{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:Z4S5MJP5X36PD33GK4HMECX5OM","short_pith_number":"pith:Z4S5MJP5","canonical_record":{"source":{"id":"2107.08242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-17T14:13:12Z","cross_cats_sorted":[],"title_canon_sha256":"d74c21c27b235a7117306ae2f1269d63c65f17bf87d17a1cdcd9e1398dc704ee","abstract_canon_sha256":"eaeb440820a8359300e1877ae1b4ba0484d8e4839a93303b793fcfb10a47fe95"},"schema_version":"1.0"},"canonical_sha256":"cf25d625fdbefcf1ef66570ec20afd731a62fe82ea13ad3e8f5c3975300def7f","source":{"kind":"arxiv","id":"2107.08242","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.08242","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"2107.08242v2","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.08242","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"Z4S5MJP5X36P","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"pith_short_16","alias_value":"Z4S5MJP5X36PD33G","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"pith_short_8","alias_value":"Z4S5MJP5","created_at":"2026-07-05T03:06:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:Z4S5MJP5X36PD33GK4HMECX5OM","target":"record","payload":{"canonical_record":{"source":{"id":"2107.08242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-17T14:13:12Z","cross_cats_sorted":[],"title_canon_sha256":"d74c21c27b235a7117306ae2f1269d63c65f17bf87d17a1cdcd9e1398dc704ee","abstract_canon_sha256":"eaeb440820a8359300e1877ae1b4ba0484d8e4839a93303b793fcfb10a47fe95"},"schema_version":"1.0"},"canonical_sha256":"cf25d625fdbefcf1ef66570ec20afd731a62fe82ea13ad3e8f5c3975300def7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:06:32.469197Z","signature_b64":"l3ECTkBl+C9FwHpLGh8pIyTMMHtSizMsmjw2T5XeDwcK0f7GHuWfejd+43XGHpkSWbAR1usQ1VMP6/o84V0SBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf25d625fdbefcf1ef66570ec20afd731a62fe82ea13ad3e8f5c3975300def7f","last_reissued_at":"2026-07-05T03:06:32.468704Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:06:32.468704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.08242","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+7u9sFXDp0ZscWnZLkGyVBqBm8fTZNh+wrSt9xEx69uzVH2LhSSgvPDDyNDBJ0c98sHwTQXOtYqRtrvtVbk7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:07:10.300922Z"},"content_sha256":"63babe56a17fa015fbd78d9b671e309c7dfae853bbddada703bbda0b1805043a","schema_version":"1.0","event_id":"sha256:63babe56a17fa015fbd78d9b671e309c7dfae853bbddada703bbda0b1805043a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:Z4S5MJP5X36PD33GK4HMECX5OM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a stiff problem in two-dimensional space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Liping Li, Wenjie Sun","submitted_at":"2021-07-17T14:13:12Z","abstract_excerpt":"In this paper we will study a stiff problem in two-dimensional space and especially its probabilistic counterpart. Roughly speaking, the heat equation with a parameter $\\varepsilon>0$ is under consideration: \\[ \\partial_t u^\\varepsilon(t,x)=\\frac{1}{2}\\nabla \\cdot \\left(\\mathbf{A}_\\varepsilon(x)\\nabla u^\\varepsilon(t,x) \\right),\\quad t\\geq 0, x\\in \\mathbb{R}^2, \\] where $\\mathbf{A}_\\varepsilon(x)=\\text{Id}_2$, the identity matrix, for $x\\notin \\Omega_\\varepsilon:=\\{x=(x_1,x_2)\\in \\mathbb{R}^2: |x_2|<\\varepsilon\\}$ while $$\\mathbf{A}_\\varepsilon(x):=\\begin{pmatrix} a_\\varepsilon^- & 0 \\\\ 0 & a^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.08242","kind":"arxiv","version":2},"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/2107.08242/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":"2026-07-05T03:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ifVavphJ3SXCtUrqAZa+qiXmuKMie0R12qWs0nIzGgEXpUcJK1jEn+yNfMOSBjLaX6SlpMS9xoGbAiMPZ7aRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:07:10.301412Z"},"content_sha256":"2b04b1b276973823b43c6788e091d1de694a4e8c55c0e67f0a8740f6dce35069","schema_version":"1.0","event_id":"sha256:2b04b1b276973823b43c6788e091d1de694a4e8c55c0e67f0a8740f6dce35069"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4S5MJP5X36PD33GK4HMECX5OM/bundle.json","state_url":"https://pith.science/pith/Z4S5MJP5X36PD33GK4HMECX5OM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4S5MJP5X36PD33GK4HMECX5OM/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":"2026-08-14T01:07:10Z","links":{"resolver":"https://pith.science/pith/Z4S5MJP5X36PD33GK4HMECX5OM","bundle":"https://pith.science/pith/Z4S5MJP5X36PD33GK4HMECX5OM/bundle.json","state":"https://pith.science/pith/Z4S5MJP5X36PD33GK4HMECX5OM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4S5MJP5X36PD33GK4HMECX5OM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:Z4S5MJP5X36PD33GK4HMECX5OM","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":"eaeb440820a8359300e1877ae1b4ba0484d8e4839a93303b793fcfb10a47fe95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-17T14:13:12Z","title_canon_sha256":"d74c21c27b235a7117306ae2f1269d63c65f17bf87d17a1cdcd9e1398dc704ee"},"schema_version":"1.0","source":{"id":"2107.08242","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.08242","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"2107.08242v2","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.08242","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"Z4S5MJP5X36P","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"pith_short_16","alias_value":"Z4S5MJP5X36PD33G","created_at":"2026-07-05T03:06:32Z"},{"alias_kind":"pith_short_8","alias_value":"Z4S5MJP5","created_at":"2026-07-05T03:06:32Z"}],"graph_snapshots":[{"event_id":"sha256:2b04b1b276973823b43c6788e091d1de694a4e8c55c0e67f0a8740f6dce35069","target":"graph","created_at":"2026-07-05T03:06:32Z","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/2107.08242/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we will study a stiff problem in two-dimensional space and especially its probabilistic counterpart. Roughly speaking, the heat equation with a parameter $\\varepsilon>0$ is under consideration: \\[ \\partial_t u^\\varepsilon(t,x)=\\frac{1}{2}\\nabla \\cdot \\left(\\mathbf{A}_\\varepsilon(x)\\nabla u^\\varepsilon(t,x) \\right),\\quad t\\geq 0, x\\in \\mathbb{R}^2, \\] where $\\mathbf{A}_\\varepsilon(x)=\\text{Id}_2$, the identity matrix, for $x\\notin \\Omega_\\varepsilon:=\\{x=(x_1,x_2)\\in \\mathbb{R}^2: |x_2|<\\varepsilon\\}$ while $$\\mathbf{A}_\\varepsilon(x):=\\begin{pmatrix} a_\\varepsilon^- & 0 \\\\ 0 & a^","authors_text":"Liping Li, Wenjie Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-17T14:13:12Z","title":"On a stiff problem in two-dimensional space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.08242","kind":"arxiv","version":2},"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":"sha256:63babe56a17fa015fbd78d9b671e309c7dfae853bbddada703bbda0b1805043a","target":"record","created_at":"2026-07-05T03:06:32Z","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":"eaeb440820a8359300e1877ae1b4ba0484d8e4839a93303b793fcfb10a47fe95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-17T14:13:12Z","title_canon_sha256":"d74c21c27b235a7117306ae2f1269d63c65f17bf87d17a1cdcd9e1398dc704ee"},"schema_version":"1.0","source":{"id":"2107.08242","kind":"arxiv","version":2}},"canonical_sha256":"cf25d625fdbefcf1ef66570ec20afd731a62fe82ea13ad3e8f5c3975300def7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf25d625fdbefcf1ef66570ec20afd731a62fe82ea13ad3e8f5c3975300def7f","first_computed_at":"2026-07-05T03:06:32.468704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:06:32.468704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l3ECTkBl+C9FwHpLGh8pIyTMMHtSizMsmjw2T5XeDwcK0f7GHuWfejd+43XGHpkSWbAR1usQ1VMP6/o84V0SBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:06:32.469197Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.08242","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63babe56a17fa015fbd78d9b671e309c7dfae853bbddada703bbda0b1805043a","sha256:2b04b1b276973823b43c6788e091d1de694a4e8c55c0e67f0a8740f6dce35069"],"state_sha256":"59a722e9d2c11e1ae920d117e93eb1eb2f8d2a30320a4eab5e455a4bb415990d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eMSxMQvzeIM0eFUjSFex9hy3e5WofJ+f/h1euIYJwWgyj8oBsHjejYLAKLh1Vu/pqXXZRkefoZuVtBW1Mx1dCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T01:07:10.305845Z","bundle_sha256":"5da8c75634485f7cd60f9a6cd51908403eb904e795db0e89872cfcc6fdab497c"}}