{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HG7PRVVA7RQCJ2JAFSGBDCJNGJ","short_pith_number":"pith:HG7PRVVA","canonical_record":{"source":{"id":"1608.01459","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SP","submitted_at":"2016-08-04T08:22:23Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"31a9c6df55260e36f13eff7b1ee3969c9b507f89ffc84e2ffb85c6408348245a","abstract_canon_sha256":"65e2e70f35365a7b8f16ddfbbda601dfb32f23011f9117efcc95a180a47e677b"},"schema_version":"1.0"},"canonical_sha256":"39bef8d6a0fc6024e9202c8c11892d326b2a97d7a132356fcbc81e7b81ffc5da","source":{"kind":"arxiv","id":"1608.01459","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01459","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01459v2","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01459","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"HG7PRVVA7RQC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HG7PRVVA7RQCJ2JA","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HG7PRVVA","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HG7PRVVA7RQCJ2JAFSGBDCJNGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01459","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SP","submitted_at":"2016-08-04T08:22:23Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"31a9c6df55260e36f13eff7b1ee3969c9b507f89ffc84e2ffb85c6408348245a","abstract_canon_sha256":"65e2e70f35365a7b8f16ddfbbda601dfb32f23011f9117efcc95a180a47e677b"},"schema_version":"1.0"},"canonical_sha256":"39bef8d6a0fc6024e9202c8c11892d326b2a97d7a132356fcbc81e7b81ffc5da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:09.479409Z","signature_b64":"48eBCzSyQ/8GcZq0GHG644h52nGhRlDiWObE3IS8xTfYbBZtckPEcEwzbjLqvb/rkz9jtAkemLNKrn7jZgi9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39bef8d6a0fc6024e9202c8c11892d326b2a97d7a132356fcbc81e7b81ffc5da","last_reissued_at":"2026-05-18T00:44:09.478897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:09.478897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01459","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Fm1h1VtC0pq3rlz7FhnY0ybj5K1EsWbkXqCNwoZ1ueWsl9aqsvbIjsVWY7oitFKu3EJEnfZBbxUsXQsiYy5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:00:03.546511Z"},"content_sha256":"0d9016250f0c5ddf0097bea3d32a65e488ca7a95b9333e4dd5194df609d5aea3","schema_version":"1.0","event_id":"sha256:0d9016250f0c5ddf0097bea3d32a65e488ca7a95b9333e4dd5194df609d5aea3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HG7PRVVA7RQCJ2JAFSGBDCJNGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the constructive solution of an inverse Sturm-Liouville problem","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.SP","authors_text":"Avetik Pahlevanyan","submitted_at":"2016-08-04T08:22:23Z","abstract_excerpt":"The necessary and sufficient conditions are found for the two sequences $\\left\\{\\mu_n \\right\\}_{n=0}^{\\infty}$ and $\\left\\{a_n \\right\\}_{n=0}^{\\infty}$ to be the spectrum and the norming constants respectively, for a boundary value problem $-y'' + q \\left( x \\right) y = \\mu y,$ $y \\left(0\\right)=0,$ $y\\left( \\pi \\right)\\cos \\beta + y'\\left( \\pi \\right)\\sin \\beta = 0,$ $\\beta \\in \\left( 0, \\pi \\right),$ with $q \\in L_{\\mathbb{R}}^1 \\left[0, \\pi \\right].$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01459","kind":"arxiv","version":2},"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":"2026-05-18T00:44:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Ib/ARyCU6yiKWSxopiExoq1qjKUbpt0OJA+cRBKi6bnh1ZbDUyyP0pEVW/JF8DmlH0JYaASHxpZbJdVDp01Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:00:03.546878Z"},"content_sha256":"2bae4ce1516f3ff2b2d11d75de96524f81281c19d39fddb83392d6b804646faa","schema_version":"1.0","event_id":"sha256:2bae4ce1516f3ff2b2d11d75de96524f81281c19d39fddb83392d6b804646faa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HG7PRVVA7RQCJ2JAFSGBDCJNGJ/bundle.json","state_url":"https://pith.science/pith/HG7PRVVA7RQCJ2JAFSGBDCJNGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HG7PRVVA7RQCJ2JAFSGBDCJNGJ/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":"2026-07-01T23:00:03Z","links":{"resolver":"https://pith.science/pith/HG7PRVVA7RQCJ2JAFSGBDCJNGJ","bundle":"https://pith.science/pith/HG7PRVVA7RQCJ2JAFSGBDCJNGJ/bundle.json","state":"https://pith.science/pith/HG7PRVVA7RQCJ2JAFSGBDCJNGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HG7PRVVA7RQCJ2JAFSGBDCJNGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HG7PRVVA7RQCJ2JAFSGBDCJNGJ","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":"65e2e70f35365a7b8f16ddfbbda601dfb32f23011f9117efcc95a180a47e677b","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SP","submitted_at":"2016-08-04T08:22:23Z","title_canon_sha256":"31a9c6df55260e36f13eff7b1ee3969c9b507f89ffc84e2ffb85c6408348245a"},"schema_version":"1.0","source":{"id":"1608.01459","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01459","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01459v2","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01459","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"HG7PRVVA7RQC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HG7PRVVA7RQCJ2JA","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HG7PRVVA","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:2bae4ce1516f3ff2b2d11d75de96524f81281c19d39fddb83392d6b804646faa","target":"graph","created_at":"2026-05-18T00:44:09Z","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":"The necessary and sufficient conditions are found for the two sequences $\\left\\{\\mu_n \\right\\}_{n=0}^{\\infty}$ and $\\left\\{a_n \\right\\}_{n=0}^{\\infty}$ to be the spectrum and the norming constants respectively, for a boundary value problem $-y'' + q \\left( x \\right) y = \\mu y,$ $y \\left(0\\right)=0,$ $y\\left( \\pi \\right)\\cos \\beta + y'\\left( \\pi \\right)\\sin \\beta = 0,$ $\\beta \\in \\left( 0, \\pi \\right),$ with $q \\in L_{\\mathbb{R}}^1 \\left[0, \\pi \\right].$","authors_text":"Avetik Pahlevanyan","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SP","submitted_at":"2016-08-04T08:22:23Z","title":"On the constructive solution of an inverse Sturm-Liouville problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01459","kind":"arxiv","version":2},"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":"sha256:0d9016250f0c5ddf0097bea3d32a65e488ca7a95b9333e4dd5194df609d5aea3","target":"record","created_at":"2026-05-18T00:44:09Z","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":"65e2e70f35365a7b8f16ddfbbda601dfb32f23011f9117efcc95a180a47e677b","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SP","submitted_at":"2016-08-04T08:22:23Z","title_canon_sha256":"31a9c6df55260e36f13eff7b1ee3969c9b507f89ffc84e2ffb85c6408348245a"},"schema_version":"1.0","source":{"id":"1608.01459","kind":"arxiv","version":2}},"canonical_sha256":"39bef8d6a0fc6024e9202c8c11892d326b2a97d7a132356fcbc81e7b81ffc5da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39bef8d6a0fc6024e9202c8c11892d326b2a97d7a132356fcbc81e7b81ffc5da","first_computed_at":"2026-05-18T00:44:09.478897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:09.478897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"48eBCzSyQ/8GcZq0GHG644h52nGhRlDiWObE3IS8xTfYbBZtckPEcEwzbjLqvb/rkz9jtAkemLNKrn7jZgi9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:09.479409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01459","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d9016250f0c5ddf0097bea3d32a65e488ca7a95b9333e4dd5194df609d5aea3","sha256:2bae4ce1516f3ff2b2d11d75de96524f81281c19d39fddb83392d6b804646faa"],"state_sha256":"abf3d67379ca610752977510ef2446d40209c2c78111a95dccdd724a79dfb0d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZX58dIuhC+rS1+PIzTkKgtbODb2LuyXtgNCja8AGKT3pZoF8IgWqNdZ43KiBGvpgRik6C29JwFZaQojQBS8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T23:00:03.549302Z","bundle_sha256":"fa7053e68f679ce7d7e43b7e1d786986699ab439ed9fbc35e101a5d44ffc6e54"}}