{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HYE3T5BBGSXLIJQI2L4XUSTLDI","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":"e789b552975c88d7c27aa10a8c72ab76826163df8fd8eedb93972247b35473e2","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-18T23:01:03Z","title_canon_sha256":"664ba1e6664ed5032fd5c8914b0bd748440510c858269b95ae9dcc9704f9d937"},"schema_version":"1.0","source":{"id":"1406.5417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5417","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5417v1","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5417","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"HYE3T5BBGSXL","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYE3T5BBGSXLIJQI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYE3T5BB","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:0cd6cb5d58df0381784811975f1f531d7ab79c9ff32e0091898bd3733d5a31a0","target":"graph","created_at":"2026-05-18T01:04:04Z","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 work is devoted to the study of a nonlocal-in-time evolutional problem for the first order differential equation in Banach space. Our primary approach, although stems from the convenient technique based on the reduction of a nonlocal problem to its classical initial value analogue, uses more advanced analysis. That is a validation of the correctness in definition of the general solution representation via the Dunford-Cauchy formula. Such approach allows us to reduce the given existence problem to the problem of locating zeros of a certain entire function. It results in the necessary and s","authors_text":"Dmytro Sytnyk, Vitalii Vasylyk, Volodymyr Makarov","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-18T23:01:03Z","title":"Existence of the solution to a nonlocal-in-time evolutional problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5417","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":"sha256:088659ba52a3702beccbe95d22021e0d04a793fac9c706ed3a84440d7aac3983","target":"record","created_at":"2026-05-18T01:04:04Z","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":"e789b552975c88d7c27aa10a8c72ab76826163df8fd8eedb93972247b35473e2","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-18T23:01:03Z","title_canon_sha256":"664ba1e6664ed5032fd5c8914b0bd748440510c858269b95ae9dcc9704f9d937"},"schema_version":"1.0","source":{"id":"1406.5417","kind":"arxiv","version":1}},"canonical_sha256":"3e09b9f42134aeb42608d2f97a4a6b1a136e2d5a41a6c0bd7fe707c680dd713d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e09b9f42134aeb42608d2f97a4a6b1a136e2d5a41a6c0bd7fe707c680dd713d","first_computed_at":"2026-05-18T01:04:04.346783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:04.346783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LEJsFbB1uJ9SMAAqu5nmZH++MUWGXfRdkY2CTyx0d9yD1mIItXv6Awk+SbX/IMtg/K5r73vY1PvzdmpqxUCtCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:04.347458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:088659ba52a3702beccbe95d22021e0d04a793fac9c706ed3a84440d7aac3983","sha256:0cd6cb5d58df0381784811975f1f531d7ab79c9ff32e0091898bd3733d5a31a0"],"state_sha256":"62cdbee3d6c6dfb3804826c874be63c497d635befe7ab9c4649c026816aedc38"}