{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5S5V2L2RZS6B2ADHTA6T3A7SCV","short_pith_number":"pith:5S5V2L2R","canonical_record":{"source":{"id":"1110.0258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-03T03:25:54Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"eae740e8d513766afb2378ede7ef03a415fcf5cc236cdd59dfec34b71cb17d5d","abstract_canon_sha256":"d736320315c11fd2497aff24d7814483007507b9f05725a0cea18608d1d61465"},"schema_version":"1.0"},"canonical_sha256":"ecbb5d2f51ccbc1d0067983d3d83f215768801419080dbdc8f79a9828815deb5","source":{"kind":"arxiv","id":"1110.0258","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0258","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0258v2","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0258","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"5S5V2L2RZS6B","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5S5V2L2RZS6B2ADH","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5S5V2L2R","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5S5V2L2RZS6B2ADHTA6T3A7SCV","target":"record","payload":{"canonical_record":{"source":{"id":"1110.0258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-03T03:25:54Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"eae740e8d513766afb2378ede7ef03a415fcf5cc236cdd59dfec34b71cb17d5d","abstract_canon_sha256":"d736320315c11fd2497aff24d7814483007507b9f05725a0cea18608d1d61465"},"schema_version":"1.0"},"canonical_sha256":"ecbb5d2f51ccbc1d0067983d3d83f215768801419080dbdc8f79a9828815deb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:26.975115Z","signature_b64":"yf17hxKUsDMmKOoROTkPrmw4KQ0Dh6lYn/Iq9BECWWlWwyiDmapi9z+qM9jqmJm2ee1dRP6G8v/MFpBUX8w3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecbb5d2f51ccbc1d0067983d3d83f215768801419080dbdc8f79a9828815deb5","last_reissued_at":"2026-05-18T04:05:26.974208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:26.974208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.0258","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":"2026-05-18T04:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8d7s068ExoUtbgFdmGQ3zewhUVGeuR6srlOj0BE4Tm0SK3JdvYRsLTwPpubHHZEZ4xGeI0C0wHXVz/uh8V4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:28:29.478851Z"},"content_sha256":"33cf9a4728ea75c6ba47b0475677fa0e126894bf39c7eb61fcb80afb652dc94c","schema_version":"1.0","event_id":"sha256:33cf9a4728ea75c6ba47b0475677fa0e126894bf39c7eb61fcb80afb652dc94c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5S5V2L2RZS6B2ADHTA6T3A7SCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relations between Transfer and Scattering Matrices in the presence of Hyperbolic Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christian Sadel","submitted_at":"2011-10-03T03:25:54Z","abstract_excerpt":"We consider a cable described by a discrete, space-homogeneous, quasi one-dimensional Schr\\\"odinger operator $H_0$. We study the scattering by a finite disordered piece (the scatterer) inserted inside this cable. For energies $E$ where $H_0$ has only elliptic channels we use the Lippmann-Schwinger equations to show that the scattering matrix and the transfer matrix, written in an appropriate basis, are related by a certain polar decomposition. For energies $E$ where $H_0$ has hyperbolic channels we show that the scattering matrix is related to a reduced transfer matrix and both are of smaller "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0258","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":"2026-05-18T04:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G/G36fPjfmiSGPvIF79WPZXQ93eY4R0x8tu2rQ4o/f75gJnoIBE5hLf8To7mRYsXbyqsxEaVd1c5Gc1h80bgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:28:29.479186Z"},"content_sha256":"596d6bb689294e94d5928af93208e97c1c65b0302c31043e8095d1c309b427a7","schema_version":"1.0","event_id":"sha256:596d6bb689294e94d5928af93208e97c1c65b0302c31043e8095d1c309b427a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5S5V2L2RZS6B2ADHTA6T3A7SCV/bundle.json","state_url":"https://pith.science/pith/5S5V2L2RZS6B2ADHTA6T3A7SCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5S5V2L2RZS6B2ADHTA6T3A7SCV/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":"2026-06-01T15:28:29Z","links":{"resolver":"https://pith.science/pith/5S5V2L2RZS6B2ADHTA6T3A7SCV","bundle":"https://pith.science/pith/5S5V2L2RZS6B2ADHTA6T3A7SCV/bundle.json","state":"https://pith.science/pith/5S5V2L2RZS6B2ADHTA6T3A7SCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5S5V2L2RZS6B2ADHTA6T3A7SCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5S5V2L2RZS6B2ADHTA6T3A7SCV","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":"d736320315c11fd2497aff24d7814483007507b9f05725a0cea18608d1d61465","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-03T03:25:54Z","title_canon_sha256":"eae740e8d513766afb2378ede7ef03a415fcf5cc236cdd59dfec34b71cb17d5d"},"schema_version":"1.0","source":{"id":"1110.0258","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0258","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0258v2","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0258","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"5S5V2L2RZS6B","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5S5V2L2RZS6B2ADH","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5S5V2L2R","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:596d6bb689294e94d5928af93208e97c1c65b0302c31043e8095d1c309b427a7","target":"graph","created_at":"2026-05-18T04:05:26Z","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 consider a cable described by a discrete, space-homogeneous, quasi one-dimensional Schr\\\"odinger operator $H_0$. We study the scattering by a finite disordered piece (the scatterer) inserted inside this cable. For energies $E$ where $H_0$ has only elliptic channels we use the Lippmann-Schwinger equations to show that the scattering matrix and the transfer matrix, written in an appropriate basis, are related by a certain polar decomposition. For energies $E$ where $H_0$ has hyperbolic channels we show that the scattering matrix is related to a reduced transfer matrix and both are of smaller ","authors_text":"Christian Sadel","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-03T03:25:54Z","title":"Relations between Transfer and Scattering Matrices in the presence of Hyperbolic Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0258","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":"sha256:33cf9a4728ea75c6ba47b0475677fa0e126894bf39c7eb61fcb80afb652dc94c","target":"record","created_at":"2026-05-18T04:05:26Z","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":"d736320315c11fd2497aff24d7814483007507b9f05725a0cea18608d1d61465","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-03T03:25:54Z","title_canon_sha256":"eae740e8d513766afb2378ede7ef03a415fcf5cc236cdd59dfec34b71cb17d5d"},"schema_version":"1.0","source":{"id":"1110.0258","kind":"arxiv","version":2}},"canonical_sha256":"ecbb5d2f51ccbc1d0067983d3d83f215768801419080dbdc8f79a9828815deb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecbb5d2f51ccbc1d0067983d3d83f215768801419080dbdc8f79a9828815deb5","first_computed_at":"2026-05-18T04:05:26.974208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:26.974208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yf17hxKUsDMmKOoROTkPrmw4KQ0Dh6lYn/Iq9BECWWlWwyiDmapi9z+qM9jqmJm2ee1dRP6G8v/MFpBUX8w3BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:26.975115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0258","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33cf9a4728ea75c6ba47b0475677fa0e126894bf39c7eb61fcb80afb652dc94c","sha256:596d6bb689294e94d5928af93208e97c1c65b0302c31043e8095d1c309b427a7"],"state_sha256":"2ae1617f0bc77b6421bc2f1fe4c260a4b8e0a16cf8873476a8e4987f0be1fbe7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCIUonwO0yDgorUVaNjngG2bIz8A0dU+UJg8IF5bY/cmTYxkZkWJazGwvrj/sW5A3OhFjeJryCeO4IBhG/emCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:28:29.481089Z","bundle_sha256":"9e281688c1196aae9237f3f87cba82dd5e69315cdace2ecd6402bb026d592863"}}