{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C3LMFPBKZQ36IEXRLIOHTPBM7Q","short_pith_number":"pith:C3LMFPBK","canonical_record":{"source":{"id":"1809.03163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-10T07:42:20Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"416fb5e3c470c7262ab11cce61b72561531759740a3b4beaa85639e6f36a454a","abstract_canon_sha256":"cacd3beaf57977478c787b09791ee920305f6a64c67a006938224b46c16f8155"},"schema_version":"1.0"},"canonical_sha256":"16d6c2bc2acc37e412f15a1c79bc2cfc0d914f4587f3fa03383fd3300958183b","source":{"kind":"arxiv","id":"1809.03163","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03163","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03163v1","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03163","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"C3LMFPBKZQ36","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C3LMFPBKZQ36IEXR","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C3LMFPBK","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C3LMFPBKZQ36IEXRLIOHTPBM7Q","target":"record","payload":{"canonical_record":{"source":{"id":"1809.03163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-10T07:42:20Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"416fb5e3c470c7262ab11cce61b72561531759740a3b4beaa85639e6f36a454a","abstract_canon_sha256":"cacd3beaf57977478c787b09791ee920305f6a64c67a006938224b46c16f8155"},"schema_version":"1.0"},"canonical_sha256":"16d6c2bc2acc37e412f15a1c79bc2cfc0d914f4587f3fa03383fd3300958183b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:52.286622Z","signature_b64":"rzC/PycORkZdENcsu/o5acV7ViFjiLe/kgybmahZ5MytMzqx/2WAF1IT/8gt8ipXi2M9Zfsn6sXVwJPXU/vuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16d6c2bc2acc37e412f15a1c79bc2cfc0d914f4587f3fa03383fd3300958183b","last_reissued_at":"2026-05-17T23:52:52.285924Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:52.285924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.03163","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":"2026-05-17T23:52:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3Bwoi6b+EwauPtcJ1delxZFKX2ly/+V+NQ8ALWsjM5VryY9J7sS8i0hL/NEp187uxbTsv0STAY01Tok3tcMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T12:02:15.391135Z"},"content_sha256":"b0dea0f93c04a17b5327599b31e41bc5cdcdf2bf39aa6d75d86329248b6b6323","schema_version":"1.0","event_id":"sha256:b0dea0f93c04a17b5327599b31e41bc5cdcdf2bf39aa6d75d86329248b6b6323"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C3LMFPBKZQ36IEXRLIOHTPBM7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extension and Application of Deleting Items and Disturbing Mesh Theorem of Riemann Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.PR","authors_text":"Jingwei Liu","submitted_at":"2018-09-10T07:42:20Z","abstract_excerpt":"The deleting items and disturbing mesh theorems of Riemann Integral are extended to multiple integral,line integral and surface integral respectively by constructing various of incomplete Riemann sum and non-Riemann sum sequences which converge to the same limit of classical Riemann sum. And, the deleting items and disturbing mesh formulae of Green's theorem, Stokes' theorem and divergence theorem (Gauss's or Ostrogradsky 's theorem) are also deduced. Then, the deleting items and disturbing mesh theorems of general Stokes' theorem on differential manifold are also derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03163","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":"2026-05-17T23:52:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5nDEeOMBF1pVsASdEeW+MaxLO7j+u/jmwZ/GueqPLY+yznTRQ/q8dgMIWIxY/Rk6kmgMFmNXqqPP5D/r+XrlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T12:02:15.391493Z"},"content_sha256":"b5899e59808a84cc4df4d70b5bbb64fbb85dba68ae7901f96b65d969899ea81e","schema_version":"1.0","event_id":"sha256:b5899e59808a84cc4df4d70b5bbb64fbb85dba68ae7901f96b65d969899ea81e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3LMFPBKZQ36IEXRLIOHTPBM7Q/bundle.json","state_url":"https://pith.science/pith/C3LMFPBKZQ36IEXRLIOHTPBM7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3LMFPBKZQ36IEXRLIOHTPBM7Q/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":"2026-05-20T12:02:15Z","links":{"resolver":"https://pith.science/pith/C3LMFPBKZQ36IEXRLIOHTPBM7Q","bundle":"https://pith.science/pith/C3LMFPBKZQ36IEXRLIOHTPBM7Q/bundle.json","state":"https://pith.science/pith/C3LMFPBKZQ36IEXRLIOHTPBM7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3LMFPBKZQ36IEXRLIOHTPBM7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C3LMFPBKZQ36IEXRLIOHTPBM7Q","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":"cacd3beaf57977478c787b09791ee920305f6a64c67a006938224b46c16f8155","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-10T07:42:20Z","title_canon_sha256":"416fb5e3c470c7262ab11cce61b72561531759740a3b4beaa85639e6f36a454a"},"schema_version":"1.0","source":{"id":"1809.03163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03163","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03163v1","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03163","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"C3LMFPBKZQ36","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C3LMFPBKZQ36IEXR","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C3LMFPBK","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:b5899e59808a84cc4df4d70b5bbb64fbb85dba68ae7901f96b65d969899ea81e","target":"graph","created_at":"2026-05-17T23:52:52Z","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":"The deleting items and disturbing mesh theorems of Riemann Integral are extended to multiple integral,line integral and surface integral respectively by constructing various of incomplete Riemann sum and non-Riemann sum sequences which converge to the same limit of classical Riemann sum. And, the deleting items and disturbing mesh formulae of Green's theorem, Stokes' theorem and divergence theorem (Gauss's or Ostrogradsky 's theorem) are also deduced. Then, the deleting items and disturbing mesh theorems of general Stokes' theorem on differential manifold are also derived.","authors_text":"Jingwei Liu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-10T07:42:20Z","title":"Extension and Application of Deleting Items and Disturbing Mesh Theorem of Riemann Integral"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03163","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:b0dea0f93c04a17b5327599b31e41bc5cdcdf2bf39aa6d75d86329248b6b6323","target":"record","created_at":"2026-05-17T23:52:52Z","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":"cacd3beaf57977478c787b09791ee920305f6a64c67a006938224b46c16f8155","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-10T07:42:20Z","title_canon_sha256":"416fb5e3c470c7262ab11cce61b72561531759740a3b4beaa85639e6f36a454a"},"schema_version":"1.0","source":{"id":"1809.03163","kind":"arxiv","version":1}},"canonical_sha256":"16d6c2bc2acc37e412f15a1c79bc2cfc0d914f4587f3fa03383fd3300958183b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16d6c2bc2acc37e412f15a1c79bc2cfc0d914f4587f3fa03383fd3300958183b","first_computed_at":"2026-05-17T23:52:52.285924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:52.285924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rzC/PycORkZdENcsu/o5acV7ViFjiLe/kgybmahZ5MytMzqx/2WAF1IT/8gt8ipXi2M9Zfsn6sXVwJPXU/vuCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:52.286622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0dea0f93c04a17b5327599b31e41bc5cdcdf2bf39aa6d75d86329248b6b6323","sha256:b5899e59808a84cc4df4d70b5bbb64fbb85dba68ae7901f96b65d969899ea81e"],"state_sha256":"c421930122747926cc3d41f48f7549bc1dbec46b0364c2b3b795df636e42824f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dh7pDme5SKQN7/811+lIvB87HBoLRAXv7xHPiPIYs4395KBSgr9mloEKOVpkln06Jehc56sDRDW1ODA+1B4gAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T12:02:15.393892Z","bundle_sha256":"999a781a83b69da824f95e36264b34b45d66016d72d3f18191631a62def2ea0b"}}