{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7B2TBC3RZ2OHDBYVDYWWCVR53G","short_pith_number":"pith:7B2TBC3R","canonical_record":{"source":{"id":"1206.1168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-06T10:10:26Z","cross_cats_sorted":[],"title_canon_sha256":"77beb6052f5c688037c3ccdd0856568928b2df523133553ebca2e7ba2abf496d","abstract_canon_sha256":"68e34db8dfacdb06db3fcd5f887bcc8a8345874817954b05ea45923045c3af24"},"schema_version":"1.0"},"canonical_sha256":"f875308b71ce9c7187151e2d61563dd9995f06be082a5a036f7485bdf493b01e","source":{"kind":"arxiv","id":"1206.1168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1168","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1168v1","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1168","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"7B2TBC3RZ2OH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7B2TBC3RZ2OHDBYV","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7B2TBC3R","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7B2TBC3RZ2OHDBYVDYWWCVR53G","target":"record","payload":{"canonical_record":{"source":{"id":"1206.1168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-06T10:10:26Z","cross_cats_sorted":[],"title_canon_sha256":"77beb6052f5c688037c3ccdd0856568928b2df523133553ebca2e7ba2abf496d","abstract_canon_sha256":"68e34db8dfacdb06db3fcd5f887bcc8a8345874817954b05ea45923045c3af24"},"schema_version":"1.0"},"canonical_sha256":"f875308b71ce9c7187151e2d61563dd9995f06be082a5a036f7485bdf493b01e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:06.763428Z","signature_b64":"/0Uq07IEbftoNigRIW+ICuVPbuFkoAXBvuNzamlOc3sW3KqpaZ+cJGfVuUoBiLlJM2unaKWVWx5ldvRL2AqEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f875308b71ce9c7187151e2d61563dd9995f06be082a5a036f7485bdf493b01e","last_reissued_at":"2026-05-18T03:54:06.762706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:06.762706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.1168","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":"2026-05-18T03:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ToSV30pW1SLa2HKby4nje3pC8MysitBqyYiG/ZB0f7v5igQBEaYDBA3UZap8TwDOUCpz/9qOGy3do0xgRkW8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:32:59.979391Z"},"content_sha256":"f11dbb8b8f189af56435b194e12dd3b331ef0fb08f01965e37407deaa3dd18d4","schema_version":"1.0","event_id":"sha256:f11dbb8b8f189af56435b194e12dd3b331ef0fb08f01965e37407deaa3dd18d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7B2TBC3RZ2OHDBYVDYWWCVR53G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new Kontorovich-Lebedev-like transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Semyon Yakubovich","submitted_at":"2012-06-06T10:10:26Z","abstract_excerpt":"A different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution operator and inversion formula are established. Solvability conditions and explicit solutions of the corresponding class of convolution integral equations are exhibited."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1168","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":"2026-05-18T03:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kgNTf6PYc/IbzRh6lNi9ndpx4SxVMZ+cQBvkIZiHI9AHsurHyHfvFSh1NU+Exn8D3Veh4GeIK8rQBo7mNaMDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:32:59.979731Z"},"content_sha256":"cf7df9dbbe7b734827bc51c7b96f73b390d1d4c9ca53425d368a42f66dfaeee2","schema_version":"1.0","event_id":"sha256:cf7df9dbbe7b734827bc51c7b96f73b390d1d4c9ca53425d368a42f66dfaeee2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7B2TBC3RZ2OHDBYVDYWWCVR53G/bundle.json","state_url":"https://pith.science/pith/7B2TBC3RZ2OHDBYVDYWWCVR53G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7B2TBC3RZ2OHDBYVDYWWCVR53G/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":"2026-06-26T09:32:59Z","links":{"resolver":"https://pith.science/pith/7B2TBC3RZ2OHDBYVDYWWCVR53G","bundle":"https://pith.science/pith/7B2TBC3RZ2OHDBYVDYWWCVR53G/bundle.json","state":"https://pith.science/pith/7B2TBC3RZ2OHDBYVDYWWCVR53G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7B2TBC3RZ2OHDBYVDYWWCVR53G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7B2TBC3RZ2OHDBYVDYWWCVR53G","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":"68e34db8dfacdb06db3fcd5f887bcc8a8345874817954b05ea45923045c3af24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-06T10:10:26Z","title_canon_sha256":"77beb6052f5c688037c3ccdd0856568928b2df523133553ebca2e7ba2abf496d"},"schema_version":"1.0","source":{"id":"1206.1168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1168","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1168v1","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1168","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"7B2TBC3RZ2OH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7B2TBC3RZ2OHDBYV","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7B2TBC3R","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:cf7df9dbbe7b734827bc51c7b96f73b390d1d4c9ca53425d368a42f66dfaeee2","target":"graph","created_at":"2026-05-18T03:54:06Z","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 different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution operator and inversion formula are established. Solvability conditions and explicit solutions of the corresponding class of convolution integral equations are exhibited.","authors_text":"Semyon Yakubovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-06T10:10:26Z","title":"A new Kontorovich-Lebedev-like transformation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1168","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:f11dbb8b8f189af56435b194e12dd3b331ef0fb08f01965e37407deaa3dd18d4","target":"record","created_at":"2026-05-18T03:54:06Z","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":"68e34db8dfacdb06db3fcd5f887bcc8a8345874817954b05ea45923045c3af24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-06T10:10:26Z","title_canon_sha256":"77beb6052f5c688037c3ccdd0856568928b2df523133553ebca2e7ba2abf496d"},"schema_version":"1.0","source":{"id":"1206.1168","kind":"arxiv","version":1}},"canonical_sha256":"f875308b71ce9c7187151e2d61563dd9995f06be082a5a036f7485bdf493b01e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f875308b71ce9c7187151e2d61563dd9995f06be082a5a036f7485bdf493b01e","first_computed_at":"2026-05-18T03:54:06.762706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:06.762706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/0Uq07IEbftoNigRIW+ICuVPbuFkoAXBvuNzamlOc3sW3KqpaZ+cJGfVuUoBiLlJM2unaKWVWx5ldvRL2AqEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:06.763428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f11dbb8b8f189af56435b194e12dd3b331ef0fb08f01965e37407deaa3dd18d4","sha256:cf7df9dbbe7b734827bc51c7b96f73b390d1d4c9ca53425d368a42f66dfaeee2"],"state_sha256":"0895cf8e2923979451a71b9ab431888f632bc96cad701a7a4272e218e2b50ae9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4UboUHdjoKdc4i4XJrl1t5sCXOUcmb7KAk31CzLSdKFLqUxfquj9xvtAv41ghPjymxq1cM9a/eGKTss1HoU6BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:32:59.981527Z","bundle_sha256":"96dda9a50ece5a296500e0a7a1a2e7c65cb0a3aacf6b664fcbb6717525bfa875"}}