{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:27ID6AYWM4GWZGURHXGFUXN2MX","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":"7d1b23f04294646fc4eb75d84462deb5079ccbfe5194bd881f314de912082e52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-18T17:19:21Z","title_canon_sha256":"d54f0f25075dd5e1fa11a97d6d4ae5c482b01ab19726c75e1673388cb024fc3c"},"schema_version":"1.0","source":{"id":"1206.3996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3996","created_at":"2026-05-18T03:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3996v1","created_at":"2026-05-18T03:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3996","created_at":"2026-05-18T03:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"27ID6AYWM4GW","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"27ID6AYWM4GWZGUR","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"27ID6AYW","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:ce704ce3029080340fae117d7a93906838099967b2a1e3d86cd31cab0e6beace","target":"graph","created_at":"2026-05-18T03:53:06Z","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, using a fixed point theorem in a Banach algebra, an existence result for a fractional functional differential equation in the Riemann-Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result are also derived.","authors_text":"Delfim F. M. Torres, El Hassan El Kinani, Moulay Rchid Sidi Ammi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-18T17:19:21Z","title":"Existence and Uniqueness of Solution to a Functional Integro-differential Fractional Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3996","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":"sha256:21d314c0e30f6f9b3e28acd9c5a1d95b3361541713393104b14e62a62826e1b2","target":"record","created_at":"2026-05-18T03:53:06Z","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":"7d1b23f04294646fc4eb75d84462deb5079ccbfe5194bd881f314de912082e52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-18T17:19:21Z","title_canon_sha256":"d54f0f25075dd5e1fa11a97d6d4ae5c482b01ab19726c75e1673388cb024fc3c"},"schema_version":"1.0","source":{"id":"1206.3996","kind":"arxiv","version":1}},"canonical_sha256":"d7d03f0316670d6c9a913dcc5a5dba65f6feadc1a2f911aeced3204d764f3806","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7d03f0316670d6c9a913dcc5a5dba65f6feadc1a2f911aeced3204d764f3806","first_computed_at":"2026-05-18T03:53:06.296563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:06.296563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fliSKVskzw1KqvxWijAHAz4UyYT2QnatK4YGEKNKwi9ykiUyoKmYM1sRp1tcgg5Zc2xOLfKdCdCiw8XR3+4HCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:06.297356Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21d314c0e30f6f9b3e28acd9c5a1d95b3361541713393104b14e62a62826e1b2","sha256:ce704ce3029080340fae117d7a93906838099967b2a1e3d86cd31cab0e6beace"],"state_sha256":"0b45747a39310aed18ec37622add7ff027453e9a5e73d0eb7b3518d1c143d25b"}