{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:2SEVIYBOS5TG42JH32ES2LM2D6","short_pith_number":"pith:2SEVIYBO","canonical_record":{"source":{"id":"1905.02109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-06T15:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"b4cdcfd0a821263915d7bbbf3db8d22fd9e874f16d25b20fa763d033b7b02a20","abstract_canon_sha256":"b2e9236acf5b617fe2d120fedcccc28712f806aaae0e95d321d144e034e172d9"},"schema_version":"1.0"},"canonical_sha256":"d48954602e97666e6927de892d2d9a1fbc09c3c424a91d3cf6c651bbab919af5","source":{"kind":"arxiv","id":"1905.02109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02109","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02109v1","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02109","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"2SEVIYBOS5TG","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2SEVIYBOS5TG42JH","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2SEVIYBO","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:2SEVIYBOS5TG42JH32ES2LM2D6","target":"record","payload":{"canonical_record":{"source":{"id":"1905.02109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-06T15:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"b4cdcfd0a821263915d7bbbf3db8d22fd9e874f16d25b20fa763d033b7b02a20","abstract_canon_sha256":"b2e9236acf5b617fe2d120fedcccc28712f806aaae0e95d321d144e034e172d9"},"schema_version":"1.0"},"canonical_sha256":"d48954602e97666e6927de892d2d9a1fbc09c3c424a91d3cf6c651bbab919af5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:56.330368Z","signature_b64":"JmBS3lUFwlCuSYcJ8AezjxQkI0mDDkP070T3Dayz+CZKHEA4mL3eLYz3qmVHN1zMNsvsxj4Ul1Fdj4abykfUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d48954602e97666e6927de892d2d9a1fbc09c3c424a91d3cf6c651bbab919af5","last_reissued_at":"2026-05-17T23:46:56.329636Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:56.329636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.02109","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":"2026-05-17T23:46:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Rrz9zJiilM5SqqKmvtXtBod1eGSpFyZmqz3faX6rMQl8z89zNhXyL8YQ2o87t0KaJe4yvLN3oo6Jjg13PI1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T04:33:57.928031Z"},"content_sha256":"1c7f0d1be78be0145f4adb168e10e7a255098f7ef5fc73deb23acca58cd710e5","schema_version":"1.0","event_id":"sha256:1c7f0d1be78be0145f4adb168e10e7a255098f7ef5fc73deb23acca58cd710e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:2SEVIYBOS5TG42JH32ES2LM2D6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jiayang Yu, Xu Zhang","submitted_at":"2019-05-06T15:47:00Z","abstract_excerpt":"The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with infinite number of variables. We adopt von Koch and Hilbert's definition of analyticity of functions as monomial expansions. Our Cauchy-Kowalevski type theorem is derived by modifying the classical method of majorants. Based on this result, by employing some tools from abstract Wiener spaces, we establish our Holmgren type theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02109","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":"2026-05-17T23:46:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XxXATuVviwgHn+1EqDG1m8W8MmG/LbEkVbzGC9LIywWsT7HavjSqkuoy8ljpt1qRxJrUlwCF7uUZtzdeegMXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T04:33:57.928383Z"},"content_sha256":"3e3ee2458103a5706470c152fae9cc8f84f99607c7c58cebd8e33b2b3d165064","schema_version":"1.0","event_id":"sha256:3e3ee2458103a5706470c152fae9cc8f84f99607c7c58cebd8e33b2b3d165064"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2SEVIYBOS5TG42JH32ES2LM2D6/bundle.json","state_url":"https://pith.science/pith/2SEVIYBOS5TG42JH32ES2LM2D6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2SEVIYBOS5TG42JH32ES2LM2D6/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":"2026-07-03T04:33:57Z","links":{"resolver":"https://pith.science/pith/2SEVIYBOS5TG42JH32ES2LM2D6","bundle":"https://pith.science/pith/2SEVIYBOS5TG42JH32ES2LM2D6/bundle.json","state":"https://pith.science/pith/2SEVIYBOS5TG42JH32ES2LM2D6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2SEVIYBOS5TG42JH32ES2LM2D6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2SEVIYBOS5TG42JH32ES2LM2D6","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":"b2e9236acf5b617fe2d120fedcccc28712f806aaae0e95d321d144e034e172d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-06T15:47:00Z","title_canon_sha256":"b4cdcfd0a821263915d7bbbf3db8d22fd9e874f16d25b20fa763d033b7b02a20"},"schema_version":"1.0","source":{"id":"1905.02109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02109","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02109v1","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02109","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"2SEVIYBOS5TG","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2SEVIYBOS5TG42JH","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2SEVIYBO","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:3e3ee2458103a5706470c152fae9cc8f84f99607c7c58cebd8e33b2b3d165064","target":"graph","created_at":"2026-05-17T23:46:56Z","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 aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with infinite number of variables. We adopt von Koch and Hilbert's definition of analyticity of functions as monomial expansions. Our Cauchy-Kowalevski type theorem is derived by modifying the classical method of majorants. Based on this result, by employing some tools from abstract Wiener spaces, we establish our Holmgren type theorem.","authors_text":"Jiayang Yu, Xu Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-06T15:47:00Z","title":"Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02109","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":"sha256:1c7f0d1be78be0145f4adb168e10e7a255098f7ef5fc73deb23acca58cd710e5","target":"record","created_at":"2026-05-17T23:46:56Z","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":"b2e9236acf5b617fe2d120fedcccc28712f806aaae0e95d321d144e034e172d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-06T15:47:00Z","title_canon_sha256":"b4cdcfd0a821263915d7bbbf3db8d22fd9e874f16d25b20fa763d033b7b02a20"},"schema_version":"1.0","source":{"id":"1905.02109","kind":"arxiv","version":1}},"canonical_sha256":"d48954602e97666e6927de892d2d9a1fbc09c3c424a91d3cf6c651bbab919af5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d48954602e97666e6927de892d2d9a1fbc09c3c424a91d3cf6c651bbab919af5","first_computed_at":"2026-05-17T23:46:56.329636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:56.329636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JmBS3lUFwlCuSYcJ8AezjxQkI0mDDkP070T3Dayz+CZKHEA4mL3eLYz3qmVHN1zMNsvsxj4Ul1Fdj4abykfUBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:56.330368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c7f0d1be78be0145f4adb168e10e7a255098f7ef5fc73deb23acca58cd710e5","sha256:3e3ee2458103a5706470c152fae9cc8f84f99607c7c58cebd8e33b2b3d165064"],"state_sha256":"670dcdeddcf0b08497fb8040e63e8123ccb914faff8106d58fed48f016fde8e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tf9EBPG0A6XWe0VTsmSqENp0iIsF9alOYy9Otoj+QsBI90NJohj+sXVYThbsVj3kprW559S4tu07zolIyPxXAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T04:33:57.930288Z","bundle_sha256":"8e11e55335143d4658fd9df2f3e86c46eaa33c44463757b4d97831a432aeb000"}}