{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:P4JPZNXRKKLFD3DWWPED6E7SFZ","short_pith_number":"pith:P4JPZNXR","canonical_record":{"source":{"id":"1205.4136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T11:06:11Z","cross_cats_sorted":[],"title_canon_sha256":"e5e71dfad34d4ea6b41f77237c20966d679fe9b2d54fa336d7777083789bc525","abstract_canon_sha256":"ad55e42da101f4107240fe48d1de99582a6cbdaaf7b31ef7bd3a43b7b2ee07bd"},"schema_version":"1.0"},"canonical_sha256":"7f12fcb6f1529651ec76b3c83f13f22e6fb37576b756fb56b6c2a94bd520b36c","source":{"kind":"arxiv","id":"1205.4136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4136","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4136v1","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4136","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"P4JPZNXRKKLF","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P4JPZNXRKKLFD3DW","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P4JPZNXR","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:P4JPZNXRKKLFD3DWWPED6E7SFZ","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T11:06:11Z","cross_cats_sorted":[],"title_canon_sha256":"e5e71dfad34d4ea6b41f77237c20966d679fe9b2d54fa336d7777083789bc525","abstract_canon_sha256":"ad55e42da101f4107240fe48d1de99582a6cbdaaf7b31ef7bd3a43b7b2ee07bd"},"schema_version":"1.0"},"canonical_sha256":"7f12fcb6f1529651ec76b3c83f13f22e6fb37576b756fb56b6c2a94bd520b36c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:25.711103Z","signature_b64":"gdJuOyOaFOIPpWh5qKgTgvirhxLgsWNc6VCSW9Gd2InUZtVxDdIHN/z721Ywy3DJgTxuwqWlkkxmXQEjkE7eCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f12fcb6f1529651ec76b3c83f13f22e6fb37576b756fb56b6c2a94bd520b36c","last_reissued_at":"2026-05-18T01:57:25.710578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:25.710578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4136","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5BpZwETPTjTidhbeCmjIz59Wx2H7EyhSS2vqn8E0n4L7YkDpY5yWY83KEKwrYV/dNZstokwvwdvo+RagaGBwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:11:11.119866Z"},"content_sha256":"154b2340793190c6dbc718b9a5b08019700117ab180b70eaaf1e2dedcba10ca9","schema_version":"1.0","event_id":"sha256:154b2340793190c6dbc718b9a5b08019700117ab180b70eaaf1e2dedcba10ca9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:P4JPZNXRKKLFD3DWWPED6E7SFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schroedinger current for discontinuous states from the first passage time decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dmitri Sokolovski","submitted_at":"2012-05-18T11:06:11Z","abstract_excerpt":"We revisit the problem of calculating the probability current for discontinuous states, such that may arise in atom trapping or as a result of projective measurements. In the first passage time representation, the problem reduces to evaluation of a localised wave originating from the discontinuity, whose interference with the initial state determines the transfer of probability. Depending on the type of discontinuity, the current behaves as $t^{1/2}$, $t^{3/2}$ or $const(t)$. Our approach generalises earlier work on this subject."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4136","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"edavW6vnWKjQMcdPpa6ZldPS6BWe7ClNMOAXSpjs0SYDNXtoMncS9LE2AwFrlrrzSSlvV/STy8HpTh7DzA8EAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:11:11.120434Z"},"content_sha256":"17911ec2ba5a48303ee291de238052cd0d83f6982ebc90ab403827e53fb97434","schema_version":"1.0","event_id":"sha256:17911ec2ba5a48303ee291de238052cd0d83f6982ebc90ab403827e53fb97434"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4JPZNXRKKLFD3DWWPED6E7SFZ/bundle.json","state_url":"https://pith.science/pith/P4JPZNXRKKLFD3DWWPED6E7SFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4JPZNXRKKLFD3DWWPED6E7SFZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T18:11:11Z","links":{"resolver":"https://pith.science/pith/P4JPZNXRKKLFD3DWWPED6E7SFZ","bundle":"https://pith.science/pith/P4JPZNXRKKLFD3DWWPED6E7SFZ/bundle.json","state":"https://pith.science/pith/P4JPZNXRKKLFD3DWWPED6E7SFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4JPZNXRKKLFD3DWWPED6E7SFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:P4JPZNXRKKLFD3DWWPED6E7SFZ","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":"ad55e42da101f4107240fe48d1de99582a6cbdaaf7b31ef7bd3a43b7b2ee07bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T11:06:11Z","title_canon_sha256":"e5e71dfad34d4ea6b41f77237c20966d679fe9b2d54fa336d7777083789bc525"},"schema_version":"1.0","source":{"id":"1205.4136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4136","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4136v1","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4136","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"P4JPZNXRKKLF","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P4JPZNXRKKLFD3DW","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P4JPZNXR","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:17911ec2ba5a48303ee291de238052cd0d83f6982ebc90ab403827e53fb97434","target":"graph","created_at":"2026-05-18T01:57:25Z","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 revisit the problem of calculating the probability current for discontinuous states, such that may arise in atom trapping or as a result of projective measurements. In the first passage time representation, the problem reduces to evaluation of a localised wave originating from the discontinuity, whose interference with the initial state determines the transfer of probability. Depending on the type of discontinuity, the current behaves as $t^{1/2}$, $t^{3/2}$ or $const(t)$. Our approach generalises earlier work on this subject.","authors_text":"Dmitri Sokolovski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T11:06:11Z","title":"Schroedinger current for discontinuous states from the first passage time decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4136","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":"sha256:154b2340793190c6dbc718b9a5b08019700117ab180b70eaaf1e2dedcba10ca9","target":"record","created_at":"2026-05-18T01:57:25Z","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":"ad55e42da101f4107240fe48d1de99582a6cbdaaf7b31ef7bd3a43b7b2ee07bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T11:06:11Z","title_canon_sha256":"e5e71dfad34d4ea6b41f77237c20966d679fe9b2d54fa336d7777083789bc525"},"schema_version":"1.0","source":{"id":"1205.4136","kind":"arxiv","version":1}},"canonical_sha256":"7f12fcb6f1529651ec76b3c83f13f22e6fb37576b756fb56b6c2a94bd520b36c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f12fcb6f1529651ec76b3c83f13f22e6fb37576b756fb56b6c2a94bd520b36c","first_computed_at":"2026-05-18T01:57:25.710578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:25.710578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gdJuOyOaFOIPpWh5qKgTgvirhxLgsWNc6VCSW9Gd2InUZtVxDdIHN/z721Ywy3DJgTxuwqWlkkxmXQEjkE7eCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:25.711103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:154b2340793190c6dbc718b9a5b08019700117ab180b70eaaf1e2dedcba10ca9","sha256:17911ec2ba5a48303ee291de238052cd0d83f6982ebc90ab403827e53fb97434"],"state_sha256":"ea4e349474cb30774cb45c6aa6869579841764daa8de85656035e7fc750f6109"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Uo5uLC3Ery/zHifimhBQBdhmHLUVMm2c98IfxnXLkYpZSqYCiE327Q3IrbiEBTTGRVB2PZaL5HCsFZAuLtGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:11:11.123073Z","bundle_sha256":"0e48ca82a7bafe76cb3eef21d845b6c6431e2ea936882f1dbcd2771c9a122c70"}}