{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2T6WWHXJGQKGRU6CAMS7VVSWJ5","short_pith_number":"pith:2T6WWHXJ","canonical_record":{"source":{"id":"2502.19117","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-26T13:12:38Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9ccefa72b653c65b42112f20150bcddf3d4073edffed8116fd5935f31fb87bf5","abstract_canon_sha256":"702f9670d85aabe1ca1bb7061efa80147cc67caae89283f460b51dfaeb440ee6"},"schema_version":"1.0"},"canonical_sha256":"d4fd6b1ee9341468d3c20325fad6564f76806cde4730a6abe93500d819b69b0d","source":{"kind":"arxiv","id":"2502.19117","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.19117","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"arxiv_version","alias_value":"2502.19117v1","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.19117","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"pith_short_12","alias_value":"2T6WWHXJGQKG","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"pith_short_16","alias_value":"2T6WWHXJGQKGRU6C","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"pith_short_8","alias_value":"2T6WWHXJ","created_at":"2026-07-05T10:20:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2T6WWHXJGQKGRU6CAMS7VVSWJ5","target":"record","payload":{"canonical_record":{"source":{"id":"2502.19117","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-26T13:12:38Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9ccefa72b653c65b42112f20150bcddf3d4073edffed8116fd5935f31fb87bf5","abstract_canon_sha256":"702f9670d85aabe1ca1bb7061efa80147cc67caae89283f460b51dfaeb440ee6"},"schema_version":"1.0"},"canonical_sha256":"d4fd6b1ee9341468d3c20325fad6564f76806cde4730a6abe93500d819b69b0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:26.936234Z","signature_b64":"DjqoS3REsKDV9FID0AqeZopfoZuzQGLAefSXC8lwQOdAyvny1iN4DRjgd3DJlK+Hdxsebp/Z5La8qRJ3Cdt9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4fd6b1ee9341468d3c20325fad6564f76806cde4730a6abe93500d819b69b0d","last_reissued_at":"2026-07-05T10:20:26.935735Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:26.935735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.19117","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":"2026-07-05T10:20:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s62WwTm0sv20nGjOVm1/zx9UYERlUOYm8MaRSKnQHzEEP88LhARBE+sWwa0t+oEzLO8Gqq3GlVwhf3wXagt7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:39:43.751732Z"},"content_sha256":"d2e18837fab268a053e832e4bcfa841a7168a671830f925514929fb863a0e5a6","schema_version":"1.0","event_id":"sha256:d2e18837fab268a053e832e4bcfa841a7168a671830f925514929fb863a0e5a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2T6WWHXJGQKGRU6CAMS7VVSWJ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Ergodicity and Optimal Error Estimates for a Class of Novel Tamed Schemes to Super-linear Stochastic PDEs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jie Shen, Zhihui Liu","submitted_at":"2025-02-26T13:12:38Z","abstract_excerpt":"We construct a class of novel tamed schemes that can preserve the original Lyapunov functional for super-linear stochastic PDEs (SPDEs), including the stochastic Allen--Cahn equation, driven by multiplicative or additive noise, and provide a rigorous analysis of their long-time unconditional stability. We also show that the corresponding Galerkin-based fully discrete tamed schemes inherit the geometric ergodicity of the SPDEs and establish their convergence towards the SPDEs with optimal strong rates in both the multiplicative and additive noise cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19117","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.19117/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:20:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5HeIbE3fDZVY6CdtRWVXpCUUoA9MFVYVdsvojyIEihnG9p8EHys85al3eX4Kz+Z5FLFMZS84ujIFIF/iLD9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:39:43.752278Z"},"content_sha256":"f654787c7837172ab199cc9516431dfa21879cdaab24585e575598ba63aadffd","schema_version":"1.0","event_id":"sha256:f654787c7837172ab199cc9516431dfa21879cdaab24585e575598ba63aadffd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2T6WWHXJGQKGRU6CAMS7VVSWJ5/bundle.json","state_url":"https://pith.science/pith/2T6WWHXJGQKGRU6CAMS7VVSWJ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2T6WWHXJGQKGRU6CAMS7VVSWJ5/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":"2026-08-09T00:39:43Z","links":{"resolver":"https://pith.science/pith/2T6WWHXJGQKGRU6CAMS7VVSWJ5","bundle":"https://pith.science/pith/2T6WWHXJGQKGRU6CAMS7VVSWJ5/bundle.json","state":"https://pith.science/pith/2T6WWHXJGQKGRU6CAMS7VVSWJ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2T6WWHXJGQKGRU6CAMS7VVSWJ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2T6WWHXJGQKGRU6CAMS7VVSWJ5","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":"702f9670d85aabe1ca1bb7061efa80147cc67caae89283f460b51dfaeb440ee6","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-26T13:12:38Z","title_canon_sha256":"9ccefa72b653c65b42112f20150bcddf3d4073edffed8116fd5935f31fb87bf5"},"schema_version":"1.0","source":{"id":"2502.19117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.19117","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"arxiv_version","alias_value":"2502.19117v1","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.19117","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"pith_short_12","alias_value":"2T6WWHXJGQKG","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"pith_short_16","alias_value":"2T6WWHXJGQKGRU6C","created_at":"2026-07-05T10:20:26Z"},{"alias_kind":"pith_short_8","alias_value":"2T6WWHXJ","created_at":"2026-07-05T10:20:26Z"}],"graph_snapshots":[{"event_id":"sha256:f654787c7837172ab199cc9516431dfa21879cdaab24585e575598ba63aadffd","target":"graph","created_at":"2026-07-05T10:20:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.19117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a class of novel tamed schemes that can preserve the original Lyapunov functional for super-linear stochastic PDEs (SPDEs), including the stochastic Allen--Cahn equation, driven by multiplicative or additive noise, and provide a rigorous analysis of their long-time unconditional stability. We also show that the corresponding Galerkin-based fully discrete tamed schemes inherit the geometric ergodicity of the SPDEs and establish their convergence towards the SPDEs with optimal strong rates in both the multiplicative and additive noise cases.","authors_text":"Jie Shen, Zhihui Liu","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-26T13:12:38Z","title":"Geometric Ergodicity and Optimal Error Estimates for a Class of Novel Tamed Schemes to Super-linear Stochastic PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19117","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:d2e18837fab268a053e832e4bcfa841a7168a671830f925514929fb863a0e5a6","target":"record","created_at":"2026-07-05T10:20:26Z","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":"702f9670d85aabe1ca1bb7061efa80147cc67caae89283f460b51dfaeb440ee6","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-26T13:12:38Z","title_canon_sha256":"9ccefa72b653c65b42112f20150bcddf3d4073edffed8116fd5935f31fb87bf5"},"schema_version":"1.0","source":{"id":"2502.19117","kind":"arxiv","version":1}},"canonical_sha256":"d4fd6b1ee9341468d3c20325fad6564f76806cde4730a6abe93500d819b69b0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4fd6b1ee9341468d3c20325fad6564f76806cde4730a6abe93500d819b69b0d","first_computed_at":"2026-07-05T10:20:26.935735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:20:26.935735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DjqoS3REsKDV9FID0AqeZopfoZuzQGLAefSXC8lwQOdAyvny1iN4DRjgd3DJlK+Hdxsebp/Z5La8qRJ3Cdt9Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:20:26.936234Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.19117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2e18837fab268a053e832e4bcfa841a7168a671830f925514929fb863a0e5a6","sha256:f654787c7837172ab199cc9516431dfa21879cdaab24585e575598ba63aadffd"],"state_sha256":"23db2b04cd129c46a56375c12f2612765b3da2c851dcbcfe909d94c0e706aeb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+fTLjxwBfuiJdHpvZ6lBTeBc06+q9GWrVn6JLeRPJL39Blm4ACo5eiPNdmRmaEadva3Qyr3HwC1mCGstTyTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T00:39:43.755671Z","bundle_sha256":"1608c6e30b13158ce8a69692791ffd3376fa309908d7f174086a03c5a60c4d34"}}