{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:45Y3ZI7L4SV5DK3XU7GDLK3534","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":"b92e10dca7fc8d8b649b249858142d7fa1cab788ac9830ad5ce27b23b6c13900","cross_cats_sorted":["math.AP","math.FA","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-08T15:01:34Z","title_canon_sha256":"4f80bb0087e5ce2d4b32fa4a19df5342c9f661f2f4ffaa8eb3f881a33f108c17"},"schema_version":"1.0","source":{"id":"1010.1712","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1712","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1712v3","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1712","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"45Y3ZI7L4SV5","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"45Y3ZI7L4SV5DK3X","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"45Y3ZI7L","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:eafe6b67153a7cbd27ffa2db8d60afb9ee00cefe9e65d7722efd1245f45b1df5","target":"graph","created_at":"2026-05-18T01:29:12Z","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 a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\\\"odinger operator. More precisely, let K_{a}^{m}(\\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \\sum_{1 \\le j \\le N} \\frac{b_j}{|x_j|} + \\sum_{1 \\le i < j \\le N} \\frac{c_{ij}}{|x_i-x_j|}, x in \\mathbb{R}^{3N}, b_j, c_{ij} in \\mathbb{R}. If u in L^2(\\mathbb{R}^{3N}) satisfies (-\\Delta + V) u = \\lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \\in \\mathbb{Z}_+ and all a ","authors_text":"Bernd Ammann, Catarina Carvalho, Victor Nistor","cross_cats":["math.AP","math.FA","math.MP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-08T15:01:34Z","title":"Regularity for eigenfunctions of Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1712","kind":"arxiv","version":3},"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":"sha256:0f6206851d7d34f77157fc9b466ad92e14bfa50b360a625d3ab3ad4648b1b69a","target":"record","created_at":"2026-05-18T01:29:12Z","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":"b92e10dca7fc8d8b649b249858142d7fa1cab788ac9830ad5ce27b23b6c13900","cross_cats_sorted":["math.AP","math.FA","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-08T15:01:34Z","title_canon_sha256":"4f80bb0087e5ce2d4b32fa4a19df5342c9f661f2f4ffaa8eb3f881a33f108c17"},"schema_version":"1.0","source":{"id":"1010.1712","kind":"arxiv","version":3}},"canonical_sha256":"e771bca3ebe4abd1ab77a7cc35ab7ddf0825bfc5f4c3e72393ddf6cddd618e22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e771bca3ebe4abd1ab77a7cc35ab7ddf0825bfc5f4c3e72393ddf6cddd618e22","first_computed_at":"2026-05-18T01:29:12.113355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:12.113355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PXGOgUfoSze3oZwznxH7v9sCUGIB3oPCpNvMSdbqXk86JaexJp9enlxrog7PMNGA7Yy/YseGkfx3iEo8hkTNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:12.113944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1712","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f6206851d7d34f77157fc9b466ad92e14bfa50b360a625d3ab3ad4648b1b69a","sha256:eafe6b67153a7cbd27ffa2db8d60afb9ee00cefe9e65d7722efd1245f45b1df5"],"state_sha256":"837bb0b6e8e9af388df5dc45c2e4703c2d6f09deee4052829722a0e73ce26251"}