{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DISLACIJIHQ5CINR6JSI3KP5MP","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":"1ed073816550a8a3f599a064b41e486e7427f06c0198823c72075881232e0530","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T20:17:55Z","title_canon_sha256":"434b40986414aa655edd82dbfde0c10f81c01a1972da8e0bab2be7011ad9ead8"},"schema_version":"1.0","source":{"id":"1810.04232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04232","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04232v1","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04232","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"DISLACIJIHQ5","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DISLACIJIHQ5CINR","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DISLACIJ","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:53ec0cbe32474d1f0dea341d8c1abecfe21519c2a9f6feb475f5b71fafa98dd1","target":"graph","created_at":"2026-05-18T00:03:40Z","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 $(M,g)$ be a compact Riemannian manifold and $P_1:=-h^2\\Delta_g+V(x)-E_1$ so that $dp_1\\neq 0$ on $p_1=0$. We assume that $P_1$ is quantum completely integrable in the sense that there exist functionally independent pseuodifferential operators $P_2,\\dots P_n$ with $[P_i,P_j]=0$, $i,j=1,\\dots ,n$. We study the pointwise bounds for the joint eigenfunctions, $u_h$ of the system $\\{P_i\\}_{i=1}^n$ with $P_1u_h=E_1u_h+o(1)$. We first give polynomial improvements over the standard H\\\"ormander bounds for typical points in $M$. In two and three dimensions, these estimates agree with the Hardy expon","authors_text":"Jeffrey Galkowski, John A. Toth","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T20:17:55Z","title":"Pointwise bounds for joint eigenfunctions of quantum completely integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04232","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:c89acac0183fae0adf6e946c206e7b6899bee3e6db7b5a735c19445e75759f6e","target":"record","created_at":"2026-05-18T00:03:40Z","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":"1ed073816550a8a3f599a064b41e486e7427f06c0198823c72075881232e0530","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T20:17:55Z","title_canon_sha256":"434b40986414aa655edd82dbfde0c10f81c01a1972da8e0bab2be7011ad9ead8"},"schema_version":"1.0","source":{"id":"1810.04232","kind":"arxiv","version":1}},"canonical_sha256":"1a24b0090941e1d121b1f2648da9fd63f659335bacbb933e6f85fb54177ce9af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a24b0090941e1d121b1f2648da9fd63f659335bacbb933e6f85fb54177ce9af","first_computed_at":"2026-05-18T00:03:40.757815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:40.757815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4sZiJ940XObedwyEvmsea0wsjOB1ccPe/60ncZxcIGcfqEGiVIBGDmPCnk6mH+DY1a081lWwwYH87ldtBVPCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:40.758416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c89acac0183fae0adf6e946c206e7b6899bee3e6db7b5a735c19445e75759f6e","sha256:53ec0cbe32474d1f0dea341d8c1abecfe21519c2a9f6feb475f5b71fafa98dd1"],"state_sha256":"54c7ecde282e02b9ed2f51dfc9f6d83a73da628ea432676e41b64a41ccc2bb04"}