{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5QQGOGSIUI5U5JGSK4VXOIRYTD","short_pith_number":"pith:5QQGOGSI","canonical_record":{"source":{"id":"1509.08525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-28T22:28:12Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"fbc5606e75b414b302fbf6a5d9404fae05afd6de42d2b3ddbe46eae0034c8aa6","abstract_canon_sha256":"1a50391e76396f95770682f7c744096567d4a57fb81042ce42a2e40df23613dd"},"schema_version":"1.0"},"canonical_sha256":"ec20671a48a23b4ea4d2572b77223898e217f668ce055959562e06f8b6baa85a","source":{"kind":"arxiv","id":"1509.08525","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08525","created_at":"2026-05-18T01:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08525v1","created_at":"2026-05-18T01:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08525","created_at":"2026-05-18T01:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"5QQGOGSIUI5U","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5QQGOGSIUI5U5JGS","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5QQGOGSI","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5QQGOGSIUI5U5JGSK4VXOIRYTD","target":"record","payload":{"canonical_record":{"source":{"id":"1509.08525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-28T22:28:12Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"fbc5606e75b414b302fbf6a5d9404fae05afd6de42d2b3ddbe46eae0034c8aa6","abstract_canon_sha256":"1a50391e76396f95770682f7c744096567d4a57fb81042ce42a2e40df23613dd"},"schema_version":"1.0"},"canonical_sha256":"ec20671a48a23b4ea4d2572b77223898e217f668ce055959562e06f8b6baa85a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:52.442758Z","signature_b64":"PFo+nCz2V59IO2CCXSx033zGw3CiH7nSeSN3xvg4kjD1pi7i1pESp+sv12yLTmNbphakeRSFDiEDAHpeg0J3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec20671a48a23b4ea4d2572b77223898e217f668ce055959562e06f8b6baa85a","last_reissued_at":"2026-05-18T01:31:52.442334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:52.442334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.08525","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":"2026-05-18T01:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gq/HGsI2KhwyGX7ZhTtFaqDPSbq+Np8r1vh7NdXNpLxZ/vde/pqaQ14Q9kEpYhCjYtoX5IlNrlkTPX2QVxv8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:03:06.961579Z"},"content_sha256":"424196eb700b047e247f4ee5fb52c55b37706bf331a17e728f158bbfb4a252b3","schema_version":"1.0","event_id":"sha256:424196eb700b047e247f4ee5fb52c55b37706bf331a17e728f158bbfb4a252b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5QQGOGSIUI5U5JGSK4VXOIRYTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reflection probabilities of one-dimensional Schroedinger operators and scattering theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Annalisa Panati, Benjamin Landon, Jane Panangaden, Justine Zwicker","submitted_at":"2015-09-28T22:28:12Z","abstract_excerpt":"The dynamic reflection probability and the spectral reflection probability for a one-dimensional Schroedinger operator $H = - \\Delta + V$ are characterized in terms of the scattering theory of the pair $(H, H_\\infty)$ where $H_\\infty$ is the operator obtained by decoupling the left and right half-lines $\\mathbb{R}_{\\leq 0}$ and $\\mathbb{R}_{\\geq 0}$. An immediate consequence is that these reflection probabilities are in fact the same, thus providing a short and transparent proof of the main result of Breuer, J., E. Ryckman, and B. Simon (2010) . This approach is inspired by recent developments"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08525","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":"2026-05-18T01:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j0U6ZHl7HqtyqMVgPuTiHMvUQ1t5lw/K9GSbOoFo48Uf/YQrC+MZPE+rc0kH/0RJgx9BVKmK4nZE3tAmzJx+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:03:06.962106Z"},"content_sha256":"dd304e85e03d05ab8279e56500c85201785367832debd90166db7db55e45228a","schema_version":"1.0","event_id":"sha256:dd304e85e03d05ab8279e56500c85201785367832debd90166db7db55e45228a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5QQGOGSIUI5U5JGSK4VXOIRYTD/bundle.json","state_url":"https://pith.science/pith/5QQGOGSIUI5U5JGSK4VXOIRYTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5QQGOGSIUI5U5JGSK4VXOIRYTD/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":"2026-06-06T19:03:06Z","links":{"resolver":"https://pith.science/pith/5QQGOGSIUI5U5JGSK4VXOIRYTD","bundle":"https://pith.science/pith/5QQGOGSIUI5U5JGSK4VXOIRYTD/bundle.json","state":"https://pith.science/pith/5QQGOGSIUI5U5JGSK4VXOIRYTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5QQGOGSIUI5U5JGSK4VXOIRYTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5QQGOGSIUI5U5JGSK4VXOIRYTD","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":"1a50391e76396f95770682f7c744096567d4a57fb81042ce42a2e40df23613dd","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-28T22:28:12Z","title_canon_sha256":"fbc5606e75b414b302fbf6a5d9404fae05afd6de42d2b3ddbe46eae0034c8aa6"},"schema_version":"1.0","source":{"id":"1509.08525","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08525","created_at":"2026-05-18T01:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08525v1","created_at":"2026-05-18T01:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08525","created_at":"2026-05-18T01:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"5QQGOGSIUI5U","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5QQGOGSIUI5U5JGS","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5QQGOGSI","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:dd304e85e03d05ab8279e56500c85201785367832debd90166db7db55e45228a","target":"graph","created_at":"2026-05-18T01:31:52Z","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 dynamic reflection probability and the spectral reflection probability for a one-dimensional Schroedinger operator $H = - \\Delta + V$ are characterized in terms of the scattering theory of the pair $(H, H_\\infty)$ where $H_\\infty$ is the operator obtained by decoupling the left and right half-lines $\\mathbb{R}_{\\leq 0}$ and $\\mathbb{R}_{\\geq 0}$. An immediate consequence is that these reflection probabilities are in fact the same, thus providing a short and transparent proof of the main result of Breuer, J., E. Ryckman, and B. Simon (2010) . This approach is inspired by recent developments","authors_text":"Annalisa Panati, Benjamin Landon, Jane Panangaden, Justine Zwicker","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-28T22:28:12Z","title":"Reflection probabilities of one-dimensional Schroedinger operators and scattering theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08525","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":"sha256:424196eb700b047e247f4ee5fb52c55b37706bf331a17e728f158bbfb4a252b3","target":"record","created_at":"2026-05-18T01:31:52Z","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":"1a50391e76396f95770682f7c744096567d4a57fb81042ce42a2e40df23613dd","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-28T22:28:12Z","title_canon_sha256":"fbc5606e75b414b302fbf6a5d9404fae05afd6de42d2b3ddbe46eae0034c8aa6"},"schema_version":"1.0","source":{"id":"1509.08525","kind":"arxiv","version":1}},"canonical_sha256":"ec20671a48a23b4ea4d2572b77223898e217f668ce055959562e06f8b6baa85a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec20671a48a23b4ea4d2572b77223898e217f668ce055959562e06f8b6baa85a","first_computed_at":"2026-05-18T01:31:52.442334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:52.442334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PFo+nCz2V59IO2CCXSx033zGw3CiH7nSeSN3xvg4kjD1pi7i1pESp+sv12yLTmNbphakeRSFDiEDAHpeg0J3Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:52.442758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08525","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:424196eb700b047e247f4ee5fb52c55b37706bf331a17e728f158bbfb4a252b3","sha256:dd304e85e03d05ab8279e56500c85201785367832debd90166db7db55e45228a"],"state_sha256":"5e21a8b27c70351e9b1a1bd1bd1cb5b0c234e8e14b95597c398a8dcf1312b3d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JATIEfvGgsrcKf1d5YheQSTdy/B1ATGBi4qwjTxkEKvSBfhLe+bIzxJz+Z/nKgeCCNwws20kZsCE9rFZJpDVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:03:06.965173Z","bundle_sha256":"7e16e6e154fd44dc5f8cb5281bf2315c189a3839d6559e91fd162d60c7cb7e8c"}}