{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:22XJ6VQY7VRXRYASHAE4II3DKH","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":"0ad8b8614ca94f3747c7c296b09c72bd3ef3e689bb8c6c3177594c30b7350d03","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-07-04T23:14:23Z","title_canon_sha256":"d3248fc77fff076a31122eea0503454a0cb602e5060e361084e771a01adb4dbc"},"schema_version":"1.0","source":{"id":"1907.02617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02617","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02617v1","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02617","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"22XJ6VQY7VRX","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"22XJ6VQY7VRXRYAS","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"22XJ6VQY","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:b14c33a6979c85202ad9c8b594f1303adb4ac6552fdaa80e874293938b1411fa","target":"graph","created_at":"2026-05-17T23:41:23Z","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 define rigorously operators of the form $f(\\partial_t)$, in which $f$ is an analytic function on a simply connected domain. Our formalism is based on the Borel transform on entire functions of exponential type. We study existence and regularity of real-valued solutions for the nonlocal in time equation \\begin{equation*} f(\\partial_t) \\phi = J(t) \\; \\; , \\quad t\\in \\mathbb{R}\\; , \\end{equation*}. and we find its more general solution as a restriction to $\\mathbb{R}$ of an entire function of exponential type.\n  As an important special case, we solve explicitly the linear nonlocal zeta field e","authors_text":"Alan Ch\\'avez, Enr\\'ique G. Reyes, Humberto Prado","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-07-04T23:14:23Z","title":"The Borel transform and linear nonlocal equations: applications to zeta-nonlocal field models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02617","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:d9ff4abce1b5fc76251a3a3db02854fe6ffdf76926d2e9f7613f7444c128f118","target":"record","created_at":"2026-05-17T23:41:23Z","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":"0ad8b8614ca94f3747c7c296b09c72bd3ef3e689bb8c6c3177594c30b7350d03","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-07-04T23:14:23Z","title_canon_sha256":"d3248fc77fff076a31122eea0503454a0cb602e5060e361084e771a01adb4dbc"},"schema_version":"1.0","source":{"id":"1907.02617","kind":"arxiv","version":1}},"canonical_sha256":"d6ae9f5618fd6378e0123809c4236351e7c4eeae1f4995cfedaf20bd3263aab7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6ae9f5618fd6378e0123809c4236351e7c4eeae1f4995cfedaf20bd3263aab7","first_computed_at":"2026-05-17T23:41:23.765047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:23.765047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bb67mNyO6Cwkz2m+k6/oGjy9GpzmNE+NMfKdqxJY4mlDq5j8la35Sf8+rcedw6DGZUuOYPOqnAv80O4DnEI/Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:23.765796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9ff4abce1b5fc76251a3a3db02854fe6ffdf76926d2e9f7613f7444c128f118","sha256:b14c33a6979c85202ad9c8b594f1303adb4ac6552fdaa80e874293938b1411fa"],"state_sha256":"abe17d35a77ee8a831af28041c6395b8baf8e24546722f27065c0d77d718f0bd"}