{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PD4FTNOR4YD5RN25RYG2Y6LAXM","short_pith_number":"pith:PD4FTNOR","canonical_record":{"source":{"id":"1002.3051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-16T10:53:51Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"54efda5d1c3f9655aaee97aa2f178879f72e2c676b1a77194654515038eef355","abstract_canon_sha256":"3628039240b559af15777c0c9b70446d4387bfc8d17bb21428e5305f4bdfa63b"},"schema_version":"1.0"},"canonical_sha256":"78f859b5d1e607d8b75d8e0dac7960bb0cbcbf9b4b93409352b7c06de9329f65","source":{"kind":"arxiv","id":"1002.3051","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3051","created_at":"2026-05-18T02:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3051v1","created_at":"2026-05-18T02:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3051","created_at":"2026-05-18T02:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"PD4FTNOR4YD5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PD4FTNOR4YD5RN25","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PD4FTNOR","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PD4FTNOR4YD5RN25RYG2Y6LAXM","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-16T10:53:51Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"54efda5d1c3f9655aaee97aa2f178879f72e2c676b1a77194654515038eef355","abstract_canon_sha256":"3628039240b559af15777c0c9b70446d4387bfc8d17bb21428e5305f4bdfa63b"},"schema_version":"1.0"},"canonical_sha256":"78f859b5d1e607d8b75d8e0dac7960bb0cbcbf9b4b93409352b7c06de9329f65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:07.869512Z","signature_b64":"Xoa6t5oea/go0iGwNz/jCa/JsTK3OgljTwHpYNnyr5ROTC0UObXbGXqdFUZxWiRrbG7DmcltO2G3rIW/DwMJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78f859b5d1e607d8b75d8e0dac7960bb0cbcbf9b4b93409352b7c06de9329f65","last_reissued_at":"2026-05-18T02:09:07.866118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:07.866118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3051","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":"2026-05-18T02:09:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kkLrQKVS41XE082eoJ3lF4BY76W0sRiSHnilwtlDQKlKRaK6ZAE4Po32mqKoqKvCjmIgaX36LYafqRvo3ksaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:33:41.952348Z"},"content_sha256":"a62286e7525a99e60f213be4ff930f9da6d074d35571ea527edbdf7b8bf12017","schema_version":"1.0","event_id":"sha256:a62286e7525a99e60f213be4ff930f9da6d074d35571ea527edbdf7b8bf12017"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PD4FTNOR4YD5RN25RYG2Y6LAXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inner products of resonance solutions in 1-D quantum barriers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"F. J. de Urries, J. Julve","submitted_at":"2010-02-16T10:53:51Z","abstract_excerpt":"The properties of a prescription for the inner products of the resonance (Gamow states), scattering (Dirac kets), and bound states for 1-dimensional quantum barriers are worked out. The divergent asypmtotic behaviour of the Gamow states is regularized using a Gaussian convergence factor first introduced by Zel'dovich. With this prescription, most of these states (with discrete complex energies) are found to be orthogonal to each other, to the bound states, and to the Dirac kets, except when they are neighbors, in which case the inner product is divergent. Therefore, as it happens for the conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3051","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":"2026-05-18T02:09:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJRZB8jZ0EFEWlVwkIX8IFtLNj/k0J3d23PYk0aGafGu/no2L4qm2ZgLsG+0U6S1MF0nnmA4P391pQ4/RYSIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:33:41.952702Z"},"content_sha256":"0d5c5747330c46c2171f2631d4f4f70113f93919d4adb8ba235b87656ba55bbd","schema_version":"1.0","event_id":"sha256:0d5c5747330c46c2171f2631d4f4f70113f93919d4adb8ba235b87656ba55bbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PD4FTNOR4YD5RN25RYG2Y6LAXM/bundle.json","state_url":"https://pith.science/pith/PD4FTNOR4YD5RN25RYG2Y6LAXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PD4FTNOR4YD5RN25RYG2Y6LAXM/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":"2026-05-28T08:33:41Z","links":{"resolver":"https://pith.science/pith/PD4FTNOR4YD5RN25RYG2Y6LAXM","bundle":"https://pith.science/pith/PD4FTNOR4YD5RN25RYG2Y6LAXM/bundle.json","state":"https://pith.science/pith/PD4FTNOR4YD5RN25RYG2Y6LAXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PD4FTNOR4YD5RN25RYG2Y6LAXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PD4FTNOR4YD5RN25RYG2Y6LAXM","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":"3628039240b559af15777c0c9b70446d4387bfc8d17bb21428e5305f4bdfa63b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-16T10:53:51Z","title_canon_sha256":"54efda5d1c3f9655aaee97aa2f178879f72e2c676b1a77194654515038eef355"},"schema_version":"1.0","source":{"id":"1002.3051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3051","created_at":"2026-05-18T02:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3051v1","created_at":"2026-05-18T02:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3051","created_at":"2026-05-18T02:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"PD4FTNOR4YD5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PD4FTNOR4YD5RN25","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PD4FTNOR","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:0d5c5747330c46c2171f2631d4f4f70113f93919d4adb8ba235b87656ba55bbd","target":"graph","created_at":"2026-05-18T02:09:07Z","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 properties of a prescription for the inner products of the resonance (Gamow states), scattering (Dirac kets), and bound states for 1-dimensional quantum barriers are worked out. The divergent asypmtotic behaviour of the Gamow states is regularized using a Gaussian convergence factor first introduced by Zel'dovich. With this prescription, most of these states (with discrete complex energies) are found to be orthogonal to each other, to the bound states, and to the Dirac kets, except when they are neighbors, in which case the inner product is divergent. Therefore, as it happens for the conti","authors_text":"F. J. de Urries, J. Julve","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-16T10:53:51Z","title":"Inner products of resonance solutions in 1-D quantum barriers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3051","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:a62286e7525a99e60f213be4ff930f9da6d074d35571ea527edbdf7b8bf12017","target":"record","created_at":"2026-05-18T02:09:07Z","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":"3628039240b559af15777c0c9b70446d4387bfc8d17bb21428e5305f4bdfa63b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-16T10:53:51Z","title_canon_sha256":"54efda5d1c3f9655aaee97aa2f178879f72e2c676b1a77194654515038eef355"},"schema_version":"1.0","source":{"id":"1002.3051","kind":"arxiv","version":1}},"canonical_sha256":"78f859b5d1e607d8b75d8e0dac7960bb0cbcbf9b4b93409352b7c06de9329f65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78f859b5d1e607d8b75d8e0dac7960bb0cbcbf9b4b93409352b7c06de9329f65","first_computed_at":"2026-05-18T02:09:07.866118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:07.866118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xoa6t5oea/go0iGwNz/jCa/JsTK3OgljTwHpYNnyr5ROTC0UObXbGXqdFUZxWiRrbG7DmcltO2G3rIW/DwMJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:07.869512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a62286e7525a99e60f213be4ff930f9da6d074d35571ea527edbdf7b8bf12017","sha256:0d5c5747330c46c2171f2631d4f4f70113f93919d4adb8ba235b87656ba55bbd"],"state_sha256":"34797cc4b332a9f6363693df7ae0e64aeca532d7cb6459865108941cda171bc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLiB0+tp1ccrOHPYMOIPfCPicQXvcts/08xbb1BCoeQd/7ABs30OMl0BrScaDT6nHrEGm9DPS7dL/gFl4FHjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:33:41.954708Z","bundle_sha256":"1403416e0add46dd01d92ef390d1390794bf44f85f0b13c0ebf74863a3706efd"}}