{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XBGAD32CGN2WOGZWI3LFVDE4U6","short_pith_number":"pith:XBGAD32C","canonical_record":{"source":{"id":"1012.5483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-12-25T16:39:44Z","cross_cats_sorted":[],"title_canon_sha256":"aa3005f8f85212462872f8adbd8c47171619760f67ee8fa2229377289f95710a","abstract_canon_sha256":"2ff2ab7d41029723266bd386da8be00518304c3c36d52b665113faabb8361a2f"},"schema_version":"1.0"},"canonical_sha256":"b84c01ef423375671b3646d65a8c9ca7947732eab8ae4effa92a5f8df02bb09b","source":{"kind":"arxiv","id":"1012.5483","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5483","created_at":"2026-05-18T04:27:27Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5483v2","created_at":"2026-05-18T04:27:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5483","created_at":"2026-05-18T04:27:27Z"},{"alias_kind":"pith_short_12","alias_value":"XBGAD32CGN2W","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XBGAD32CGN2WOGZW","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XBGAD32C","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XBGAD32CGN2WOGZWI3LFVDE4U6","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-12-25T16:39:44Z","cross_cats_sorted":[],"title_canon_sha256":"aa3005f8f85212462872f8adbd8c47171619760f67ee8fa2229377289f95710a","abstract_canon_sha256":"2ff2ab7d41029723266bd386da8be00518304c3c36d52b665113faabb8361a2f"},"schema_version":"1.0"},"canonical_sha256":"b84c01ef423375671b3646d65a8c9ca7947732eab8ae4effa92a5f8df02bb09b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:27.887479Z","signature_b64":"B3QgDc7P5mcDPp3YjdKoxVN/gyCkeZkMY/nuzBu9Wiukc7ZK23bLiCI4bKnIE6+0hkpydLIf7BSjtapfBVHBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b84c01ef423375671b3646d65a8c9ca7947732eab8ae4effa92a5f8df02bb09b","last_reissued_at":"2026-05-18T04:27:27.887034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:27.887034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5483","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":"2026-05-18T04:27:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJfB9FV2zlen2lNbO40hy3t43Be2+lvCRHIenVnAOYCNYVpaeRv3RV9HHm9vCyQQcJOXqP3GWeDXXvdW6e8oBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:30:23.033799Z"},"content_sha256":"f4521f540be9a1bb5ac9fc5839a43a5647b8913026759ec6ca320133ddded3cc","schema_version":"1.0","event_id":"sha256:f4521f540be9a1bb5ac9fc5839a43a5647b8913026759ec6ca320133ddded3cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XBGAD32CGN2WOGZWI3LFVDE4U6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentiation by integration with Jacobi polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Da-Yan Liu (LAGIS, INRIA Lille - Nord Europe), L2MA), Olivier Gibaru (INRIA Lille - Nord Europe, Wilfrid Perruquetti (LAGIS","submitted_at":"2010-12-25T16:39:44Z","abstract_excerpt":"In this paper, the numerical differentiation by integration method based on Jacobi polynomials originally introduced by Mboup, Fliess and Join is revisited in the central case where the used integration window is centered. Such method based on Jacobi polynomials was introduced through an algebraic approach and extends the numerical differentiation by integration method introduced by Lanczos. The here proposed method is used to estimate the $n^{th}$ ($n \\in \\mathbb{N}$) order derivative from noisy data of a smooth function belonging to at least $C^{n+1+q}$ $(q \\in \\mathbb{N})$. In the recent pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5483","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":"2026-05-18T04:27:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPlmpwCBer6WTFJaCpMfHbaM6BU+ctkpj7OGWJNH7T68C53enVt8O0FJUpblc1qnhqKVH7nZ0xiqOQMr+lMzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:30:23.034179Z"},"content_sha256":"d9fa9ce2613bcc5d63c2fba0f8d95b841a3bc1acb725fbe78b488155c34c2f19","schema_version":"1.0","event_id":"sha256:d9fa9ce2613bcc5d63c2fba0f8d95b841a3bc1acb725fbe78b488155c34c2f19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBGAD32CGN2WOGZWI3LFVDE4U6/bundle.json","state_url":"https://pith.science/pith/XBGAD32CGN2WOGZWI3LFVDE4U6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBGAD32CGN2WOGZWI3LFVDE4U6/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":"2026-06-01T17:30:23Z","links":{"resolver":"https://pith.science/pith/XBGAD32CGN2WOGZWI3LFVDE4U6","bundle":"https://pith.science/pith/XBGAD32CGN2WOGZWI3LFVDE4U6/bundle.json","state":"https://pith.science/pith/XBGAD32CGN2WOGZWI3LFVDE4U6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBGAD32CGN2WOGZWI3LFVDE4U6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XBGAD32CGN2WOGZWI3LFVDE4U6","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":"2ff2ab7d41029723266bd386da8be00518304c3c36d52b665113faabb8361a2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-12-25T16:39:44Z","title_canon_sha256":"aa3005f8f85212462872f8adbd8c47171619760f67ee8fa2229377289f95710a"},"schema_version":"1.0","source":{"id":"1012.5483","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5483","created_at":"2026-05-18T04:27:27Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5483v2","created_at":"2026-05-18T04:27:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5483","created_at":"2026-05-18T04:27:27Z"},{"alias_kind":"pith_short_12","alias_value":"XBGAD32CGN2W","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XBGAD32CGN2WOGZW","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XBGAD32C","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d9fa9ce2613bcc5d63c2fba0f8d95b841a3bc1acb725fbe78b488155c34c2f19","target":"graph","created_at":"2026-05-18T04:27:27Z","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":"In this paper, the numerical differentiation by integration method based on Jacobi polynomials originally introduced by Mboup, Fliess and Join is revisited in the central case where the used integration window is centered. Such method based on Jacobi polynomials was introduced through an algebraic approach and extends the numerical differentiation by integration method introduced by Lanczos. The here proposed method is used to estimate the $n^{th}$ ($n \\in \\mathbb{N}$) order derivative from noisy data of a smooth function belonging to at least $C^{n+1+q}$ $(q \\in \\mathbb{N})$. In the recent pa","authors_text":"Da-Yan Liu (LAGIS, INRIA Lille - Nord Europe), L2MA), Olivier Gibaru (INRIA Lille - Nord Europe, Wilfrid Perruquetti (LAGIS","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-12-25T16:39:44Z","title":"Differentiation by integration with Jacobi polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5483","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:f4521f540be9a1bb5ac9fc5839a43a5647b8913026759ec6ca320133ddded3cc","target":"record","created_at":"2026-05-18T04:27:27Z","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":"2ff2ab7d41029723266bd386da8be00518304c3c36d52b665113faabb8361a2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-12-25T16:39:44Z","title_canon_sha256":"aa3005f8f85212462872f8adbd8c47171619760f67ee8fa2229377289f95710a"},"schema_version":"1.0","source":{"id":"1012.5483","kind":"arxiv","version":2}},"canonical_sha256":"b84c01ef423375671b3646d65a8c9ca7947732eab8ae4effa92a5f8df02bb09b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b84c01ef423375671b3646d65a8c9ca7947732eab8ae4effa92a5f8df02bb09b","first_computed_at":"2026-05-18T04:27:27.887034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:27.887034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3QgDc7P5mcDPp3YjdKoxVN/gyCkeZkMY/nuzBu9Wiukc7ZK23bLiCI4bKnIE6+0hkpydLIf7BSjtapfBVHBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:27.887479Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5483","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4521f540be9a1bb5ac9fc5839a43a5647b8913026759ec6ca320133ddded3cc","sha256:d9fa9ce2613bcc5d63c2fba0f8d95b841a3bc1acb725fbe78b488155c34c2f19"],"state_sha256":"bc036fd4f5a9227fee212025b43cb0d626b23a87f8d45736fb662e7d2fa03b27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0iDAJh9fG1c2TU2buHgPfyUsayv2cdblVwlIHGv954KcSl1gNAvt/ZXa9Jta2NEkDPMiu5J8m/CSp21rJqxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:30:23.036375Z","bundle_sha256":"192b5208e546c2b77398b72c0548c76c211af7e5e52f862ae77b82082bb691aa"}}