{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BC7M4V5Q7MDDUZITLWO3FUTMYO","short_pith_number":"pith:BC7M4V5Q","canonical_record":{"source":{"id":"1208.5958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-29T16:15:02Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"1b474aba6fc60820ef9bd261a90f81355327ab4d1e8fb80ddcfb1dbec1b1a3c9","abstract_canon_sha256":"e39ef6795590b4a171da8043fe106a940244200900df9d4224473674eb676851"},"schema_version":"1.0"},"canonical_sha256":"08bece57b0fb063a65135d9db2d26cc3aec8eb099989b120d43863429791f516","source":{"kind":"arxiv","id":"1208.5958","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5958","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5958v1","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5958","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"BC7M4V5Q7MDD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BC7M4V5Q7MDDUZIT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BC7M4V5Q","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BC7M4V5Q7MDDUZITLWO3FUTMYO","target":"record","payload":{"canonical_record":{"source":{"id":"1208.5958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-29T16:15:02Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"1b474aba6fc60820ef9bd261a90f81355327ab4d1e8fb80ddcfb1dbec1b1a3c9","abstract_canon_sha256":"e39ef6795590b4a171da8043fe106a940244200900df9d4224473674eb676851"},"schema_version":"1.0"},"canonical_sha256":"08bece57b0fb063a65135d9db2d26cc3aec8eb099989b120d43863429791f516","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:48.227063Z","signature_b64":"zgA+1/nZYbovgVv6PT8t3dzIPY+C1BGse3NGJwvOICmJO0jXYf2S0K6EVktYwgXyFi9gyAYPOcYefmaYf6TLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08bece57b0fb063a65135d9db2d26cc3aec8eb099989b120d43863429791f516","last_reissued_at":"2026-05-18T03:46:48.226380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:48.226380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.5958","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":"2026-05-18T03:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7jvl0CuC3f3Elps6j1SvP3omoqJ30DoZofdWaveAfJ++wM1VIVBVfojeAVyKxe+8VWpb6T2fhLV1IamQNN9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:24:48.580640Z"},"content_sha256":"a1e08aca3c7ebf5dc4804095ecbb6c165fbb3977d21388ac51fda0e21e5a04ef","schema_version":"1.0","event_id":"sha256:a1e08aca3c7ebf5dc4804095ecbb6c165fbb3977d21388ac51fda0e21e5a04ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BC7M4V5Q7MDDUZITLWO3FUTMYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"C. M. Elliott, M. Hairer, M. R. Scott","submitted_at":"2012-08-29T16:15:02Z","abstract_excerpt":"We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly linear stochastic partial differential equations, we establish various existence and uniqueness theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5958","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":"2026-05-18T03:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2iQZVGndczhUyqCPf5jyq3O5WCYWJhGVJUFNeEK8zbYBdudQ4+TST39TsqZEvjVNhwMu5qZApO1L/baffM4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:24:48.580976Z"},"content_sha256":"f657cb3bb6b356c905c14f67a13f9435ceda886b4ec9eb09de5dd31a537f3a5b","schema_version":"1.0","event_id":"sha256:f657cb3bb6b356c905c14f67a13f9435ceda886b4ec9eb09de5dd31a537f3a5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BC7M4V5Q7MDDUZITLWO3FUTMYO/bundle.json","state_url":"https://pith.science/pith/BC7M4V5Q7MDDUZITLWO3FUTMYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BC7M4V5Q7MDDUZITLWO3FUTMYO/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":"2026-05-27T21:24:48Z","links":{"resolver":"https://pith.science/pith/BC7M4V5Q7MDDUZITLWO3FUTMYO","bundle":"https://pith.science/pith/BC7M4V5Q7MDDUZITLWO3FUTMYO/bundle.json","state":"https://pith.science/pith/BC7M4V5Q7MDDUZITLWO3FUTMYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BC7M4V5Q7MDDUZITLWO3FUTMYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BC7M4V5Q7MDDUZITLWO3FUTMYO","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":"e39ef6795590b4a171da8043fe106a940244200900df9d4224473674eb676851","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-29T16:15:02Z","title_canon_sha256":"1b474aba6fc60820ef9bd261a90f81355327ab4d1e8fb80ddcfb1dbec1b1a3c9"},"schema_version":"1.0","source":{"id":"1208.5958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5958","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5958v1","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5958","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"BC7M4V5Q7MDD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BC7M4V5Q7MDDUZIT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BC7M4V5Q","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:f657cb3bb6b356c905c14f67a13f9435ceda886b4ec9eb09de5dd31a537f3a5b","target":"graph","created_at":"2026-05-18T03:46:48Z","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 formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly linear stochastic partial differential equations, we establish various existence and uniqueness theorems.","authors_text":"C. M. Elliott, M. Hairer, M. R. Scott","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-29T16:15:02Z","title":"Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5958","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:a1e08aca3c7ebf5dc4804095ecbb6c165fbb3977d21388ac51fda0e21e5a04ef","target":"record","created_at":"2026-05-18T03:46:48Z","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":"e39ef6795590b4a171da8043fe106a940244200900df9d4224473674eb676851","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-29T16:15:02Z","title_canon_sha256":"1b474aba6fc60820ef9bd261a90f81355327ab4d1e8fb80ddcfb1dbec1b1a3c9"},"schema_version":"1.0","source":{"id":"1208.5958","kind":"arxiv","version":1}},"canonical_sha256":"08bece57b0fb063a65135d9db2d26cc3aec8eb099989b120d43863429791f516","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08bece57b0fb063a65135d9db2d26cc3aec8eb099989b120d43863429791f516","first_computed_at":"2026-05-18T03:46:48.226380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:48.226380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zgA+1/nZYbovgVv6PT8t3dzIPY+C1BGse3NGJwvOICmJO0jXYf2S0K6EVktYwgXyFi9gyAYPOcYefmaYf6TLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:48.227063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1e08aca3c7ebf5dc4804095ecbb6c165fbb3977d21388ac51fda0e21e5a04ef","sha256:f657cb3bb6b356c905c14f67a13f9435ceda886b4ec9eb09de5dd31a537f3a5b"],"state_sha256":"850ecc400ed061991f63a0aef85411fec84fd35c3b483052b32379a7a4cc13c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"erV/0d77QjQe7te84DhAeSqpAmmxRhnQMCDGcHG+dVrHgOOVpSX77glkDlT5g9v/zkc27/QEjhmU0C0bX6sIBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:24:48.583197Z","bundle_sha256":"c09247e07a75f304de03d1c4cbc306c14b61de20d340a93d418fc087e8f2d113"}}