{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7QPHDLUGI4EMVWQS4FM6E6BH64","short_pith_number":"pith:7QPHDLUG","canonical_record":{"source":{"id":"1008.2378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-13T19:45:59Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"b6e2c47cd2678c75d109860767712d76939062dfa816d5e66a6e5a4ee2003f7a","abstract_canon_sha256":"373dc0933b23484e88749e286f42a2e5cf119ba09edb861d19d9409789eb477b"},"schema_version":"1.0"},"canonical_sha256":"fc1e71ae864708cada12e159e27827f706177b808f8716ee7af0c5e70cabac4d","source":{"kind":"arxiv","id":"1008.2378","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2378","created_at":"2026-05-18T02:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2378v1","created_at":"2026-05-18T02:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2378","created_at":"2026-05-18T02:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"7QPHDLUGI4EM","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"7QPHDLUGI4EMVWQS","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"7QPHDLUG","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7QPHDLUGI4EMVWQS4FM6E6BH64","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-13T19:45:59Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"b6e2c47cd2678c75d109860767712d76939062dfa816d5e66a6e5a4ee2003f7a","abstract_canon_sha256":"373dc0933b23484e88749e286f42a2e5cf119ba09edb861d19d9409789eb477b"},"schema_version":"1.0"},"canonical_sha256":"fc1e71ae864708cada12e159e27827f706177b808f8716ee7af0c5e70cabac4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:48.469357Z","signature_b64":"mV4xM6N3ukTOmo325w2Cr7KMZ4GBycTmIKNgzEwtNgNfm8CFAYEz1KMbyTLRJiWjgG3euNOEsQXDT+AxYV/ABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc1e71ae864708cada12e159e27827f706177b808f8716ee7af0c5e70cabac4d","last_reissued_at":"2026-05-18T02:05:48.468587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:48.468587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2378","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":"2026-05-18T02:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g0sta5nMPmvJBn/SwDxAUvSuSyqoIZ83Zu36xlsbJHY9zcdob0BNqZuBkN/edmRhnKIR7oRBiq8EZAar97ymAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:40:23.745803Z"},"content_sha256":"6a9be6d78fd58d0251f91db7e2c62b256e88a6334cdd1c1ed60c53523930a92f","schema_version":"1.0","event_id":"sha256:6a9be6d78fd58d0251f91db7e2c62b256e88a6334cdd1c1ed60c53523930a92f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7QPHDLUGI4EMVWQS4FM6E6BH64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Escape Problem in a Classical Field Theory With Two Coupled Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"D. L. Stein, Lan Gong","submitted_at":"2010-08-13T19:45:59Z","abstract_excerpt":"We introduce and analyze a system of two coupled partial differential equations with external noise. The equations are constructed to model transitions of monovalent metallic nanowires with non-axisymmetric intermediate or end states, but also have more general applicability. They provide a rare example of a system for which an exact solution of nonuniform stationary states can be found. We find a transition in activation behavior as the interval length on which the fields are defined is varied. We discuss several applications to physical problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2378","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":"2026-05-18T02:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qtx6ZRrmfFeiXtPpR2XAuaJPoYqF6OK6DKidwCCdvK9XJy6njI7+RwK9Eta2McVqf7cFgoRHzbI6AQwAZ0zHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:40:23.746402Z"},"content_sha256":"3807815de4050150b18df75307a90de717c0e08c6cb9593c22e6d59fa15060b3","schema_version":"1.0","event_id":"sha256:3807815de4050150b18df75307a90de717c0e08c6cb9593c22e6d59fa15060b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QPHDLUGI4EMVWQS4FM6E6BH64/bundle.json","state_url":"https://pith.science/pith/7QPHDLUGI4EMVWQS4FM6E6BH64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QPHDLUGI4EMVWQS4FM6E6BH64/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":"2026-05-28T08:40:23Z","links":{"resolver":"https://pith.science/pith/7QPHDLUGI4EMVWQS4FM6E6BH64","bundle":"https://pith.science/pith/7QPHDLUGI4EMVWQS4FM6E6BH64/bundle.json","state":"https://pith.science/pith/7QPHDLUGI4EMVWQS4FM6E6BH64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QPHDLUGI4EMVWQS4FM6E6BH64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7QPHDLUGI4EMVWQS4FM6E6BH64","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":"373dc0933b23484e88749e286f42a2e5cf119ba09edb861d19d9409789eb477b","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-13T19:45:59Z","title_canon_sha256":"b6e2c47cd2678c75d109860767712d76939062dfa816d5e66a6e5a4ee2003f7a"},"schema_version":"1.0","source":{"id":"1008.2378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2378","created_at":"2026-05-18T02:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2378v1","created_at":"2026-05-18T02:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2378","created_at":"2026-05-18T02:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"7QPHDLUGI4EM","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"7QPHDLUGI4EMVWQS","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"7QPHDLUG","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:3807815de4050150b18df75307a90de717c0e08c6cb9593c22e6d59fa15060b3","target":"graph","created_at":"2026-05-18T02:05:48Z","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 introduce and analyze a system of two coupled partial differential equations with external noise. The equations are constructed to model transitions of monovalent metallic nanowires with non-axisymmetric intermediate or end states, but also have more general applicability. They provide a rare example of a system for which an exact solution of nonuniform stationary states can be found. We find a transition in activation behavior as the interval length on which the fields are defined is varied. We discuss several applications to physical problems.","authors_text":"D. L. Stein, Lan Gong","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-13T19:45:59Z","title":"The Escape Problem in a Classical Field Theory With Two Coupled Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2378","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":"sha256:6a9be6d78fd58d0251f91db7e2c62b256e88a6334cdd1c1ed60c53523930a92f","target":"record","created_at":"2026-05-18T02:05:48Z","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":"373dc0933b23484e88749e286f42a2e5cf119ba09edb861d19d9409789eb477b","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-13T19:45:59Z","title_canon_sha256":"b6e2c47cd2678c75d109860767712d76939062dfa816d5e66a6e5a4ee2003f7a"},"schema_version":"1.0","source":{"id":"1008.2378","kind":"arxiv","version":1}},"canonical_sha256":"fc1e71ae864708cada12e159e27827f706177b808f8716ee7af0c5e70cabac4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc1e71ae864708cada12e159e27827f706177b808f8716ee7af0c5e70cabac4d","first_computed_at":"2026-05-18T02:05:48.468587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:48.468587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mV4xM6N3ukTOmo325w2Cr7KMZ4GBycTmIKNgzEwtNgNfm8CFAYEz1KMbyTLRJiWjgG3euNOEsQXDT+AxYV/ABQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:48.469357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a9be6d78fd58d0251f91db7e2c62b256e88a6334cdd1c1ed60c53523930a92f","sha256:3807815de4050150b18df75307a90de717c0e08c6cb9593c22e6d59fa15060b3"],"state_sha256":"d2bc5d1cf789949c56d7b97f994daadd1824bdfee3bba8cc936a950ebf960abc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1Hh+ODdLYI/gXh+RgQgKb30P2HepVQ+M2U/FEJT0PiCFfSv8D2xtUMsUPMumKW8utmefM909Xa9zUazNLeZAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:40:23.749145Z","bundle_sha256":"e6ef55e58e2aa31d8ba60f3ff30ec567fde9cdf2bd8f4e0f42a337167c86ace2"}}