{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:G4PFUOMWQW3NIESB7C3R53RVJE","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":"c0448468cc34d1c19c0ff247c5ebd94a91a0df1d53bcebbe4b4c2563465b41ff","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2002-11-11T21:38:27Z","title_canon_sha256":"861818f3c02efb524a46257eb925b9469add9dce7151fe3cfd61087241eeb1f8"},"schema_version":"1.0","source":{"id":"quant-ph/0211062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0211062","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0211062v2","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0211062","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"pith_short_12","alias_value":"G4PFUOMWQW3N","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"G4PFUOMWQW3NIESB","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"G4PFUOMW","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:e948b316f895979606b7a16822d48290e75841c54b564abc0f3d6cfedb9c15e4","target":"graph","created_at":"2026-05-18T03:24:20Z","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":"The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states in a given m-th partial wave is related to the phase shift and the singularity strength of the potential. For the m-wave phase shift the asymptotic behaviour is calculated for short wavelengths.","authors_text":"Boris A. Ivanov, Denis D. Sheka, Franz G. Mertens","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2002-11-11T21:38:27Z","title":"Asymptotic phase shifts and Levinson theorem for 2D potentials with inverse square singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0211062","kind":"arxiv","version":2},"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":"sha256:09c2b3983c3865c5b33c7f22d9390d7f1275d024f41c295d8c6d2e2cc837af68","target":"record","created_at":"2026-05-18T03:24:20Z","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":"c0448468cc34d1c19c0ff247c5ebd94a91a0df1d53bcebbe4b4c2563465b41ff","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2002-11-11T21:38:27Z","title_canon_sha256":"861818f3c02efb524a46257eb925b9469add9dce7151fe3cfd61087241eeb1f8"},"schema_version":"1.0","source":{"id":"quant-ph/0211062","kind":"arxiv","version":2}},"canonical_sha256":"371e5a399685b6d41241f8b71eee354928b3048e4b6e1c650f36959c0e919c88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"371e5a399685b6d41241f8b71eee354928b3048e4b6e1c650f36959c0e919c88","first_computed_at":"2026-05-18T03:24:20.258623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:20.258623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dJemdBB7lu/NmJ8LfuteprTGFbqUPVGpsbb6hJzgvymJdnqoXrruDO0+5fepKxQDk05yDwQ4PpHo/AnMTbB/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:20.259228Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0211062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09c2b3983c3865c5b33c7f22d9390d7f1275d024f41c295d8c6d2e2cc837af68","sha256:e948b316f895979606b7a16822d48290e75841c54b564abc0f3d6cfedb9c15e4"],"state_sha256":"cbf72785ea06e402ea70b845cda711e8af50e92f7a2bbb499c447a332514ab0a"}