{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QXQ42EMOSZXF4ZKW53QBQNJMF6","short_pith_number":"pith:QXQ42EMO","canonical_record":{"source":{"id":"1501.05288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-21T20:36:46Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"82a9e7c254a4b754599222b78116360e4cf762c8213eda42791ff5e726ec852b","abstract_canon_sha256":"b6cc2b3312bfc6feba1672c312af5d4de5b22f96f96f2beafb68cf9e5cf2de88"},"schema_version":"1.0"},"canonical_sha256":"85e1cd118e966e5e6556eee018352c2fb7e9268db6a0eec4ca048033d5500d49","source":{"kind":"arxiv","id":"1501.05288","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05288","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05288v1","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05288","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"QXQ42EMOSZXF","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QXQ42EMOSZXF4ZKW","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QXQ42EMO","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QXQ42EMOSZXF4ZKW53QBQNJMF6","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-21T20:36:46Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"82a9e7c254a4b754599222b78116360e4cf762c8213eda42791ff5e726ec852b","abstract_canon_sha256":"b6cc2b3312bfc6feba1672c312af5d4de5b22f96f96f2beafb68cf9e5cf2de88"},"schema_version":"1.0"},"canonical_sha256":"85e1cd118e966e5e6556eee018352c2fb7e9268db6a0eec4ca048033d5500d49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:55.577445Z","signature_b64":"IykwA6nyeNvouVjXTFNsFKkbI1z+ncq7agViKkcgyAXF8KBoefUDTICK8wu9zbBBYZc7iz5fGlj5PhOqa0aPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85e1cd118e966e5e6556eee018352c2fb7e9268db6a0eec4ca048033d5500d49","last_reissued_at":"2026-05-18T02:28:55.576909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:55.576909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05288","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":"2026-05-18T02:28:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RuYO0MN4R9xUFbgUmTfvQv4Iy5VyuxwoY5DaRp0nn9rs6XZaO/KMi7rEKv2hGt/UaA2dUAifcHZJWxMXIl/9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:39:47.146143Z"},"content_sha256":"7458ecdfe91cf686bc6c8815b5b31d596ce008deceb91732f627684570bc00fa","schema_version":"1.0","event_id":"sha256:7458ecdfe91cf686bc6c8815b5b31d596ce008deceb91732f627684570bc00fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QXQ42EMOSZXF4ZKW53QBQNJMF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Dimitra C. Antonopoulou, Dirk Bl\\\"omker, Georgia D. Karali, Peter W. Bates","submitted_at":"2015-01-21T20:36:46Z","abstract_excerpt":"We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It\\^o calculus to derive the stochastic dynamics of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco for the deterministic problem. In the stochastic case depending on the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05288","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":"2026-05-18T02:28:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+Yv4FAWRHk6E3LbaaH2ypWnp0Nki9Pi+Cz4bAPnrAYVAJbP0anM15PjmINAWrThFu5EmVfk1E/ZEKtaLTq3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:39:47.146504Z"},"content_sha256":"ef2bf1508df1b40e3a6bc8510fd36062c8d5c215162b1473a03f259bcc45657d","schema_version":"1.0","event_id":"sha256:ef2bf1508df1b40e3a6bc8510fd36062c8d5c215162b1473a03f259bcc45657d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXQ42EMOSZXF4ZKW53QBQNJMF6/bundle.json","state_url":"https://pith.science/pith/QXQ42EMOSZXF4ZKW53QBQNJMF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXQ42EMOSZXF4ZKW53QBQNJMF6/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":"2026-06-02T15:39:47Z","links":{"resolver":"https://pith.science/pith/QXQ42EMOSZXF4ZKW53QBQNJMF6","bundle":"https://pith.science/pith/QXQ42EMOSZXF4ZKW53QBQNJMF6/bundle.json","state":"https://pith.science/pith/QXQ42EMOSZXF4ZKW53QBQNJMF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXQ42EMOSZXF4ZKW53QBQNJMF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QXQ42EMOSZXF4ZKW53QBQNJMF6","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":"b6cc2b3312bfc6feba1672c312af5d4de5b22f96f96f2beafb68cf9e5cf2de88","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-21T20:36:46Z","title_canon_sha256":"82a9e7c254a4b754599222b78116360e4cf762c8213eda42791ff5e726ec852b"},"schema_version":"1.0","source":{"id":"1501.05288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05288","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05288v1","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05288","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"QXQ42EMOSZXF","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QXQ42EMOSZXF4ZKW","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QXQ42EMO","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:ef2bf1508df1b40e3a6bc8510fd36062c8d5c215162b1473a03f259bcc45657d","target":"graph","created_at":"2026-05-18T02:28:55Z","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 stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It\\^o calculus to derive the stochastic dynamics of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco for the deterministic problem. In the stochastic case depending on the s","authors_text":"Dimitra C. Antonopoulou, Dirk Bl\\\"omker, Georgia D. Karali, Peter W. Bates","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-21T20:36:46Z","title":"Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05288","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":"sha256:7458ecdfe91cf686bc6c8815b5b31d596ce008deceb91732f627684570bc00fa","target":"record","created_at":"2026-05-18T02:28:55Z","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":"b6cc2b3312bfc6feba1672c312af5d4de5b22f96f96f2beafb68cf9e5cf2de88","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-21T20:36:46Z","title_canon_sha256":"82a9e7c254a4b754599222b78116360e4cf762c8213eda42791ff5e726ec852b"},"schema_version":"1.0","source":{"id":"1501.05288","kind":"arxiv","version":1}},"canonical_sha256":"85e1cd118e966e5e6556eee018352c2fb7e9268db6a0eec4ca048033d5500d49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85e1cd118e966e5e6556eee018352c2fb7e9268db6a0eec4ca048033d5500d49","first_computed_at":"2026-05-18T02:28:55.576909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:55.576909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IykwA6nyeNvouVjXTFNsFKkbI1z+ncq7agViKkcgyAXF8KBoefUDTICK8wu9zbBBYZc7iz5fGlj5PhOqa0aPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:55.577445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7458ecdfe91cf686bc6c8815b5b31d596ce008deceb91732f627684570bc00fa","sha256:ef2bf1508df1b40e3a6bc8510fd36062c8d5c215162b1473a03f259bcc45657d"],"state_sha256":"597fe484f6ecf25905284c861725c96a24dacd1a4dbf79c0b09e29f8c808ad2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZzcbyixITt7gXqcxW2bLLFtI+oryV9Rd7frQb2xF/lJDvAKja3LOQHolb/HOqgqENOrixLb0Al5s46IlFnIcBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:39:47.148456Z","bundle_sha256":"2d459f2d7de8c267d0b3076660d03663b34edac82cec8ca2e913af8f9dcc2686"}}