{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FH7X6EJGJV5O3MK36VROJ44FNV","short_pith_number":"pith:FH7X6EJG","canonical_record":{"source":{"id":"2605.25176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-24T17:16:47Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4fb7e8baf9eb519cc3a927541e9631cdcfa7a0ba667d823320c78cafee0e7cc0","abstract_canon_sha256":"323c09e8a30925395afe9173b46f0005a8d261e5a8a82c93492ed93d0a1ec4b7"},"schema_version":"1.0"},"canonical_sha256":"29ff7f11264d7aedb15bf562e4f3856d56fca73953e30148bc1c23f2ebe4664a","source":{"kind":"arxiv","id":"2605.25176","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25176","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25176v1","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25176","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"FH7X6EJGJV5O","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"pith_short_16","alias_value":"FH7X6EJGJV5O3MK3","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"pith_short_8","alias_value":"FH7X6EJG","created_at":"2026-05-26T02:04:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FH7X6EJGJV5O3MK36VROJ44FNV","target":"record","payload":{"canonical_record":{"source":{"id":"2605.25176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-24T17:16:47Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4fb7e8baf9eb519cc3a927541e9631cdcfa7a0ba667d823320c78cafee0e7cc0","abstract_canon_sha256":"323c09e8a30925395afe9173b46f0005a8d261e5a8a82c93492ed93d0a1ec4b7"},"schema_version":"1.0"},"canonical_sha256":"29ff7f11264d7aedb15bf562e4f3856d56fca73953e30148bc1c23f2ebe4664a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:21.615818Z","signature_b64":"yozfD9OJkSHlScbKTJnI0twDjvvPUxirUOawFA08l99li/5QYLyu5d6p26l5Hk+EGeRZdSgFNXao0kMIZPZCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29ff7f11264d7aedb15bf562e4f3856d56fca73953e30148bc1c23f2ebe4664a","last_reissued_at":"2026-05-26T02:04:21.614498Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:21.614498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.25176","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":"2026-05-26T02:04:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vUezzlFfDnoWRe2Qa8rvwKoVkrAslQEUzgEN4FSnnuPJuuPInw2bEFAl256D0ZkXM+yZwsnV1HGn+vddMIPhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:49:10.897907Z"},"content_sha256":"722a8b3c5b32f5d3a5c78346dd3d1c1f0bd5bde00f7a7a34694e2fca3ed2c26c","schema_version":"1.0","event_id":"sha256:722a8b3c5b32f5d3a5c78346dd3d1c1f0bd5bde00f7a7a34694e2fca3ed2c26c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FH7X6EJGJV5O3MK36VROJ44FNV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arnoldi-Enhanced Multivariate Hermite Interpolation of Manifold-Valued Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Qiang Niu, Wubin Zhou, Yuxuan Li","submitted_at":"2026-05-24T17:16:47Z","abstract_excerpt":"This paper presents a robust enhancement of the Tangent space Hermite Interpolation (THI) method for manifold-valued data by integrating the multivariate Arnoldi process. To circumvent the inherent numerical instability of multivariate confluent Vandermonde matrices, we use a $G$-Arnoldi-based recurrence to construct a discrete orthogonal polynomial basis directly on the tangent space. The method generates better numerical conditioning for high-order approximations. We analyze the convergence rates for both $C^0$ and $C^1$ errors in the multivariate setting. When only function values are used,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25176","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/2605.25176/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":"2026-05-26T02:04:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R88Q4NdBMVSfQn6xkIQwWJVOdTjk/8YxfH82FYl9/5Qs+dMYexpdbthW6V85qZAgiywQC/r2Do4ePiuWH8NQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:49:10.898260Z"},"content_sha256":"94fd485092bfe75043478e52248562e94f1f101802aa5246061aaef9ece38174","schema_version":"1.0","event_id":"sha256:94fd485092bfe75043478e52248562e94f1f101802aa5246061aaef9ece38174"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FH7X6EJGJV5O3MK36VROJ44FNV/bundle.json","state_url":"https://pith.science/pith/FH7X6EJGJV5O3MK36VROJ44FNV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FH7X6EJGJV5O3MK36VROJ44FNV/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":"2026-06-26T23:49:10Z","links":{"resolver":"https://pith.science/pith/FH7X6EJGJV5O3MK36VROJ44FNV","bundle":"https://pith.science/pith/FH7X6EJGJV5O3MK36VROJ44FNV/bundle.json","state":"https://pith.science/pith/FH7X6EJGJV5O3MK36VROJ44FNV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FH7X6EJGJV5O3MK36VROJ44FNV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FH7X6EJGJV5O3MK36VROJ44FNV","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":"323c09e8a30925395afe9173b46f0005a8d261e5a8a82c93492ed93d0a1ec4b7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-24T17:16:47Z","title_canon_sha256":"4fb7e8baf9eb519cc3a927541e9631cdcfa7a0ba667d823320c78cafee0e7cc0"},"schema_version":"1.0","source":{"id":"2605.25176","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25176","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25176v1","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25176","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"FH7X6EJGJV5O","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"pith_short_16","alias_value":"FH7X6EJGJV5O3MK3","created_at":"2026-05-26T02:04:21Z"},{"alias_kind":"pith_short_8","alias_value":"FH7X6EJG","created_at":"2026-05-26T02:04:21Z"}],"graph_snapshots":[{"event_id":"sha256:94fd485092bfe75043478e52248562e94f1f101802aa5246061aaef9ece38174","target":"graph","created_at":"2026-05-26T02:04:21Z","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/2605.25176/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents a robust enhancement of the Tangent space Hermite Interpolation (THI) method for manifold-valued data by integrating the multivariate Arnoldi process. To circumvent the inherent numerical instability of multivariate confluent Vandermonde matrices, we use a $G$-Arnoldi-based recurrence to construct a discrete orthogonal polynomial basis directly on the tangent space. The method generates better numerical conditioning for high-order approximations. We analyze the convergence rates for both $C^0$ and $C^1$ errors in the multivariate setting. When only function values are used,","authors_text":"Qiang Niu, Wubin Zhou, Yuxuan Li","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-24T17:16:47Z","title":"Arnoldi-Enhanced Multivariate Hermite Interpolation of Manifold-Valued Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25176","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":"sha256:722a8b3c5b32f5d3a5c78346dd3d1c1f0bd5bde00f7a7a34694e2fca3ed2c26c","target":"record","created_at":"2026-05-26T02:04:21Z","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":"323c09e8a30925395afe9173b46f0005a8d261e5a8a82c93492ed93d0a1ec4b7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-24T17:16:47Z","title_canon_sha256":"4fb7e8baf9eb519cc3a927541e9631cdcfa7a0ba667d823320c78cafee0e7cc0"},"schema_version":"1.0","source":{"id":"2605.25176","kind":"arxiv","version":1}},"canonical_sha256":"29ff7f11264d7aedb15bf562e4f3856d56fca73953e30148bc1c23f2ebe4664a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29ff7f11264d7aedb15bf562e4f3856d56fca73953e30148bc1c23f2ebe4664a","first_computed_at":"2026-05-26T02:04:21.614498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:21.614498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yozfD9OJkSHlScbKTJnI0twDjvvPUxirUOawFA08l99li/5QYLyu5d6p26l5Hk+EGeRZdSgFNXao0kMIZPZCAQ==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:21.615818Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25176","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:722a8b3c5b32f5d3a5c78346dd3d1c1f0bd5bde00f7a7a34694e2fca3ed2c26c","sha256:94fd485092bfe75043478e52248562e94f1f101802aa5246061aaef9ece38174"],"state_sha256":"dc775fa4d7560d8529d649ded6d8df8a8651ac05deadcd90ac62ec6479d3bc2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LzhgecdqgB0nFnbLwKzHrtVYPABUogXhY+efwwzrp4Fz9iCYG5IdXGrPDn/eU5DGyd9sNWPOipiCvowH1rI6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:49:10.900132Z","bundle_sha256":"199cd8a63f39c2d73c9154ca90d9efdfddcd81128de9b874f5431bc8c082970d"}}