{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3ST7FKJ7HEIMBYSZYQC6HJKQ3U","short_pith_number":"pith:3ST7FKJ7","canonical_record":{"source":{"id":"1208.6166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-30T13:21:11Z","cross_cats_sorted":["math-ph","math.CA","math.CV","math.MP"],"title_canon_sha256":"aaa7e89be494cdb34ff193c3d9d6c293354689f3d05af1ab3bd7863776d006d6","abstract_canon_sha256":"1ed76fb0edb7365d6376a211f4f2f95e66243ba94be90937ec81aad96701b78a"},"schema_version":"1.0"},"canonical_sha256":"dca7f2a93f3910c0e259c405e3a550dd338c75a6f902bc9dadde0724eabc52da","source":{"kind":"arxiv","id":"1208.6166","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6166","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6166v2","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6166","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"3ST7FKJ7HEIM","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3ST7FKJ7HEIMBYSZ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3ST7FKJ7","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3ST7FKJ7HEIMBYSZYQC6HJKQ3U","target":"record","payload":{"canonical_record":{"source":{"id":"1208.6166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-30T13:21:11Z","cross_cats_sorted":["math-ph","math.CA","math.CV","math.MP"],"title_canon_sha256":"aaa7e89be494cdb34ff193c3d9d6c293354689f3d05af1ab3bd7863776d006d6","abstract_canon_sha256":"1ed76fb0edb7365d6376a211f4f2f95e66243ba94be90937ec81aad96701b78a"},"schema_version":"1.0"},"canonical_sha256":"dca7f2a93f3910c0e259c405e3a550dd338c75a6f902bc9dadde0724eabc52da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:59.859811Z","signature_b64":"PhIwBP8qv+mPvWAPH2BNPOTDT3GeILd1xKtqLXT2AiwnlYGFVZUeDrxYt+r1+rUOvrfl5O8YLh2QWVKI4UNEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dca7f2a93f3910c0e259c405e3a550dd338c75a6f902bc9dadde0724eabc52da","last_reissued_at":"2026-05-18T02:20:59.859118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:59.859118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.6166","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":"2026-05-18T02:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Q+P7U2VkQI47ln9ptIvD9RcS6xTc1NPzkqUoY0nNXstx7NI4YK7sTqaKvcQJZIghrPPcJf8+bet5tn1jhQwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:14:48.966910Z"},"content_sha256":"18ad0f06e930652094ec517764b1fb6abf083c5a72075f1b9edea919ad0b6ea8","schema_version":"1.0","event_id":"sha256:18ad0f06e930652094ec517764b1fb6abf083c5a72075f1b9edea919ad0b6ea8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3ST7FKJ7HEIMBYSZYQC6HJKQ3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of transmutation operators and hyperbolic pseudoanalytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.CV","math.MP"],"primary_cat":"math.AP","authors_text":"Sergii M. Torba, Vladislav V. Kravchenko","submitted_at":"2012-08-30T13:21:11Z","abstract_excerpt":"A representation for integral kernels of Delsarte transmutation operators is obtained in the form of a functional series with the exact formulas for the terms of the series. It is based on the application of hyperbolic pseudoanalytic function theory and recent results on mapping properties of the transmutation operators.\n  The kernel $K_1$ of the transmutation operator relating $A=-\\frac{d^2}{dx^2}+q_1(x)$ and $B=-\\frac{d^2}{dx^2}$ results to be one of the complex components of a bicomplex-valued hyperbolic pseudoanalytic function satisfying a Vekua-type hyperbolic equation of a special form. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6166","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":"2026-05-18T02:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5YWUpYJAPH7BGqids79FJMNfvtfyjPLqRmCyyuF1Hw+EYbivj2SmQ6OoiNBJZT5q6Hd9w0+aO2oFSpbjBojsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:14:48.967248Z"},"content_sha256":"d4c71e878d9b222ce7e13e3104a03ea705bb7261549594c5f06bb730af00065f","schema_version":"1.0","event_id":"sha256:d4c71e878d9b222ce7e13e3104a03ea705bb7261549594c5f06bb730af00065f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ST7FKJ7HEIMBYSZYQC6HJKQ3U/bundle.json","state_url":"https://pith.science/pith/3ST7FKJ7HEIMBYSZYQC6HJKQ3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ST7FKJ7HEIMBYSZYQC6HJKQ3U/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":"2026-06-27T16:14:48Z","links":{"resolver":"https://pith.science/pith/3ST7FKJ7HEIMBYSZYQC6HJKQ3U","bundle":"https://pith.science/pith/3ST7FKJ7HEIMBYSZYQC6HJKQ3U/bundle.json","state":"https://pith.science/pith/3ST7FKJ7HEIMBYSZYQC6HJKQ3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ST7FKJ7HEIMBYSZYQC6HJKQ3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3ST7FKJ7HEIMBYSZYQC6HJKQ3U","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":"1ed76fb0edb7365d6376a211f4f2f95e66243ba94be90937ec81aad96701b78a","cross_cats_sorted":["math-ph","math.CA","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-30T13:21:11Z","title_canon_sha256":"aaa7e89be494cdb34ff193c3d9d6c293354689f3d05af1ab3bd7863776d006d6"},"schema_version":"1.0","source":{"id":"1208.6166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6166","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6166v2","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6166","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"3ST7FKJ7HEIM","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3ST7FKJ7HEIMBYSZ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3ST7FKJ7","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:d4c71e878d9b222ce7e13e3104a03ea705bb7261549594c5f06bb730af00065f","target":"graph","created_at":"2026-05-18T02:20:59Z","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":"A representation for integral kernels of Delsarte transmutation operators is obtained in the form of a functional series with the exact formulas for the terms of the series. It is based on the application of hyperbolic pseudoanalytic function theory and recent results on mapping properties of the transmutation operators.\n  The kernel $K_1$ of the transmutation operator relating $A=-\\frac{d^2}{dx^2}+q_1(x)$ and $B=-\\frac{d^2}{dx^2}$ results to be one of the complex components of a bicomplex-valued hyperbolic pseudoanalytic function satisfying a Vekua-type hyperbolic equation of a special form. ","authors_text":"Sergii M. Torba, Vladislav V. Kravchenko","cross_cats":["math-ph","math.CA","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-30T13:21:11Z","title":"Construction of transmutation operators and hyperbolic pseudoanalytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6166","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":"sha256:18ad0f06e930652094ec517764b1fb6abf083c5a72075f1b9edea919ad0b6ea8","target":"record","created_at":"2026-05-18T02:20:59Z","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":"1ed76fb0edb7365d6376a211f4f2f95e66243ba94be90937ec81aad96701b78a","cross_cats_sorted":["math-ph","math.CA","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-30T13:21:11Z","title_canon_sha256":"aaa7e89be494cdb34ff193c3d9d6c293354689f3d05af1ab3bd7863776d006d6"},"schema_version":"1.0","source":{"id":"1208.6166","kind":"arxiv","version":2}},"canonical_sha256":"dca7f2a93f3910c0e259c405e3a550dd338c75a6f902bc9dadde0724eabc52da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dca7f2a93f3910c0e259c405e3a550dd338c75a6f902bc9dadde0724eabc52da","first_computed_at":"2026-05-18T02:20:59.859118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:59.859118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PhIwBP8qv+mPvWAPH2BNPOTDT3GeILd1xKtqLXT2AiwnlYGFVZUeDrxYt+r1+rUOvrfl5O8YLh2QWVKI4UNEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:59.859811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18ad0f06e930652094ec517764b1fb6abf083c5a72075f1b9edea919ad0b6ea8","sha256:d4c71e878d9b222ce7e13e3104a03ea705bb7261549594c5f06bb730af00065f"],"state_sha256":"c7ca77cb012528a6b017665fa1ead14e82396c893924c42ad0086937ddb7d07c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+7v9TiKsg76KlOTdIHERlHWEHAzeoP8LM2zwbEJvDxtz2Pbj5pDLrp+uQJCe3uTxos36si3BQOSyy0DV9p7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:14:48.969156Z","bundle_sha256":"fe5becac5f79aa4f051a8be811de3ffbfd721f069587c79f85a5303eecdad663"}}