{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PK46VMDTSFTCS4UP7GK56X4WIT","short_pith_number":"pith:PK46VMDT","canonical_record":{"source":{"id":"1912.10735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-12-23T11:14:06Z","cross_cats_sorted":[],"title_canon_sha256":"fa723a36d35d4d3068e6c35b60a3a7a7336353822f7d68ed1e94b9f924c9ca0e","abstract_canon_sha256":"53656d460da6bd9ef2947527096d3bfddc6da575f6d8714df0a2e01d4830aefa"},"schema_version":"1.0"},"canonical_sha256":"7ab9eab073916629728ff995df5f9644fbaa679b5635156f7a758402995be9fc","source":{"kind":"arxiv","id":"1912.10735","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.10735","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1912.10735v1","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.10735","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"PK46VMDTSFTC","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"PK46VMDTSFTCS4UP","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"PK46VMDT","created_at":"2026-07-05T00:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PK46VMDTSFTCS4UP7GK56X4WIT","target":"record","payload":{"canonical_record":{"source":{"id":"1912.10735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-12-23T11:14:06Z","cross_cats_sorted":[],"title_canon_sha256":"fa723a36d35d4d3068e6c35b60a3a7a7336353822f7d68ed1e94b9f924c9ca0e","abstract_canon_sha256":"53656d460da6bd9ef2947527096d3bfddc6da575f6d8714df0a2e01d4830aefa"},"schema_version":"1.0"},"canonical_sha256":"7ab9eab073916629728ff995df5f9644fbaa679b5635156f7a758402995be9fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:28:02.071056Z","signature_b64":"tpejNm9hICh4QxzBEhTklloASyZpaWT3B2ekl+7T+qCjLHRxr8Z8z6k68SF0JHWtN2IFkvIw/feh9h/UbiJZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ab9eab073916629728ff995df5f9644fbaa679b5635156f7a758402995be9fc","last_reissued_at":"2026-07-05T00:28:02.070682Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:28:02.070682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.10735","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":"2026-07-05T00:28:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aswAdh7+X0Cglwp9lDC9IelD2xELcU8h95bJTtVhDuNhX8j46elXQXXdMUMX+hGZOlgREpi//yAzQyhtwhNQCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T13:29:53.375964Z"},"content_sha256":"418d33912109757d9beed185bc9e56bcf1f56a6d290c715604e82e347a8eda71","schema_version":"1.0","event_id":"sha256:418d33912109757d9beed185bc9e56bcf1f56a6d290c715604e82e347a8eda71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PK46VMDTSFTCS4UP7GK56X4WIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on an expansion formula with application to nonlinear DAE's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Matthias Stiefenhofer","submitted_at":"2019-12-23T11:14:06Z","abstract_excerpt":"In [DL] systems of differential polynomials are investigated with respect to properties of Artin approximation type. The key tool in [DL] is an extended version of a formula by Hurwitz [Hu] expressing high order derivatives of an expansion by lower ones. The formula is further refined in [VFZ] to deliver sufficient conditions concerning the existence of power series solutions of scalar algebraic differential equations of order n. In the paper at hand, the main results from [VFZ] are first reproduced and further extended to systems of nonlinear differential algebraic equations. In addition, a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.10735","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.10735/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:28:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTuGaSpwh7PgsteJW+OCFEMH5qG16XNZy0xXlfyKJEFllSNOonNoSrbNlnqQ25tjKz9d8Gy4Keh0mMN45ydBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T13:29:53.376347Z"},"content_sha256":"17a78c38392cc3b452ec1e68f506a7027b5e1be955f795e63297512e25d16843","schema_version":"1.0","event_id":"sha256:17a78c38392cc3b452ec1e68f506a7027b5e1be955f795e63297512e25d16843"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PK46VMDTSFTCS4UP7GK56X4WIT/bundle.json","state_url":"https://pith.science/pith/PK46VMDTSFTCS4UP7GK56X4WIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PK46VMDTSFTCS4UP7GK56X4WIT/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":"2026-08-13T13:29:53Z","links":{"resolver":"https://pith.science/pith/PK46VMDTSFTCS4UP7GK56X4WIT","bundle":"https://pith.science/pith/PK46VMDTSFTCS4UP7GK56X4WIT/bundle.json","state":"https://pith.science/pith/PK46VMDTSFTCS4UP7GK56X4WIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PK46VMDTSFTCS4UP7GK56X4WIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PK46VMDTSFTCS4UP7GK56X4WIT","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":"53656d460da6bd9ef2947527096d3bfddc6da575f6d8714df0a2e01d4830aefa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-12-23T11:14:06Z","title_canon_sha256":"fa723a36d35d4d3068e6c35b60a3a7a7336353822f7d68ed1e94b9f924c9ca0e"},"schema_version":"1.0","source":{"id":"1912.10735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.10735","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1912.10735v1","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.10735","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"PK46VMDTSFTC","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"PK46VMDTSFTCS4UP","created_at":"2026-07-05T00:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"PK46VMDT","created_at":"2026-07-05T00:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:17a78c38392cc3b452ec1e68f506a7027b5e1be955f795e63297512e25d16843","target":"graph","created_at":"2026-07-05T00:28:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.10735/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In [DL] systems of differential polynomials are investigated with respect to properties of Artin approximation type. The key tool in [DL] is an extended version of a formula by Hurwitz [Hu] expressing high order derivatives of an expansion by lower ones. The formula is further refined in [VFZ] to deliver sufficient conditions concerning the existence of power series solutions of scalar algebraic differential equations of order n. In the paper at hand, the main results from [VFZ] are first reproduced and further extended to systems of nonlinear differential algebraic equations. In addition, a s","authors_text":"Matthias Stiefenhofer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-12-23T11:14:06Z","title":"A note on an expansion formula with application to nonlinear DAE's"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.10735","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":"sha256:418d33912109757d9beed185bc9e56bcf1f56a6d290c715604e82e347a8eda71","target":"record","created_at":"2026-07-05T00:28:02Z","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":"53656d460da6bd9ef2947527096d3bfddc6da575f6d8714df0a2e01d4830aefa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-12-23T11:14:06Z","title_canon_sha256":"fa723a36d35d4d3068e6c35b60a3a7a7336353822f7d68ed1e94b9f924c9ca0e"},"schema_version":"1.0","source":{"id":"1912.10735","kind":"arxiv","version":1}},"canonical_sha256":"7ab9eab073916629728ff995df5f9644fbaa679b5635156f7a758402995be9fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ab9eab073916629728ff995df5f9644fbaa679b5635156f7a758402995be9fc","first_computed_at":"2026-07-05T00:28:02.070682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:28:02.070682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tpejNm9hICh4QxzBEhTklloASyZpaWT3B2ekl+7T+qCjLHRxr8Z8z6k68SF0JHWtN2IFkvIw/feh9h/UbiJZDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:28:02.071056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.10735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:418d33912109757d9beed185bc9e56bcf1f56a6d290c715604e82e347a8eda71","sha256:17a78c38392cc3b452ec1e68f506a7027b5e1be955f795e63297512e25d16843"],"state_sha256":"78be15719aaf8a7cdddfaee8b8bcd69c8504ab3aedc406f99dcff8164ab44199"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fq1KDlnfKbuhxWc8YE8YkIOP0WeZAusmRdw8rTcDAEeFz7E4DjQps/Zjowqxw3bptwFNzgSvcrys8cf8EcP8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T13:29:53.379311Z","bundle_sha256":"d01ce044651b7385b4b904a8de1f16d464a9f2f791cbc49f41d762c1dc684426"}}