{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DS4UNOPW4HKNGMGBSJTO5AWL6D","short_pith_number":"pith:DS4UNOPW","canonical_record":{"source":{"id":"1705.06445","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-18T07:28:30Z","cross_cats_sorted":[],"title_canon_sha256":"bad530a784d0c023fecb0fb9ab202ff6b80fa9d3b33f78b94602351d94ab01af","abstract_canon_sha256":"35e80d2c872bb2b91241c7f1095684a4a73125b11cbb6aca13b5eaf09f088af4"},"schema_version":"1.0"},"canonical_sha256":"1cb946b9f6e1d4d330c19266ee82cbf0f4ee4091c1a2236adaf017e0381ee340","source":{"kind":"arxiv","id":"1705.06445","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06445","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06445v2","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06445","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"DS4UNOPW4HKN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DS4UNOPW4HKNGMGB","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DS4UNOPW","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DS4UNOPW4HKNGMGBSJTO5AWL6D","target":"record","payload":{"canonical_record":{"source":{"id":"1705.06445","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-18T07:28:30Z","cross_cats_sorted":[],"title_canon_sha256":"bad530a784d0c023fecb0fb9ab202ff6b80fa9d3b33f78b94602351d94ab01af","abstract_canon_sha256":"35e80d2c872bb2b91241c7f1095684a4a73125b11cbb6aca13b5eaf09f088af4"},"schema_version":"1.0"},"canonical_sha256":"1cb946b9f6e1d4d330c19266ee82cbf0f4ee4091c1a2236adaf017e0381ee340","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:56.105717Z","signature_b64":"dEXOX0OQuEqLVjHtJ0z1r48BhvbYJciIRXeueRI8mFkLKPBxOOk0Dk6Xoj88B33Ak7n6v7dUJdEb5aH+R4HwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cb946b9f6e1d4d330c19266ee82cbf0f4ee4091c1a2236adaf017e0381ee340","last_reissued_at":"2026-05-17T23:52:56.105159Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:56.105159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.06445","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjl/hoL62bnmTV/vdAxLbd83y+lfC2mn8yXZBNgbsFQVp7702CI3auEzwEvu6wm1AEfEiSfzxo0G0Q1Qqe0LBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:36:54.723331Z"},"content_sha256":"36dd79fc59e490f948289db01d5bc7d608e0e2c143092c241b2a03d52e0afa80","schema_version":"1.0","event_id":"sha256:36dd79fc59e490f948289db01d5bc7d608e0e2c143092c241b2a03d52e0afa80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DS4UNOPW4HKNGMGBSJTO5AWL6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias Black","submitted_at":"2017-05-18T07:28:30Z","abstract_excerpt":"We investigate the parabolic-elliptic Keller-Segel model \\begin{align*}\\left\\{\\begin{array}{r@{\\,}l@{\\quad}l@{\\quad}l@{\\,}c} u_{t}&=\\Delta u-\\,\\chi\\nabla\\!\\cdot(\\frac{u}{v}\\nabla v),\\ &x\\in\\Omega,& t>0,\\\\ 0&=\\Delta v-\\,v+u,\\ &x\\in\\Omega,& t>0,\\\\ \\frac{\\partial u}{\\partial\\nu}&=\\frac{\\partial v}{\\partial\\nu}=0,\\ &x\\in\\partial\\Omega,& t>0,\\\\ u(&x,0)=u_0(x),\\ &x\\in\\Omega,& \\end{array}\\right. \\end{align*} in a bounded domain $\\Omega\\subset\\mathbb{R}^n$ $(n\\geq2)$ with smooth boundary.\n  \\noindent We introduce a notion of generalized solvability which is consistent with the classical solution conce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06445","kind":"arxiv","version":2},"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":"2026-05-17T23:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7kmQGQCO+Yo1yWtGvXB/5D+lzlnNVys932kc8wfNEXrO8i8iUjeUmTfrZMg/2DQ4Q0dMVBV9PZ9w7NfsGC1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:36:54.723686Z"},"content_sha256":"59715a306f6e290a4d6edadddb684dbffe2f02ce7e1f5d85907c318935585d12","schema_version":"1.0","event_id":"sha256:59715a306f6e290a4d6edadddb684dbffe2f02ce7e1f5d85907c318935585d12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DS4UNOPW4HKNGMGBSJTO5AWL6D/bundle.json","state_url":"https://pith.science/pith/DS4UNOPW4HKNGMGBSJTO5AWL6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DS4UNOPW4HKNGMGBSJTO5AWL6D/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":"2026-06-21T23:36:54Z","links":{"resolver":"https://pith.science/pith/DS4UNOPW4HKNGMGBSJTO5AWL6D","bundle":"https://pith.science/pith/DS4UNOPW4HKNGMGBSJTO5AWL6D/bundle.json","state":"https://pith.science/pith/DS4UNOPW4HKNGMGBSJTO5AWL6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DS4UNOPW4HKNGMGBSJTO5AWL6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DS4UNOPW4HKNGMGBSJTO5AWL6D","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":"35e80d2c872bb2b91241c7f1095684a4a73125b11cbb6aca13b5eaf09f088af4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-18T07:28:30Z","title_canon_sha256":"bad530a784d0c023fecb0fb9ab202ff6b80fa9d3b33f78b94602351d94ab01af"},"schema_version":"1.0","source":{"id":"1705.06445","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06445","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06445v2","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06445","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"DS4UNOPW4HKN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DS4UNOPW4HKNGMGB","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DS4UNOPW","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:59715a306f6e290a4d6edadddb684dbffe2f02ce7e1f5d85907c318935585d12","target":"graph","created_at":"2026-05-17T23:52:56Z","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 investigate the parabolic-elliptic Keller-Segel model \\begin{align*}\\left\\{\\begin{array}{r@{\\,}l@{\\quad}l@{\\quad}l@{\\,}c} u_{t}&=\\Delta u-\\,\\chi\\nabla\\!\\cdot(\\frac{u}{v}\\nabla v),\\ &x\\in\\Omega,& t>0,\\\\ 0&=\\Delta v-\\,v+u,\\ &x\\in\\Omega,& t>0,\\\\ \\frac{\\partial u}{\\partial\\nu}&=\\frac{\\partial v}{\\partial\\nu}=0,\\ &x\\in\\partial\\Omega,& t>0,\\\\ u(&x,0)=u_0(x),\\ &x\\in\\Omega,& \\end{array}\\right. \\end{align*} in a bounded domain $\\Omega\\subset\\mathbb{R}^n$ $(n\\geq2)$ with smooth boundary.\n  \\noindent We introduce a notion of generalized solvability which is consistent with the classical solution conce","authors_text":"Tobias Black","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-18T07:28:30Z","title":"Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06445","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":"sha256:36dd79fc59e490f948289db01d5bc7d608e0e2c143092c241b2a03d52e0afa80","target":"record","created_at":"2026-05-17T23:52:56Z","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":"35e80d2c872bb2b91241c7f1095684a4a73125b11cbb6aca13b5eaf09f088af4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-18T07:28:30Z","title_canon_sha256":"bad530a784d0c023fecb0fb9ab202ff6b80fa9d3b33f78b94602351d94ab01af"},"schema_version":"1.0","source":{"id":"1705.06445","kind":"arxiv","version":2}},"canonical_sha256":"1cb946b9f6e1d4d330c19266ee82cbf0f4ee4091c1a2236adaf017e0381ee340","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cb946b9f6e1d4d330c19266ee82cbf0f4ee4091c1a2236adaf017e0381ee340","first_computed_at":"2026-05-17T23:52:56.105159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:56.105159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dEXOX0OQuEqLVjHtJ0z1r48BhvbYJciIRXeueRI8mFkLKPBxOOk0Dk6Xoj88B33Ak7n6v7dUJdEb5aH+R4HwCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:56.105717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06445","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36dd79fc59e490f948289db01d5bc7d608e0e2c143092c241b2a03d52e0afa80","sha256:59715a306f6e290a4d6edadddb684dbffe2f02ce7e1f5d85907c318935585d12"],"state_sha256":"9deb83893ba6f6e68eee895a8bc4d4107556f3347d614f648d62069147b1e8d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XysO+CkegUQ4gB8qxhWYIzQ5//b9nQwOR6sYn1Mpl4XbkW4s+D2f7so2p5CTOa+65T5rhgf8qnADRBoXgd3YDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:36:54.725598Z","bundle_sha256":"7adda7be5f7b38283f788f53e7e8816f9aec58076d2b551494739b1ed17fb7a8"}}