{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PBLYUMQA3NT3RJ5DQ6K3V7RYPM","short_pith_number":"pith:PBLYUMQA","canonical_record":{"source":{"id":"1802.02031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-06T16:19:00Z","cross_cats_sorted":[],"title_canon_sha256":"5904f260311186fdb9b034c3069620381e5ea7c97b6a43162196dbe52160e5d6","abstract_canon_sha256":"9b46fd76bd60320e8968bff4183911be4acedd73c8f538b17ec1ee511a8e460e"},"schema_version":"1.0"},"canonical_sha256":"78578a3200db67b8a7a38795bafe387b3fbafd81f42219bf13bc283ad19b49a6","source":{"kind":"arxiv","id":"1802.02031","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02031","created_at":"2026-05-18T00:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02031v1","created_at":"2026-05-18T00:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02031","created_at":"2026-05-18T00:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"PBLYUMQA3NT3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PBLYUMQA3NT3RJ5D","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PBLYUMQA","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PBLYUMQA3NT3RJ5DQ6K3V7RYPM","target":"record","payload":{"canonical_record":{"source":{"id":"1802.02031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-06T16:19:00Z","cross_cats_sorted":[],"title_canon_sha256":"5904f260311186fdb9b034c3069620381e5ea7c97b6a43162196dbe52160e5d6","abstract_canon_sha256":"9b46fd76bd60320e8968bff4183911be4acedd73c8f538b17ec1ee511a8e460e"},"schema_version":"1.0"},"canonical_sha256":"78578a3200db67b8a7a38795bafe387b3fbafd81f42219bf13bc283ad19b49a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:11.136094Z","signature_b64":"WNc5NjHAF+7Z/0si5xj1+6uSKltZSiaBNOxu0lo1ebTLbWNCMAY3L7dQ85C+nHRxZCXbgw+Vrz/k+pVR4Ax2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78578a3200db67b8a7a38795bafe387b3fbafd81f42219bf13bc283ad19b49a6","last_reissued_at":"2026-05-18T00:24:11.135374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:11.135374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.02031","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":"2026-05-18T00:24:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XgqFrLYT51os6AX0GQu7dXX8nbApDnyNBjSFMzhgmyJl9XCRS2ymba2ExLVYr6N7Jwn2fJ1jz7oB5bMxc54YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:13:12.360483Z"},"content_sha256":"bdf04eb7d041d508fcefc1066c4b3ca9b4f96cb5afd4bdfefac680e1cbee6b35","schema_version":"1.0","event_id":"sha256:bdf04eb7d041d508fcefc1066c4b3ca9b4f96cb5afd4bdfefac680e1cbee6b35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PBLYUMQA3NT3RJ5DQ6K3V7RYPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite speed of propagation for the thin film equation in spherical geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Roman Taranets","submitted_at":"2018-02-06T16:19:00Z","abstract_excerpt":"We show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative strong solutions and hence there exists an interface or free boundary separating the regions where solution $u>0$ and $u=0$. Using local entropy estimates we also obtain an upper bound for the rate of the interface propagation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02031","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":"2026-05-18T00:24:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VE8u4aB+enzlHLToFXMfSHGXTova7koUyLkDOsBmNxqWOcULLDgmxwASNZQXKqYmW0DWLQhGm7ChjdhEB0SaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:13:12.361276Z"},"content_sha256":"6fe7cbb1159f84319172ca6e10bdb07a1254f99d1fb7060b19a0baddb68b28c7","schema_version":"1.0","event_id":"sha256:6fe7cbb1159f84319172ca6e10bdb07a1254f99d1fb7060b19a0baddb68b28c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBLYUMQA3NT3RJ5DQ6K3V7RYPM/bundle.json","state_url":"https://pith.science/pith/PBLYUMQA3NT3RJ5DQ6K3V7RYPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBLYUMQA3NT3RJ5DQ6K3V7RYPM/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":"2026-05-30T11:13:12Z","links":{"resolver":"https://pith.science/pith/PBLYUMQA3NT3RJ5DQ6K3V7RYPM","bundle":"https://pith.science/pith/PBLYUMQA3NT3RJ5DQ6K3V7RYPM/bundle.json","state":"https://pith.science/pith/PBLYUMQA3NT3RJ5DQ6K3V7RYPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBLYUMQA3NT3RJ5DQ6K3V7RYPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PBLYUMQA3NT3RJ5DQ6K3V7RYPM","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":"9b46fd76bd60320e8968bff4183911be4acedd73c8f538b17ec1ee511a8e460e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-06T16:19:00Z","title_canon_sha256":"5904f260311186fdb9b034c3069620381e5ea7c97b6a43162196dbe52160e5d6"},"schema_version":"1.0","source":{"id":"1802.02031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02031","created_at":"2026-05-18T00:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02031v1","created_at":"2026-05-18T00:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02031","created_at":"2026-05-18T00:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"PBLYUMQA3NT3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PBLYUMQA3NT3RJ5D","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PBLYUMQA","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:6fe7cbb1159f84319172ca6e10bdb07a1254f99d1fb7060b19a0baddb68b28c7","target":"graph","created_at":"2026-05-18T00:24:11Z","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 show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative strong solutions and hence there exists an interface or free boundary separating the regions where solution $u>0$ and $u=0$. Using local entropy estimates we also obtain an upper bound for the rate of the interface propagation.","authors_text":"Roman Taranets","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-06T16:19:00Z","title":"Finite speed of propagation for the thin film equation in spherical geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02031","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:bdf04eb7d041d508fcefc1066c4b3ca9b4f96cb5afd4bdfefac680e1cbee6b35","target":"record","created_at":"2026-05-18T00:24:11Z","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":"9b46fd76bd60320e8968bff4183911be4acedd73c8f538b17ec1ee511a8e460e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-06T16:19:00Z","title_canon_sha256":"5904f260311186fdb9b034c3069620381e5ea7c97b6a43162196dbe52160e5d6"},"schema_version":"1.0","source":{"id":"1802.02031","kind":"arxiv","version":1}},"canonical_sha256":"78578a3200db67b8a7a38795bafe387b3fbafd81f42219bf13bc283ad19b49a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78578a3200db67b8a7a38795bafe387b3fbafd81f42219bf13bc283ad19b49a6","first_computed_at":"2026-05-18T00:24:11.135374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:11.135374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WNc5NjHAF+7Z/0si5xj1+6uSKltZSiaBNOxu0lo1ebTLbWNCMAY3L7dQ85C+nHRxZCXbgw+Vrz/k+pVR4Ax2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:11.136094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdf04eb7d041d508fcefc1066c4b3ca9b4f96cb5afd4bdfefac680e1cbee6b35","sha256:6fe7cbb1159f84319172ca6e10bdb07a1254f99d1fb7060b19a0baddb68b28c7"],"state_sha256":"dcc1d39c5aefca010bb788f220cc66162836e48eb9b36b5d85e789c32461010d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KFqE4qg7dEVZnk3wK2DbuqpCzU73C2NZVzAcZMtLmNGo/YKvcnh3UXidq8CrRueqCevDoyaiFaTSmk3WlgefBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:13:12.365699Z","bundle_sha256":"45c25e67aca851706c0884b0c11a21e8f853322eed809b7cf41078fee7b4c0ef"}}