{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:G6ARKLBF4KAPS33XWYUJRMEAXM","short_pith_number":"pith:G6ARKLBF","canonical_record":{"source":{"id":"1907.03796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-08T18:22:12Z","cross_cats_sorted":[],"title_canon_sha256":"cc4b28c9d25b00d93f6428592ded4bc85c5d29d190fc86e492b6f4514bac71be","abstract_canon_sha256":"d01b1f7aa5658b64973815bdefd32dbb0d5011de204aa387052ac56d5361ab73"},"schema_version":"1.0"},"canonical_sha256":"3781152c25e280f96f77b62898b080bb1cbd250836ffb83363ad4cb7c1f07829","source":{"kind":"arxiv","id":"1907.03796","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03796","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03796v1","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03796","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"G6ARKLBF4KAP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"G6ARKLBF4KAPS33X","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"G6ARKLBF","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:G6ARKLBF4KAPS33XWYUJRMEAXM","target":"record","payload":{"canonical_record":{"source":{"id":"1907.03796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-08T18:22:12Z","cross_cats_sorted":[],"title_canon_sha256":"cc4b28c9d25b00d93f6428592ded4bc85c5d29d190fc86e492b6f4514bac71be","abstract_canon_sha256":"d01b1f7aa5658b64973815bdefd32dbb0d5011de204aa387052ac56d5361ab73"},"schema_version":"1.0"},"canonical_sha256":"3781152c25e280f96f77b62898b080bb1cbd250836ffb83363ad4cb7c1f07829","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:06.838424Z","signature_b64":"eDN+ZEjZUB5FV587fd7b59sVeUrMjk9PWyMWhgd9PjH7HrSOd36li/ceKjdWRFmd+jk7xl0TX087Gs9VqZsXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3781152c25e280f96f77b62898b080bb1cbd250836ffb83363ad4cb7c1f07829","last_reissued_at":"2026-05-17T23:41:06.837668Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:06.837668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.03796","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":"2026-05-17T23:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDqMqgpQzRmAh9kfEtsOfRE8Ac5dpIvRCsUxPTnN3rRsJhpSxzCsojGyllj9z5NUtKtTq92bqNATYQgj9bWmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:32:00.816688Z"},"content_sha256":"b9fb4d7eb2593fd60f4192792b0ae45c391368ac224e24e81eb36a734cc06353","schema_version":"1.0","event_id":"sha256:b9fb4d7eb2593fd60f4192792b0ae45c391368ac224e24e81eb36a734cc06353"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:G6ARKLBF4KAPS33XWYUJRMEAXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quenching estimates for a non-Newtonian filtration equation with singular boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Burhan Selcuk, Matthew A. Beauregard","submitted_at":"2019-07-08T18:22:12Z","abstract_excerpt":"In this paper, the quenching behavior of the non-Newtonian filtration equation $(\\phi (u))_{t}=(\\left \\vert u_{x}\\right \\vert ^{r-2}u_{x})_{x}$ with singular boundary conditions, $u_{x}\\left( 0,t\\right) =u^{-p}(0,t)$, $u_{x}\\left( a,t\\right) =(1-u(a,t))^{-q}$ is investigated. Various conditions on the initial condition are shown to guarantee quenching at either the left or right boundary. Theoretical quenching rates and lower bounds to the quenching time are determined when $\\phi(u)=u$ and $r=2$. Numerical experiments are provided to illustrate and provide additional validation of the theoreti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03796","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":"2026-05-17T23:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnFxFM5plmFShttdGs87Q8CytYVFaH7LqMFYa4tUhGhiFE5JMga3XHlHpJ9/Oz+otDP3L/4cMQFZLafYIrZeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:32:00.817192Z"},"content_sha256":"b30b459069f25a25ad63dd8b2e774415a4d450ec2794084d76199e354519bb04","schema_version":"1.0","event_id":"sha256:b30b459069f25a25ad63dd8b2e774415a4d450ec2794084d76199e354519bb04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G6ARKLBF4KAPS33XWYUJRMEAXM/bundle.json","state_url":"https://pith.science/pith/G6ARKLBF4KAPS33XWYUJRMEAXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G6ARKLBF4KAPS33XWYUJRMEAXM/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":"2026-05-25T19:32:00Z","links":{"resolver":"https://pith.science/pith/G6ARKLBF4KAPS33XWYUJRMEAXM","bundle":"https://pith.science/pith/G6ARKLBF4KAPS33XWYUJRMEAXM/bundle.json","state":"https://pith.science/pith/G6ARKLBF4KAPS33XWYUJRMEAXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G6ARKLBF4KAPS33XWYUJRMEAXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:G6ARKLBF4KAPS33XWYUJRMEAXM","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":"d01b1f7aa5658b64973815bdefd32dbb0d5011de204aa387052ac56d5361ab73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-08T18:22:12Z","title_canon_sha256":"cc4b28c9d25b00d93f6428592ded4bc85c5d29d190fc86e492b6f4514bac71be"},"schema_version":"1.0","source":{"id":"1907.03796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03796","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03796v1","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03796","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"G6ARKLBF4KAP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"G6ARKLBF4KAPS33X","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"G6ARKLBF","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:b30b459069f25a25ad63dd8b2e774415a4d450ec2794084d76199e354519bb04","target":"graph","created_at":"2026-05-17T23:41:06Z","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, the quenching behavior of the non-Newtonian filtration equation $(\\phi (u))_{t}=(\\left \\vert u_{x}\\right \\vert ^{r-2}u_{x})_{x}$ with singular boundary conditions, $u_{x}\\left( 0,t\\right) =u^{-p}(0,t)$, $u_{x}\\left( a,t\\right) =(1-u(a,t))^{-q}$ is investigated. Various conditions on the initial condition are shown to guarantee quenching at either the left or right boundary. Theoretical quenching rates and lower bounds to the quenching time are determined when $\\phi(u)=u$ and $r=2$. Numerical experiments are provided to illustrate and provide additional validation of the theoreti","authors_text":"Burhan Selcuk, Matthew A. Beauregard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-08T18:22:12Z","title":"Quenching estimates for a non-Newtonian filtration equation with singular boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03796","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:b9fb4d7eb2593fd60f4192792b0ae45c391368ac224e24e81eb36a734cc06353","target":"record","created_at":"2026-05-17T23:41:06Z","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":"d01b1f7aa5658b64973815bdefd32dbb0d5011de204aa387052ac56d5361ab73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-08T18:22:12Z","title_canon_sha256":"cc4b28c9d25b00d93f6428592ded4bc85c5d29d190fc86e492b6f4514bac71be"},"schema_version":"1.0","source":{"id":"1907.03796","kind":"arxiv","version":1}},"canonical_sha256":"3781152c25e280f96f77b62898b080bb1cbd250836ffb83363ad4cb7c1f07829","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3781152c25e280f96f77b62898b080bb1cbd250836ffb83363ad4cb7c1f07829","first_computed_at":"2026-05-17T23:41:06.837668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:06.837668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eDN+ZEjZUB5FV587fd7b59sVeUrMjk9PWyMWhgd9PjH7HrSOd36li/ceKjdWRFmd+jk7xl0TX087Gs9VqZsXCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:06.838424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.03796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9fb4d7eb2593fd60f4192792b0ae45c391368ac224e24e81eb36a734cc06353","sha256:b30b459069f25a25ad63dd8b2e774415a4d450ec2794084d76199e354519bb04"],"state_sha256":"b5ec23be6095fe5a34fbaea5c4ea9db3f316d0d5beef942d20c49fad192e7d9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/UoH8y8qMAbORx42gqm+MBvc9XhGrmOrOVfni9xFsjptCHI9p1aJsp6YMwZkdFnEPEsFzfQ5xeGyJ+EGajDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:32:00.820593Z","bundle_sha256":"dc0e11ed27d000848ead0ca41a15c781a9de020146f16564ee6fc40541383382"}}