{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PFSJOOUMWD4BY7KD5KZHAFZA26","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":"fe80bec543abd4e060a3802d1f0609a657cf800a9d57ef969a2b03db6ef2b45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-23T15:05:46Z","title_canon_sha256":"72f565c31d12a444241dd0492f5ab242414443eb2ce35fdcfdacb70c0c0cc641"},"schema_version":"1.0","source":{"id":"1701.06436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06436","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06436v1","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06436","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"PFSJOOUMWD4B","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PFSJOOUMWD4BY7KD","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PFSJOOUM","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:680ec4c318683fe3996f93839125c07d14d94eba0c32f3d98cac04a0d5fc69e8","target":"graph","created_at":"2026-05-18T00:52:18Z","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 complete the classical Schoenberg representation theorem for radial positive definite functions. We apply this result to study spectral properties of self-adjoint realizations of two- and three-dimensional Schr\\\"odinger operators with point interactions on a finite set. In particular, we prove that any realization has purely absolutely continuous non-negative spectrum.","authors_text":"M. Malamud, N. Goloshchapova, V. Zastavnyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-23T15:05:46Z","title":"Radial positive definite functions and spectral theory of the Schr\\\"odinger operators with point interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06436","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":"sha256:8ed33155c0e41e4b06232a0e680b2e23bc65bfcfe22e2f33c5470c63b420ca25","target":"record","created_at":"2026-05-18T00:52:18Z","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":"fe80bec543abd4e060a3802d1f0609a657cf800a9d57ef969a2b03db6ef2b45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-23T15:05:46Z","title_canon_sha256":"72f565c31d12a444241dd0492f5ab242414443eb2ce35fdcfdacb70c0c0cc641"},"schema_version":"1.0","source":{"id":"1701.06436","kind":"arxiv","version":1}},"canonical_sha256":"7964973a8cb0f81c7d43eab2701720d78500033fc82916f54ecdba82f48f97a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7964973a8cb0f81c7d43eab2701720d78500033fc82916f54ecdba82f48f97a6","first_computed_at":"2026-05-18T00:52:18.397075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:18.397075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OeZLw0c4C1B/mHhzXz7oWYwjtkf8Zv4H/3NZ7XZou2p6lxBcF2vAse5jpaNwTLS/cGTXDb2fgmB+eoJMRGc3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:18.397623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ed33155c0e41e4b06232a0e680b2e23bc65bfcfe22e2f33c5470c63b420ca25","sha256:680ec4c318683fe3996f93839125c07d14d94eba0c32f3d98cac04a0d5fc69e8"],"state_sha256":"8e0bd74096bb0eee2a1aa08c8c07da48f8266e7d14da824f82da54440eb37812"}