{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VSH5M2UOFUYATVZLWVDTGIP3B5","short_pith_number":"pith:VSH5M2UO","canonical_record":{"source":{"id":"1809.10422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T09:25:28Z","cross_cats_sorted":[],"title_canon_sha256":"751f2aaa03f70d9e3c6fdc3944b475e8d907e60e40fdf0db7302e5080d3cddcb","abstract_canon_sha256":"73886288f6ade55179f4b67f9850a2562baf1d92bd8a8e3ebefc3552ae5915a0"},"schema_version":"1.0"},"canonical_sha256":"ac8fd66a8e2d3009d72bb5473321fb0f51b3f34c8bbfe9085a51ab42f279cdf0","source":{"kind":"arxiv","id":"1809.10422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10422","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10422v1","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10422","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"VSH5M2UOFUYA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VSH5M2UOFUYATVZL","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VSH5M2UO","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VSH5M2UOFUYATVZLWVDTGIP3B5","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T09:25:28Z","cross_cats_sorted":[],"title_canon_sha256":"751f2aaa03f70d9e3c6fdc3944b475e8d907e60e40fdf0db7302e5080d3cddcb","abstract_canon_sha256":"73886288f6ade55179f4b67f9850a2562baf1d92bd8a8e3ebefc3552ae5915a0"},"schema_version":"1.0"},"canonical_sha256":"ac8fd66a8e2d3009d72bb5473321fb0f51b3f34c8bbfe9085a51ab42f279cdf0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:38.386980Z","signature_b64":"DvkjbDRVGk6H2TpxtVsBTtYpQiH94EELtubN7Tj3L2ahEIbmag6TrF92DoyCCTkbWazJCdsQAdp4lNx5w6toAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac8fd66a8e2d3009d72bb5473321fb0f51b3f34c8bbfe9085a51ab42f279cdf0","last_reissued_at":"2026-05-18T00:04:38.386585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:38.386585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10422","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":"2026-05-18T00:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jnqe+vrSToCtWlQQZfafdFHWOCaJwmy1BJsIBSIGeWjPXwndCbP4ahZItluc/JJZhb99dxWMqu23wObYjpcJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:08:13.931483Z"},"content_sha256":"82669471ad19efafbc4dd0ba4ab87c2843104e4c2b29b1a27646ac3327802735","schema_version":"1.0","event_id":"sha256:82669471ad19efafbc4dd0ba4ab87c2843104e4c2b29b1a27646ac3327802735"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VSH5M2UOFUYATVZLWVDTGIP3B5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multidomain spectral method for the Gauss hypergeometric function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"C. Klein, C. Vall\\'ee, M. Fasondini, N. Stoilov, S. Crespo","submitted_at":"2018-09-27T09:25:28Z","abstract_excerpt":"We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius' method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10422","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":"2026-05-18T00:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KhX+FRWLNIDCwSKs4nkf1QpUXtmssaWZNC6V7mnLAjWH0pBmCKTNFvZaYZVRsNo+Fb5GiiVyl2w9+iH74q7jAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:08:13.932130Z"},"content_sha256":"1dd8722f0b63f11274ae3aacf476668d2bc9d565e6836e042856ece2c5f00de3","schema_version":"1.0","event_id":"sha256:1dd8722f0b63f11274ae3aacf476668d2bc9d565e6836e042856ece2c5f00de3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSH5M2UOFUYATVZLWVDTGIP3B5/bundle.json","state_url":"https://pith.science/pith/VSH5M2UOFUYATVZLWVDTGIP3B5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSH5M2UOFUYATVZLWVDTGIP3B5/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":"2026-06-06T20:08:13Z","links":{"resolver":"https://pith.science/pith/VSH5M2UOFUYATVZLWVDTGIP3B5","bundle":"https://pith.science/pith/VSH5M2UOFUYATVZLWVDTGIP3B5/bundle.json","state":"https://pith.science/pith/VSH5M2UOFUYATVZLWVDTGIP3B5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSH5M2UOFUYATVZLWVDTGIP3B5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VSH5M2UOFUYATVZLWVDTGIP3B5","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":"73886288f6ade55179f4b67f9850a2562baf1d92bd8a8e3ebefc3552ae5915a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T09:25:28Z","title_canon_sha256":"751f2aaa03f70d9e3c6fdc3944b475e8d907e60e40fdf0db7302e5080d3cddcb"},"schema_version":"1.0","source":{"id":"1809.10422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10422","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10422v1","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10422","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"VSH5M2UOFUYA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VSH5M2UOFUYATVZL","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VSH5M2UO","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:1dd8722f0b63f11274ae3aacf476668d2bc9d565e6836e042856ece2c5f00de3","target":"graph","created_at":"2026-05-18T00:04:38Z","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":"We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius' method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole com","authors_text":"C. Klein, C. Vall\\'ee, M. Fasondini, N. Stoilov, S. Crespo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T09:25:28Z","title":"Multidomain spectral method for the Gauss hypergeometric function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10422","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":"sha256:82669471ad19efafbc4dd0ba4ab87c2843104e4c2b29b1a27646ac3327802735","target":"record","created_at":"2026-05-18T00:04:38Z","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":"73886288f6ade55179f4b67f9850a2562baf1d92bd8a8e3ebefc3552ae5915a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T09:25:28Z","title_canon_sha256":"751f2aaa03f70d9e3c6fdc3944b475e8d907e60e40fdf0db7302e5080d3cddcb"},"schema_version":"1.0","source":{"id":"1809.10422","kind":"arxiv","version":1}},"canonical_sha256":"ac8fd66a8e2d3009d72bb5473321fb0f51b3f34c8bbfe9085a51ab42f279cdf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac8fd66a8e2d3009d72bb5473321fb0f51b3f34c8bbfe9085a51ab42f279cdf0","first_computed_at":"2026-05-18T00:04:38.386585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:38.386585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DvkjbDRVGk6H2TpxtVsBTtYpQiH94EELtubN7Tj3L2ahEIbmag6TrF92DoyCCTkbWazJCdsQAdp4lNx5w6toAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:38.386980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82669471ad19efafbc4dd0ba4ab87c2843104e4c2b29b1a27646ac3327802735","sha256:1dd8722f0b63f11274ae3aacf476668d2bc9d565e6836e042856ece2c5f00de3"],"state_sha256":"95e878c8272c2851fac41cc4c649a689c336e9e881560dae2b32a7645d31f4e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ntj3sTt0VNqqeM2mXOp0FJ7oOPSFDEtZ4Mkt4HxNGLa6xkek84F4hW6qWkHgFMaSyfkcyod4cbtcPMxWoCDBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:08:13.935429Z","bundle_sha256":"0d69a031ad68187c45b332b864b506adea813ab165ace05e1c7277dc139a9d18"}}