{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SLGYS3IO4JS5XX4NORXKYYFG5X","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":"ba158ee1fa283a6ffb74b92b637b9eb6fddef14c85a08371311dfa8bd76073bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-08T23:47:05Z","title_canon_sha256":"5d823cccce7898f0f35a18cb1bd4372c51bcf2f35afcce0fb739039facc1932b"},"schema_version":"1.0","source":{"id":"1701.02038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02038","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02038v1","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02038","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"pith_short_12","alias_value":"SLGYS3IO4JS5","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SLGYS3IO4JS5XX4N","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SLGYS3IO","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:89937457371e0d29f72e187ebf4df6ae82bd6430be1d494c5150a0722cbb9ab1","target":"graph","created_at":"2026-05-18T00:53:11Z","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":"In this article, we investigate the method of upper and lower solutions for Volterra integral equation of the first kind on arbitrary time scale $\\mathbb{T}$. We establish some existence results in a certain sector. Moreover, monotone iterative technique is used to obtain maximal and minimal solutions of the considered equation.","authors_text":"Ahmed G. Ghallab, Alaa E. Hamza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-08T23:47:05Z","title":"Existence Results by The Method of Upper and Lower Solutions for Volterra Integral Equation on Time Scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02038","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":"sha256:77b74a28cd9227c2dfe2d7b902806ac123261e3408de3e5571bb6fa9a9f42147","target":"record","created_at":"2026-05-18T00:53:11Z","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":"ba158ee1fa283a6ffb74b92b637b9eb6fddef14c85a08371311dfa8bd76073bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-08T23:47:05Z","title_canon_sha256":"5d823cccce7898f0f35a18cb1bd4372c51bcf2f35afcce0fb739039facc1932b"},"schema_version":"1.0","source":{"id":"1701.02038","kind":"arxiv","version":1}},"canonical_sha256":"92cd896d0ee265dbdf8d746eac60a6edfecfd962666bb5625695a90e4cce0833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92cd896d0ee265dbdf8d746eac60a6edfecfd962666bb5625695a90e4cce0833","first_computed_at":"2026-05-18T00:53:11.792557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:11.792557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZvk6HdiFd03DZ34uhUgRnIdVVS/I5PoKSDhDjBQk/M6iCSddlWQC80OvisveYYQTkbHJ0ImrPUu9Rj/2tFpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:11.793042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77b74a28cd9227c2dfe2d7b902806ac123261e3408de3e5571bb6fa9a9f42147","sha256:89937457371e0d29f72e187ebf4df6ae82bd6430be1d494c5150a0722cbb9ab1"],"state_sha256":"f19db2dde818f1497c645c6150d5b5a67cd583280fe66fd85349a9c4ab8f9fc6"}