{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:2HXU2DUKVZUQ7ZHXGEDD3KDG4A","short_pith_number":"pith:2HXU2DUK","canonical_record":{"source":{"id":"0811.0133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.OH","submitted_at":"2008-11-02T06:16:49Z","cross_cats_sorted":[],"title_canon_sha256":"4f3869956302828dac00d6ccfa7e66b64f9dc8fd8688d34ce93a5a234be9a673","abstract_canon_sha256":"14c12a78b7a1b23b63ca0a7aaf5d49266dbeabbcf23bd71a2a2dfae87a72066a"},"schema_version":"1.0"},"canonical_sha256":"d1ef4d0e8aae690fe4f731063da866e02d886186d67df2337c0a1ff6750d15a5","source":{"kind":"arxiv","id":"0811.0133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0133","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0133v1","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0133","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"2HXU2DUKVZUQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"2HXU2DUKVZUQ7ZHX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"2HXU2DUK","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:2HXU2DUKVZUQ7ZHXGEDD3KDG4A","target":"record","payload":{"canonical_record":{"source":{"id":"0811.0133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.OH","submitted_at":"2008-11-02T06:16:49Z","cross_cats_sorted":[],"title_canon_sha256":"4f3869956302828dac00d6ccfa7e66b64f9dc8fd8688d34ce93a5a234be9a673","abstract_canon_sha256":"14c12a78b7a1b23b63ca0a7aaf5d49266dbeabbcf23bd71a2a2dfae87a72066a"},"schema_version":"1.0"},"canonical_sha256":"d1ef4d0e8aae690fe4f731063da866e02d886186d67df2337c0a1ff6750d15a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:11.608887Z","signature_b64":"eEHQPWaQNOXTH7jg/k2xvKKENQqGJFowafFUeG45E8DLiLIT3NsKHO7PCjU7bfpFNTo6hbFLhOY4dPEUkY9NDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1ef4d0e8aae690fe4f731063da866e02d886186d67df2337c0a1ff6750d15a5","last_reissued_at":"2026-05-18T00:59:11.608160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:11.608160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.0133","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":"2026-05-18T00:59:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgm8gNaG3WMF09jdNW4dG3Dd3VFAttdGTk90YlCrVt0QNct0W5NcXhY9jOutCKrSi+2p3t5cYcyj4KG+UygCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:47:05.463340Z"},"content_sha256":"2d7243390e26591f0002c16f1ccd79e653b0177a0c831da0ac9676f05a8ab9cc","schema_version":"1.0","event_id":"sha256:2d7243390e26591f0002c16f1ccd79e653b0177a0c831da0ac9676f05a8ab9cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:2HXU2DUKVZUQ7ZHXGEDD3KDG4A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Study of the Grunwald-Letnikov Definition for Minimizing the Effects of Random Noise on Fractional Order Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.OH","authors_text":"Amit Konar, Deepyaman Maiti, Mithun Chakraborty, Ramadoss Janarthanan","submitted_at":"2008-11-02T06:16:49Z","abstract_excerpt":"Of the many definitions for fractional order differintegral, the Grunwald-Letnikov definition is arguably the most important one. The necessity of this definition for the description and analysis of fractional order systems cannot be overstated. Unfortunately, the Fractional Order Differential Equation (FODE) describing such a systems, in its original form, highly sensitive to the effects of random noise components inevitable in a natural environment. Thus direct application of the definition in a real-life problem can yield erroneous results. In this article, we perform an in-depth mathematic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0133","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":"2026-05-18T00:59:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLiTfelUN35LeQRLKpHi8gu+M5tAbTfdZR5yAm+bF4aGYgBzRawrjDKVY1aGgp/k2006VIDRKNVmQy6bf5SyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:47:05.464009Z"},"content_sha256":"0ea0e6d0f5d1ce940f65b1f3bfb8bb4e238fdb4b31e92a600e9ca8694d47bee8","schema_version":"1.0","event_id":"sha256:0ea0e6d0f5d1ce940f65b1f3bfb8bb4e238fdb4b31e92a600e9ca8694d47bee8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HXU2DUKVZUQ7ZHXGEDD3KDG4A/bundle.json","state_url":"https://pith.science/pith/2HXU2DUKVZUQ7ZHXGEDD3KDG4A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HXU2DUKVZUQ7ZHXGEDD3KDG4A/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":"2026-05-29T20:47:05Z","links":{"resolver":"https://pith.science/pith/2HXU2DUKVZUQ7ZHXGEDD3KDG4A","bundle":"https://pith.science/pith/2HXU2DUKVZUQ7ZHXGEDD3KDG4A/bundle.json","state":"https://pith.science/pith/2HXU2DUKVZUQ7ZHXGEDD3KDG4A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HXU2DUKVZUQ7ZHXGEDD3KDG4A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:2HXU2DUKVZUQ7ZHXGEDD3KDG4A","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":"14c12a78b7a1b23b63ca0a7aaf5d49266dbeabbcf23bd71a2a2dfae87a72066a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.OH","submitted_at":"2008-11-02T06:16:49Z","title_canon_sha256":"4f3869956302828dac00d6ccfa7e66b64f9dc8fd8688d34ce93a5a234be9a673"},"schema_version":"1.0","source":{"id":"0811.0133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0133","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0133v1","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0133","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"2HXU2DUKVZUQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"2HXU2DUKVZUQ7ZHX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"2HXU2DUK","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:0ea0e6d0f5d1ce940f65b1f3bfb8bb4e238fdb4b31e92a600e9ca8694d47bee8","target":"graph","created_at":"2026-05-18T00:59:11Z","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":"Of the many definitions for fractional order differintegral, the Grunwald-Letnikov definition is arguably the most important one. The necessity of this definition for the description and analysis of fractional order systems cannot be overstated. Unfortunately, the Fractional Order Differential Equation (FODE) describing such a systems, in its original form, highly sensitive to the effects of random noise components inevitable in a natural environment. Thus direct application of the definition in a real-life problem can yield erroneous results. In this article, we perform an in-depth mathematic","authors_text":"Amit Konar, Deepyaman Maiti, Mithun Chakraborty, Ramadoss Janarthanan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.OH","submitted_at":"2008-11-02T06:16:49Z","title":"A Study of the Grunwald-Letnikov Definition for Minimizing the Effects of Random Noise on Fractional Order Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0133","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":"sha256:2d7243390e26591f0002c16f1ccd79e653b0177a0c831da0ac9676f05a8ab9cc","target":"record","created_at":"2026-05-18T00:59:11Z","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":"14c12a78b7a1b23b63ca0a7aaf5d49266dbeabbcf23bd71a2a2dfae87a72066a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.OH","submitted_at":"2008-11-02T06:16:49Z","title_canon_sha256":"4f3869956302828dac00d6ccfa7e66b64f9dc8fd8688d34ce93a5a234be9a673"},"schema_version":"1.0","source":{"id":"0811.0133","kind":"arxiv","version":1}},"canonical_sha256":"d1ef4d0e8aae690fe4f731063da866e02d886186d67df2337c0a1ff6750d15a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1ef4d0e8aae690fe4f731063da866e02d886186d67df2337c0a1ff6750d15a5","first_computed_at":"2026-05-18T00:59:11.608160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:11.608160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eEHQPWaQNOXTH7jg/k2xvKKENQqGJFowafFUeG45E8DLiLIT3NsKHO7PCjU7bfpFNTo6hbFLhOY4dPEUkY9NDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:11.608887Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.0133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d7243390e26591f0002c16f1ccd79e653b0177a0c831da0ac9676f05a8ab9cc","sha256:0ea0e6d0f5d1ce940f65b1f3bfb8bb4e238fdb4b31e92a600e9ca8694d47bee8"],"state_sha256":"2e1ee0e1a7943fe04c79c7045ca91ba8570e40bd8668313cf5c59281b79067b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nMU60AIzyJ9vlllPkyvMyY3NjjbfeTyIx6K3+dy0KQllDnOAJTonU+B+Cy8xpKIRygofwRmjqDxw7DwjGwjnAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:47:05.467038Z","bundle_sha256":"af45cfaf923a1d2b83f0e512401380ba676e83fdc9769b84b1f1f78f6ca34d3d"}}