{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZW5HZWXLRC7BUKI7I4GJA2X7DE","short_pith_number":"pith:ZW5HZWXL","canonical_record":{"source":{"id":"1305.1859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-08T15:45:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0ff83e6531236b7ed49f321efa33dd63483a4fabfd7d69385d311fe7d1b0e105","abstract_canon_sha256":"8d27a25b9115b221d47efa0c2f75946c5ea8f701581588ae81c34eaa2168cd09"},"schema_version":"1.0"},"canonical_sha256":"cdba7cdaeb88be1a291f470c906aff19133372448ec83d64fc3f58870017dbce","source":{"kind":"arxiv","id":"1305.1859","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1859","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1859v1","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1859","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZW5HZWXLRC7B","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZW5HZWXLRC7BUKI7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZW5HZWXL","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZW5HZWXLRC7BUKI7I4GJA2X7DE","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-08T15:45:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0ff83e6531236b7ed49f321efa33dd63483a4fabfd7d69385d311fe7d1b0e105","abstract_canon_sha256":"8d27a25b9115b221d47efa0c2f75946c5ea8f701581588ae81c34eaa2168cd09"},"schema_version":"1.0"},"canonical_sha256":"cdba7cdaeb88be1a291f470c906aff19133372448ec83d64fc3f58870017dbce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:40.990488Z","signature_b64":"lnMnEKWgA2fdVmHNFjD2jv8ztlQjg8VlcVLmZHG4FSJ6SUUXYXXWGUQTwQ1XU/zCVT9dlMSwD8BH8+g0mI6ACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdba7cdaeb88be1a291f470c906aff19133372448ec83d64fc3f58870017dbce","last_reissued_at":"2026-05-18T00:23:40.989831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:40.989831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1859","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":"2026-05-18T00:23:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P3Ectmq8EWJxkVTeADH9YgqK3hLk+3CCPS9Vc14sN58M4oh16Ai/6P2gE76xYlKDa4frt/NQ1LEEjUEhWiQLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:11:53.663109Z"},"content_sha256":"18d114e35ff72d5930b8a4c0a226238cae44b31dbc6697a15b0f3cdfd68da889","schema_version":"1.0","event_id":"sha256:18d114e35ff72d5930b8a4c0a226238cae44b31dbc6697a15b0f3cdfd68da889"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZW5HZWXLRC7BUKI7I4GJA2X7DE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A discrete time method to the first variation of fractional order variational functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OC","authors_text":"Delfim F. M. Torres, Ricardo Almeida, Shakoor Pooseh","submitted_at":"2013-05-08T15:45:43Z","abstract_excerpt":"The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Grunwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1859","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":"2026-05-18T00:23:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s1C1twql+GqArWiE5vLY7HeSq6KALBiNOGYS3AXIOQtJYivGXSt4ViBx06aqx+OKcqVsbRnftH+KPHjs66Q8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:11:53.663474Z"},"content_sha256":"adf636a413a00ff5a57df37343a2ce0d7ede039a45580a732ab1763fcd2826bf","schema_version":"1.0","event_id":"sha256:adf636a413a00ff5a57df37343a2ce0d7ede039a45580a732ab1763fcd2826bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZW5HZWXLRC7BUKI7I4GJA2X7DE/bundle.json","state_url":"https://pith.science/pith/ZW5HZWXLRC7BUKI7I4GJA2X7DE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZW5HZWXLRC7BUKI7I4GJA2X7DE/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":"2026-06-11T11:11:53Z","links":{"resolver":"https://pith.science/pith/ZW5HZWXLRC7BUKI7I4GJA2X7DE","bundle":"https://pith.science/pith/ZW5HZWXLRC7BUKI7I4GJA2X7DE/bundle.json","state":"https://pith.science/pith/ZW5HZWXLRC7BUKI7I4GJA2X7DE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZW5HZWXLRC7BUKI7I4GJA2X7DE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZW5HZWXLRC7BUKI7I4GJA2X7DE","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":"8d27a25b9115b221d47efa0c2f75946c5ea8f701581588ae81c34eaa2168cd09","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-08T15:45:43Z","title_canon_sha256":"0ff83e6531236b7ed49f321efa33dd63483a4fabfd7d69385d311fe7d1b0e105"},"schema_version":"1.0","source":{"id":"1305.1859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1859","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1859v1","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1859","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZW5HZWXLRC7B","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZW5HZWXLRC7BUKI7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZW5HZWXL","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:adf636a413a00ff5a57df37343a2ce0d7ede039a45580a732ab1763fcd2826bf","target":"graph","created_at":"2026-05-18T00:23:40Z","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":"The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Grunwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations.","authors_text":"Delfim F. M. Torres, Ricardo Almeida, Shakoor Pooseh","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-08T15:45:43Z","title":"A discrete time method to the first variation of fractional order variational functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1859","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":"sha256:18d114e35ff72d5930b8a4c0a226238cae44b31dbc6697a15b0f3cdfd68da889","target":"record","created_at":"2026-05-18T00:23:40Z","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":"8d27a25b9115b221d47efa0c2f75946c5ea8f701581588ae81c34eaa2168cd09","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-08T15:45:43Z","title_canon_sha256":"0ff83e6531236b7ed49f321efa33dd63483a4fabfd7d69385d311fe7d1b0e105"},"schema_version":"1.0","source":{"id":"1305.1859","kind":"arxiv","version":1}},"canonical_sha256":"cdba7cdaeb88be1a291f470c906aff19133372448ec83d64fc3f58870017dbce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdba7cdaeb88be1a291f470c906aff19133372448ec83d64fc3f58870017dbce","first_computed_at":"2026-05-18T00:23:40.989831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:40.989831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lnMnEKWgA2fdVmHNFjD2jv8ztlQjg8VlcVLmZHG4FSJ6SUUXYXXWGUQTwQ1XU/zCVT9dlMSwD8BH8+g0mI6ACg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:40.990488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18d114e35ff72d5930b8a4c0a226238cae44b31dbc6697a15b0f3cdfd68da889","sha256:adf636a413a00ff5a57df37343a2ce0d7ede039a45580a732ab1763fcd2826bf"],"state_sha256":"8cc30941af46a386a11e2522a5b511f20401a0c8684f8f02b1c88bb807659f26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O1vH8dJBaRNkn0Kj+6YIc3n63dLxWHe2JWna8QhJeO+ch3hVtd4fXQJThDIXyHDRl6cF2wbxVSSPCX0ku6eXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:11:53.665436Z","bundle_sha256":"7a5219a281aa1d39d92e6a0751ea5953d7fc45efa62d0b3ab3923ec91e6c724b"}}