{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2PFVJQDEHGZD7MDMGCLJU3FC63","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":"13b62a6f2653d568a8e38786f5c517b9b5df937fe0863f14a0bd569fad959275","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-05T19:00:13Z","title_canon_sha256":"1f0e742a22e6b140fb830ca2b5dcdd3fdeb2c6b5b023d8252889012e487084c5"},"schema_version":"1.0","source":{"id":"1608.01974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01974","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01974v1","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01974","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"pith_short_12","alias_value":"2PFVJQDEHGZD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PFVJQDEHGZD7MDM","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PFVJQDE","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:5870e059beb63f54689a184af0c3d158e4f964a6f7c72163547f8576e82df12e","target":"graph","created_at":"2026-05-18T00:52:03Z","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":"Some general properties of the wave functions of complex-valued potentials with real spectrum are studied. The main results are presented in a series of lemmas, corollaries and theorems that are satisfied by the zeros of the real and imaginary parts of the wave functions on the real line. In particular, it is shown that such zeros interlace so that the corresponding probability densities $\\rho(x)$ are never null. We find that the profile of the imaginary part $V_I(x)$ of a given complex-valued potential determines the number and distribution of the maxima and minima of the related probability ","authors_text":"Alfonso Jaimes-Najera, Oscar Rosas-Ortiz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-05T19:00:13Z","title":"Interlace properties for the real and imaginary parts of the wave functions of complex-valued potentials with real spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01974","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:de85d00857235a7c4f13d81d9636884dcdf3448430ae02c06d99cd8382768fd8","target":"record","created_at":"2026-05-18T00:52:03Z","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":"13b62a6f2653d568a8e38786f5c517b9b5df937fe0863f14a0bd569fad959275","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-05T19:00:13Z","title_canon_sha256":"1f0e742a22e6b140fb830ca2b5dcdd3fdeb2c6b5b023d8252889012e487084c5"},"schema_version":"1.0","source":{"id":"1608.01974","kind":"arxiv","version":1}},"canonical_sha256":"d3cb54c06439b23fb06c30969a6ca2f6de57b0c151e2e2fa738b01376d882d23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3cb54c06439b23fb06c30969a6ca2f6de57b0c151e2e2fa738b01376d882d23","first_computed_at":"2026-05-18T00:52:03.972405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:03.972405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lEgB5DyVFiMEvVkhxrGgo3RGkJlpZWwS6xaArM9iSWi43HxOJJVl5dcSrzQAJg2N7VVcS3TIN7ATxIcZ3PTDCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:03.973029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de85d00857235a7c4f13d81d9636884dcdf3448430ae02c06d99cd8382768fd8","sha256:5870e059beb63f54689a184af0c3d158e4f964a6f7c72163547f8576e82df12e"],"state_sha256":"7e1237b27000d3ab48c4718628c2975f1e09362560b4c6fcf58e0918337e1dc3"}