{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:S2GOSHIGFYZBFVUGIDH3D54KXT","short_pith_number":"pith:S2GOSHIG","canonical_record":{"source":{"id":"1110.4141","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-18T23:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"916d437a49ee629413b8602fcf734369614c601863f7b0be72bb9b294c3eb0ae","abstract_canon_sha256":"11e37fc4dd5774224529bb9eeb325681666c4d40820691101fa76d34f024c8d9"},"schema_version":"1.0"},"canonical_sha256":"968ce91d062e3212d68640cfb1f78abcdc5e62dfb179ac6935c1563af78f280f","source":{"kind":"arxiv","id":"1110.4141","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4141","created_at":"2026-05-18T03:34:25Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4141v2","created_at":"2026-05-18T03:34:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4141","created_at":"2026-05-18T03:34:25Z"},{"alias_kind":"pith_short_12","alias_value":"S2GOSHIGFYZB","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"S2GOSHIGFYZBFVUG","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"S2GOSHIG","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:S2GOSHIGFYZBFVUGIDH3D54KXT","target":"record","payload":{"canonical_record":{"source":{"id":"1110.4141","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-18T23:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"916d437a49ee629413b8602fcf734369614c601863f7b0be72bb9b294c3eb0ae","abstract_canon_sha256":"11e37fc4dd5774224529bb9eeb325681666c4d40820691101fa76d34f024c8d9"},"schema_version":"1.0"},"canonical_sha256":"968ce91d062e3212d68640cfb1f78abcdc5e62dfb179ac6935c1563af78f280f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:25.654640Z","signature_b64":"61ZuoMw6sMXppIjduFgnkmNVopFqTclRul/VKKp5Ep9LIcKWFayZolY5YKjF/UecWL2pDUNfT48R6mBZENKNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"968ce91d062e3212d68640cfb1f78abcdc5e62dfb179ac6935c1563af78f280f","last_reissued_at":"2026-05-18T03:34:25.653913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:25.653913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.4141","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":"2026-05-18T03:34:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZ0sfHoNM+GH4cZ5TRE9JSWXYr1hoHti2eWzGA5RliDe0bfQcUq/+duDquyzX2M7Yvj437SlDjUedHdoCN9mBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:46:09.919493Z"},"content_sha256":"e84cc8ea425a405b55dea2245f639d268212852dbeff5431e2cda096d555740d","schema_version":"1.0","event_id":"sha256:e84cc8ea425a405b55dea2245f639d268212852dbeff5431e2cda096d555740d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:S2GOSHIGFYZBFVUGIDH3D54KXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional variational calculus of variable order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Agnieszka B. Malinowska, Delfim F. M. Torres, Tatiana Odzijewicz","submitted_at":"2011-10-18T23:04:58Z","abstract_excerpt":"We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4141","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":"2026-05-18T03:34:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ty8smRF/FiyR4hPflNo3G/IN1o3+IYorLz6uB1iuZIWK05HzCSjSPP3AK8o2aVgCScAdyhMwOcQzwTVKVaN6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:46:09.920423Z"},"content_sha256":"c7f5f270127e0be24848f0a6c63d6025e944166b45f29e9883cc2552e517d71e","schema_version":"1.0","event_id":"sha256:c7f5f270127e0be24848f0a6c63d6025e944166b45f29e9883cc2552e517d71e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2GOSHIGFYZBFVUGIDH3D54KXT/bundle.json","state_url":"https://pith.science/pith/S2GOSHIGFYZBFVUGIDH3D54KXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2GOSHIGFYZBFVUGIDH3D54KXT/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":"2026-06-02T20:46:09Z","links":{"resolver":"https://pith.science/pith/S2GOSHIGFYZBFVUGIDH3D54KXT","bundle":"https://pith.science/pith/S2GOSHIGFYZBFVUGIDH3D54KXT/bundle.json","state":"https://pith.science/pith/S2GOSHIGFYZBFVUGIDH3D54KXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2GOSHIGFYZBFVUGIDH3D54KXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:S2GOSHIGFYZBFVUGIDH3D54KXT","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":"11e37fc4dd5774224529bb9eeb325681666c4d40820691101fa76d34f024c8d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-18T23:04:58Z","title_canon_sha256":"916d437a49ee629413b8602fcf734369614c601863f7b0be72bb9b294c3eb0ae"},"schema_version":"1.0","source":{"id":"1110.4141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4141","created_at":"2026-05-18T03:34:25Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4141v2","created_at":"2026-05-18T03:34:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4141","created_at":"2026-05-18T03:34:25Z"},{"alias_kind":"pith_short_12","alias_value":"S2GOSHIGFYZB","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"S2GOSHIGFYZBFVUG","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"S2GOSHIG","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:c7f5f270127e0be24848f0a6c63d6025e944166b45f29e9883cc2552e517d71e","target":"graph","created_at":"2026-05-18T03:34:25Z","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 study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.","authors_text":"Agnieszka B. Malinowska, Delfim F. M. Torres, Tatiana Odzijewicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-18T23:04:58Z","title":"Fractional variational calculus of variable order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4141","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:e84cc8ea425a405b55dea2245f639d268212852dbeff5431e2cda096d555740d","target":"record","created_at":"2026-05-18T03:34:25Z","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":"11e37fc4dd5774224529bb9eeb325681666c4d40820691101fa76d34f024c8d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-18T23:04:58Z","title_canon_sha256":"916d437a49ee629413b8602fcf734369614c601863f7b0be72bb9b294c3eb0ae"},"schema_version":"1.0","source":{"id":"1110.4141","kind":"arxiv","version":2}},"canonical_sha256":"968ce91d062e3212d68640cfb1f78abcdc5e62dfb179ac6935c1563af78f280f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"968ce91d062e3212d68640cfb1f78abcdc5e62dfb179ac6935c1563af78f280f","first_computed_at":"2026-05-18T03:34:25.653913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:25.653913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61ZuoMw6sMXppIjduFgnkmNVopFqTclRul/VKKp5Ep9LIcKWFayZolY5YKjF/UecWL2pDUNfT48R6mBZENKNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:25.654640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e84cc8ea425a405b55dea2245f639d268212852dbeff5431e2cda096d555740d","sha256:c7f5f270127e0be24848f0a6c63d6025e944166b45f29e9883cc2552e517d71e"],"state_sha256":"239608a98d9e406382637f6fe2a1bf6535a3aa00f7e091ef3328d872e7ebbd34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jfupaAuVOj87jrTXl1r2AL877vFuY5x0Lh54YGUQ6MdVoiukOhkgKuY7My6LyUpOjkvR3q9XObGD7ACq28sBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:46:09.923871Z","bundle_sha256":"6436724adf864d4a601868c852a6e8908b627e22ed9d5b72b71995e59cde7dd5"}}