{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TBMZSWEYZAKKCQPNUXPUHC7LSR","short_pith_number":"pith:TBMZSWEY","canonical_record":{"source":{"id":"1502.08021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-27T19:13:11Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f7e68f6b90494b637a8de9ead851b290b238147f2ddc603cd3cb281511f70eca","abstract_canon_sha256":"b342b6f68b723871fa40bc63667ee433c7ff9533dbe6f0bfc33abc68897b76a3"},"schema_version":"1.0"},"canonical_sha256":"9859995898c814a141eda5df438beb946b4670a623b671c62cff9331a6007ccd","source":{"kind":"arxiv","id":"1502.08021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.08021","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.08021v1","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.08021","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"TBMZSWEYZAKK","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TBMZSWEYZAKKCQPN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TBMZSWEY","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TBMZSWEYZAKKCQPNUXPUHC7LSR","target":"record","payload":{"canonical_record":{"source":{"id":"1502.08021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-27T19:13:11Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f7e68f6b90494b637a8de9ead851b290b238147f2ddc603cd3cb281511f70eca","abstract_canon_sha256":"b342b6f68b723871fa40bc63667ee433c7ff9533dbe6f0bfc33abc68897b76a3"},"schema_version":"1.0"},"canonical_sha256":"9859995898c814a141eda5df438beb946b4670a623b671c62cff9331a6007ccd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:01.567739Z","signature_b64":"Fx1VBn2YTLWpuge0Qwe/Yb9CLB89llPXh3tF2gObtiy66yxHRTtUW9sLa/gv+jRF/eIM7xlKbiu7qYFDM4k1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9859995898c814a141eda5df438beb946b4670a623b671c62cff9331a6007ccd","last_reissued_at":"2026-05-18T02:26:01.567335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:01.567335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.08021","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":"2026-05-18T02:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QEDt1RQ835q0APZRt4xj7R79iLfrJN/A4m6xkvpNBUojSeiBrjtnunVLW1JZcttTxYr8g2UbOe5NvLtCDkuqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:43:50.594039Z"},"content_sha256":"8345ab97058914f5d81d6aa2f2dc5d7bdfefb49ff10b8cb10fdf53837262e9c8","schema_version":"1.0","event_id":"sha256:8345ab97058914f5d81d6aa2f2dc5d7bdfefb49ff10b8cb10fdf53837262e9c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TBMZSWEYZAKKCQPNUXPUHC7LSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E.V. Damaskinsky, V.V. Borzov","submitted_at":"2015-02-27T19:13:11Z","abstract_excerpt":"In this note we investigate the discrete spectrum of Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples we consider a)the case when period $N$ of coefficients of recurrence relations equals three (as a particular case we consider \"parametric\" Chebyshev polynomials introduced by authors early); b)the elementary $N$-symmetrical Chebyshev polynomials ($N=3,4,5$), that was introduced by authors in the study of the \"composite model of generalized oscillator\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.08021","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":"2026-05-18T02:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oBO6LlxDKVnHCRh8ea2SOfIebvy9PARNFHrLYlosgYW+4zkEGZcpkve08g5zV9GRyiAN7p0wgGnHJrU9xvkpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:43:50.594389Z"},"content_sha256":"22026bdbdb9f345332fa4e63d09d99e72b170a997e1c7da9fc078d2f7e10debd","schema_version":"1.0","event_id":"sha256:22026bdbdb9f345332fa4e63d09d99e72b170a997e1c7da9fc078d2f7e10debd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TBMZSWEYZAKKCQPNUXPUHC7LSR/bundle.json","state_url":"https://pith.science/pith/TBMZSWEYZAKKCQPNUXPUHC7LSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TBMZSWEYZAKKCQPNUXPUHC7LSR/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":"2026-06-24T09:43:50Z","links":{"resolver":"https://pith.science/pith/TBMZSWEYZAKKCQPNUXPUHC7LSR","bundle":"https://pith.science/pith/TBMZSWEYZAKKCQPNUXPUHC7LSR/bundle.json","state":"https://pith.science/pith/TBMZSWEYZAKKCQPNUXPUHC7LSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TBMZSWEYZAKKCQPNUXPUHC7LSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TBMZSWEYZAKKCQPNUXPUHC7LSR","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":"b342b6f68b723871fa40bc63667ee433c7ff9533dbe6f0bfc33abc68897b76a3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-27T19:13:11Z","title_canon_sha256":"f7e68f6b90494b637a8de9ead851b290b238147f2ddc603cd3cb281511f70eca"},"schema_version":"1.0","source":{"id":"1502.08021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.08021","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.08021v1","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.08021","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"TBMZSWEYZAKK","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TBMZSWEYZAKKCQPN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TBMZSWEY","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:22026bdbdb9f345332fa4e63d09d99e72b170a997e1c7da9fc078d2f7e10debd","target":"graph","created_at":"2026-05-18T02:26:01Z","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":"In this note we investigate the discrete spectrum of Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples we consider a)the case when period $N$ of coefficients of recurrence relations equals three (as a particular case we consider \"parametric\" Chebyshev polynomials introduced by authors early); b)the elementary $N$-symmetrical Chebyshev polynomials ($N=3,4,5$), that was introduced by authors in the study of the \"composite model of generalized oscillator\".","authors_text":"E.V. Damaskinsky, V.V. Borzov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-27T19:13:11Z","title":"The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.08021","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":"sha256:8345ab97058914f5d81d6aa2f2dc5d7bdfefb49ff10b8cb10fdf53837262e9c8","target":"record","created_at":"2026-05-18T02:26:01Z","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":"b342b6f68b723871fa40bc63667ee433c7ff9533dbe6f0bfc33abc68897b76a3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-27T19:13:11Z","title_canon_sha256":"f7e68f6b90494b637a8de9ead851b290b238147f2ddc603cd3cb281511f70eca"},"schema_version":"1.0","source":{"id":"1502.08021","kind":"arxiv","version":1}},"canonical_sha256":"9859995898c814a141eda5df438beb946b4670a623b671c62cff9331a6007ccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9859995898c814a141eda5df438beb946b4670a623b671c62cff9331a6007ccd","first_computed_at":"2026-05-18T02:26:01.567335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:01.567335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fx1VBn2YTLWpuge0Qwe/Yb9CLB89llPXh3tF2gObtiy66yxHRTtUW9sLa/gv+jRF/eIM7xlKbiu7qYFDM4k1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:01.567739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.08021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8345ab97058914f5d81d6aa2f2dc5d7bdfefb49ff10b8cb10fdf53837262e9c8","sha256:22026bdbdb9f345332fa4e63d09d99e72b170a997e1c7da9fc078d2f7e10debd"],"state_sha256":"53b6632b1317c6cb992fc82ac309905f64b0524cb09eb27668a1ae38a310c488"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oqVyxoN0Y+gwETQjcQw7z5Oj9Xh7XW7Amx/jiRpb16hJk5jcy+EYjMTGGsrE4M8BGcjxafrjZrt2uyoyVOJIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T09:43:50.596221Z","bundle_sha256":"3fd5b02ac20d3e937782e70ed3407c60f33f5f3120ffad98ff6a3350a2d36ba3"}}