{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MNDDH2GT6VCSIW7TVM5ISHO7ZV","short_pith_number":"pith:MNDDH2GT","canonical_record":{"source":{"id":"1302.5735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-22T22:50:13Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ba77a79489e366802dcb1721df2ffaa22dced36c86a27d98d0b6cdbe702bada5","abstract_canon_sha256":"cfb61013c04b50757aa38fcaa2b58480a3c67c1977eb209406365115a56cb41f"},"schema_version":"1.0"},"canonical_sha256":"634633e8d3f545245bf3ab3a891ddfcd6d8ed06e87bde37ddbbd5e702a6232ee","source":{"kind":"arxiv","id":"1302.5735","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5735","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5735v1","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5735","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"pith_short_12","alias_value":"MNDDH2GT6VCS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MNDDH2GT6VCSIW7T","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MNDDH2GT","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MNDDH2GT6VCSIW7TVM5ISHO7ZV","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-22T22:50:13Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ba77a79489e366802dcb1721df2ffaa22dced36c86a27d98d0b6cdbe702bada5","abstract_canon_sha256":"cfb61013c04b50757aa38fcaa2b58480a3c67c1977eb209406365115a56cb41f"},"schema_version":"1.0"},"canonical_sha256":"634633e8d3f545245bf3ab3a891ddfcd6d8ed06e87bde37ddbbd5e702a6232ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:44.065545Z","signature_b64":"rTGiuyPemUdZ4ENmF3YpS+92YpkCf8St/rhjRDO6Z8QE2Ol+/VKt8JbvbGa+nNxpDBIQdsWu+9TJ4a1Oo2oYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"634633e8d3f545245bf3ab3a891ddfcd6d8ed06e87bde37ddbbd5e702a6232ee","last_reissued_at":"2026-05-18T03:32:44.064643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:44.064643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5735","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":"2026-05-18T03:32:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Aecu9F/HfytMxUNVOvBu0g/QM3OCJO935GXVRShODV1sKMGSWO1roF4BVONZKX1MSXKJUJ8K5P/85yy49a1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:24:43.913078Z"},"content_sha256":"773b0ac337fb1242e0b4d16f69dce2e0f0b14520423e3423fe7f6ad5e61c4da0","schema_version":"1.0","event_id":"sha256:773b0ac337fb1242e0b4d16f69dce2e0f0b14520423e3423fe7f6ad5e61c4da0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MNDDH2GT6VCSIW7TVM5ISHO7ZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic and rapid decay rank two self-adjoint commuting differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andrey E. Mironov","submitted_at":"2013-02-22T22:50:13Z","abstract_excerpt":"Self-adjoint rank two commuting ordinary differential operators are studied in this paper. Such operators with trigonometric, elliptic and rapid decay coefficients corresponding to hyperelliptic spectral curves are constructed. Some problems related to the Lame operator and rank two solutions of soliton equations are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5735","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":"2026-05-18T03:32:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4c5ShRXnuHvxHvNKCv3q5hSmISuF5OyG4bRfjN5Hb289KyqR6XTo8jvE70EL6FZTRXiSyFzY8aHuAeew/XtQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:24:43.913427Z"},"content_sha256":"208a3ed7f86bbb9be8d0107e226b48b3cc9d5848e4139692597c07c84c21f678","schema_version":"1.0","event_id":"sha256:208a3ed7f86bbb9be8d0107e226b48b3cc9d5848e4139692597c07c84c21f678"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MNDDH2GT6VCSIW7TVM5ISHO7ZV/bundle.json","state_url":"https://pith.science/pith/MNDDH2GT6VCSIW7TVM5ISHO7ZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MNDDH2GT6VCSIW7TVM5ISHO7ZV/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":"2026-06-24T10:24:43Z","links":{"resolver":"https://pith.science/pith/MNDDH2GT6VCSIW7TVM5ISHO7ZV","bundle":"https://pith.science/pith/MNDDH2GT6VCSIW7TVM5ISHO7ZV/bundle.json","state":"https://pith.science/pith/MNDDH2GT6VCSIW7TVM5ISHO7ZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MNDDH2GT6VCSIW7TVM5ISHO7ZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MNDDH2GT6VCSIW7TVM5ISHO7ZV","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":"cfb61013c04b50757aa38fcaa2b58480a3c67c1977eb209406365115a56cb41f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-22T22:50:13Z","title_canon_sha256":"ba77a79489e366802dcb1721df2ffaa22dced36c86a27d98d0b6cdbe702bada5"},"schema_version":"1.0","source":{"id":"1302.5735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5735","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5735v1","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5735","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"pith_short_12","alias_value":"MNDDH2GT6VCS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MNDDH2GT6VCSIW7T","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MNDDH2GT","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:208a3ed7f86bbb9be8d0107e226b48b3cc9d5848e4139692597c07c84c21f678","target":"graph","created_at":"2026-05-18T03:32:44Z","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":"Self-adjoint rank two commuting ordinary differential operators are studied in this paper. Such operators with trigonometric, elliptic and rapid decay coefficients corresponding to hyperelliptic spectral curves are constructed. Some problems related to the Lame operator and rank two solutions of soliton equations are discussed.","authors_text":"Andrey E. Mironov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-22T22:50:13Z","title":"Periodic and rapid decay rank two self-adjoint commuting differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5735","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":"sha256:773b0ac337fb1242e0b4d16f69dce2e0f0b14520423e3423fe7f6ad5e61c4da0","target":"record","created_at":"2026-05-18T03:32:44Z","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":"cfb61013c04b50757aa38fcaa2b58480a3c67c1977eb209406365115a56cb41f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-22T22:50:13Z","title_canon_sha256":"ba77a79489e366802dcb1721df2ffaa22dced36c86a27d98d0b6cdbe702bada5"},"schema_version":"1.0","source":{"id":"1302.5735","kind":"arxiv","version":1}},"canonical_sha256":"634633e8d3f545245bf3ab3a891ddfcd6d8ed06e87bde37ddbbd5e702a6232ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"634633e8d3f545245bf3ab3a891ddfcd6d8ed06e87bde37ddbbd5e702a6232ee","first_computed_at":"2026-05-18T03:32:44.064643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:44.064643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rTGiuyPemUdZ4ENmF3YpS+92YpkCf8St/rhjRDO6Z8QE2Ol+/VKt8JbvbGa+nNxpDBIQdsWu+9TJ4a1Oo2oYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:44.065545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:773b0ac337fb1242e0b4d16f69dce2e0f0b14520423e3423fe7f6ad5e61c4da0","sha256:208a3ed7f86bbb9be8d0107e226b48b3cc9d5848e4139692597c07c84c21f678"],"state_sha256":"4125f9b8c95e219e5e779bc7d37fb0ea98cf04c25af083180c3b6d2fcc107281"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+v/h5d4NfgWEiUvb5Ztvqcc799nhJrtr68Y7LoyYOOdsEJm4fiJYqvWKb7EMfv7xQsutEpUKlGSbP9m27bNVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:24:43.915216Z","bundle_sha256":"c68e51f63c49d3f1c3bc2701d33e0e6c204d3e2f130ba123578e41e4d7b4df2b"}}