{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RZH2Z6XOGCAUWYZARZMCAZWWXD","short_pith_number":"pith:RZH2Z6XO","canonical_record":{"source":{"id":"1301.0408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T10:00:12Z","cross_cats_sorted":[],"title_canon_sha256":"0a05b6a63c054356c914b27c8d218fde0a6fc7a6c4aff006b201f4765590c62c","abstract_canon_sha256":"1f9d64e55513dbb9d7f9a738d916d02e41751b094f4b01ec2a21e02ff5552adc"},"schema_version":"1.0"},"canonical_sha256":"8e4facfaee30814b63208e582066d6b8ec75b79e7d81f9f085ad1a5470042d44","source":{"kind":"arxiv","id":"1301.0408","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0408","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0408v1","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0408","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"RZH2Z6XOGCAU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RZH2Z6XOGCAUWYZA","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RZH2Z6XO","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RZH2Z6XOGCAUWYZARZMCAZWWXD","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T10:00:12Z","cross_cats_sorted":[],"title_canon_sha256":"0a05b6a63c054356c914b27c8d218fde0a6fc7a6c4aff006b201f4765590c62c","abstract_canon_sha256":"1f9d64e55513dbb9d7f9a738d916d02e41751b094f4b01ec2a21e02ff5552adc"},"schema_version":"1.0"},"canonical_sha256":"8e4facfaee30814b63208e582066d6b8ec75b79e7d81f9f085ad1a5470042d44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:10.072706Z","signature_b64":"FXx8vDDwMHy41rffEZBwBCp9KfCs4bar8A+VBNmg7ka/Je9knEsXs5/c9EuGGP9+1q61xTwHCFd2YBacuYuoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e4facfaee30814b63208e582066d6b8ec75b79e7d81f9f085ad1a5470042d44","last_reissued_at":"2026-05-18T01:13:10.072336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:10.072336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0408","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":"2026-05-18T01:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqtfpQk+tb8KB5ivU2XKNQ6n1PxnS+UIcgaoLplKi4es+yspsuJ6vmYCLbAkvPyCMQFso430bGKp1rSgR1HMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:37:37.780309Z"},"content_sha256":"01158b348f4992692c4bcd7dc859fd7cd3d49e5b8daab403efa6fe157601cfeb","schema_version":"1.0","event_id":"sha256:01158b348f4992692c4bcd7dc859fd7cd3d49e5b8daab403efa6fe157601cfeb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RZH2Z6XOGCAUWYZARZMCAZWWXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Felix Otto, Hendrik Weber, Maria Westdickenberg","submitted_at":"2013-01-03T10:00:12Z","abstract_excerpt":"We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one transition from -1 to 1. (Our methods can be applied to other boundary conditions as well.) We are interested in the competition between the energy that should be minimized due to the small noise strength and the entropy that is induced by the large system size.\n  Our methods handle system sizes that are exponential with respect to the inverse noise strength, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0408","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":"2026-05-18T01:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aFRei2j0PEal5TqBow0qh4a8E7U+7QCTc4BKg0Pby3TP/qx0XrvEQJldk4OvcycpN0cF0g2sY6XwbEdWmZWeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:37:37.780683Z"},"content_sha256":"15d890c60177b697c87bfa55aa328a49c7611fd396cb8e41d83d34e0d8434b01","schema_version":"1.0","event_id":"sha256:15d890c60177b697c87bfa55aa328a49c7611fd396cb8e41d83d34e0d8434b01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZH2Z6XOGCAUWYZARZMCAZWWXD/bundle.json","state_url":"https://pith.science/pith/RZH2Z6XOGCAUWYZARZMCAZWWXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZH2Z6XOGCAUWYZARZMCAZWWXD/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":"2026-05-29T18:37:37Z","links":{"resolver":"https://pith.science/pith/RZH2Z6XOGCAUWYZARZMCAZWWXD","bundle":"https://pith.science/pith/RZH2Z6XOGCAUWYZARZMCAZWWXD/bundle.json","state":"https://pith.science/pith/RZH2Z6XOGCAUWYZARZMCAZWWXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZH2Z6XOGCAUWYZARZMCAZWWXD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RZH2Z6XOGCAUWYZARZMCAZWWXD","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":"1f9d64e55513dbb9d7f9a738d916d02e41751b094f4b01ec2a21e02ff5552adc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T10:00:12Z","title_canon_sha256":"0a05b6a63c054356c914b27c8d218fde0a6fc7a6c4aff006b201f4765590c62c"},"schema_version":"1.0","source":{"id":"1301.0408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0408","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0408v1","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0408","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"RZH2Z6XOGCAU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RZH2Z6XOGCAUWYZA","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RZH2Z6XO","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:15d890c60177b697c87bfa55aa328a49c7611fd396cb8e41d83d34e0d8434b01","target":"graph","created_at":"2026-05-18T01:13:10Z","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":"We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one transition from -1 to 1. (Our methods can be applied to other boundary conditions as well.) We are interested in the competition between the energy that should be minimized due to the small noise strength and the entropy that is induced by the large system size.\n  Our methods handle system sizes that are exponential with respect to the inverse noise strength, ","authors_text":"Felix Otto, Hendrik Weber, Maria Westdickenberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T10:00:12Z","title":"Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0408","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":"sha256:01158b348f4992692c4bcd7dc859fd7cd3d49e5b8daab403efa6fe157601cfeb","target":"record","created_at":"2026-05-18T01:13:10Z","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":"1f9d64e55513dbb9d7f9a738d916d02e41751b094f4b01ec2a21e02ff5552adc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T10:00:12Z","title_canon_sha256":"0a05b6a63c054356c914b27c8d218fde0a6fc7a6c4aff006b201f4765590c62c"},"schema_version":"1.0","source":{"id":"1301.0408","kind":"arxiv","version":1}},"canonical_sha256":"8e4facfaee30814b63208e582066d6b8ec75b79e7d81f9f085ad1a5470042d44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e4facfaee30814b63208e582066d6b8ec75b79e7d81f9f085ad1a5470042d44","first_computed_at":"2026-05-18T01:13:10.072336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:10.072336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FXx8vDDwMHy41rffEZBwBCp9KfCs4bar8A+VBNmg7ka/Je9knEsXs5/c9EuGGP9+1q61xTwHCFd2YBacuYuoBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:10.072706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01158b348f4992692c4bcd7dc859fd7cd3d49e5b8daab403efa6fe157601cfeb","sha256:15d890c60177b697c87bfa55aa328a49c7611fd396cb8e41d83d34e0d8434b01"],"state_sha256":"d79384121f7604fee016fa0feb14643fd12202f5bc76a76fb524073b28ae7cbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4NtkcGQXBEv1a7hffOrGT70cN5PdU2uqNKvhfYhTYuK+HoCnE5fyiAw5VmTqpVCfpMSmuUqdJ3S6KzdH4pyhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:37:37.782774Z","bundle_sha256":"97d271527cc2373c0cfbb3453394d521d52f8ae217820df24c8fbfaaece236e4"}}