{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3RNLNVXSTYK7IJEFDMB34MDYT5","short_pith_number":"pith:3RNLNVXS","canonical_record":{"source":{"id":"1802.04574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-13T11:45:26Z","cross_cats_sorted":[],"title_canon_sha256":"b8399801cb652a56bf458e3d52fb63e99bdc4967c9a64a50f0a8ca8e6b144e9a","abstract_canon_sha256":"1154d3ed1d8f165b33bc00c6c49fae19105b354d5bd7dadae2d392a1b18ddb5b"},"schema_version":"1.0"},"canonical_sha256":"dc5ab6d6f29e15f424851b03be30789f59550086877ae5bded84905600aa0235","source":{"kind":"arxiv","id":"1802.04574","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04574","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04574v1","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04574","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"pith_short_12","alias_value":"3RNLNVXSTYK7","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3RNLNVXSTYK7IJEF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3RNLNVXS","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3RNLNVXSTYK7IJEFDMB34MDYT5","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-13T11:45:26Z","cross_cats_sorted":[],"title_canon_sha256":"b8399801cb652a56bf458e3d52fb63e99bdc4967c9a64a50f0a8ca8e6b144e9a","abstract_canon_sha256":"1154d3ed1d8f165b33bc00c6c49fae19105b354d5bd7dadae2d392a1b18ddb5b"},"schema_version":"1.0"},"canonical_sha256":"dc5ab6d6f29e15f424851b03be30789f59550086877ae5bded84905600aa0235","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:42.083351Z","signature_b64":"h/QQZiR+mtBXTzQSb4KWLZC/mfpEEwtB2jCHoXJtm9eLm6P6Fyh6ziPj7O5uIJ/ssxDXdsblZv9Wiz/rYvFnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc5ab6d6f29e15f424851b03be30789f59550086877ae5bded84905600aa0235","last_reissued_at":"2026-05-18T00:23:42.082835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:42.082835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04574","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":"2026-05-18T00:23:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmaa0llL+ENlf9Ju7aXyIFgwp24NVZz7pqtMpJTkdVgaVt1nqENdTpEwlRGL0AQovKRQyZ4rUjyRw4lMfAleCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:15:56.045219Z"},"content_sha256":"a88d78978473e329d2e1f6f33b6cc6a05edf42c0e5ba35a7db333fb298f67ed1","schema_version":"1.0","event_id":"sha256:a88d78978473e329d2e1f6f33b6cc6a05edf42c0e5ba35a7db333fb298f67ed1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3RNLNVXSTYK7IJEFDMB34MDYT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The effect of noise intensity on stochastic parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangying Lv, Hongjun Gao, Jiang-Lun Wu, Jinlong Wei","submitted_at":"2018-02-13T11:45:26Z","abstract_excerpt":"In the present paper, the effect of noise intensity on stochastic parabolic equations is discussed. We focus on the effect of noise on the energy solutions of the stochastic parabolic equations. By utilising It\\^o's formula and the energy estimate method, we obtain the excitation indices of the energy solutions $u$ at any finite time $t$. Furthermore, we improve certain existing results in the literature by presenting a comparably simple method to show those existing results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04574","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":"2026-05-18T00:23:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hm7vUR5hshw4r34J8T0AeorY90JzrCxhY4C8wMQUtu/D54sQxeH457b5/4Rmo6PAPYgtvo6CSDnP42qjBLI9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:15:56.045825Z"},"content_sha256":"f3ca3ef98b1b7f95e7e9850269aca32849c97cca2bb267bd7c36146dce60b39f","schema_version":"1.0","event_id":"sha256:f3ca3ef98b1b7f95e7e9850269aca32849c97cca2bb267bd7c36146dce60b39f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RNLNVXSTYK7IJEFDMB34MDYT5/bundle.json","state_url":"https://pith.science/pith/3RNLNVXSTYK7IJEFDMB34MDYT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RNLNVXSTYK7IJEFDMB34MDYT5/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":"2026-05-25T23:15:56Z","links":{"resolver":"https://pith.science/pith/3RNLNVXSTYK7IJEFDMB34MDYT5","bundle":"https://pith.science/pith/3RNLNVXSTYK7IJEFDMB34MDYT5/bundle.json","state":"https://pith.science/pith/3RNLNVXSTYK7IJEFDMB34MDYT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RNLNVXSTYK7IJEFDMB34MDYT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3RNLNVXSTYK7IJEFDMB34MDYT5","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":"1154d3ed1d8f165b33bc00c6c49fae19105b354d5bd7dadae2d392a1b18ddb5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-13T11:45:26Z","title_canon_sha256":"b8399801cb652a56bf458e3d52fb63e99bdc4967c9a64a50f0a8ca8e6b144e9a"},"schema_version":"1.0","source":{"id":"1802.04574","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04574","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04574v1","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04574","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"pith_short_12","alias_value":"3RNLNVXSTYK7","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3RNLNVXSTYK7IJEF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3RNLNVXS","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:f3ca3ef98b1b7f95e7e9850269aca32849c97cca2bb267bd7c36146dce60b39f","target":"graph","created_at":"2026-05-18T00:23:42Z","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 the present paper, the effect of noise intensity on stochastic parabolic equations is discussed. We focus on the effect of noise on the energy solutions of the stochastic parabolic equations. By utilising It\\^o's formula and the energy estimate method, we obtain the excitation indices of the energy solutions $u$ at any finite time $t$. Furthermore, we improve certain existing results in the literature by presenting a comparably simple method to show those existing results.","authors_text":"Guangying Lv, Hongjun Gao, Jiang-Lun Wu, Jinlong Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-13T11:45:26Z","title":"The effect of noise intensity on stochastic parabolic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04574","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:a88d78978473e329d2e1f6f33b6cc6a05edf42c0e5ba35a7db333fb298f67ed1","target":"record","created_at":"2026-05-18T00:23:42Z","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":"1154d3ed1d8f165b33bc00c6c49fae19105b354d5bd7dadae2d392a1b18ddb5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-13T11:45:26Z","title_canon_sha256":"b8399801cb652a56bf458e3d52fb63e99bdc4967c9a64a50f0a8ca8e6b144e9a"},"schema_version":"1.0","source":{"id":"1802.04574","kind":"arxiv","version":1}},"canonical_sha256":"dc5ab6d6f29e15f424851b03be30789f59550086877ae5bded84905600aa0235","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc5ab6d6f29e15f424851b03be30789f59550086877ae5bded84905600aa0235","first_computed_at":"2026-05-18T00:23:42.082835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:42.082835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h/QQZiR+mtBXTzQSb4KWLZC/mfpEEwtB2jCHoXJtm9eLm6P6Fyh6ziPj7O5uIJ/ssxDXdsblZv9Wiz/rYvFnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:42.083351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04574","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a88d78978473e329d2e1f6f33b6cc6a05edf42c0e5ba35a7db333fb298f67ed1","sha256:f3ca3ef98b1b7f95e7e9850269aca32849c97cca2bb267bd7c36146dce60b39f"],"state_sha256":"ae2b0944fb20bbf5a6d0a1af788206452a9b945283ebcdc39326f1d84fb63af8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5U2l4opUWs6tzYsLnIyZ7Ev8gsWhUeicf3XWA2eTC2EB8nVCbrCTyJGdjOgjIkrRZYGdRFVSJxdOT7j2EQJWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:15:56.049651Z","bundle_sha256":"4e47fd7d74298ddf917d426f7ddaa52e5a8b68569686d7419a222f9ac98d76a4"}}