{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DFSKGLCA7XS5FCELHOMPIFXN5X","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":"a10f2020f88dd8392f7aa32519e1f276791054299c35764118ca8b9ad0da3935","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-09T23:49:00Z","title_canon_sha256":"51f119a628c28f97a2ddea2e1d699b04aa425c7f16fab44a196e3f2b72bc46ef"},"schema_version":"1.0","source":{"id":"1205.2124","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2124","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2124v1","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2124","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"pith_short_12","alias_value":"DFSKGLCA7XS5","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DFSKGLCA7XS5FCEL","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DFSKGLCA","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:ea4dba3ff2810d8afb5f58bc5f9e72ffb46cbafc79c6f281712f803d242152ab","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 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 $Z$ continuous on $\\RR^3$ with $Z(p) > -1/4$ for $p \\in \\maS$. Also assume that $\\rho$ and $Z$ are smooth outside $\\maS$ and $Z$ is smooth in polar coordinates around each singular point. We either assume that $V$ is periodic or that the set $\\maS$ is finite and $V$ extends to a smooth function on the radial compactification of $\\RR^3$ that is bounded outside a compact set containing $\\maS$. I","authors_text":"Eugenie Hunsicker, Hengguang Li, Victor Nistor, Ville Uski","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-09T23:49:00Z","title":"Analysis of Schr\\\"odinger operators with inverse square potentials I: regularity results in 3D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2124","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":"sha256:04eda84f891529ffaee79463c58117c8765cc96420a8c3c6fac3c17a519e7b69","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":"a10f2020f88dd8392f7aa32519e1f276791054299c35764118ca8b9ad0da3935","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-09T23:49:00Z","title_canon_sha256":"51f119a628c28f97a2ddea2e1d699b04aa425c7f16fab44a196e3f2b72bc46ef"},"schema_version":"1.0","source":{"id":"1205.2124","kind":"arxiv","version":1}},"canonical_sha256":"1964a32c40fde5d2888b3b98f416edede30ee3076d5e8f5761c91a2e046e3748","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1964a32c40fde5d2888b3b98f416edede30ee3076d5e8f5761c91a2e046e3748","first_computed_at":"2026-05-18T03:55:56.991640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:56.991640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3G8jGhTj8A1xQSTE0C8uXd/NVvMVGT3Vz040tS9/r2USAcmNEWnGgdO/RQEtxTiD7TqtlYO30Wjc6yiJ0rfFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:56.992247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2124","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04eda84f891529ffaee79463c58117c8765cc96420a8c3c6fac3c17a519e7b69","sha256:ea4dba3ff2810d8afb5f58bc5f9e72ffb46cbafc79c6f281712f803d242152ab"],"state_sha256":"5cbdd404de9ed0df794f22ec4a107c65c99570260ad641251ee3a783c8636cf8"}