{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CPYK3C6GPZPOI2WJZP5CZMRPSI","short_pith_number":"pith:CPYK3C6G","canonical_record":{"source":{"id":"1608.04827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-17T01:23:39Z","cross_cats_sorted":[],"title_canon_sha256":"12313ad22828333dd20d99f19fc3c0d46c8c8ce3e31d2d0f127930d0ef572761","abstract_canon_sha256":"6d68f98f0aa644b8327264302ac308eadafeb04b981a839b1ce643e6d9d6f2d8"},"schema_version":"1.0"},"canonical_sha256":"13f0ad8bc67e5ee46ac9cbfa2cb22f92206bf86234b17a432c21fd13f5f521c1","source":{"kind":"arxiv","id":"1608.04827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04827","created_at":"2026-05-18T01:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04827v1","created_at":"2026-05-18T01:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04827","created_at":"2026-05-18T01:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"CPYK3C6GPZPO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CPYK3C6GPZPOI2WJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CPYK3C6G","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CPYK3C6GPZPOI2WJZP5CZMRPSI","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-17T01:23:39Z","cross_cats_sorted":[],"title_canon_sha256":"12313ad22828333dd20d99f19fc3c0d46c8c8ce3e31d2d0f127930d0ef572761","abstract_canon_sha256":"6d68f98f0aa644b8327264302ac308eadafeb04b981a839b1ce643e6d9d6f2d8"},"schema_version":"1.0"},"canonical_sha256":"13f0ad8bc67e5ee46ac9cbfa2cb22f92206bf86234b17a432c21fd13f5f521c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:33.433518Z","signature_b64":"koNiuJBASs9J3cQtD5WiomnxL3Lq1Bcv4CYNE+0YvtYE94E/gvmWNTOw49cPOGLLz34T36AY1VvauG+Y5DumBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13f0ad8bc67e5ee46ac9cbfa2cb22f92206bf86234b17a432c21fd13f5f521c1","last_reissued_at":"2026-05-18T01:08:33.432770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:33.432770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04827","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":"2026-05-18T01:08:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SMxDN/TAOwYPpjnXSGbYVgR8hTBcGZeklGJVcqWDziHbBZImMnTeBX34Tmh0jCBib8ul8K6M9h6k2p6FW0sVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:40:16.807231Z"},"content_sha256":"d883ac538088c5fe9a2291c468e1ab8dfef722547594f368d8e86bf2be1ef2b5","schema_version":"1.0","event_id":"sha256:d883ac538088c5fe9a2291c468e1ab8dfef722547594f368d8e86bf2be1ef2b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CPYK3C6GPZPOI2WJZP5CZMRPSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-Posedness of some nonlinear Volterra-Fredholm integral and integro-dynamic equations on time scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ahmed G. Ghallab, Alaa E.Hamza","submitted_at":"2016-08-17T01:23:39Z","abstract_excerpt":"In this paper we study well posedness of a certain nonlinear Volterra-Fredholm dynamic integral and integro-dynamic equations on unbounded interval from arbitrary time scale. We derive the time scale analogue of certain integral inequalities of Pachpatte type and using them with Banach's fixed-point theorem to establish the results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04827","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":"2026-05-18T01:08:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4u+3N4PDT3Gr+HK0aYvbaEwosIp5xj9baVa4vxIG2JziU954s8SDxdb4SZe9kgzgoJXY4T3StV3hW3HR/21fBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:40:16.807582Z"},"content_sha256":"bb768ca8b1f27d7803ae47164d53807ded30218d2ae497a90a69fcf9b305b813","schema_version":"1.0","event_id":"sha256:bb768ca8b1f27d7803ae47164d53807ded30218d2ae497a90a69fcf9b305b813"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPYK3C6GPZPOI2WJZP5CZMRPSI/bundle.json","state_url":"https://pith.science/pith/CPYK3C6GPZPOI2WJZP5CZMRPSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPYK3C6GPZPOI2WJZP5CZMRPSI/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":"2026-06-05T01:40:16Z","links":{"resolver":"https://pith.science/pith/CPYK3C6GPZPOI2WJZP5CZMRPSI","bundle":"https://pith.science/pith/CPYK3C6GPZPOI2WJZP5CZMRPSI/bundle.json","state":"https://pith.science/pith/CPYK3C6GPZPOI2WJZP5CZMRPSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPYK3C6GPZPOI2WJZP5CZMRPSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CPYK3C6GPZPOI2WJZP5CZMRPSI","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":"6d68f98f0aa644b8327264302ac308eadafeb04b981a839b1ce643e6d9d6f2d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-17T01:23:39Z","title_canon_sha256":"12313ad22828333dd20d99f19fc3c0d46c8c8ce3e31d2d0f127930d0ef572761"},"schema_version":"1.0","source":{"id":"1608.04827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04827","created_at":"2026-05-18T01:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04827v1","created_at":"2026-05-18T01:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04827","created_at":"2026-05-18T01:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"CPYK3C6GPZPO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CPYK3C6GPZPOI2WJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CPYK3C6G","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:bb768ca8b1f27d7803ae47164d53807ded30218d2ae497a90a69fcf9b305b813","target":"graph","created_at":"2026-05-18T01:08:33Z","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 paper we study well posedness of a certain nonlinear Volterra-Fredholm dynamic integral and integro-dynamic equations on unbounded interval from arbitrary time scale. We derive the time scale analogue of certain integral inequalities of Pachpatte type and using them with Banach's fixed-point theorem to establish the results.","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":"2016-08-17T01:23:39Z","title":"Well-Posedness of some nonlinear Volterra-Fredholm integral and integro-dynamic equations on time scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04827","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:d883ac538088c5fe9a2291c468e1ab8dfef722547594f368d8e86bf2be1ef2b5","target":"record","created_at":"2026-05-18T01:08:33Z","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":"6d68f98f0aa644b8327264302ac308eadafeb04b981a839b1ce643e6d9d6f2d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-17T01:23:39Z","title_canon_sha256":"12313ad22828333dd20d99f19fc3c0d46c8c8ce3e31d2d0f127930d0ef572761"},"schema_version":"1.0","source":{"id":"1608.04827","kind":"arxiv","version":1}},"canonical_sha256":"13f0ad8bc67e5ee46ac9cbfa2cb22f92206bf86234b17a432c21fd13f5f521c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13f0ad8bc67e5ee46ac9cbfa2cb22f92206bf86234b17a432c21fd13f5f521c1","first_computed_at":"2026-05-18T01:08:33.432770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:33.432770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"koNiuJBASs9J3cQtD5WiomnxL3Lq1Bcv4CYNE+0YvtYE94E/gvmWNTOw49cPOGLLz34T36AY1VvauG+Y5DumBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:33.433518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d883ac538088c5fe9a2291c468e1ab8dfef722547594f368d8e86bf2be1ef2b5","sha256:bb768ca8b1f27d7803ae47164d53807ded30218d2ae497a90a69fcf9b305b813"],"state_sha256":"ac317ff900f268f979c1f2e4c933438a8768a6f7cadab6f6277a80d1b9f6aac2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uOHL3AcgLQdNxFiIa45wNu8fqTXcsoPdcd6yx1RqGOVw+2B5AJthLfd1YelN7dDeQRIuXIY+nwzAsVk3B2lmBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:40:16.809613Z","bundle_sha256":"5d6cad2b0480a2ea334adae3ae3822b1645a3546caa339560754dc2e2870e2ec"}}