{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6ANKZOJLM3RPQPSZCQDPII4JKR","short_pith_number":"pith:6ANKZOJL","canonical_record":{"source":{"id":"1903.08530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-20T14:51:55Z","cross_cats_sorted":[],"title_canon_sha256":"955b887a3bb7d3760b0e57e9d9e0f083e552f129c8ae802f42cbffbad257b437","abstract_canon_sha256":"bfb6ec7daa909d307d3b06bdf70a8cb21fc1fd31a9e6844da660820f7066281a"},"schema_version":"1.0"},"canonical_sha256":"f01aacb92b66e2f83e591406f4238954775467117b184b7d3743b89095dd6f71","source":{"kind":"arxiv","id":"1903.08530","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.08530","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1903.08530v1","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08530","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"6ANKZOJLM3RP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6ANKZOJLM3RPQPSZ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6ANKZOJL","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6ANKZOJLM3RPQPSZCQDPII4JKR","target":"record","payload":{"canonical_record":{"source":{"id":"1903.08530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-20T14:51:55Z","cross_cats_sorted":[],"title_canon_sha256":"955b887a3bb7d3760b0e57e9d9e0f083e552f129c8ae802f42cbffbad257b437","abstract_canon_sha256":"bfb6ec7daa909d307d3b06bdf70a8cb21fc1fd31a9e6844da660820f7066281a"},"schema_version":"1.0"},"canonical_sha256":"f01aacb92b66e2f83e591406f4238954775467117b184b7d3743b89095dd6f71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:47.846627Z","signature_b64":"Ueq+kL2NLyqFaBNF4BpSwjg2KFqbvPQAHcCcHaDq/FZJ40AxfP8gM9ua3r7/0qRr3mbD3PJGRcSyVrYnfbjJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f01aacb92b66e2f83e591406f4238954775467117b184b7d3743b89095dd6f71","last_reissued_at":"2026-05-17T23:50:47.845956Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:47.845956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.08530","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":"2026-05-17T23:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"00XhU4WpvS1LqqBvLlIMVCGqPidPPzCPhyB9QvhQr/ScK8t0tWFPYUPMKW4KZ1S3QihG/rqddQeQ30ZU/lNfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:16:35.838235Z"},"content_sha256":"79560aaa627d834b45d0f0be9a557a357942e38e3c778a6d73ab788e71607ec7","schema_version":"1.0","event_id":"sha256:79560aaa627d834b45d0f0be9a557a357942e38e3c778a6d73ab788e71607ec7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6ANKZOJLM3RPQPSZCQDPII4JKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic Dirac operator on the half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Dmitrii Mokeev, Evgeny Korotyaev","submitted_at":"2019-03-20T14:51:55Z","abstract_excerpt":"We consider the Dirac operator with a periodic potential on the half-line with the Dirichlet boundary condition at zero. Its spectrum consists of an absolutely continuous part plus at most one eigenvalue in each open gap. The Dirac resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface with a unique simple pole on each open gap: on the first sheet (an eigenvalue) or on the second sheet (a resonance). These poles are called states and there are no other poles. If the potential is shifted by real parameter t, then the continuous spectrum does not change but the states can"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08530","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":"2026-05-17T23:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWnDdvDYt/DjN+Bb62cA/6SnlGhhU30ZHm6uQrBsXhJdifbZCsyj5PQBetncYc6KLtTppcJuFdg/8vtYGUyuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:16:35.839022Z"},"content_sha256":"1f940eaf0669f43bf5519c27320f2a54398127f365cd3c4a6d5d7a2b8838891d","schema_version":"1.0","event_id":"sha256:1f940eaf0669f43bf5519c27320f2a54398127f365cd3c4a6d5d7a2b8838891d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ANKZOJLM3RPQPSZCQDPII4JKR/bundle.json","state_url":"https://pith.science/pith/6ANKZOJLM3RPQPSZCQDPII4JKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ANKZOJLM3RPQPSZCQDPII4JKR/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":"2026-05-31T18:16:35Z","links":{"resolver":"https://pith.science/pith/6ANKZOJLM3RPQPSZCQDPII4JKR","bundle":"https://pith.science/pith/6ANKZOJLM3RPQPSZCQDPII4JKR/bundle.json","state":"https://pith.science/pith/6ANKZOJLM3RPQPSZCQDPII4JKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ANKZOJLM3RPQPSZCQDPII4JKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6ANKZOJLM3RPQPSZCQDPII4JKR","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":"bfb6ec7daa909d307d3b06bdf70a8cb21fc1fd31a9e6844da660820f7066281a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-20T14:51:55Z","title_canon_sha256":"955b887a3bb7d3760b0e57e9d9e0f083e552f129c8ae802f42cbffbad257b437"},"schema_version":"1.0","source":{"id":"1903.08530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.08530","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1903.08530v1","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08530","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"6ANKZOJLM3RP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6ANKZOJLM3RPQPSZ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6ANKZOJL","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:1f940eaf0669f43bf5519c27320f2a54398127f365cd3c4a6d5d7a2b8838891d","target":"graph","created_at":"2026-05-17T23:50:47Z","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 the Dirac operator with a periodic potential on the half-line with the Dirichlet boundary condition at zero. Its spectrum consists of an absolutely continuous part plus at most one eigenvalue in each open gap. The Dirac resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface with a unique simple pole on each open gap: on the first sheet (an eigenvalue) or on the second sheet (a resonance). These poles are called states and there are no other poles. If the potential is shifted by real parameter t, then the continuous spectrum does not change but the states can","authors_text":"Dmitrii Mokeev, Evgeny Korotyaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-20T14:51:55Z","title":"Periodic Dirac operator on the half-line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08530","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":"sha256:79560aaa627d834b45d0f0be9a557a357942e38e3c778a6d73ab788e71607ec7","target":"record","created_at":"2026-05-17T23:50:47Z","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":"bfb6ec7daa909d307d3b06bdf70a8cb21fc1fd31a9e6844da660820f7066281a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-20T14:51:55Z","title_canon_sha256":"955b887a3bb7d3760b0e57e9d9e0f083e552f129c8ae802f42cbffbad257b437"},"schema_version":"1.0","source":{"id":"1903.08530","kind":"arxiv","version":1}},"canonical_sha256":"f01aacb92b66e2f83e591406f4238954775467117b184b7d3743b89095dd6f71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f01aacb92b66e2f83e591406f4238954775467117b184b7d3743b89095dd6f71","first_computed_at":"2026-05-17T23:50:47.845956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:47.845956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ueq+kL2NLyqFaBNF4BpSwjg2KFqbvPQAHcCcHaDq/FZJ40AxfP8gM9ua3r7/0qRr3mbD3PJGRcSyVrYnfbjJAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:47.846627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.08530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79560aaa627d834b45d0f0be9a557a357942e38e3c778a6d73ab788e71607ec7","sha256:1f940eaf0669f43bf5519c27320f2a54398127f365cd3c4a6d5d7a2b8838891d"],"state_sha256":"41c26c0df7a79fc1cfc5c71b16f1467559223598d186391404aa9c16698a83c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3QCOJwKO6z/mUjFUUyZcUAW9SmtRCg1adeUkXwWpDFZB6f+tyYq0JB/ijpzKQF8xM3q/ffHClTOwkpZa8shCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:16:35.843155Z","bundle_sha256":"b065aca7dbb32fe913d11dd384460a5eac843dbb131178f8bf1535ac03fe7b4b"}}