{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IDSW4OHYAP2QZELXWP6L6MNHKH","short_pith_number":"pith:IDSW4OHY","canonical_record":{"source":{"id":"1906.06584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-15T16:13:25Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6b711fcb0f2bb4de347a0aa303cfae8529191e151ba555291958a117fa7d7933","abstract_canon_sha256":"ba1dffe9ad86758035a8c9ab432ac0d1d4cd68019cbbc789daf3fa7b07ad0a74"},"schema_version":"1.0"},"canonical_sha256":"40e56e38f803f50c9177b3fcbf31a751df785ece0c2117b363f6e8450a9eff5d","source":{"kind":"arxiv","id":"1906.06584","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.06584","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"arxiv_version","alias_value":"1906.06584v1","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06584","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"pith_short_12","alias_value":"IDSW4OHYAP2Q","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IDSW4OHYAP2QZELX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IDSW4OHY","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IDSW4OHYAP2QZELXWP6L6MNHKH","target":"record","payload":{"canonical_record":{"source":{"id":"1906.06584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-15T16:13:25Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6b711fcb0f2bb4de347a0aa303cfae8529191e151ba555291958a117fa7d7933","abstract_canon_sha256":"ba1dffe9ad86758035a8c9ab432ac0d1d4cd68019cbbc789daf3fa7b07ad0a74"},"schema_version":"1.0"},"canonical_sha256":"40e56e38f803f50c9177b3fcbf31a751df785ece0c2117b363f6e8450a9eff5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:13.288419Z","signature_b64":"QiLq4MeC2kraOULTzN25Gtx0o7uDXHbjsV+VYMIMzIJ2QOh/GbLblpxCrBBeOMkigXSGUdljg+X6eQTE3JzUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40e56e38f803f50c9177b3fcbf31a751df785ece0c2117b363f6e8450a9eff5d","last_reissued_at":"2026-05-17T23:43:13.287829Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:13.287829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.06584","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":"2026-05-17T23:43:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwMyr/NNm/0L5Azke8YcUTuTeowU8L64q/+1qMMETkHh3Fi45y2eNCLwW1jTAZgeTeMwPbpjV6RdmeKz/faZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:22:14.603682Z"},"content_sha256":"1d2874dd0df45101556562a0d15fa768a4906d5d35d106daf73e05260e6b5120","schema_version":"1.0","event_id":"sha256:1d2874dd0df45101556562a0d15fa768a4906d5d35d106daf73e05260e6b5120"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IDSW4OHYAP2QZELXWP6L6MNHKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jiang Yang, Qiang Du, Zhi Zhou","submitted_at":"2019-06-15T16:13:25Z","abstract_excerpt":"In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $\\alpha\\in(0,1)$. First, the well-posedness and (limited) smoothing property are systematically analyzed, by using the maximal $L^p$ regularity of fractional evolution equations and the fractional Gr\\\"onwall's inequality. We also show the maximum principle like their conventional local-in-time counterpart. Precisely, the time-fractional equation preserves the property that the solution only takes value between the wells of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06584","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":"2026-05-17T23:43:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HNKmU3HHWxjxL5lmt/wssg18wXvkseAq6P0wfJfl5brArkjVhxOovR03S5Qpf01JXcaaDzO8dHnWMQyCzw40Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:22:14.604428Z"},"content_sha256":"6a2052a762d1429a7d1255be06e0e54d4d3534b785c5345e8591886741fa90d8","schema_version":"1.0","event_id":"sha256:6a2052a762d1429a7d1255be06e0e54d4d3534b785c5345e8591886741fa90d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDSW4OHYAP2QZELXWP6L6MNHKH/bundle.json","state_url":"https://pith.science/pith/IDSW4OHYAP2QZELXWP6L6MNHKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDSW4OHYAP2QZELXWP6L6MNHKH/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":"2026-06-08T21:22:14Z","links":{"resolver":"https://pith.science/pith/IDSW4OHYAP2QZELXWP6L6MNHKH","bundle":"https://pith.science/pith/IDSW4OHYAP2QZELXWP6L6MNHKH/bundle.json","state":"https://pith.science/pith/IDSW4OHYAP2QZELXWP6L6MNHKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDSW4OHYAP2QZELXWP6L6MNHKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IDSW4OHYAP2QZELXWP6L6MNHKH","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":"ba1dffe9ad86758035a8c9ab432ac0d1d4cd68019cbbc789daf3fa7b07ad0a74","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-15T16:13:25Z","title_canon_sha256":"6b711fcb0f2bb4de347a0aa303cfae8529191e151ba555291958a117fa7d7933"},"schema_version":"1.0","source":{"id":"1906.06584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.06584","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"arxiv_version","alias_value":"1906.06584v1","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06584","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"pith_short_12","alias_value":"IDSW4OHYAP2Q","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IDSW4OHYAP2QZELX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IDSW4OHY","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:6a2052a762d1429a7d1255be06e0e54d4d3534b785c5345e8591886741fa90d8","target":"graph","created_at":"2026-05-17T23:43:13Z","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 work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $\\alpha\\in(0,1)$. First, the well-posedness and (limited) smoothing property are systematically analyzed, by using the maximal $L^p$ regularity of fractional evolution equations and the fractional Gr\\\"onwall's inequality. We also show the maximum principle like their conventional local-in-time counterpart. Precisely, the time-fractional equation preserves the property that the solution only takes value between the wells of ","authors_text":"Jiang Yang, Qiang Du, Zhi Zhou","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-15T16:13:25Z","title":"Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06584","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":"sha256:1d2874dd0df45101556562a0d15fa768a4906d5d35d106daf73e05260e6b5120","target":"record","created_at":"2026-05-17T23:43:13Z","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":"ba1dffe9ad86758035a8c9ab432ac0d1d4cd68019cbbc789daf3fa7b07ad0a74","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-15T16:13:25Z","title_canon_sha256":"6b711fcb0f2bb4de347a0aa303cfae8529191e151ba555291958a117fa7d7933"},"schema_version":"1.0","source":{"id":"1906.06584","kind":"arxiv","version":1}},"canonical_sha256":"40e56e38f803f50c9177b3fcbf31a751df785ece0c2117b363f6e8450a9eff5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40e56e38f803f50c9177b3fcbf31a751df785ece0c2117b363f6e8450a9eff5d","first_computed_at":"2026-05-17T23:43:13.287829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:13.287829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QiLq4MeC2kraOULTzN25Gtx0o7uDXHbjsV+VYMIMzIJ2QOh/GbLblpxCrBBeOMkigXSGUdljg+X6eQTE3JzUDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:13.288419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.06584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d2874dd0df45101556562a0d15fa768a4906d5d35d106daf73e05260e6b5120","sha256:6a2052a762d1429a7d1255be06e0e54d4d3534b785c5345e8591886741fa90d8"],"state_sha256":"55c18673ae5f814713bdfb32617178c259f4f54f5c48b025a165011915bbdb9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qa4ANJfB/u5bMw3j7opvJLrOhEm6sByOtFGZ4x1VNvUC4IdBKOO+Ucpcv9KGyJ20Co7e2QxJK1rwcAmDxV3zAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:22:14.608441Z","bundle_sha256":"ffb9d72259020b358e3f96113b37f3ddc1c8117bcdcaf5eab58a9f1ac516100c"}}