{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VZCBBUXWRLZ3Q4NNB3ODRWOGX7","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":"79c8498537038b4c06ff12e77806f0c5cc084f8830c48316fab9db57c77a2575","cross_cats_sorted":["math.AP","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-10T00:11:48Z","title_canon_sha256":"4321677e47ec53bcf3bf168fda157f9e6de50ad22d02f1a4ace4d6a2c97f9bed"},"schema_version":"1.0","source":{"id":"1205.2127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2127","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2127v1","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2127","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"pith_short_12","alias_value":"VZCBBUXWRLZ3","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VZCBBUXWRLZ3Q4NN","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VZCBBUXW","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:a1120f387b2f0c77397ff53a897388c86615ce00ccb29f9c35aa034d66c10bc1","target":"graph","created_at":"2026-05-18T03:55:56Z","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 $V$ be a {\\em periodic} potential on $\\RR^3$ that is smooth everywhere except at a discrete set $\\maS$ of points, where it has singularities of the form $Z/\\rho^2$, with $\\rho(x) = |x - p|$ for $x$ close to $p$ and $Z$ is continuous, $Z(p) > -1/4$ for $p \\in \\maS$. We also assume that $\\rho$ and $Z$ are smooth outside $\\maS$ and $Z$ is smooth in polar coordinates around each singular point. Let us denote by $\\Lambda$ the periodicity lattice and set $\\TT := \\RR^3/ \\Lambda$. In the first paper of this series \\cite{HLNU1}, we obtained regularity results in weighted Sobolev space for the eigen","authors_text":"Eugenie Hunsicker, Hengguang Li, Victor Nistor, Ville Uski","cross_cats":["math.AP","math.MP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-10T00:11:48Z","title":"Analysis of Schr\\\"odinger operators with inverse square potentials {II}: FEM and approximation of eigenfunctions in the periodic case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2127","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":"sha256:81accae6f770c69dfd438d033759576517116b6de5d8429462d36c968356e46e","target":"record","created_at":"2026-05-18T03:55:56Z","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":"79c8498537038b4c06ff12e77806f0c5cc084f8830c48316fab9db57c77a2575","cross_cats_sorted":["math.AP","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-10T00:11:48Z","title_canon_sha256":"4321677e47ec53bcf3bf168fda157f9e6de50ad22d02f1a4ace4d6a2c97f9bed"},"schema_version":"1.0","source":{"id":"1205.2127","kind":"arxiv","version":1}},"canonical_sha256":"ae4410d2f68af3b871ad0edc38d9c6bfdfe3e0a04edcd97ab376cd41b534f03a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae4410d2f68af3b871ad0edc38d9c6bfdfe3e0a04edcd97ab376cd41b534f03a","first_computed_at":"2026-05-18T03:55:56.982503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:56.982503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JR/8aCSxSWV+6gpjv/F1lJISvGTivlL0tohhedKVjjCsK3mVZaVyJCbduODFARNLcGItT5+cG0dp7BWdj2DMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:56.983146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81accae6f770c69dfd438d033759576517116b6de5d8429462d36c968356e46e","sha256:a1120f387b2f0c77397ff53a897388c86615ce00ccb29f9c35aa034d66c10bc1"],"state_sha256":"0e145556e91bdfd6c14d5ea73d1dc5aa185c7c8555a70e7ff6234b6a36eb0211"}