{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DREV2SRHLVJOZAQO6B5KK255W6","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":"814b9173a226f1bc62eb4fe736f1f10ec1a3521e221732762d10e9932c7da6c6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-05-19T15:39:31Z","title_canon_sha256":"93ebf332ce135efe7791970a59f4473db2fc1ab88d5ef52a1323175be4184a25"},"schema_version":"1.0","source":{"id":"2505.13256","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13256","created_at":"2026-07-05T12:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13256v2","created_at":"2026-07-05T12:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13256","created_at":"2026-07-05T12:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"DREV2SRHLVJO","created_at":"2026-07-05T12:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"DREV2SRHLVJOZAQO","created_at":"2026-07-05T12:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"DREV2SRH","created_at":"2026-07-05T12:09:44Z"}],"graph_snapshots":[{"event_id":"sha256:6b70ce861a0ab4fa55fe8580d1d30c97ae0b7b2ad7421f3ce4a70b261f20bcbd","target":"graph","created_at":"2026-07-05T12:09:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.13256/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity (QUE) from subconvexity.","authors_text":"Paul D. Nelson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13256","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":"sha256:204577c0288b912bb8e64d0f91a50a1a92a7fd6a91a390901fd972f2b81fc33a","target":"record","created_at":"2026-07-05T12:09:44Z","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":"814b9173a226f1bc62eb4fe736f1f10ec1a3521e221732762d10e9932c7da6c6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-05-19T15:39:31Z","title_canon_sha256":"93ebf332ce135efe7791970a59f4473db2fc1ab88d5ef52a1323175be4184a25"},"schema_version":"1.0","source":{"id":"2505.13256","kind":"arxiv","version":2}},"canonical_sha256":"1c495d4a275d52ec820ef07aa56bbdb7abead7ceb4cc585393b510623b168413","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c495d4a275d52ec820ef07aa56bbdb7abead7ceb4cc585393b510623b168413","first_computed_at":"2026-07-05T12:09:44.362587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:09:44.362587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LE6psc9YPgRydQnlXlHAQzchKmHl4gz6p/0EgZ/DPGmhvFxLXTcqaHjOLIa1PETl8EZaT11xS5u0z8DLiJz6Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:09:44.363026Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13256","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:204577c0288b912bb8e64d0f91a50a1a92a7fd6a91a390901fd972f2b81fc33a","sha256:6b70ce861a0ab4fa55fe8580d1d30c97ae0b7b2ad7421f3ce4a70b261f20bcbd"],"state_sha256":"c39d6ccb0e91c27cbd71b904515dfcb8f85068e12d3c8356fb37f215b5ab7334"}