{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XV3NV56GVWTAMCEYHQYPUX573L","short_pith_number":"pith:XV3NV56G","canonical_record":{"source":{"id":"1302.2400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T05:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"b2717c1ac6067fb0839dea8a0079614b810dd3ed891b7f7db8d6a521fafaad94","abstract_canon_sha256":"7d15e95e509a0565d2bd0368015c6f2e85475c92e9d69c0461ffc5e854d2d6c1"},"schema_version":"1.0"},"canonical_sha256":"bd76daf7c6ada60608983c30fa5fbfdaf991cb13aa0fc4e716c42de5c4297a7d","source":{"kind":"arxiv","id":"1302.2400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2400","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2400v1","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2400","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"XV3NV56GVWTA","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XV3NV56GVWTAMCEY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XV3NV56G","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XV3NV56GVWTAMCEYHQYPUX573L","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T05:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"b2717c1ac6067fb0839dea8a0079614b810dd3ed891b7f7db8d6a521fafaad94","abstract_canon_sha256":"7d15e95e509a0565d2bd0368015c6f2e85475c92e9d69c0461ffc5e854d2d6c1"},"schema_version":"1.0"},"canonical_sha256":"bd76daf7c6ada60608983c30fa5fbfdaf991cb13aa0fc4e716c42de5c4297a7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:01.268235Z","signature_b64":"Ujv1IXSBVQUkAJxdlIKKUkrs3R3fm95uqtgU/mi8wWzoKnlKGA+IhfSJ/E++h5MgQerhGlwfCJzPmIXge3A/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd76daf7c6ada60608983c30fa5fbfdaf991cb13aa0fc4e716c42de5c4297a7d","last_reissued_at":"2026-05-18T03:34:01.267455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:01.267455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2400","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":"2026-05-18T03:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Gq/W2TRqhDqFNeaGXZhfK5PYBfXgXfvalAuI6/p7YM+mtEaDcVhZBlqQ7gAaL7hzuNYJ6kEh+ewKTipiOT2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:38:14.397661Z"},"content_sha256":"12a0a137cd3e53ba98d64911ad59772a1ccd87428aa6bfe2b6c23f54301644a8","schema_version":"1.0","event_id":"sha256:12a0a137cd3e53ba98d64911ad59772a1ccd87428aa6bfe2b6c23f54301644a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XV3NV56GVWTAMCEYHQYPUX573L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bj\\\"orn Schmalfuss, Hakima Bessaih, Mar\\'ia J. Garrido-Atienza","submitted_at":"2013-02-11T05:28:37Z","abstract_excerpt":"In this paper we study the longtime dynamics of mild solutions to retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a preparation for this purpose we have to show the existence and uniqueness of a cocycle solution of such an equation. We do not assume that the noise is given in additive form or that it is a very simple multiplicative noise. However, we need some smoothing property for the coefficient in front of the noise. The main idea of this paper consists of expressing the stochastic integral in terms of non-stochastic integrals and the noisy path by usin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2400","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":"2026-05-18T03:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9rjTI6O800emnVIf76eSMOzGwtHSyt8ZsbWLNPvCVer0RACHRfjJNFb94358UR33xDWsUNgP1lD4hYPgx1KgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:38:14.398297Z"},"content_sha256":"50212e4cfec109f043eea95436a3bab219dc093f34d46c37641388c3f15e3d61","schema_version":"1.0","event_id":"sha256:50212e4cfec109f043eea95436a3bab219dc093f34d46c37641388c3f15e3d61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XV3NV56GVWTAMCEYHQYPUX573L/bundle.json","state_url":"https://pith.science/pith/XV3NV56GVWTAMCEYHQYPUX573L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XV3NV56GVWTAMCEYHQYPUX573L/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":"2026-06-04T13:38:14Z","links":{"resolver":"https://pith.science/pith/XV3NV56GVWTAMCEYHQYPUX573L","bundle":"https://pith.science/pith/XV3NV56GVWTAMCEYHQYPUX573L/bundle.json","state":"https://pith.science/pith/XV3NV56GVWTAMCEYHQYPUX573L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XV3NV56GVWTAMCEYHQYPUX573L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XV3NV56GVWTAMCEYHQYPUX573L","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":"7d15e95e509a0565d2bd0368015c6f2e85475c92e9d69c0461ffc5e854d2d6c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T05:28:37Z","title_canon_sha256":"b2717c1ac6067fb0839dea8a0079614b810dd3ed891b7f7db8d6a521fafaad94"},"schema_version":"1.0","source":{"id":"1302.2400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2400","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2400v1","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2400","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"XV3NV56GVWTA","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XV3NV56GVWTAMCEY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XV3NV56G","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:50212e4cfec109f043eea95436a3bab219dc093f34d46c37641388c3f15e3d61","target":"graph","created_at":"2026-05-18T03:34:01Z","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 the longtime dynamics of mild solutions to retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a preparation for this purpose we have to show the existence and uniqueness of a cocycle solution of such an equation. We do not assume that the noise is given in additive form or that it is a very simple multiplicative noise. However, we need some smoothing property for the coefficient in front of the noise. The main idea of this paper consists of expressing the stochastic integral in terms of non-stochastic integrals and the noisy path by usin","authors_text":"Bj\\\"orn Schmalfuss, Hakima Bessaih, Mar\\'ia J. Garrido-Atienza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T05:28:37Z","title":"Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2400","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":"sha256:12a0a137cd3e53ba98d64911ad59772a1ccd87428aa6bfe2b6c23f54301644a8","target":"record","created_at":"2026-05-18T03:34:01Z","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":"7d15e95e509a0565d2bd0368015c6f2e85475c92e9d69c0461ffc5e854d2d6c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T05:28:37Z","title_canon_sha256":"b2717c1ac6067fb0839dea8a0079614b810dd3ed891b7f7db8d6a521fafaad94"},"schema_version":"1.0","source":{"id":"1302.2400","kind":"arxiv","version":1}},"canonical_sha256":"bd76daf7c6ada60608983c30fa5fbfdaf991cb13aa0fc4e716c42de5c4297a7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd76daf7c6ada60608983c30fa5fbfdaf991cb13aa0fc4e716c42de5c4297a7d","first_computed_at":"2026-05-18T03:34:01.267455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:01.267455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ujv1IXSBVQUkAJxdlIKKUkrs3R3fm95uqtgU/mi8wWzoKnlKGA+IhfSJ/E++h5MgQerhGlwfCJzPmIXge3A/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:01.268235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12a0a137cd3e53ba98d64911ad59772a1ccd87428aa6bfe2b6c23f54301644a8","sha256:50212e4cfec109f043eea95436a3bab219dc093f34d46c37641388c3f15e3d61"],"state_sha256":"d029937ce3c758bf3365b31ca608ba3205fde3e309131bb112d82c3798db71ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2arSOYyj9Ef37vtojlbD+H7bwuVBda62slcfEUNI/BBnt5MzVrnb76TWHKY94tltIdb9NrJtHrVDCJWYOGd4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T13:38:14.401665Z","bundle_sha256":"fb691c2c00ff6d22c71e871f31278de7633ccf237033376e736f2891673902f1"}}