{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KA7FC5JDTDNEJEG34CJSMHNJ6U","short_pith_number":"pith:KA7FC5JD","canonical_record":{"source":{"id":"1011.1291","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-04T22:46:10Z","cross_cats_sorted":[],"title_canon_sha256":"edd14d1b51f12b68f253a96755f44f156d2189be99bdbacb33392407932dcb29","abstract_canon_sha256":"446a53c55bd5a30171ce38b9699bc0775c51ca0495d282024418d8949ed0e337"},"schema_version":"1.0"},"canonical_sha256":"503e51752398da4490dbe093261da9f50e6f99b66ce31736da5c2abed22a8ba5","source":{"kind":"arxiv","id":"1011.1291","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1291","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1291v2","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1291","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"KA7FC5JDTDNE","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KA7FC5JDTDNEJEG3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KA7FC5JD","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KA7FC5JDTDNEJEG34CJSMHNJ6U","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1291","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-04T22:46:10Z","cross_cats_sorted":[],"title_canon_sha256":"edd14d1b51f12b68f253a96755f44f156d2189be99bdbacb33392407932dcb29","abstract_canon_sha256":"446a53c55bd5a30171ce38b9699bc0775c51ca0495d282024418d8949ed0e337"},"schema_version":"1.0"},"canonical_sha256":"503e51752398da4490dbe093261da9f50e6f99b66ce31736da5c2abed22a8ba5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:23.342205Z","signature_b64":"EMucqhHwXQeWMSzZFJ47ScYoYi/yidbHy3LKRZJfeok17oAfeb9r2761RIf526ZnIGlh/mh4pCPh6AzGixDfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"503e51752398da4490dbe093261da9f50e6f99b66ce31736da5c2abed22a8ba5","last_reissued_at":"2026-05-18T04:01:23.341708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:23.341708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1291","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZBptH85ompld319QEtfwVvFRywbzl/JgaM+8X+ApMcRveaC+710uRAlquMgYYLjoNbGLfkOGIhpCrGAVUjLVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:50:52.578645Z"},"content_sha256":"d761b4b6e6a5c76d65ea657ba92d534f8524c8bb2a0dfa8dfbe24990124da426","schema_version":"1.0","event_id":"sha256:d761b4b6e6a5c76d65ea657ba92d534f8524c8bb2a0dfa8dfbe24990124da426"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KA7FC5JDTDNEJEG34CJSMHNJ6U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mass equidistribution of Hilbert modular eigenforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul D. Nelson","submitted_at":"2010-11-04T22:46:10Z","abstract_excerpt":"Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity.\n  Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1291","kind":"arxiv","version":2},"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":"2026-05-18T04:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gb6os2SVFpputy2CXnN9qqeko0FISdNqG8myZW7UjHX1isTV0RazZWWQUMVpcnzvfcKwHNegND71bEvNiLv0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:50:52.579337Z"},"content_sha256":"8be443a659fdba3372a69961a299e8fe9ce025b97b91470631872cbf370beea2","schema_version":"1.0","event_id":"sha256:8be443a659fdba3372a69961a299e8fe9ce025b97b91470631872cbf370beea2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KA7FC5JDTDNEJEG34CJSMHNJ6U/bundle.json","state_url":"https://pith.science/pith/KA7FC5JDTDNEJEG34CJSMHNJ6U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KA7FC5JDTDNEJEG34CJSMHNJ6U/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":"2026-06-06T12:50:52Z","links":{"resolver":"https://pith.science/pith/KA7FC5JDTDNEJEG34CJSMHNJ6U","bundle":"https://pith.science/pith/KA7FC5JDTDNEJEG34CJSMHNJ6U/bundle.json","state":"https://pith.science/pith/KA7FC5JDTDNEJEG34CJSMHNJ6U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KA7FC5JDTDNEJEG34CJSMHNJ6U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KA7FC5JDTDNEJEG34CJSMHNJ6U","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":"446a53c55bd5a30171ce38b9699bc0775c51ca0495d282024418d8949ed0e337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-04T22:46:10Z","title_canon_sha256":"edd14d1b51f12b68f253a96755f44f156d2189be99bdbacb33392407932dcb29"},"schema_version":"1.0","source":{"id":"1011.1291","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1291","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1291v2","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1291","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"KA7FC5JDTDNE","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KA7FC5JDTDNEJEG3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KA7FC5JD","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:8be443a659fdba3372a69961a299e8fe9ce025b97b91470631872cbf370beea2","target":"graph","created_at":"2026-05-18T04:01:23Z","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":"Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity.\n  Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the","authors_text":"Paul D. Nelson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-04T22:46:10Z","title":"Mass equidistribution of Hilbert modular eigenforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1291","kind":"arxiv","version":2},"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:d761b4b6e6a5c76d65ea657ba92d534f8524c8bb2a0dfa8dfbe24990124da426","target":"record","created_at":"2026-05-18T04:01:23Z","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":"446a53c55bd5a30171ce38b9699bc0775c51ca0495d282024418d8949ed0e337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-04T22:46:10Z","title_canon_sha256":"edd14d1b51f12b68f253a96755f44f156d2189be99bdbacb33392407932dcb29"},"schema_version":"1.0","source":{"id":"1011.1291","kind":"arxiv","version":2}},"canonical_sha256":"503e51752398da4490dbe093261da9f50e6f99b66ce31736da5c2abed22a8ba5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"503e51752398da4490dbe093261da9f50e6f99b66ce31736da5c2abed22a8ba5","first_computed_at":"2026-05-18T04:01:23.341708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:23.341708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EMucqhHwXQeWMSzZFJ47ScYoYi/yidbHy3LKRZJfeok17oAfeb9r2761RIf526ZnIGlh/mh4pCPh6AzGixDfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:23.342205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1291","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d761b4b6e6a5c76d65ea657ba92d534f8524c8bb2a0dfa8dfbe24990124da426","sha256:8be443a659fdba3372a69961a299e8fe9ce025b97b91470631872cbf370beea2"],"state_sha256":"0a477273881b25ab52e05715b8417a5c82c945934c20dc84eab88fa166b52c67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rXG8w59w2OoJAns/jMZPwZE9DBLf/YYGFNzt2ysEkzZvawqKtBOX6w2635hpdObj3+oou3WR6HYe6f93pyTPDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T12:50:52.582842Z","bundle_sha256":"a2118c336edbd4c7fe2d7a4ee594a88f2627ee22bbf4aa43d66dbca5886cf3ab"}}