{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YDHZQWZCU6L4L77MQXRS4XIW2Y","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":"76174d0a0ce54c47d6f740e7b45ba302acec8566ee980a2f963dab9c8ce4cac8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-24T20:20:54Z","title_canon_sha256":"d45759ff35157c80d6bc43bd9820894eb7e535d8f16c5df87ac7632725c867f5"},"schema_version":"1.0","source":{"id":"1708.07542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07542","created_at":"2026-05-17T23:51:09Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07542v2","created_at":"2026-05-17T23:51:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07542","created_at":"2026-05-17T23:51:09Z"},{"alias_kind":"pith_short_12","alias_value":"YDHZQWZCU6L4","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YDHZQWZCU6L4L77M","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YDHZQWZC","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:9ca5f9ecc1c8004f8f30132bd148563b11e5221b155b784f9647b94e7e2a8d34","target":"graph","created_at":"2026-05-17T23:51:09Z","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 study the porous medium equation on manifolds with conical singularities. Given strictly positive initial values, we show that the solution exists in the maximal $L^{q}$-regularity space for all times and is instantaneously smooth in space and time, where the maximal $L^{q}$-regularity is obtained in the sense of Mellin-Sobolev spaces. Moreover, we obtain precise information concerning the asymptotic behavior of the solution close to the singularity. Finally, we show the existence of generalized solutions for non-negative initial data.","authors_text":"Elmar Schrohe, Nikolaos Roidos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-24T20:20:54Z","title":"Smoothness and long time existence for solutions of the porous medium equation on manifolds with conical singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07542","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":"sha256:105f0fd546ef7c2d94fa2f5522ab1c9d2f8718141d3accf5bc33c05382a63f0a","target":"record","created_at":"2026-05-17T23:51:09Z","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":"76174d0a0ce54c47d6f740e7b45ba302acec8566ee980a2f963dab9c8ce4cac8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-24T20:20:54Z","title_canon_sha256":"d45759ff35157c80d6bc43bd9820894eb7e535d8f16c5df87ac7632725c867f5"},"schema_version":"1.0","source":{"id":"1708.07542","kind":"arxiv","version":2}},"canonical_sha256":"c0cf985b22a797c5ffec85e32e5d16d6129b970791705b17ae86726af3d894d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0cf985b22a797c5ffec85e32e5d16d6129b970791705b17ae86726af3d894d8","first_computed_at":"2026-05-17T23:51:09.856472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:09.856472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+aLGlQ2GYakNQe2xdfFyEKPCJNHaqu+qPf0askAp041byX9T+OUMKdVN0OX1Qbl4eUiYKvZVVKZZU8fy/Me8CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:09.857288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:105f0fd546ef7c2d94fa2f5522ab1c9d2f8718141d3accf5bc33c05382a63f0a","sha256:9ca5f9ecc1c8004f8f30132bd148563b11e5221b155b784f9647b94e7e2a8d34"],"state_sha256":"89e38b5c57903b89a51c6575188999688619665fecf7f841d42a82829ddfef7e"}