{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:233PWE2CFPTTSPMEWYCDDDHLKD","short_pith_number":"pith:233PWE2C","canonical_record":{"source":{"id":"1309.1211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T00:21:09Z","cross_cats_sorted":[],"title_canon_sha256":"7dc9145674f1059a81bb098177db94dcbb53edbd1c67db220b8f54c4f8523cb8","abstract_canon_sha256":"f36052c774a37d800b3994f5b4958b939a92e71e50a67093644e16280e50fde7"},"schema_version":"1.0"},"canonical_sha256":"d6f6fb13422be7393d84b604318ceb50d159a8f7d6de5b2fe0540fe0f3bfd599","source":{"kind":"arxiv","id":"1309.1211","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1211","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1211v1","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1211","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"233PWE2CFPTT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"233PWE2CFPTTSPME","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"233PWE2C","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:233PWE2CFPTTSPMEWYCDDDHLKD","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T00:21:09Z","cross_cats_sorted":[],"title_canon_sha256":"7dc9145674f1059a81bb098177db94dcbb53edbd1c67db220b8f54c4f8523cb8","abstract_canon_sha256":"f36052c774a37d800b3994f5b4958b939a92e71e50a67093644e16280e50fde7"},"schema_version":"1.0"},"canonical_sha256":"d6f6fb13422be7393d84b604318ceb50d159a8f7d6de5b2fe0540fe0f3bfd599","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:42.181411Z","signature_b64":"DSd3VkVdNFFXPq0LpVAbxfTRVkOYB1KZRUqMtFRWNWKWSJ3EmvEMtpVtwSSSNeAoH634Cdo51bRHGapdzPNDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6f6fb13422be7393d84b604318ceb50d159a8f7d6de5b2fe0540fe0f3bfd599","last_reissued_at":"2026-05-18T02:41:42.180767Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:42.180767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1211","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":"2026-05-18T02:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/QpA5XrSQgD56umeeNs9axoDBNhuzt7GIi6gWF6/eIvcRwNcIJNPYAiKuSXck07QaVwCGO2BZJgRQ8ugU2oCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:27:48.325041Z"},"content_sha256":"861646119afc158ad9a05c5a77000f61fab7f31003c142469e380b46378ad49f","schema_version":"1.0","event_id":"sha256:861646119afc158ad9a05c5a77000f61fab7f31003c142469e380b46378ad49f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:233PWE2CFPTTSPMEWYCDDDHLKD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pullback Attractors of Non-autonomous Stochastic Degenerate Parabolic Equations on Unbounded Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Krause, Bixiang Wang","submitted_at":"2013-09-05T00:21:09Z","abstract_excerpt":"This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R^n. We first establish the asymptotic compactness of the equation in L^2(R^n) and then prove the existence and uniqueness of non-autonomous random attractors. This attractor is pathwise periodic if the non-autonomous deterministic forcing is time periodic. The difficulty of non-compactness of Sobolev embeddings on R^n is overcome by the uniform smallness of solutions outside a bounded domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1211","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":"2026-05-18T02:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEvTyJ9WRdXt8iG4c8WRY02RgaaI10Nuev211b3tQNCuNvxKGbBWsHFQiHrg0oJbtHxs8CvFmnHpofkpzm/ZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:27:48.325395Z"},"content_sha256":"6e3c197dc92704f3efc74fbcaf43fa025002ef4ba51ac38bb6f893af3e6f441e","schema_version":"1.0","event_id":"sha256:6e3c197dc92704f3efc74fbcaf43fa025002ef4ba51ac38bb6f893af3e6f441e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/233PWE2CFPTTSPMEWYCDDDHLKD/bundle.json","state_url":"https://pith.science/pith/233PWE2CFPTTSPMEWYCDDDHLKD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/233PWE2CFPTTSPMEWYCDDDHLKD/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":"2026-06-04T21:27:48Z","links":{"resolver":"https://pith.science/pith/233PWE2CFPTTSPMEWYCDDDHLKD","bundle":"https://pith.science/pith/233PWE2CFPTTSPMEWYCDDDHLKD/bundle.json","state":"https://pith.science/pith/233PWE2CFPTTSPMEWYCDDDHLKD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/233PWE2CFPTTSPMEWYCDDDHLKD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:233PWE2CFPTTSPMEWYCDDDHLKD","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":"f36052c774a37d800b3994f5b4958b939a92e71e50a67093644e16280e50fde7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T00:21:09Z","title_canon_sha256":"7dc9145674f1059a81bb098177db94dcbb53edbd1c67db220b8f54c4f8523cb8"},"schema_version":"1.0","source":{"id":"1309.1211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1211","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1211v1","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1211","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"233PWE2CFPTT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"233PWE2CFPTTSPME","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"233PWE2C","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:6e3c197dc92704f3efc74fbcaf43fa025002ef4ba51ac38bb6f893af3e6f441e","target":"graph","created_at":"2026-05-18T02:41:42Z","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":"This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R^n. We first establish the asymptotic compactness of the equation in L^2(R^n) and then prove the existence and uniqueness of non-autonomous random attractors. This attractor is pathwise periodic if the non-autonomous deterministic forcing is time periodic. The difficulty of non-compactness of Sobolev embeddings on R^n is overcome by the uniform smallness of solutions outside a bounded domain.","authors_text":"Andrew Krause, Bixiang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T00:21:09Z","title":"Pullback Attractors of Non-autonomous Stochastic Degenerate Parabolic Equations on Unbounded Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1211","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":"sha256:861646119afc158ad9a05c5a77000f61fab7f31003c142469e380b46378ad49f","target":"record","created_at":"2026-05-18T02:41:42Z","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":"f36052c774a37d800b3994f5b4958b939a92e71e50a67093644e16280e50fde7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T00:21:09Z","title_canon_sha256":"7dc9145674f1059a81bb098177db94dcbb53edbd1c67db220b8f54c4f8523cb8"},"schema_version":"1.0","source":{"id":"1309.1211","kind":"arxiv","version":1}},"canonical_sha256":"d6f6fb13422be7393d84b604318ceb50d159a8f7d6de5b2fe0540fe0f3bfd599","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6f6fb13422be7393d84b604318ceb50d159a8f7d6de5b2fe0540fe0f3bfd599","first_computed_at":"2026-05-18T02:41:42.180767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:42.180767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DSd3VkVdNFFXPq0LpVAbxfTRVkOYB1KZRUqMtFRWNWKWSJ3EmvEMtpVtwSSSNeAoH634Cdo51bRHGapdzPNDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:42.181411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:861646119afc158ad9a05c5a77000f61fab7f31003c142469e380b46378ad49f","sha256:6e3c197dc92704f3efc74fbcaf43fa025002ef4ba51ac38bb6f893af3e6f441e"],"state_sha256":"7fedb2591c5a020b2965235da0507e3862c1110944b61e383eee5fb38f3199e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hoq+j92sDOQyWTW6UX2hrC2m9To+JcMkMDKTNbYA4uHkkSYPwMR1x4is8eNT+Bh+Asw5YbDmzrbZMppTqOlhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:27:48.327255Z","bundle_sha256":"d1e6092aea992f15969b09bd1becbcb9f1d70a85a4ba564903f9a721a36c5d34"}}