{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:WDEMWGN5GAN44DKDG43ZQNZ3EF","short_pith_number":"pith:WDEMWGN5","canonical_record":{"source":{"id":"1908.07158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-20T04:16:56Z","cross_cats_sorted":[],"title_canon_sha256":"0de102090e2420e92d9fb4307bd428b035060e38656c27eb798c69bd33e8268d","abstract_canon_sha256":"8f1e71b52a0cd1c5717cd285714ec494ffc5e48e6e874f965d226ffe5c39d0ee"},"schema_version":"1.0"},"canonical_sha256":"b0c8cb19bd301bce0d43373798373b216e3a18253a579c5d47836fc5eb017c3d","source":{"kind":"arxiv","id":"1908.07158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07158","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07158v1","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07158","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"WDEMWGN5GAN4","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"pith_short_16","alias_value":"WDEMWGN5GAN44DKD","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"pith_short_8","alias_value":"WDEMWGN5","created_at":"2026-07-04T23:58:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:WDEMWGN5GAN44DKDG43ZQNZ3EF","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-20T04:16:56Z","cross_cats_sorted":[],"title_canon_sha256":"0de102090e2420e92d9fb4307bd428b035060e38656c27eb798c69bd33e8268d","abstract_canon_sha256":"8f1e71b52a0cd1c5717cd285714ec494ffc5e48e6e874f965d226ffe5c39d0ee"},"schema_version":"1.0"},"canonical_sha256":"b0c8cb19bd301bce0d43373798373b216e3a18253a579c5d47836fc5eb017c3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:31.502488Z","signature_b64":"5lCn5Z1S0Lx7MvtulMG5uMRzOP59n+DeARerOeKm+IMqFw2l5kHS4tbkQyJbXE5k5sZpLfL2NIk4uSJqXOgeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0c8cb19bd301bce0d43373798373b216e3a18253a579c5d47836fc5eb017c3d","last_reissued_at":"2026-07-04T23:58:31.502129Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:31.502129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07158","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":"2026-07-04T23:58:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E4uIx4oEI6FDEsr7CCGdWwH+I/xr54DRkqUMhpF2O++3GEvJKu9Ze2XXWUvxDtP/Eh8+bGON13hobcryy07qAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:32:15.223440Z"},"content_sha256":"f342665917bd4725c49b0598f231f5e54ccd48c122df7ec5f1bf070e8960cc2e","schema_version":"1.0","event_id":"sha256:f342665917bd4725c49b0598f231f5e54ccd48c122df7ec5f1bf070e8960cc2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:WDEMWGN5GAN44DKDG43ZQNZ3EF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tuhtasin Ergashev","submitted_at":"2019-08-20T04:16:56Z","abstract_excerpt":"In this paper, we introduce a new class of confluent hypergeometric functions of many variables, study their properties, and determine a system of partial differential equations that this function satisfies. It turns out that all the fundamental solutions of the generalized Helmholtz equation with several singular coefficients are written out through the newly introduced confluent hypergeometric function. Using the expansion formula established here for the confluent function, the order of the singularity of the fundamental solutions of the elliptic equation under this consideration is determi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07158","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07158/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:58:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MCNRV2+ASEofDNIoHM/+bGTrF4ka/tcSFQa6nM01jBbmmZppWFfnJHQ7vpwKjkPEghaXrAi/E5VXIg8ejO1ZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:32:15.224926Z"},"content_sha256":"e5e3af4e4c8f0339df9af8cce575b87db0dbc10751dc79da967ebe7ec29ed97c","schema_version":"1.0","event_id":"sha256:e5e3af4e4c8f0339df9af8cce575b87db0dbc10751dc79da967ebe7ec29ed97c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WDEMWGN5GAN44DKDG43ZQNZ3EF/bundle.json","state_url":"https://pith.science/pith/WDEMWGN5GAN44DKDG43ZQNZ3EF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WDEMWGN5GAN44DKDG43ZQNZ3EF/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":"2026-08-16T10:32:15Z","links":{"resolver":"https://pith.science/pith/WDEMWGN5GAN44DKDG43ZQNZ3EF","bundle":"https://pith.science/pith/WDEMWGN5GAN44DKDG43ZQNZ3EF/bundle.json","state":"https://pith.science/pith/WDEMWGN5GAN44DKDG43ZQNZ3EF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WDEMWGN5GAN44DKDG43ZQNZ3EF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WDEMWGN5GAN44DKDG43ZQNZ3EF","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":"8f1e71b52a0cd1c5717cd285714ec494ffc5e48e6e874f965d226ffe5c39d0ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-20T04:16:56Z","title_canon_sha256":"0de102090e2420e92d9fb4307bd428b035060e38656c27eb798c69bd33e8268d"},"schema_version":"1.0","source":{"id":"1908.07158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07158","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07158v1","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07158","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"WDEMWGN5GAN4","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"pith_short_16","alias_value":"WDEMWGN5GAN44DKD","created_at":"2026-07-04T23:58:31Z"},{"alias_kind":"pith_short_8","alias_value":"WDEMWGN5","created_at":"2026-07-04T23:58:31Z"}],"graph_snapshots":[{"event_id":"sha256:e5e3af4e4c8f0339df9af8cce575b87db0dbc10751dc79da967ebe7ec29ed97c","target":"graph","created_at":"2026-07-04T23:58:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07158/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce a new class of confluent hypergeometric functions of many variables, study their properties, and determine a system of partial differential equations that this function satisfies. It turns out that all the fundamental solutions of the generalized Helmholtz equation with several singular coefficients are written out through the newly introduced confluent hypergeometric function. Using the expansion formula established here for the confluent function, the order of the singularity of the fundamental solutions of the elliptic equation under this consideration is determi","authors_text":"Tuhtasin Ergashev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-20T04:16:56Z","title":"Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07158","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:f342665917bd4725c49b0598f231f5e54ccd48c122df7ec5f1bf070e8960cc2e","target":"record","created_at":"2026-07-04T23:58:31Z","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":"8f1e71b52a0cd1c5717cd285714ec494ffc5e48e6e874f965d226ffe5c39d0ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-20T04:16:56Z","title_canon_sha256":"0de102090e2420e92d9fb4307bd428b035060e38656c27eb798c69bd33e8268d"},"schema_version":"1.0","source":{"id":"1908.07158","kind":"arxiv","version":1}},"canonical_sha256":"b0c8cb19bd301bce0d43373798373b216e3a18253a579c5d47836fc5eb017c3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0c8cb19bd301bce0d43373798373b216e3a18253a579c5d47836fc5eb017c3d","first_computed_at":"2026-07-04T23:58:31.502129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:31.502129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5lCn5Z1S0Lx7MvtulMG5uMRzOP59n+DeARerOeKm+IMqFw2l5kHS4tbkQyJbXE5k5sZpLfL2NIk4uSJqXOgeCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:31.502488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f342665917bd4725c49b0598f231f5e54ccd48c122df7ec5f1bf070e8960cc2e","sha256:e5e3af4e4c8f0339df9af8cce575b87db0dbc10751dc79da967ebe7ec29ed97c"],"state_sha256":"03f2f230b174481f65f1b1a9aeb6690068de6bb5af8c41bdd5fba0553d951006"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t0x60eGQKUqBgkMyLA0bE2/ALe3hy9esCq1Cl2ymBdrBvl/t+jP/icNJkoaaQ+OB4yjrFw29wqxk9EplYbQ0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:32:15.234737Z","bundle_sha256":"52a425c5d0d6c2c1d68451330882fb2c41e7b8d9066ccdfa46b7297a4dc67bcf"}}