{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KIKARV7E4MQV56QXTSSEYULHMF","short_pith_number":"pith:KIKARV7E","canonical_record":{"source":{"id":"1903.00125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-01T02:01:29Z","cross_cats_sorted":[],"title_canon_sha256":"1dcd8def4a9ebc33400071ce6c9b0c36d3c01cee4c0c0cde1d01b612cdbd9995","abstract_canon_sha256":"0575c671733143f3f643e09b1528a6855ed1ed220b9e7b81b483e3293254c18f"},"schema_version":"1.0"},"canonical_sha256":"521408d7e4e3215efa179ca44c516761517b87f81f985656e7a516c348d6fe71","source":{"kind":"arxiv","id":"1903.00125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00125","created_at":"2026-05-17T23:51:38Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00125v1","created_at":"2026-05-17T23:51:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00125","created_at":"2026-05-17T23:51:38Z"},{"alias_kind":"pith_short_12","alias_value":"KIKARV7E4MQV","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KIKARV7E4MQV56QX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KIKARV7E","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KIKARV7E4MQV56QXTSSEYULHMF","target":"record","payload":{"canonical_record":{"source":{"id":"1903.00125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-01T02:01:29Z","cross_cats_sorted":[],"title_canon_sha256":"1dcd8def4a9ebc33400071ce6c9b0c36d3c01cee4c0c0cde1d01b612cdbd9995","abstract_canon_sha256":"0575c671733143f3f643e09b1528a6855ed1ed220b9e7b81b483e3293254c18f"},"schema_version":"1.0"},"canonical_sha256":"521408d7e4e3215efa179ca44c516761517b87f81f985656e7a516c348d6fe71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:38.932192Z","signature_b64":"l69VZkUpwEDsy9oWHOb/YXYLja7z5xPb5uT1h2A524TeqcQHu7C0PKWJE0n41EPEtPjyrvLDS1DjSZk/ihFiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"521408d7e4e3215efa179ca44c516761517b87f81f985656e7a516c348d6fe71","last_reissued_at":"2026-05-17T23:51:38.931593Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:38.931593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.00125","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":"2026-05-17T23:51:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/m1wIKz2lUES1rYgprNFZaUoP5C08yL7LSAtGG7+cd1coJhKxk9BM5l+CCU2cYt5oauTxoKhA+HP8BkydlT+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:06:59.070151Z"},"content_sha256":"ebeeffab78cfedb1b9f73439257f2d1f77fc35a7db006feb20a5abed33ca3a40","schema_version":"1.0","event_id":"sha256:ebeeffab78cfedb1b9f73439257f2d1f77fc35a7db006feb20a5abed33ca3a40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KIKARV7E4MQV56QXTSSEYULHMF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Tomomi Yokota, Yuka Chiyoda","submitted_at":"2019-03-01T02:01:29Z","abstract_excerpt":"This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \\begin{align*} \\begin{cases} u_t = \\nabla\\cdot\\left(\\dfrac{u^p \\nabla u}{\\sqrt{u^2 + |\\nabla u|^2}} \\right) -\\chi \\nabla\\cdot\\left( \\dfrac{u^q\\nabla v}{\\sqrt{1 + |\\nabla v|^2}}\\right), &x\\in \\Omega,\\ t>0, \\\\[1mm] 0 = \\Delta v - \\mu + u, &x\\in \\Omega,\\ t>0, \\end{cases} \\end{align*} where $\\Omega := B_R(0) \\subset \\mathbb{R}^n$ ($n \\in \\mathbb{N}$) is a ball with some $R>0$, and $\\chi >0$, $p,q\\geq1$, $\\mu := \\frac 1{|\\Omega|} \\int_\\Omega u_0$ and $u_0$ is an initial data of an unknown function $u$. Bellomo--"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00125","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":"2026-05-17T23:51:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NFxGvOKho7s3r8H9FKlkGgz++hARMn7Hg2UgZslciar3fh2m7nBMZ4xyn9v0Uvm60cUZavcL9DiirsllG6fvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:06:59.070570Z"},"content_sha256":"9cf2e630a03a80bc558a15f98c107557db144c3947a81d5470e4001eac17c88c","schema_version":"1.0","event_id":"sha256:9cf2e630a03a80bc558a15f98c107557db144c3947a81d5470e4001eac17c88c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/bundle.json","state_url":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIKARV7E4MQV56QXTSSEYULHMF/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":"2026-06-22T07:06:59Z","links":{"resolver":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF","bundle":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/bundle.json","state":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIKARV7E4MQV56QXTSSEYULHMF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KIKARV7E4MQV56QXTSSEYULHMF","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":"0575c671733143f3f643e09b1528a6855ed1ed220b9e7b81b483e3293254c18f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-01T02:01:29Z","title_canon_sha256":"1dcd8def4a9ebc33400071ce6c9b0c36d3c01cee4c0c0cde1d01b612cdbd9995"},"schema_version":"1.0","source":{"id":"1903.00125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00125","created_at":"2026-05-17T23:51:38Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00125v1","created_at":"2026-05-17T23:51:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00125","created_at":"2026-05-17T23:51:38Z"},{"alias_kind":"pith_short_12","alias_value":"KIKARV7E4MQV","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KIKARV7E4MQV56QX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KIKARV7E","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:9cf2e630a03a80bc558a15f98c107557db144c3947a81d5470e4001eac17c88c","target":"graph","created_at":"2026-05-17T23:51:38Z","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":"This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \\begin{align*} \\begin{cases} u_t = \\nabla\\cdot\\left(\\dfrac{u^p \\nabla u}{\\sqrt{u^2 + |\\nabla u|^2}} \\right) -\\chi \\nabla\\cdot\\left( \\dfrac{u^q\\nabla v}{\\sqrt{1 + |\\nabla v|^2}}\\right), &x\\in \\Omega,\\ t>0, \\\\[1mm] 0 = \\Delta v - \\mu + u, &x\\in \\Omega,\\ t>0, \\end{cases} \\end{align*} where $\\Omega := B_R(0) \\subset \\mathbb{R}^n$ ($n \\in \\mathbb{N}$) is a ball with some $R>0$, and $\\chi >0$, $p,q\\geq1$, $\\mu := \\frac 1{|\\Omega|} \\int_\\Omega u_0$ and $u_0$ is an initial data of an unknown function $u$. Bellomo--","authors_text":"Masaaki Mizukami, Tomomi Yokota, Yuka Chiyoda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-01T02:01:29Z","title":"Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00125","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:ebeeffab78cfedb1b9f73439257f2d1f77fc35a7db006feb20a5abed33ca3a40","target":"record","created_at":"2026-05-17T23:51:38Z","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":"0575c671733143f3f643e09b1528a6855ed1ed220b9e7b81b483e3293254c18f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-01T02:01:29Z","title_canon_sha256":"1dcd8def4a9ebc33400071ce6c9b0c36d3c01cee4c0c0cde1d01b612cdbd9995"},"schema_version":"1.0","source":{"id":"1903.00125","kind":"arxiv","version":1}},"canonical_sha256":"521408d7e4e3215efa179ca44c516761517b87f81f985656e7a516c348d6fe71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"521408d7e4e3215efa179ca44c516761517b87f81f985656e7a516c348d6fe71","first_computed_at":"2026-05-17T23:51:38.931593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:38.931593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l69VZkUpwEDsy9oWHOb/YXYLja7z5xPb5uT1h2A524TeqcQHu7C0PKWJE0n41EPEtPjyrvLDS1DjSZk/ihFiCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:38.932192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebeeffab78cfedb1b9f73439257f2d1f77fc35a7db006feb20a5abed33ca3a40","sha256:9cf2e630a03a80bc558a15f98c107557db144c3947a81d5470e4001eac17c88c"],"state_sha256":"026d3e22f7cb3f0c98bd05432749a47d59a893648433cf487838361267e6f319"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UpSiCoQ38lmCH34nBgsRhmOR61aoq0vpOeYLWdjDhb913jqTLbQuOYspkdGcE7hlG52HH43khBW22FTUSclQBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T07:06:59.072556Z","bundle_sha256":"aa6ac3c05264fab1da0928c63dc99223dd6ec74146d5b0736b632b80ee79ee6a"}}