxfy75pCXMMBjIKTa/5Ym2JQO+3B/Glwh4G3wymjDHEcKnidItMx+HH5rTeCQgKsdUXaDMTvSg2YP/2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ee8126adb87a4db9a95f28347b501c5ed045ab83dbbdddf0349a7a4326ae375","last_reissued_at":"2026-05-18T00:20:59.482675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:59.482675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02057","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":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9JpfPpp8OXh+l+7k0SwsTd33je1mRYPeuyGK2VeCiQtS+Immj58Vy/fuWPk14E++6bpZWdE3MDd67kUNzGiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:56:56.971424Z"},"content_sha256":"c1c9f7157a905de06eb20b2ac428dd32a4db4422a10cb6aea46afaa333eb962d","schema_version":"1.0","event_id":"sha256:c1c9f7157a905de06eb20b2ac428dd32a4db4422a10cb6aea46afaa333eb962d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:B3UBE2W3Q6SNXGUV6KBUPNIBYX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications of small scale quantum ergodicity in nodal sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Hamid Hezari","submitted_at":"2016-06-07T08:26:28Z","abstract_excerpt":"The goal of this article is to draw new applications of small scale quantum ergodicity in nodal sets of eigenfunctions. We show that if quantum ergodicity holds on balls of shrinking radius $r(\\lambda) \\to 0$, then one can achieve improvements on the recent upper bounds of Logunov and Logunov-Malinnikova on the size of nodal sets, according to a certain power of $r(\\lambda)$. We also show that the order of vanishing results of Donnelly-Fefferman and Dong can be improved. Since by the results of Han and Hezari-Rivi\\`ere small scale QE holds on negatively curved manifolds at logarithmically shri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02057","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":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RUQbDraKGaOT/xklm2uwWAoe3Bu/icgujklY2ARmz86pRwAvPBAyfDJZC58eODLzIltoNaakIg+BuLhQfbs7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:56:56.972153Z"},"content_sha256":"95a420a8c1e1aaa0c8731cbc38cb550506adc260301f85992ae43ccc9f8a11ac","schema_version":"1.0","event_id":"sha256:95a420a8c1e1aaa0c8731cbc38cb550506adc260301f85992ae43ccc9f8a11ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3UBE2W3Q6SNXGUV6KBUPNIBYX/bundle.json","state_url":"https://pith.science/pith/B3UBE2W3Q6SNXGUV6KBUPNIBYX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3UBE2W3Q6SNXGUV6KBUPNIBYX/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":"2026-06-11T02:56:56Z","links":{"resolver":"https://pith.science/pith/B3UBE2W3Q6SNXGUV6KBUPNIBYX","bundle":"https://pith.science/pith/B3UBE2W3Q6SNXGUV6KBUPNIBYX/bundle.json","state":"https://pith.science/pith/B3UBE2W3Q6SNXGUV6KBUPNIBYX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3UBE2W3Q6SNXGUV6KBUPNIBYX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:B3UBE2W3Q6SNXGUV6KBUPNIBYX","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":"e7e09925fb89abb01241778f9cc6fdc7cb75b781a62df4b9c71acfc4bc7331b8","cross_cats_sorted":["math.CA","math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-07T08:26:28Z","title_canon_sha256":"e0aa93890e71d15ecbeedba382fe68872dbe742ee64f2651a771bf82f93c19b0"},"schema_version":"1.0","source":{"id":"1606.02057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02057","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02057v1","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02057","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"B3UBE2W3Q6SN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B3UBE2W3Q6SNXGUV","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B3UBE2W3","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:95a420a8c1e1aaa0c8731cbc38cb550506adc260301f85992ae43ccc9f8a11ac","target":"graph","created_at":"2026-05-18T00:20:59Z","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":"The goal of this article is to draw new applications of small scale quantum ergodicity in nodal sets of eigenfunctions. We show that if quantum ergodicity holds on balls of shrinking radius $r(\\lambda) \\to 0$, then one can achieve improvements on the recent upper bounds of Logunov and Logunov-Malinnikova on the size of nodal sets, according to a certain power of $r(\\lambda)$. We also show that the order of vanishing results of Donnelly-Fefferman and Dong can be improved. Since by the results of Han and Hezari-Rivi\\`ere small scale QE holds on negatively curved manifolds at logarithmically shri","authors_text":"Hamid Hezari","cross_cats":["math.CA","math.DG","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-07T08:26:28Z","title":"Applications of small scale quantum ergodicity in nodal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02057","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:c1c9f7157a905de06eb20b2ac428dd32a4db4422a10cb6aea46afaa333eb962d","target":"record","created_at":"2026-05-18T00:20:59Z","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":"e7e09925fb89abb01241778f9cc6fdc7cb75b781a62df4b9c71acfc4bc7331b8","cross_cats_sorted":["math.CA","math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-07T08:26:28Z","title_canon_sha256":"e0aa93890e71d15ecbeedba382fe68872dbe742ee64f2651a771bf82f93c19b0"},"schema_version":"1.0","source":{"id":"1606.02057","kind":"arxiv","version":1}},"canonical_sha256":"0ee8126adb87a4db9a95f28347b501c5ed045ab83dbbdddf0349a7a4326ae375","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ee8126adb87a4db9a95f28347b501c5ed045ab83dbbdddf0349a7a4326ae375","first_computed_at":"2026-05-18T00:20:59.482675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:59.482675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+obGVmxfy75pCXMMBjIKTa/5Ym2JQO+3B/Glwh4G3wymjDHEcKnidItMx+HH5rTeCQgKsdUXaDMTvSg2YP/2BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:59.483099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1c9f7157a905de06eb20b2ac428dd32a4db4422a10cb6aea46afaa333eb962d","sha256:95a420a8c1e1aaa0c8731cbc38cb550506adc260301f85992ae43ccc9f8a11ac"],"state_sha256":"f40ba5201ac01bd8bcb56e528b96cf0d5e396a37065444f49365d3bcc38ec499"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CoIsMUVjNG2wvv55ohsEfv5EJGpUAx7JJ3nkzJl59QjQTooV0RyjHjxVGA6cHGBUM7ojuRFfYDfyVVKFkgwKAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:56:56.976455Z","bundle_sha256":"ad493d2b60510ccfb7c5eea1845a37e346982c7ca34c8c7f9327c686b2483639"}}