{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DMWDV7S3KK6AEMW6HTLEJVWMMI","short_pith_number":"pith:DMWDV7S3","canonical_record":{"source":{"id":"1808.05311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-16T00:10:11Z","cross_cats_sorted":["q-fin.CP"],"title_canon_sha256":"01a27dbc2a2285ae45c9c2904a56b8739c5a40cf7a0365f22efcd44aeaf4a226","abstract_canon_sha256":"b246052fdf55940b734140c7d4771bd97bb9bcb66e5380baafa8ee7f9f5c19aa"},"schema_version":"1.0"},"canonical_sha256":"1b2c3afe5b52bc0232de3cd644d6cc62152572893f8666bdd3cd032962e84369","source":{"kind":"arxiv","id":"1808.05311","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05311","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05311v2","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05311","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"DMWDV7S3KK6A","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMWDV7S3KK6AEMW6","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMWDV7S3","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DMWDV7S3KK6AEMW6HTLEJVWMMI","target":"record","payload":{"canonical_record":{"source":{"id":"1808.05311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-16T00:10:11Z","cross_cats_sorted":["q-fin.CP"],"title_canon_sha256":"01a27dbc2a2285ae45c9c2904a56b8739c5a40cf7a0365f22efcd44aeaf4a226","abstract_canon_sha256":"b246052fdf55940b734140c7d4771bd97bb9bcb66e5380baafa8ee7f9f5c19aa"},"schema_version":"1.0"},"canonical_sha256":"1b2c3afe5b52bc0232de3cd644d6cc62152572893f8666bdd3cd032962e84369","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:16.988466Z","signature_b64":"e5PFd5mP2QtMeLqrh6q+SW4uHKk7JrEbScm7vXmnqOTTpGK8Ya0Lq1gaKBdbWkV9bryicgrpeKRqC0mEb53WAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b2c3afe5b52bc0232de3cd644d6cc62152572893f8666bdd3cd032962e84369","last_reissued_at":"2026-05-18T00:07:16.987875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:16.987875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.05311","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":"2026-05-18T00:07:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UAMIvi+8aNWnwH23AEAPtG2AqpJBy9/SvJXELKfJa7XAKiqeQFbFhJdVUcq60A1UKwOuyWYbM3/bQ7EuxswJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:31:32.807642Z"},"content_sha256":"7297ced9a6f8a987a3d67ad732a0045d9ba15b1c67f0ff3d62157757379142da","schema_version":"1.0","event_id":"sha256:7297ced9a6f8a987a3d67ad732a0045d9ba15b1c67f0ff3d62157757379142da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DMWDV7S3KK6AEMW6HTLEJVWMMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.CP"],"primary_cat":"math.NA","authors_text":"Alexander Lipton, Christoph Reisinger, Vadim Kaushansky","submitted_at":"2018-08-16T00:10:11Z","abstract_excerpt":"In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the method of heat potentials, we derive a coupled system of Volterra integral equations for the transition density and for the loss through absorption. An approximation by expansion is given for a small interaction parameter. We also present a numerical solution algorithm and conduct com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05311","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":""},"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":"2026-05-18T00:07:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/VFVV+RzaSXIkhf4FFExAJ7GyVffFwG+cyx/ys3haRkR3m1GOCbF9DR5x/dJgB0hAdJ6L8rXp1UilHgKK40ABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:31:32.808378Z"},"content_sha256":"c692e9a7f53b1cd629c87ddeabedf5d17af8166c6396b116a58dd99b232aad2c","schema_version":"1.0","event_id":"sha256:c692e9a7f53b1cd629c87ddeabedf5d17af8166c6396b116a58dd99b232aad2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMWDV7S3KK6AEMW6HTLEJVWMMI/bundle.json","state_url":"https://pith.science/pith/DMWDV7S3KK6AEMW6HTLEJVWMMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMWDV7S3KK6AEMW6HTLEJVWMMI/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":"2026-05-20T04:31:32Z","links":{"resolver":"https://pith.science/pith/DMWDV7S3KK6AEMW6HTLEJVWMMI","bundle":"https://pith.science/pith/DMWDV7S3KK6AEMW6HTLEJVWMMI/bundle.json","state":"https://pith.science/pith/DMWDV7S3KK6AEMW6HTLEJVWMMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMWDV7S3KK6AEMW6HTLEJVWMMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DMWDV7S3KK6AEMW6HTLEJVWMMI","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":"b246052fdf55940b734140c7d4771bd97bb9bcb66e5380baafa8ee7f9f5c19aa","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-16T00:10:11Z","title_canon_sha256":"01a27dbc2a2285ae45c9c2904a56b8739c5a40cf7a0365f22efcd44aeaf4a226"},"schema_version":"1.0","source":{"id":"1808.05311","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05311","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05311v2","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05311","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"DMWDV7S3KK6A","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMWDV7S3KK6AEMW6","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMWDV7S3","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:c692e9a7f53b1cd629c87ddeabedf5d17af8166c6396b116a58dd99b232aad2c","target":"graph","created_at":"2026-05-18T00:07:16Z","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":"In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the method of heat potentials, we derive a coupled system of Volterra integral equations for the transition density and for the loss through absorption. An approximation by expansion is given for a small interaction parameter. We also present a numerical solution algorithm and conduct com","authors_text":"Alexander Lipton, Christoph Reisinger, Vadim Kaushansky","cross_cats":["q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-16T00:10:11Z","title":"Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05311","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":"sha256:7297ced9a6f8a987a3d67ad732a0045d9ba15b1c67f0ff3d62157757379142da","target":"record","created_at":"2026-05-18T00:07:16Z","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":"b246052fdf55940b734140c7d4771bd97bb9bcb66e5380baafa8ee7f9f5c19aa","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-16T00:10:11Z","title_canon_sha256":"01a27dbc2a2285ae45c9c2904a56b8739c5a40cf7a0365f22efcd44aeaf4a226"},"schema_version":"1.0","source":{"id":"1808.05311","kind":"arxiv","version":2}},"canonical_sha256":"1b2c3afe5b52bc0232de3cd644d6cc62152572893f8666bdd3cd032962e84369","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b2c3afe5b52bc0232de3cd644d6cc62152572893f8666bdd3cd032962e84369","first_computed_at":"2026-05-18T00:07:16.987875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:16.987875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e5PFd5mP2QtMeLqrh6q+SW4uHKk7JrEbScm7vXmnqOTTpGK8Ya0Lq1gaKBdbWkV9bryicgrpeKRqC0mEb53WAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:16.988466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.05311","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7297ced9a6f8a987a3d67ad732a0045d9ba15b1c67f0ff3d62157757379142da","sha256:c692e9a7f53b1cd629c87ddeabedf5d17af8166c6396b116a58dd99b232aad2c"],"state_sha256":"7f7d54d6db78dff582880f76e3b12bab89e410b6ea4f3068b128157b63e0c021"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3GeI49avgbUubMNhRc7N+Z9RG2q2raLnACvzLdtnVciO0Tj8rFsNJRes3dy/4xKf2yXuGJDTVubt3cH51JPDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T04:31:32.812208Z","bundle_sha256":"a1887c6d83de8c743b675bd69635da54cd1f1657b2e09436820843dcf81d5439"}}