{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HNKNV3T6RSLZZ5RDJWUENTOBV3","short_pith_number":"pith:HNKNV3T6","canonical_record":{"source":{"id":"1907.04250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-09T15:32:52Z","cross_cats_sorted":[],"title_canon_sha256":"9bc24caee680120bf02674e2165b42e42cf7e67cdf70198479598e13a1c388aa","abstract_canon_sha256":"dd76f2fd3cf3c467775e3c8a75916ff3ba08318411eaae632ced24f033380dd5"},"schema_version":"1.0"},"canonical_sha256":"3b54daee7e8c979cf6234da846cdc1aefc849904a587a0320a0ebde6486d504c","source":{"kind":"arxiv","id":"1907.04250","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04250","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04250v1","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04250","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"HNKNV3T6RSLZ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HNKNV3T6RSLZZ5RD","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HNKNV3T6","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HNKNV3T6RSLZZ5RDJWUENTOBV3","target":"record","payload":{"canonical_record":{"source":{"id":"1907.04250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-09T15:32:52Z","cross_cats_sorted":[],"title_canon_sha256":"9bc24caee680120bf02674e2165b42e42cf7e67cdf70198479598e13a1c388aa","abstract_canon_sha256":"dd76f2fd3cf3c467775e3c8a75916ff3ba08318411eaae632ced24f033380dd5"},"schema_version":"1.0"},"canonical_sha256":"3b54daee7e8c979cf6234da846cdc1aefc849904a587a0320a0ebde6486d504c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:02.876732Z","signature_b64":"32rJJ9Y0Gmv6ZjiSofHV0nCcNLtE/jBmyHD1Qv3wegaJs9cDVnl7CvzuW452ZWmojyEjStL2mquKCcOVgMYLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b54daee7e8c979cf6234da846cdc1aefc849904a587a0320a0ebde6486d504c","last_reissued_at":"2026-05-17T23:41:02.876149Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:02.876149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.04250","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":"2026-05-17T23:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yDqOfnbgA/KTI2iFfy4PTX5jICJ4C+6XFqxTPocIe4fom/rxM93iJWRwkcVrMEj0Kx/HIe7NkcIeRiPGpfxnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:40:48.603963Z"},"content_sha256":"0894df31d42664370dd879a2e5b8dae677f46031839a1b2bab2d344772c4205d","schema_version":"1.0","event_id":"sha256:0894df31d42664370dd879a2e5b8dae677f46031839a1b2bab2d344772c4205d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HNKNV3T6RSLZZ5RDJWUENTOBV3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular limits of the quasi-linear Kolmogorov-type equation with a source term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ivan Kuznetsov, Sergey Sazhenkov","submitted_at":"2019-07-09T15:32:52Z","abstract_excerpt":"Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem for the Kolmogorov-type genuinely nonlinear ultra-parabolic equation with a smooth source term is established. After this, we consider the case when the source term contains a small positive parameter and collapses to the Dirac delta-function, as this parameter tends to zero. In this case, the limiting passage from the original equation with the smooth source to the impulsive ultra-parabolic equation is fulfilled and rigorously justified. The proofs rely on the method of kinetic equation and on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04250","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":"2026-05-17T23:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2r/dHPvDbc0KQHbL+R9g1VjXamYKKjrJY+VJbhuRaG1AUoZdt9l2igE3v/4vw/gqpFc5x3B9YXcQ++1HE/pTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:40:48.604630Z"},"content_sha256":"3dcebe504ce1f06457d54344f16e01ce534f80a992b40f111e0504af6601ee21","schema_version":"1.0","event_id":"sha256:3dcebe504ce1f06457d54344f16e01ce534f80a992b40f111e0504af6601ee21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNKNV3T6RSLZZ5RDJWUENTOBV3/bundle.json","state_url":"https://pith.science/pith/HNKNV3T6RSLZZ5RDJWUENTOBV3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNKNV3T6RSLZZ5RDJWUENTOBV3/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":"2026-05-28T18:40:48Z","links":{"resolver":"https://pith.science/pith/HNKNV3T6RSLZZ5RDJWUENTOBV3","bundle":"https://pith.science/pith/HNKNV3T6RSLZZ5RDJWUENTOBV3/bundle.json","state":"https://pith.science/pith/HNKNV3T6RSLZZ5RDJWUENTOBV3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNKNV3T6RSLZZ5RDJWUENTOBV3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HNKNV3T6RSLZZ5RDJWUENTOBV3","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":"dd76f2fd3cf3c467775e3c8a75916ff3ba08318411eaae632ced24f033380dd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-09T15:32:52Z","title_canon_sha256":"9bc24caee680120bf02674e2165b42e42cf7e67cdf70198479598e13a1c388aa"},"schema_version":"1.0","source":{"id":"1907.04250","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04250","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04250v1","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04250","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"HNKNV3T6RSLZ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HNKNV3T6RSLZZ5RD","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HNKNV3T6","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:3dcebe504ce1f06457d54344f16e01ce534f80a992b40f111e0504af6601ee21","target":"graph","created_at":"2026-05-17T23:41:02Z","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":"Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem for the Kolmogorov-type genuinely nonlinear ultra-parabolic equation with a smooth source term is established. After this, we consider the case when the source term contains a small positive parameter and collapses to the Dirac delta-function, as this parameter tends to zero. In this case, the limiting passage from the original equation with the smooth source to the impulsive ultra-parabolic equation is fulfilled and rigorously justified. The proofs rely on the method of kinetic equation and on t","authors_text":"Ivan Kuznetsov, Sergey Sazhenkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-09T15:32:52Z","title":"Singular limits of the quasi-linear Kolmogorov-type equation with a source term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04250","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":"sha256:0894df31d42664370dd879a2e5b8dae677f46031839a1b2bab2d344772c4205d","target":"record","created_at":"2026-05-17T23:41:02Z","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":"dd76f2fd3cf3c467775e3c8a75916ff3ba08318411eaae632ced24f033380dd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-09T15:32:52Z","title_canon_sha256":"9bc24caee680120bf02674e2165b42e42cf7e67cdf70198479598e13a1c388aa"},"schema_version":"1.0","source":{"id":"1907.04250","kind":"arxiv","version":1}},"canonical_sha256":"3b54daee7e8c979cf6234da846cdc1aefc849904a587a0320a0ebde6486d504c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b54daee7e8c979cf6234da846cdc1aefc849904a587a0320a0ebde6486d504c","first_computed_at":"2026-05-17T23:41:02.876149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:02.876149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"32rJJ9Y0Gmv6ZjiSofHV0nCcNLtE/jBmyHD1Qv3wegaJs9cDVnl7CvzuW452ZWmojyEjStL2mquKCcOVgMYLAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:02.876732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04250","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0894df31d42664370dd879a2e5b8dae677f46031839a1b2bab2d344772c4205d","sha256:3dcebe504ce1f06457d54344f16e01ce534f80a992b40f111e0504af6601ee21"],"state_sha256":"bf1da595445ea1354e1689fbe5d6b1bae77b52157883d5e1672aa3ef8a180e87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+TKnC29AMSHjZeNsZ8ZkCNdhrJCs6iFxj5qRY4DFI9FjKR9tQv5mq/cXD1TEA5EabTOYD0Y95CO82yW7NdgAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:40:48.607439Z","bundle_sha256":"0dcd0f90adc5914befdb1dbb77fb73cd736072c2fa46ea2237d1aa0332e7580d"}}