{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:G2D2JS5WEBMDNZJBXACQEHNPVY","short_pith_number":"pith:G2D2JS5W","canonical_record":{"source":{"id":"1610.05524","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-18T10:27:02Z","cross_cats_sorted":[],"title_canon_sha256":"ace0ca53e69e2615186dbf18bf95c959cb1b49bcb0db08af66f9d7690acaac02","abstract_canon_sha256":"e9b8c99af4ef3cc8fd54bac58bcbb9eaa0b450220f5bf8e453b7fcab3c9d0dd8"},"schema_version":"1.0"},"canonical_sha256":"3687a4cbb6205836e521b805021dafae2a0608a03c662d57fbf600fcf498045f","source":{"kind":"arxiv","id":"1610.05524","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05524","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05524v2","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05524","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"G2D2JS5WEBMD","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G2D2JS5WEBMDNZJB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G2D2JS5W","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:G2D2JS5WEBMDNZJBXACQEHNPVY","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05524","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-18T10:27:02Z","cross_cats_sorted":[],"title_canon_sha256":"ace0ca53e69e2615186dbf18bf95c959cb1b49bcb0db08af66f9d7690acaac02","abstract_canon_sha256":"e9b8c99af4ef3cc8fd54bac58bcbb9eaa0b450220f5bf8e453b7fcab3c9d0dd8"},"schema_version":"1.0"},"canonical_sha256":"3687a4cbb6205836e521b805021dafae2a0608a03c662d57fbf600fcf498045f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:37.265003Z","signature_b64":"qSk6Jr0z81Q30eLPQams/bx+B2aTLqyMKJrrHHCAlzZup7FYWZ168+tjCVL97/wBdqJxFtqNqr6iz5/v8I3nBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3687a4cbb6205836e521b805021dafae2a0608a03c662d57fbf600fcf498045f","last_reissued_at":"2026-05-18T00:57:37.264289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:37.264289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05524","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":"2026-05-18T00:57:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u5W/HhgR5t7ufxbVf/P+eY8+ARLdnTyxHMDlrEyiHtoEynJjmHaOnVQpzV6Ah5rcJ2zFIbmSMADCrzy2G+YVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:45.672363Z"},"content_sha256":"7ea211364b8300a062295643c25ffd9b4128d34792d1770cfe32f7b97f93da45","schema_version":"1.0","event_id":"sha256:7ea211364b8300a062295643c25ffd9b4128d34792d1770cfe32f7b97f93da45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:G2D2JS5WEBMDNZJBXACQEHNPVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Initial boundary value problems for a fractional differential equation with hyper-Bessel operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erkinjon Karimov, Fatma Al-Musalhi, Nasser Al-Salti","submitted_at":"2016-10-18T10:27:02Z","abstract_excerpt":"Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart hyper-Bessel operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansion and results on existence and uniqueness are established. To solve the resultant equations, a solution to a non-homogeneous fractional differential equation with regularized Caputo-like counterpart hyper-Bessel operator is also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05524","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":"2026-05-18T00:57:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hu/PsvgXqT4xSUQkQ2QSYnYvLn1Vpz1EA7ubBxaZACZpU1RDaExl1aSflK+KLy0a0KCMpU/AjTk3JT53LzLQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:45.673007Z"},"content_sha256":"d53f0e099a3ff160dac208520046785bcbba9ed4766b454799b643edd34e9ad1","schema_version":"1.0","event_id":"sha256:d53f0e099a3ff160dac208520046785bcbba9ed4766b454799b643edd34e9ad1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G2D2JS5WEBMDNZJBXACQEHNPVY/bundle.json","state_url":"https://pith.science/pith/G2D2JS5WEBMDNZJBXACQEHNPVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G2D2JS5WEBMDNZJBXACQEHNPVY/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":"2026-06-01T18:39:45Z","links":{"resolver":"https://pith.science/pith/G2D2JS5WEBMDNZJBXACQEHNPVY","bundle":"https://pith.science/pith/G2D2JS5WEBMDNZJBXACQEHNPVY/bundle.json","state":"https://pith.science/pith/G2D2JS5WEBMDNZJBXACQEHNPVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G2D2JS5WEBMDNZJBXACQEHNPVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G2D2JS5WEBMDNZJBXACQEHNPVY","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":"e9b8c99af4ef3cc8fd54bac58bcbb9eaa0b450220f5bf8e453b7fcab3c9d0dd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-18T10:27:02Z","title_canon_sha256":"ace0ca53e69e2615186dbf18bf95c959cb1b49bcb0db08af66f9d7690acaac02"},"schema_version":"1.0","source":{"id":"1610.05524","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05524","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05524v2","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05524","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"G2D2JS5WEBMD","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G2D2JS5WEBMDNZJB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G2D2JS5W","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:d53f0e099a3ff160dac208520046785bcbba9ed4766b454799b643edd34e9ad1","target":"graph","created_at":"2026-05-18T00:57:37Z","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":"Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart hyper-Bessel operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansion and results on existence and uniqueness are established. To solve the resultant equations, a solution to a non-homogeneous fractional differential equation with regularized Caputo-like counterpart hyper-Bessel operator is also presented.","authors_text":"Erkinjon Karimov, Fatma Al-Musalhi, Nasser Al-Salti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-18T10:27:02Z","title":"Initial boundary value problems for a fractional differential equation with hyper-Bessel operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05524","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":"sha256:7ea211364b8300a062295643c25ffd9b4128d34792d1770cfe32f7b97f93da45","target":"record","created_at":"2026-05-18T00:57:37Z","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":"e9b8c99af4ef3cc8fd54bac58bcbb9eaa0b450220f5bf8e453b7fcab3c9d0dd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-18T10:27:02Z","title_canon_sha256":"ace0ca53e69e2615186dbf18bf95c959cb1b49bcb0db08af66f9d7690acaac02"},"schema_version":"1.0","source":{"id":"1610.05524","kind":"arxiv","version":2}},"canonical_sha256":"3687a4cbb6205836e521b805021dafae2a0608a03c662d57fbf600fcf498045f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3687a4cbb6205836e521b805021dafae2a0608a03c662d57fbf600fcf498045f","first_computed_at":"2026-05-18T00:57:37.264289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:37.264289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qSk6Jr0z81Q30eLPQams/bx+B2aTLqyMKJrrHHCAlzZup7FYWZ168+tjCVL97/wBdqJxFtqNqr6iz5/v8I3nBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:37.265003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05524","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ea211364b8300a062295643c25ffd9b4128d34792d1770cfe32f7b97f93da45","sha256:d53f0e099a3ff160dac208520046785bcbba9ed4766b454799b643edd34e9ad1"],"state_sha256":"9742bac4588e5faf002cc798e7d248bf0d55d81cc6a1711a76fb63f8382aa50a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CN1aLIQ0CvQ733pUC1hDTxOj8CHm38Pb+4VtH0j1TH0MJCAlqK3H8YknqnrDPA1Cx1oikKIKO42jABtUMGuTBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:39:45.676432Z","bundle_sha256":"54f5e5d82e78ac1d1db6d3ade3afb07e2e1f537bce9207309bc3d33ff724e838"}}