{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DR4TEWHAOE3DBD7ZU5EOP6673M","short_pith_number":"pith:DR4TEWHA","canonical_record":{"source":{"id":"1110.3710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-17T15:53:52Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4f4f8643332167e598b13a1d7ab0bb53b383beef705d2c38d9cc5259862142e7","abstract_canon_sha256":"dc6d201fe6156e67909d20b9c8b6d9e1bd29b0fdcd012ff596e2ad3d3bb1a067"},"schema_version":"1.0"},"canonical_sha256":"1c793258e07136308ff9a748e7fbdfdb0649d248550693d4e3cda338364bf881","source":{"kind":"arxiv","id":"1110.3710","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3710","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3710v1","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3710","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"pith_short_12","alias_value":"DR4TEWHAOE3D","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DR4TEWHAOE3DBD7Z","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DR4TEWHA","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DR4TEWHAOE3DBD7ZU5EOP6673M","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-17T15:53:52Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4f4f8643332167e598b13a1d7ab0bb53b383beef705d2c38d9cc5259862142e7","abstract_canon_sha256":"dc6d201fe6156e67909d20b9c8b6d9e1bd29b0fdcd012ff596e2ad3d3bb1a067"},"schema_version":"1.0"},"canonical_sha256":"1c793258e07136308ff9a748e7fbdfdb0649d248550693d4e3cda338364bf881","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:11.490018Z","signature_b64":"F0OsTNY5OUnvTtRl7XWlPcVPJSLRtIyTretlb3ILVszPDAjv7VejhJNYkYwDO0w3AY7NFNC5Qr5zo94hjkIcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c793258e07136308ff9a748e7fbdfdb0649d248550693d4e3cda338364bf881","last_reissued_at":"2026-05-18T02:00:11.489581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:11.489581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3710","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":"2026-05-18T02:00:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wxVpYeqmYoJpqqt7I6DsG1n1c6MeM1EeJ2WJvYAAmn3jHEExPYnnk4Arl+KGalqvpn30G/Y+LyhcU7bzj3M+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:02:31.133325Z"},"content_sha256":"2d01e4789d3f6962a738964d684ce9bd0a4342f84e03646b1c9e0dc197bae826","schema_version":"1.0","event_id":"sha256:2d01e4789d3f6962a738964d684ce9bd0a4342f84e03646b1c9e0dc197bae826"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DR4TEWHAOE3DBD7ZU5EOP6673M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spectral density of the scattering matrix for high energies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski, Daniel Bulger","submitted_at":"2011-10-17T15:53:52Z","abstract_excerpt":"We determine the density of eigenvalues of the scattering matrix of the Schrodinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of the potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3710","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":"2026-05-18T02:00:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2MSTr++r1sZDADOzOr+3BG27V+r7CK3XdL/XTvDAbw5cSdHAzpMyN9wRj/pTs4sqvIXDa5TgyWaCQeGgI+O/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:02:31.133969Z"},"content_sha256":"f0266bf224792782f5b40ff8aa41292f2fc0c587ef53d4c1cb27285b82fb29dd","schema_version":"1.0","event_id":"sha256:f0266bf224792782f5b40ff8aa41292f2fc0c587ef53d4c1cb27285b82fb29dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DR4TEWHAOE3DBD7ZU5EOP6673M/bundle.json","state_url":"https://pith.science/pith/DR4TEWHAOE3DBD7ZU5EOP6673M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DR4TEWHAOE3DBD7ZU5EOP6673M/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":"2026-06-01T20:02:31Z","links":{"resolver":"https://pith.science/pith/DR4TEWHAOE3DBD7ZU5EOP6673M","bundle":"https://pith.science/pith/DR4TEWHAOE3DBD7ZU5EOP6673M/bundle.json","state":"https://pith.science/pith/DR4TEWHAOE3DBD7ZU5EOP6673M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DR4TEWHAOE3DBD7ZU5EOP6673M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DR4TEWHAOE3DBD7ZU5EOP6673M","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":"dc6d201fe6156e67909d20b9c8b6d9e1bd29b0fdcd012ff596e2ad3d3bb1a067","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-17T15:53:52Z","title_canon_sha256":"4f4f8643332167e598b13a1d7ab0bb53b383beef705d2c38d9cc5259862142e7"},"schema_version":"1.0","source":{"id":"1110.3710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3710","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3710v1","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3710","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"pith_short_12","alias_value":"DR4TEWHAOE3D","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DR4TEWHAOE3DBD7Z","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DR4TEWHA","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:f0266bf224792782f5b40ff8aa41292f2fc0c587ef53d4c1cb27285b82fb29dd","target":"graph","created_at":"2026-05-18T02:00:11Z","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 determine the density of eigenvalues of the scattering matrix of the Schrodinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of the potential.","authors_text":"Alexander Pushnitski, Daniel Bulger","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-17T15:53:52Z","title":"The spectral density of the scattering matrix for high energies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3710","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":"sha256:2d01e4789d3f6962a738964d684ce9bd0a4342f84e03646b1c9e0dc197bae826","target":"record","created_at":"2026-05-18T02:00:11Z","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":"dc6d201fe6156e67909d20b9c8b6d9e1bd29b0fdcd012ff596e2ad3d3bb1a067","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-17T15:53:52Z","title_canon_sha256":"4f4f8643332167e598b13a1d7ab0bb53b383beef705d2c38d9cc5259862142e7"},"schema_version":"1.0","source":{"id":"1110.3710","kind":"arxiv","version":1}},"canonical_sha256":"1c793258e07136308ff9a748e7fbdfdb0649d248550693d4e3cda338364bf881","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c793258e07136308ff9a748e7fbdfdb0649d248550693d4e3cda338364bf881","first_computed_at":"2026-05-18T02:00:11.489581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:11.489581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F0OsTNY5OUnvTtRl7XWlPcVPJSLRtIyTretlb3ILVszPDAjv7VejhJNYkYwDO0w3AY7NFNC5Qr5zo94hjkIcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:11.490018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d01e4789d3f6962a738964d684ce9bd0a4342f84e03646b1c9e0dc197bae826","sha256:f0266bf224792782f5b40ff8aa41292f2fc0c587ef53d4c1cb27285b82fb29dd"],"state_sha256":"01371c8a671f0c4b81173f4319f4aa0a683fa67ca189ba2ad0f32d092f557563"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"932FC5E9f+QT0TNdPg9h0PBfGcX8u0rcM33khwgaXv4QPQYWD4XsXuDxr6n9Sdw0LirUBYSQlPDxC1iUqxv7AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:02:31.137018Z","bundle_sha256":"eb55cb28536d7f37a9be144c0ae1ff724a57e023d0674ce2d514fba2c1cf3624"}}