{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:ST2MLLFE5YOHLTGHI3S43GHE22","short_pith_number":"pith:ST2MLLFE","canonical_record":{"source":{"id":"math-ph/0208035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-08-25T17:29:35Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"27f213a5cea319ae7039fe098d271fe3f8edcd967373f0e14165c00f0a868028","abstract_canon_sha256":"a0201bcbd2f767d4d2f9df27e040cd4678c027659105658b4fb2d34becbdd112"},"schema_version":"1.0"},"canonical_sha256":"94f4c5aca4ee1c75ccc746e5cd98e4d6905533a45092ad81937a74e22f42521c","source":{"kind":"arxiv","id":"math-ph/0208035","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0208035","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0208035v1","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0208035","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"ST2MLLFE5YOH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"ST2MLLFE5YOHLTGH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"ST2MLLFE","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:ST2MLLFE5YOHLTGHI3S43GHE22","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0208035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-08-25T17:29:35Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"27f213a5cea319ae7039fe098d271fe3f8edcd967373f0e14165c00f0a868028","abstract_canon_sha256":"a0201bcbd2f767d4d2f9df27e040cd4678c027659105658b4fb2d34becbdd112"},"schema_version":"1.0"},"canonical_sha256":"94f4c5aca4ee1c75ccc746e5cd98e4d6905533a45092ad81937a74e22f42521c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:16.553258Z","signature_b64":"buzTloBetwLZ5zc4NYCYemJgwVhP8whmw1iN57b15Mua+4SRMMrDJ8AKsZgGEFOZIaM+IvAc1kcD4ef5hTaMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94f4c5aca4ee1c75ccc746e5cd98e4d6905533a45092ad81937a74e22f42521c","last_reissued_at":"2026-05-18T02:30:16.552861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:16.552861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0208035","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":"2026-05-18T02:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrL7K86j4SlTVaLGrs3hAeoLPm8eoHzFqSLzLtP0O/awb4d/AaDoTukLz5h4v8MClIrng53ItbWkUKH62TdQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:34:19.247422Z"},"content_sha256":"3005e2cc55cd666aa23ea307bf3b4187709d3cbd8b64bae48ce5b12db872991f","schema_version":"1.0","event_id":"sha256:3005e2cc55cd666aa23ea307bf3b4187709d3cbd8b64bae48ce5b12db872991f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:ST2MLLFE5YOHLTGHI3S43GHE22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bound States and the Szego Condition for Jacobi Matrices and Schrodinger Operators","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Barry Simon (Caltech), David Damanik (Caltech), Dirk Hundertmark (Caltech)","submitted_at":"2002-08-25T17:29:35Z","abstract_excerpt":"For Jacobi matrices with a_n = 1+(-1)^n alpha n^{-gamma}, b_n = (-1)^n beta n^{-gamma}, we study bound states and the SzegHo condition. We provide a new proof of Nevai's result that if gamma > 1/2, the Szego condition holds, which works also if one replaces (-1)^n by cos(mu n). We show that if alpha = 0, beta not equal to 0, and gamma < 1/2, the Szego condition fails. We also show that if gamma = 1, alpha and beta are small enough (beta^2 + 8 alpha^2 < 1/24 will do), then the Jacobi matrix has finitely many bound states (for alpha = 0, beta large, it has infinitely many)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0208035","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":"2026-05-18T02:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q/qfQKpzmcafiCHvFPvdF2xqba7gwwqS1GfZrGYGv2bVs5aUS3T1/puX1oKmKbd1FM0hptZnCkyzEsUvJfl6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:34:19.248035Z"},"content_sha256":"38578c5de1f7e7dccbf7fc2bbdbf79dc823f9ffafd60fe0c9ef1e790a583bfe4","schema_version":"1.0","event_id":"sha256:38578c5de1f7e7dccbf7fc2bbdbf79dc823f9ffafd60fe0c9ef1e790a583bfe4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ST2MLLFE5YOHLTGHI3S43GHE22/bundle.json","state_url":"https://pith.science/pith/ST2MLLFE5YOHLTGHI3S43GHE22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ST2MLLFE5YOHLTGHI3S43GHE22/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":"2026-06-04T06:34:19Z","links":{"resolver":"https://pith.science/pith/ST2MLLFE5YOHLTGHI3S43GHE22","bundle":"https://pith.science/pith/ST2MLLFE5YOHLTGHI3S43GHE22/bundle.json","state":"https://pith.science/pith/ST2MLLFE5YOHLTGHI3S43GHE22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ST2MLLFE5YOHLTGHI3S43GHE22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:ST2MLLFE5YOHLTGHI3S43GHE22","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":"a0201bcbd2f767d4d2f9df27e040cd4678c027659105658b4fb2d34becbdd112","cross_cats_sorted":["math.MP","math.SP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-08-25T17:29:35Z","title_canon_sha256":"27f213a5cea319ae7039fe098d271fe3f8edcd967373f0e14165c00f0a868028"},"schema_version":"1.0","source":{"id":"math-ph/0208035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0208035","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0208035v1","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0208035","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"ST2MLLFE5YOH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"ST2MLLFE5YOHLTGH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"ST2MLLFE","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:38578c5de1f7e7dccbf7fc2bbdbf79dc823f9ffafd60fe0c9ef1e790a583bfe4","target":"graph","created_at":"2026-05-18T02:30:16Z","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":"For Jacobi matrices with a_n = 1+(-1)^n alpha n^{-gamma}, b_n = (-1)^n beta n^{-gamma}, we study bound states and the SzegHo condition. We provide a new proof of Nevai's result that if gamma > 1/2, the Szego condition holds, which works also if one replaces (-1)^n by cos(mu n). We show that if alpha = 0, beta not equal to 0, and gamma < 1/2, the Szego condition fails. We also show that if gamma = 1, alpha and beta are small enough (beta^2 + 8 alpha^2 < 1/24 will do), then the Jacobi matrix has finitely many bound states (for alpha = 0, beta large, it has infinitely many).","authors_text":"Barry Simon (Caltech), David Damanik (Caltech), Dirk Hundertmark (Caltech)","cross_cats":["math.MP","math.SP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-08-25T17:29:35Z","title":"Bound States and the Szego Condition for Jacobi Matrices and Schrodinger Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0208035","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":"sha256:3005e2cc55cd666aa23ea307bf3b4187709d3cbd8b64bae48ce5b12db872991f","target":"record","created_at":"2026-05-18T02:30:16Z","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":"a0201bcbd2f767d4d2f9df27e040cd4678c027659105658b4fb2d34becbdd112","cross_cats_sorted":["math.MP","math.SP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-08-25T17:29:35Z","title_canon_sha256":"27f213a5cea319ae7039fe098d271fe3f8edcd967373f0e14165c00f0a868028"},"schema_version":"1.0","source":{"id":"math-ph/0208035","kind":"arxiv","version":1}},"canonical_sha256":"94f4c5aca4ee1c75ccc746e5cd98e4d6905533a45092ad81937a74e22f42521c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94f4c5aca4ee1c75ccc746e5cd98e4d6905533a45092ad81937a74e22f42521c","first_computed_at":"2026-05-18T02:30:16.552861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:16.552861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"buzTloBetwLZ5zc4NYCYemJgwVhP8whmw1iN57b15Mua+4SRMMrDJ8AKsZgGEFOZIaM+IvAc1kcD4ef5hTaMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:16.553258Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0208035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3005e2cc55cd666aa23ea307bf3b4187709d3cbd8b64bae48ce5b12db872991f","sha256:38578c5de1f7e7dccbf7fc2bbdbf79dc823f9ffafd60fe0c9ef1e790a583bfe4"],"state_sha256":"6c9994e6626c1d37c0c3b763787415e548f4a5414e9397e2d1343cd63b9d3764"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7cbjK+JBlCYV/dSZTrtyX575k6FWGTEfBLQDVQDB1SY0/RsBJPu6RIhqdL9Gjs0q/MxwXzd4FmJiT/fs+P6bAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:34:19.250894Z","bundle_sha256":"55666b6870a3f04799b128def6d63fb6fff6a8571f6742e4e8941491e5baf0d1"}}