{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BBQ7YZ436N6B7TFMOB7VDNOTHE","short_pith_number":"pith:BBQ7YZ43","canonical_record":{"source":{"id":"1311.1388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-06T13:36:44Z","cross_cats_sorted":[],"title_canon_sha256":"01c10e8ba3792f0d8ccc66cc5906b55fbedef40b83f5b9e1b9741fa7cda16325","abstract_canon_sha256":"afb5df4b279adad8577db7e10c3ea77477a2096150649841e4c3ebdc5d357f29"},"schema_version":"1.0"},"canonical_sha256":"0861fc679bf37c1fccac707f51b5d339055d83a972e6a94d93a3a3a909bdc8b6","source":{"kind":"arxiv","id":"1311.1388","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1388","created_at":"2026-05-18T02:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1388v1","created_at":"2026-05-18T02:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1388","created_at":"2026-05-18T02:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"BBQ7YZ436N6B","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BBQ7YZ436N6B7TFM","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BBQ7YZ43","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BBQ7YZ436N6B7TFMOB7VDNOTHE","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-06T13:36:44Z","cross_cats_sorted":[],"title_canon_sha256":"01c10e8ba3792f0d8ccc66cc5906b55fbedef40b83f5b9e1b9741fa7cda16325","abstract_canon_sha256":"afb5df4b279adad8577db7e10c3ea77477a2096150649841e4c3ebdc5d357f29"},"schema_version":"1.0"},"canonical_sha256":"0861fc679bf37c1fccac707f51b5d339055d83a972e6a94d93a3a3a909bdc8b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:47.696046Z","signature_b64":"Qx0pCKGcXLGuxGG1H9mkPAI1AR9zwwddRxso+5TIH3ah5xEFbQ+KFsMZ0tp9cFrwRY8cgta38hqXV3MGX+odDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0861fc679bf37c1fccac707f51b5d339055d83a972e6a94d93a3a3a909bdc8b6","last_reissued_at":"2026-05-18T02:20:47.695201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:47.695201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1388","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":"2026-05-18T02:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5lIrD9rLc/JbU0uY0rTuWYHIBpufgaiJIeOOi1hQn7o0o/CpCL+iamwS4t6qOmtxvzu0aWKKf7A4t6850wYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:51:22.655380Z"},"content_sha256":"fb8f4c8a923ab81a47c60912d0e0ceedda570d0d6fac817002172cf20eb0eb70","schema_version":"1.0","event_id":"sha256:fb8f4c8a923ab81a47c60912d0e0ceedda570d0d6fac817002172cf20eb0eb70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BBQ7YZ436N6B7TFMOB7VDNOTHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential quadrature rules for linear fractional differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Marina Popolizio, Roberto Garrappa","submitted_at":"2013-11-06T13:36:44Z","abstract_excerpt":"This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized Mittag-Leffler function. Then suitable quadrature rules are devised and order conditions of algebraic type are derived. Theoretical findings are validated by means of numerical experiments and the effectiveness of the proposed approach is illustrated by means of comparisons with other standard methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1388","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":"2026-05-18T02:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38Fhqci8LQq3VmONMeW3XXy11HlIYL0zrHTkNLePaQnDlXwR9YiCIb4K5U6eOHQnrgIDwYxzysF1/LC5T8EUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:51:22.655718Z"},"content_sha256":"3304c6c1b804c5183eba0141e2dbe40e792eb7ac9bd5284ffef26765efe1fc96","schema_version":"1.0","event_id":"sha256:3304c6c1b804c5183eba0141e2dbe40e792eb7ac9bd5284ffef26765efe1fc96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBQ7YZ436N6B7TFMOB7VDNOTHE/bundle.json","state_url":"https://pith.science/pith/BBQ7YZ436N6B7TFMOB7VDNOTHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBQ7YZ436N6B7TFMOB7VDNOTHE/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":"2026-06-05T12:51:22Z","links":{"resolver":"https://pith.science/pith/BBQ7YZ436N6B7TFMOB7VDNOTHE","bundle":"https://pith.science/pith/BBQ7YZ436N6B7TFMOB7VDNOTHE/bundle.json","state":"https://pith.science/pith/BBQ7YZ436N6B7TFMOB7VDNOTHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBQ7YZ436N6B7TFMOB7VDNOTHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BBQ7YZ436N6B7TFMOB7VDNOTHE","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":"afb5df4b279adad8577db7e10c3ea77477a2096150649841e4c3ebdc5d357f29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-06T13:36:44Z","title_canon_sha256":"01c10e8ba3792f0d8ccc66cc5906b55fbedef40b83f5b9e1b9741fa7cda16325"},"schema_version":"1.0","source":{"id":"1311.1388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1388","created_at":"2026-05-18T02:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1388v1","created_at":"2026-05-18T02:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1388","created_at":"2026-05-18T02:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"BBQ7YZ436N6B","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BBQ7YZ436N6B7TFM","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BBQ7YZ43","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:3304c6c1b804c5183eba0141e2dbe40e792eb7ac9bd5284ffef26765efe1fc96","target":"graph","created_at":"2026-05-18T02:20:47Z","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":"This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized Mittag-Leffler function. Then suitable quadrature rules are devised and order conditions of algebraic type are derived. Theoretical findings are validated by means of numerical experiments and the effectiveness of the proposed approach is illustrated by means of comparisons with other standard methods.","authors_text":"Marina Popolizio, Roberto Garrappa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-06T13:36:44Z","title":"Exponential quadrature rules for linear fractional differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1388","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:fb8f4c8a923ab81a47c60912d0e0ceedda570d0d6fac817002172cf20eb0eb70","target":"record","created_at":"2026-05-18T02:20:47Z","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":"afb5df4b279adad8577db7e10c3ea77477a2096150649841e4c3ebdc5d357f29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-06T13:36:44Z","title_canon_sha256":"01c10e8ba3792f0d8ccc66cc5906b55fbedef40b83f5b9e1b9741fa7cda16325"},"schema_version":"1.0","source":{"id":"1311.1388","kind":"arxiv","version":1}},"canonical_sha256":"0861fc679bf37c1fccac707f51b5d339055d83a972e6a94d93a3a3a909bdc8b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0861fc679bf37c1fccac707f51b5d339055d83a972e6a94d93a3a3a909bdc8b6","first_computed_at":"2026-05-18T02:20:47.695201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:47.695201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qx0pCKGcXLGuxGG1H9mkPAI1AR9zwwddRxso+5TIH3ah5xEFbQ+KFsMZ0tp9cFrwRY8cgta38hqXV3MGX+odDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:47.696046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb8f4c8a923ab81a47c60912d0e0ceedda570d0d6fac817002172cf20eb0eb70","sha256:3304c6c1b804c5183eba0141e2dbe40e792eb7ac9bd5284ffef26765efe1fc96"],"state_sha256":"cfd506b7d4a8aed12c754d475281fe9089ee4088aa3101d47d79297b163ee2cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"49FtIeAjPeHqVoS4fVmVpWkhBWuH2oxIaGKzcjFvPLB16Df8b7qmS9HO1iCShTadg5dWLpzygQzErHL0crifCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:51:22.657638Z","bundle_sha256":"cf9a36a0756ec88dc920654e6ea3b22e060d6f89063a8dbcb57983c138efeb85"}}