{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3SXNWVJRP2KX5F3ZH4FHF2BVEM","short_pith_number":"pith:3SXNWVJR","canonical_record":{"source":{"id":"1202.4389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-20T17:19:48Z","cross_cats_sorted":["math.DS","math.NA"],"title_canon_sha256":"d64100b8c32625fc9848b1213e114b2c2572069ed97679575329e5addfbf4df5","abstract_canon_sha256":"36c77f28400efe33def76dcee7383f018fecfdcdf000785c71dee74008d7e0a6"},"schema_version":"1.0"},"canonical_sha256":"dcaedb55317e957e97793f0a72e835233ca301505a793956132399c7fd1fec98","source":{"kind":"arxiv","id":"1202.4389","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4389","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4389v2","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4389","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"pith_short_12","alias_value":"3SXNWVJRP2KX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3SXNWVJRP2KX5F3Z","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3SXNWVJR","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3SXNWVJRP2KX5F3ZH4FHF2BVEM","target":"record","payload":{"canonical_record":{"source":{"id":"1202.4389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-20T17:19:48Z","cross_cats_sorted":["math.DS","math.NA"],"title_canon_sha256":"d64100b8c32625fc9848b1213e114b2c2572069ed97679575329e5addfbf4df5","abstract_canon_sha256":"36c77f28400efe33def76dcee7383f018fecfdcdf000785c71dee74008d7e0a6"},"schema_version":"1.0"},"canonical_sha256":"dcaedb55317e957e97793f0a72e835233ca301505a793956132399c7fd1fec98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:41.787025Z","signature_b64":"Q/E5Lq51oK2VcGzvvx05yL2Xbs8/AC9blmIn1U6OnGQ6Ag1MHVgLwb0bR6tBQqW97CmvalEuEdVYJFM8A5acAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcaedb55317e957e97793f0a72e835233ca301505a793956132399c7fd1fec98","last_reissued_at":"2026-05-18T03:39:41.786427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:41.786427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.4389","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3q9k7U68enVrQWcN/dx7pLg80di/5Xlrdb7/wUCEtrCkbfUC+ntBey9hsZgy7Y6Psn4Vz3i3seKTVCypQt5oCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:16:11.517876Z"},"content_sha256":"4f130433a55078712e8cb968923faab913614123569f06b862cfadebda3b0179","schema_version":"1.0","event_id":"sha256:4f130433a55078712e8cb968923faab913614123569f06b862cfadebda3b0179"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3SXNWVJRP2KX5F3ZH4FHF2BVEM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator splitting for nonautonomous delay equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NA"],"primary_cat":"math.FA","authors_text":"Andr\\'as B\\'atkai, B\\'alint Farkas, Petra Csom\\'os","submitted_at":"2012-02-20T17:19:48Z","abstract_excerpt":"We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the theoretical results are demonstrated on some typical numerical examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4389","kind":"arxiv","version":2},"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":"2026-05-18T03:39:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SX+64VIJZylSuicMApszngilPPzUOF+hElS4ZNMlh8NsBmq5Cg8kj28D5gtaqIGkLwFyz/KnTxBFSKKiv0LABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:16:11.518227Z"},"content_sha256":"b1f26128044146e25f81d34c9085f6ee0a0bbf5b7b1bca3f143fc30458e3f332","schema_version":"1.0","event_id":"sha256:b1f26128044146e25f81d34c9085f6ee0a0bbf5b7b1bca3f143fc30458e3f332"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3SXNWVJRP2KX5F3ZH4FHF2BVEM/bundle.json","state_url":"https://pith.science/pith/3SXNWVJRP2KX5F3ZH4FHF2BVEM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3SXNWVJRP2KX5F3ZH4FHF2BVEM/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":"2026-06-24T15:16:11Z","links":{"resolver":"https://pith.science/pith/3SXNWVJRP2KX5F3ZH4FHF2BVEM","bundle":"https://pith.science/pith/3SXNWVJRP2KX5F3ZH4FHF2BVEM/bundle.json","state":"https://pith.science/pith/3SXNWVJRP2KX5F3ZH4FHF2BVEM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3SXNWVJRP2KX5F3ZH4FHF2BVEM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3SXNWVJRP2KX5F3ZH4FHF2BVEM","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":"36c77f28400efe33def76dcee7383f018fecfdcdf000785c71dee74008d7e0a6","cross_cats_sorted":["math.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-20T17:19:48Z","title_canon_sha256":"d64100b8c32625fc9848b1213e114b2c2572069ed97679575329e5addfbf4df5"},"schema_version":"1.0","source":{"id":"1202.4389","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4389","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4389v2","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4389","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"pith_short_12","alias_value":"3SXNWVJRP2KX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3SXNWVJRP2KX5F3Z","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3SXNWVJR","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:b1f26128044146e25f81d34c9085f6ee0a0bbf5b7b1bca3f143fc30458e3f332","target":"graph","created_at":"2026-05-18T03:39:41Z","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":"We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the theoretical results are demonstrated on some typical numerical examples.","authors_text":"Andr\\'as B\\'atkai, B\\'alint Farkas, Petra Csom\\'os","cross_cats":["math.DS","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-20T17:19:48Z","title":"Operator splitting for nonautonomous delay equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4389","kind":"arxiv","version":2},"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":"sha256:4f130433a55078712e8cb968923faab913614123569f06b862cfadebda3b0179","target":"record","created_at":"2026-05-18T03:39:41Z","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":"36c77f28400efe33def76dcee7383f018fecfdcdf000785c71dee74008d7e0a6","cross_cats_sorted":["math.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-20T17:19:48Z","title_canon_sha256":"d64100b8c32625fc9848b1213e114b2c2572069ed97679575329e5addfbf4df5"},"schema_version":"1.0","source":{"id":"1202.4389","kind":"arxiv","version":2}},"canonical_sha256":"dcaedb55317e957e97793f0a72e835233ca301505a793956132399c7fd1fec98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcaedb55317e957e97793f0a72e835233ca301505a793956132399c7fd1fec98","first_computed_at":"2026-05-18T03:39:41.786427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:41.786427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q/E5Lq51oK2VcGzvvx05yL2Xbs8/AC9blmIn1U6OnGQ6Ag1MHVgLwb0bR6tBQqW97CmvalEuEdVYJFM8A5acAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:41.787025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4389","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f130433a55078712e8cb968923faab913614123569f06b862cfadebda3b0179","sha256:b1f26128044146e25f81d34c9085f6ee0a0bbf5b7b1bca3f143fc30458e3f332"],"state_sha256":"bf3c864a652ca494e94b8e52d7e2bcf20c27ecc8534c08c5290440e6e3c02c22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Y+5gBifPAVuNpChVkHofgBMeZcozyPHT8KpZViH4UkU7h5CwhDPBauBLyIHkhQl2i01cV5YNlwnI9KFion9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T15:16:11.520182Z","bundle_sha256":"4cf23035a3e4d7861647baca025b26c16a0b9e6bfbe9d9dbd89c0f347ea2964e"}}