{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ACI76FR7LYI6SWR7G7KCNRNGCU","short_pith_number":"pith:ACI76FR7","canonical_record":{"source":{"id":"1308.1980","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-08T21:12:32Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"abd408eabaff8bf4628219aef4b430c6039b2c7de6f544f92b61b79a9820d4a0","abstract_canon_sha256":"fb9519c18f6db5b1433d0b1f397f20fd3e798527b7d6cbe3a12f83e82369742f"},"schema_version":"1.0"},"canonical_sha256":"0091ff163f5e11e95a3f37d426c5a61522f679bee00bd6e5f4ec47cc90d8defd","source":{"kind":"arxiv","id":"1308.1980","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1980","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1980v2","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1980","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"pith_short_12","alias_value":"ACI76FR7LYI6","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ACI76FR7LYI6SWR7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ACI76FR7","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ACI76FR7LYI6SWR7G7KCNRNGCU","target":"record","payload":{"canonical_record":{"source":{"id":"1308.1980","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-08T21:12:32Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"abd408eabaff8bf4628219aef4b430c6039b2c7de6f544f92b61b79a9820d4a0","abstract_canon_sha256":"fb9519c18f6db5b1433d0b1f397f20fd3e798527b7d6cbe3a12f83e82369742f"},"schema_version":"1.0"},"canonical_sha256":"0091ff163f5e11e95a3f37d426c5a61522f679bee00bd6e5f4ec47cc90d8defd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:21.994069Z","signature_b64":"U5J0ln31WR39KMPXZZQd+M01OcxbEKyFodAM/rpnabGBrdcjZ5+0gchoy2bBpluBbCY7vDiB6zwWNG94FSqdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0091ff163f5e11e95a3f37d426c5a61522f679bee00bd6e5f4ec47cc90d8defd","last_reissued_at":"2026-05-18T01:48:21.993571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:21.993571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.1980","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:48:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fqV93TDknWE+NBgVCbV4HCXT3hEEBRWxObLGQeGnuDcJ1HTDbKYm15+Vbbs7SaH9E4AvlHWIsCpo+ml1u6P0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:08:03.490297Z"},"content_sha256":"f7203002deb367a1f7d82237b593e292495c8c9439d9a3224282afb55da1bccb","schema_version":"1.0","event_id":"sha256:f7203002deb367a1f7d82237b593e292495c8c9439d9a3224282afb55da1bccb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ACI76FR7LYI6SWR7G7KCNRNGCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on reflectionless Jacobi matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Annalisa Panati, Benjamin Landon, Vojkan Jaksic","submitted_at":"2013-08-08T21:12:32Z","abstract_excerpt":"The property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl m-functions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a characterization in terms of stationary scattering theory (the vanishing of the reflection coefficients) and prove that this characterization is equivalent to the usual ones. We also show that the new characterization is equivalent to the notion of being dynamically reflectionless, thus providing a short proof of an important result of [Breuer-Ryckman-Simon]. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1980","kind":"arxiv","version":2},"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":"2026-05-18T01:48:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"peckL8h4CJ5LKpNOPsCXLvb7rNBN5WpJyPJjA+wuRtpyCoAqvLyu3gFVU6fVY1WHPQPyn4x9KsKikwvTazNRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:08:03.490685Z"},"content_sha256":"145f4ae6e0fbe74b93911c9450463da7aebec1df311e0973c7fab929ce78a138","schema_version":"1.0","event_id":"sha256:145f4ae6e0fbe74b93911c9450463da7aebec1df311e0973c7fab929ce78a138"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ACI76FR7LYI6SWR7G7KCNRNGCU/bundle.json","state_url":"https://pith.science/pith/ACI76FR7LYI6SWR7G7KCNRNGCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ACI76FR7LYI6SWR7G7KCNRNGCU/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":"2026-05-26T23:08:03Z","links":{"resolver":"https://pith.science/pith/ACI76FR7LYI6SWR7G7KCNRNGCU","bundle":"https://pith.science/pith/ACI76FR7LYI6SWR7G7KCNRNGCU/bundle.json","state":"https://pith.science/pith/ACI76FR7LYI6SWR7G7KCNRNGCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ACI76FR7LYI6SWR7G7KCNRNGCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ACI76FR7LYI6SWR7G7KCNRNGCU","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":"fb9519c18f6db5b1433d0b1f397f20fd3e798527b7d6cbe3a12f83e82369742f","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-08T21:12:32Z","title_canon_sha256":"abd408eabaff8bf4628219aef4b430c6039b2c7de6f544f92b61b79a9820d4a0"},"schema_version":"1.0","source":{"id":"1308.1980","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1980","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1980v2","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1980","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"pith_short_12","alias_value":"ACI76FR7LYI6","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ACI76FR7LYI6SWR7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ACI76FR7","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:145f4ae6e0fbe74b93911c9450463da7aebec1df311e0973c7fab929ce78a138","target":"graph","created_at":"2026-05-18T01:48:21Z","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 property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl m-functions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a characterization in terms of stationary scattering theory (the vanishing of the reflection coefficients) and prove that this characterization is equivalent to the usual ones. We also show that the new characterization is equivalent to the notion of being dynamically reflectionless, thus providing a short proof of an important result of [Breuer-Ryckman-Simon]. The","authors_text":"Annalisa Panati, Benjamin Landon, Vojkan Jaksic","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-08T21:12:32Z","title":"A note on reflectionless Jacobi matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1980","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:f7203002deb367a1f7d82237b593e292495c8c9439d9a3224282afb55da1bccb","target":"record","created_at":"2026-05-18T01:48:21Z","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":"fb9519c18f6db5b1433d0b1f397f20fd3e798527b7d6cbe3a12f83e82369742f","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-08T21:12:32Z","title_canon_sha256":"abd408eabaff8bf4628219aef4b430c6039b2c7de6f544f92b61b79a9820d4a0"},"schema_version":"1.0","source":{"id":"1308.1980","kind":"arxiv","version":2}},"canonical_sha256":"0091ff163f5e11e95a3f37d426c5a61522f679bee00bd6e5f4ec47cc90d8defd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0091ff163f5e11e95a3f37d426c5a61522f679bee00bd6e5f4ec47cc90d8defd","first_computed_at":"2026-05-18T01:48:21.993571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:21.993571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U5J0ln31WR39KMPXZZQd+M01OcxbEKyFodAM/rpnabGBrdcjZ5+0gchoy2bBpluBbCY7vDiB6zwWNG94FSqdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:21.994069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1980","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7203002deb367a1f7d82237b593e292495c8c9439d9a3224282afb55da1bccb","sha256:145f4ae6e0fbe74b93911c9450463da7aebec1df311e0973c7fab929ce78a138"],"state_sha256":"86d5c245c084e6a2b2ae3b676eb8b5cba47024f70bd34f32062819d59a951492"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GI28D1za6aDWgHbaV5Z7ZzGqHYWkSU925qUV+xg4Xp2Dy+h3raQUpD1E8p6JZ0FXf7kiLnk+5OQJQCwi2RWpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:08:03.493341Z","bundle_sha256":"fe21c5e80f0117da49d722ec9d364ab85cc9655f300f95ec06d723af5fab9f92"}}