{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7WHQ2WFKSHWIZ7NTYL42YLNVXB","short_pith_number":"pith:7WHQ2WFK","canonical_record":{"source":{"id":"1605.07088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-23T16:42:29Z","cross_cats_sorted":[],"title_canon_sha256":"13f46b76a7d639d21b31fd3ffbc274efe1cd3ffc9db179f6b605191c77499ac9","abstract_canon_sha256":"c6b0f7c5f974c95f35ce9d236ff8d679662d9ce712608500604245abf218d535"},"schema_version":"1.0"},"canonical_sha256":"fd8f0d58aa91ec8cfdb3c2f9ac2db5b84b2c87e3b43db0b1762250f24e8f1cce","source":{"kind":"arxiv","id":"1605.07088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07088","created_at":"2026-05-18T01:14:10Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07088v1","created_at":"2026-05-18T01:14:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07088","created_at":"2026-05-18T01:14:10Z"},{"alias_kind":"pith_short_12","alias_value":"7WHQ2WFKSHWI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7WHQ2WFKSHWIZ7NT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7WHQ2WFK","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7WHQ2WFKSHWIZ7NTYL42YLNVXB","target":"record","payload":{"canonical_record":{"source":{"id":"1605.07088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-23T16:42:29Z","cross_cats_sorted":[],"title_canon_sha256":"13f46b76a7d639d21b31fd3ffbc274efe1cd3ffc9db179f6b605191c77499ac9","abstract_canon_sha256":"c6b0f7c5f974c95f35ce9d236ff8d679662d9ce712608500604245abf218d535"},"schema_version":"1.0"},"canonical_sha256":"fd8f0d58aa91ec8cfdb3c2f9ac2db5b84b2c87e3b43db0b1762250f24e8f1cce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:10.058401Z","signature_b64":"8RhytEmonPXNPWVt+XmNXniqlSSVUqx0mkwI5eS/5pL3MFPPjWmVwFTesPQPROEV0kuZFpHqqA/1T8w9uOTQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd8f0d58aa91ec8cfdb3c2f9ac2db5b84b2c87e3b43db0b1762250f24e8f1cce","last_reissued_at":"2026-05-18T01:14:10.057712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:10.057712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.07088","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":"2026-05-18T01:14:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6BRu+lf1aSS9WmVpGSoQFlfSWehToPlPnV+tfA5tsUlBx+WH7nxrBjxHaQkhQMwRaOF3YDzIfIYOsY6FJCVJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:02:48.509729Z"},"content_sha256":"d92983e6fa07699993ec5950887f5f444d2dc6b1c84ef89ab6609e36a555c07b","schema_version":"1.0","event_id":"sha256:d92983e6fa07699993ec5950887f5f444d2dc6b1c84ef89ab6609e36a555c07b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7WHQ2WFKSHWIZ7NTYL42YLNVXB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-local fractional derivatives. Discrete and continuous","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e L. Torrea, Luciano Abad\\'ias, Marta de Le\\'on-Contreras","submitted_at":"2016-05-23T16:42:29Z","abstract_excerpt":"We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When the functions are good enough, these approximation procedures give a measure of the order of approximation. These results also allows us to prove the coincidence, for good enough functions, of the Marchaud and Gr\\\"unwald-Letnikov derivatives in every point and the speed of convergence to the Gr\\\"unwald-Letnikov derivative. The fractional discrete derivative w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07088","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":"2026-05-18T01:14:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KDysl9O2RBfS7lPPGDu7kLgfOe2AXkn17YI14Ohr/xDVg79uLK3ydPXmgyyaFrUKGcdangh9ghdaPtxefah+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:02:48.510409Z"},"content_sha256":"c5cc13bdb23f3fd66afe19033eaeff90b19d6f06973d91fda71f229139f9c5c7","schema_version":"1.0","event_id":"sha256:c5cc13bdb23f3fd66afe19033eaeff90b19d6f06973d91fda71f229139f9c5c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7WHQ2WFKSHWIZ7NTYL42YLNVXB/bundle.json","state_url":"https://pith.science/pith/7WHQ2WFKSHWIZ7NTYL42YLNVXB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7WHQ2WFKSHWIZ7NTYL42YLNVXB/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":"2026-06-08T21:02:48Z","links":{"resolver":"https://pith.science/pith/7WHQ2WFKSHWIZ7NTYL42YLNVXB","bundle":"https://pith.science/pith/7WHQ2WFKSHWIZ7NTYL42YLNVXB/bundle.json","state":"https://pith.science/pith/7WHQ2WFKSHWIZ7NTYL42YLNVXB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7WHQ2WFKSHWIZ7NTYL42YLNVXB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7WHQ2WFKSHWIZ7NTYL42YLNVXB","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":"c6b0f7c5f974c95f35ce9d236ff8d679662d9ce712608500604245abf218d535","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-23T16:42:29Z","title_canon_sha256":"13f46b76a7d639d21b31fd3ffbc274efe1cd3ffc9db179f6b605191c77499ac9"},"schema_version":"1.0","source":{"id":"1605.07088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07088","created_at":"2026-05-18T01:14:10Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07088v1","created_at":"2026-05-18T01:14:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07088","created_at":"2026-05-18T01:14:10Z"},{"alias_kind":"pith_short_12","alias_value":"7WHQ2WFKSHWI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7WHQ2WFKSHWIZ7NT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7WHQ2WFK","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:c5cc13bdb23f3fd66afe19033eaeff90b19d6f06973d91fda71f229139f9c5c7","target":"graph","created_at":"2026-05-18T01:14:10Z","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 prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When the functions are good enough, these approximation procedures give a measure of the order of approximation. These results also allows us to prove the coincidence, for good enough functions, of the Marchaud and Gr\\\"unwald-Letnikov derivatives in every point and the speed of convergence to the Gr\\\"unwald-Letnikov derivative. The fractional discrete derivative w","authors_text":"Jos\\'e L. Torrea, Luciano Abad\\'ias, Marta de Le\\'on-Contreras","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-23T16:42:29Z","title":"Non-local fractional derivatives. Discrete and continuous"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07088","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:d92983e6fa07699993ec5950887f5f444d2dc6b1c84ef89ab6609e36a555c07b","target":"record","created_at":"2026-05-18T01:14:10Z","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":"c6b0f7c5f974c95f35ce9d236ff8d679662d9ce712608500604245abf218d535","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-23T16:42:29Z","title_canon_sha256":"13f46b76a7d639d21b31fd3ffbc274efe1cd3ffc9db179f6b605191c77499ac9"},"schema_version":"1.0","source":{"id":"1605.07088","kind":"arxiv","version":1}},"canonical_sha256":"fd8f0d58aa91ec8cfdb3c2f9ac2db5b84b2c87e3b43db0b1762250f24e8f1cce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd8f0d58aa91ec8cfdb3c2f9ac2db5b84b2c87e3b43db0b1762250f24e8f1cce","first_computed_at":"2026-05-18T01:14:10.057712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:10.057712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8RhytEmonPXNPWVt+XmNXniqlSSVUqx0mkwI5eS/5pL3MFPPjWmVwFTesPQPROEV0kuZFpHqqA/1T8w9uOTQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:10.058401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d92983e6fa07699993ec5950887f5f444d2dc6b1c84ef89ab6609e36a555c07b","sha256:c5cc13bdb23f3fd66afe19033eaeff90b19d6f06973d91fda71f229139f9c5c7"],"state_sha256":"fa8125d8b759990e6274396bfb42e0bcbc5d6e8d3e2014e4d7e23a031461d871"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OCaM4mt+IyqYiQJfCutaFukfdbV4I5dcrgwfeQ+9T/AH0YzQVlrl/X8T8a6GpKD7d0dQRXGL+J+vyAqyFEw1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:02:48.514769Z","bundle_sha256":"2141b2c5840567868e04b6f3d5fab0b074d8355110a60e3cbb969cd06fa99007"}}