{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EYQQVZERLZNMU6PUUMAEW6JND2","short_pith_number":"pith:EYQQVZER","canonical_record":{"source":{"id":"1301.5389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-23T02:58:35Z","cross_cats_sorted":[],"title_canon_sha256":"25f363caa54ecadd5d1320bd249a526308a7c1c74dedf9c39b35a9e3449232a1","abstract_canon_sha256":"e564db408b6054a141a0f3ebff4859325bbe0b106eef60b54d8a5b777d009bfc"},"schema_version":"1.0"},"canonical_sha256":"26210ae4915e5aca79f4a3004b792d1eb0e76edd25f3fc78fc462408dcd2484b","source":{"kind":"arxiv","id":"1301.5389","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5389","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5389v2","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5389","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"pith_short_12","alias_value":"EYQQVZERLZNM","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EYQQVZERLZNMU6PU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EYQQVZER","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EYQQVZERLZNMU6PUUMAEW6JND2","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-23T02:58:35Z","cross_cats_sorted":[],"title_canon_sha256":"25f363caa54ecadd5d1320bd249a526308a7c1c74dedf9c39b35a9e3449232a1","abstract_canon_sha256":"e564db408b6054a141a0f3ebff4859325bbe0b106eef60b54d8a5b777d009bfc"},"schema_version":"1.0"},"canonical_sha256":"26210ae4915e5aca79f4a3004b792d1eb0e76edd25f3fc78fc462408dcd2484b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:46.823084Z","signature_b64":"b/hkNRbJq7+gWf8dpwNK5D7K8gRY3+7l5aTqWJdUBeMbVR6S6peW1b6Reb5D/spXPf6tyXok46C/Kci+5sCaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26210ae4915e5aca79f4a3004b792d1eb0e76edd25f3fc78fc462408dcd2484b","last_reissued_at":"2026-05-18T03:01:46.822645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:46.822645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5389","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":"2026-05-18T03:01:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTD5r7W+489najQBk9cMB8qsI0WJBfmyZBZwF5cGUMhEVDM3QE1hOJdTBuol2ZNI+mpzWvSMbxZ1Y6+SbAt3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:50:56.130785Z"},"content_sha256":"7d702180bc47dfd24b285196c68a289b319e5dfb8ce263d96f550cb7f767b266","schema_version":"1.0","event_id":"sha256:7d702180bc47dfd24b285196c68a289b319e5dfb8ce263d96f550cb7f767b266"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EYQQVZERLZNMU6PUUMAEW6JND2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Aiguo Xiao, Desheng Wang, Siqing Gan","submitted_at":"2013-01-23T02:58:35Z","abstract_excerpt":"This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean square of the solutions for nonlinear SDDEs. The results provide a unified theoretical treatment for SDDEs with constant delay and variable delay (including bounded and unbounded variable delays). Then the stability, contractivity and asymptotic contractivity in mean square are investigated for the backward Euler method. It is shown that the backward Euler metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5389","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":"2026-05-18T03:01:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ni7uRqnweklL4c6GxMKNITgDmadgTtfcMdiWYzRwm2hmvS2y5tTuUFfzmlykMY8DqZvGXET4EkFPs7XKkqLJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:50:56.131435Z"},"content_sha256":"089e5d5fcede207c4413a50579dac16944a6e41994c4b268d69cc3bbb0ad214e","schema_version":"1.0","event_id":"sha256:089e5d5fcede207c4413a50579dac16944a6e41994c4b268d69cc3bbb0ad214e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYQQVZERLZNMU6PUUMAEW6JND2/bundle.json","state_url":"https://pith.science/pith/EYQQVZERLZNMU6PUUMAEW6JND2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYQQVZERLZNMU6PUUMAEW6JND2/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":"2026-05-30T21:50:56Z","links":{"resolver":"https://pith.science/pith/EYQQVZERLZNMU6PUUMAEW6JND2","bundle":"https://pith.science/pith/EYQQVZERLZNMU6PUUMAEW6JND2/bundle.json","state":"https://pith.science/pith/EYQQVZERLZNMU6PUUMAEW6JND2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYQQVZERLZNMU6PUUMAEW6JND2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EYQQVZERLZNMU6PUUMAEW6JND2","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":"e564db408b6054a141a0f3ebff4859325bbe0b106eef60b54d8a5b777d009bfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-23T02:58:35Z","title_canon_sha256":"25f363caa54ecadd5d1320bd249a526308a7c1c74dedf9c39b35a9e3449232a1"},"schema_version":"1.0","source":{"id":"1301.5389","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5389","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5389v2","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5389","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"pith_short_12","alias_value":"EYQQVZERLZNM","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EYQQVZERLZNMU6PU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EYQQVZER","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:089e5d5fcede207c4413a50579dac16944a6e41994c4b268d69cc3bbb0ad214e","target":"graph","created_at":"2026-05-18T03:01:46Z","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":"This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean square of the solutions for nonlinear SDDEs. The results provide a unified theoretical treatment for SDDEs with constant delay and variable delay (including bounded and unbounded variable delays). Then the stability, contractivity and asymptotic contractivity in mean square are investigated for the backward Euler method. It is shown that the backward Euler metho","authors_text":"Aiguo Xiao, Desheng Wang, Siqing Gan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-23T02:58:35Z","title":"Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5389","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":"sha256:7d702180bc47dfd24b285196c68a289b319e5dfb8ce263d96f550cb7f767b266","target":"record","created_at":"2026-05-18T03:01:46Z","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":"e564db408b6054a141a0f3ebff4859325bbe0b106eef60b54d8a5b777d009bfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-23T02:58:35Z","title_canon_sha256":"25f363caa54ecadd5d1320bd249a526308a7c1c74dedf9c39b35a9e3449232a1"},"schema_version":"1.0","source":{"id":"1301.5389","kind":"arxiv","version":2}},"canonical_sha256":"26210ae4915e5aca79f4a3004b792d1eb0e76edd25f3fc78fc462408dcd2484b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26210ae4915e5aca79f4a3004b792d1eb0e76edd25f3fc78fc462408dcd2484b","first_computed_at":"2026-05-18T03:01:46.822645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:46.822645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b/hkNRbJq7+gWf8dpwNK5D7K8gRY3+7l5aTqWJdUBeMbVR6S6peW1b6Reb5D/spXPf6tyXok46C/Kci+5sCaBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:46.823084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5389","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d702180bc47dfd24b285196c68a289b319e5dfb8ce263d96f550cb7f767b266","sha256:089e5d5fcede207c4413a50579dac16944a6e41994c4b268d69cc3bbb0ad214e"],"state_sha256":"42c183677475f5d54dce5aac7cf88d524f4e33ee4f645bfd6a5043d1ec03f049"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CzEIycSQC3J6vMeX73xBOy2s/IZ22GFEcYaaqM1Ep0QsypTAAcotk8c7t1H4D3bZluFmMrzzSKJ5385CoatMDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:50:56.134939Z","bundle_sha256":"2cec2e35bc0e49be4f03bec7da2048d9e81dc9e51d660785a63f517da412b9cc"}}