{"as_of":"2026-08-11T17:45:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3bf96664eaf5cd3c7f0462c7c95e641d14e14a0f6fb6075edd8b9fb24ea350d7","coverage":[{"denominator":48,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":48,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T06:33:18.586775Z","state":"measured"},{"denominator":48,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":48,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.11165/citation-record","integrity":"/paper/2607.11165/integrity","json":"/paper/2607.11165/citation-record.json","paper":"/paper/2607.11165"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Bandle, H","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:142dab991d68c6d016726013079d9e40325ebae5ce5c94a405f3d41d43fc5d16","observation_id":"3be26c22-676e-4341-a1da-8a21b360453f","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Budd and J","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:97dec42d6a4cbbbd933077d68c0bb5a4e6668811fee5005c6c37e9f8bd975f7a","observation_id":"b94aa0ef-efc1-4429-b31f-75846807f8fd","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:b1f2714e6d0342fabcb955b4d4a8d77630b24fe26d41378e486253e96218335d","observation_id":"350555ed-bb05-476d-9ebb-930d902f96ed","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Collot, Type II blow up manifolds for the energy supercritical semilinear wave equation, Mem","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:5de96b35c63409538ae176267013ef29bf227202c147792375e470f4c3a2cdcb","observation_id":"8cb63224-63b3-478d-8a4f-ba7e72baf7ea","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Collot, F","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:d53b5a7732326eae849a5d4e8d50f81e542d960ccbfd8a57540bdbec6b224807","observation_id":"37c30772-1e0b-480c-a535-bdfffbe80722","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Collot, P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:884d8ae505a7b4d263594ff683e3c2d2fb0502e06231e40939fced702b07997a","observation_id":"0e17d47d-ea25-4b82-9a83-8307fbf87008","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.11358","last_updated":"2024-08-02T02:09:11Z","snapshot_observed_at":"2026-08-08T20:29:57.244952Z","submitted_at":"2024-06-17T09:25:18Z","title":"On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.11358","snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Collot and K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"cited_paper":"/paper/2406.11358","citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:dd12e1735908e671d310ed8dea6230d187d105b805f8049617527ce284126d22","observation_id":"8cdb9d9d-a937-4c1c-95b7-423be6b35306","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Cort´ azar, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:a669b103be67d4eb8f30df9c349d6a94e96eb65ea925ae5e4158b0e592683a7d","observation_id":"9d39b46c-fca0-4b01-87ab-a7d28af1d39a","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"D´ avila, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:b9ab348a38aa1f8b17026a112b436abab37c93118fcb1d4cedc99f5db5924970","observation_id":"b6bca327-93ca-4467-8b6b-bc470ed153e7","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Donninger and M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:e105c93c735b17f45aac169fef3d57c2902200ec24f9d0987148a56eb08264c1","observation_id":"fd9622a1-9f16-4494-aa94-a545b49f7b21","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Fujita, On the blowing up of solutions of the Cauchy problem foru t = ∆u+u 1+α,J","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:304993482f99338568580cb98f9f49c215937ec5c8b62d480f38afea16434f28","observation_id":"3c3e4fb8-2cca-42da-a25c-35900fe34adc","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Giga and R","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:9145b9305331032643820550547ed4829e3d1a2b618ee0fef55a279c92acbeab","observation_id":"f1abd5f1-33c5-4e9e-8172-a6a37c112a2b","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Giga and R","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:648d46424f9fe87381a302094e16d0f6acde42a58b4cab7964a4b6e2c23f02e6","observation_id":"ff76de2d-37ad-425b-9f5f-a83d75213622","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2604.19389","last_updated":"2026-04-21T12:16:01Z","snapshot_observed_at":"2026-07-06T23:06:02.635464Z","submitted_at":"2026-04-21T12:16:01Z","title":"Stable blowup profile for a semilinear Heat Equation with spatially inhomogeneous nonlinearity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.19389","snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Glogi´ c, S","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"cited_paper":"/paper/2604.19389","citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:c13067df7fc0b23d085e1613a75c5fd664a6519ab86af84058014286c6dc9c5e","observation_id":"7af480ad-ba55-43ad-9185-bccc4d907d46","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Glogi´ c, Globally stable blowup profile for supercritical wave maps in all dimensions.Calc","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:560525077ab93b6afcd052fec960af2965576385c447c1255504535d4499ac69","observation_id":"bd6a4b3d-3558-43b9-b28c-296ea1ce8f5a","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Harada, Dynamics near the ground state for the Sobolev critical Fujita equation in 6D.Calc","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:94d9e396b42c4c76abe419d29c339efe41c55e7a2fc371981ccd2a7ec7ee7978","observation_id":"ec7015b1-afa2-40a6-96e9-129d3456f818","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:6538ffd1240fc6d0b1eb8a65ed99369d46134ebb212e9f2827456b2f924be943","observation_id":"e522b695-35b3-4cbb-a1a3-2eb0bc25b0fb","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:bd5162a66e0d8d4f458e888acbf96e4b9f3991783fac86954ce2c69dac2e6132","observation_id":"d853169a-b137-424a-8901-75f198aa2de6","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Ikehata, M","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:63efe42c223ad6c61cb255f231f49d5d2574c908a86e962f7a1cf4ac9569abd5","observation_id":"d882621a-0575-422e-a1e0-a7fdf64c5225","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Ishige, T","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:189397fa76ea440fedad88031056644d68f944c3eb831823841a02aa3e8070e5","observation_id":"5627911f-13ce-40b8-bb4c-50d9366c2739","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:a27e06fece5494788e7fc37368f2dbaa55f873c19a8013a8ef12eedec1fa20f8","observation_id":"6237e18b-2ebd-44cc-bf5f-26195f5096e8","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:21782d88ac1eb86e3a89f571bd579ebceb9db34594f1c093e21c2553e7825e50","observation_id":"ba8810d8-1373-472d-899d-528b378efcbf","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:c94fbfb93e1e3b106694fe2f592761c14957ecf86de8c2b03278ecbdb2b47224","observation_id":"b539c01d-193f-4478-99ae-3035a6940ac6","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:6bea9914b4cae74a2201a78fb78c51906c293e8507eb460f49989c098a0629e5","observation_id":"2b240fed-cf5c-4922-abaf-ffa4e2fd6dd2","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.07073","last_updated":"2025-03-30T15:24:56Z","snapshot_observed_at":"2026-08-11T10:09:56.305676Z","submitted_at":"2025-01-13T06:05:01Z","title":"Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.07073","snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Li and T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"cited_paper":"/paper/2501.07073","citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:651857eda894e88ace7968dabba408dbd4e95f1e4055997172295e376449c5c5","observation_id":"d42bc6b1-7fc7-4b21-ae14-ac2538833a9f","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Liu and F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:514f4d80a2763dac48034d0b8a7dacc84f1e351441768bfb7f200c2c341697ab","observation_id":"f7e12828-345d-4fe4-98d5-3406b64208c7","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:43797bd12b7a23f077d9cfc881b47b78bdf4060230cf8913ebd63b0608eef976","observation_id":"d800fcd2-96a7-4a4d-af9d-d606ae191af9","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Martel, F","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:61033f1fc1c6d17e5ab33ff966e26463ffb53bdf92887b5e93f60761cc4a94c6","observation_id":"e28c9f78-576c-425a-bdd7-5c3b265443fa","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Matano and F","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:c32178875e96729719df9d74fadf1cc8e5c8ab1b7dd29e49b504d7b1dc8c7646","observation_id":"87eb631b-74ec-4eb2-9400-d290605d78a6","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Matano and F","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:6295f9290d32f4c272a999769a0a3d1b54197a8c51801c365073f0561b3d25e6","observation_id":"8714c5d3-b2b5-4976-95a0-470d1a18ec3e","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Merle and P","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:e01f5d95e62e7752b6fa742966f2f08cf89c74e9f1c5a947ff8ff2c69c5d16e6","observation_id":"01e559dc-932c-4849-84be-a7d7f9eaaffc","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Merle and P","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:0c8f15a7f13afa8bef407dde593e5e2d6e87b8a175e37c0aa533de6535c82253","observation_id":"db867d69-7028-4ca3-9a7c-06c86f7bfaa4","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Merle and H","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:51d452b818296d7c39e7f0b2b9bcf19c0abfb5e2ea7c9147da64391d114aa34c","observation_id":"af1cd156-a98d-4dcf-ba52-141fc5249e03","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:5eb085d551ae34d4d268effbc20724af3acff9f6e0e6dbacd75ef7423a59c275","observation_id":"dcda4a6a-8bac-4962-819d-c3cc65627ccf","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"del Pino, M","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:89ea1cc50593c06455fa5dfe81c58b350799071de33d687dc42941c8453f7cdd","observation_id":"81013105-ba90-4142-ab15-39915072e2c6","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"del Pino, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:902302b7bb3e6eebbae5cf81ebfb055f7a7eeb6cfcb92d405ead266bea27b08a","observation_id":"100573cc-51b5-4195-9070-8d147e34b450","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"del Pino, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:17ec5e7d476096063d49fce56b2c1751fb19155323111f80f6969c9ea6425d23","observation_id":"8ced7887-aa44-43b1-86ba-6f07777dbec2","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Quittner and P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:4fd5fa99b650ffe2b1e82ef7b6107aa38d97970fe4f6c12d9bf1efd24ac65a9e","observation_id":"4958968e-821e-4177-9289-bd2bed4f82f7","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Roland and B","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:2958167154e43cb87e8a98175981fb71dea209de9fe210c636ecbb33df93fb68","observation_id":"5c35e65e-53e8-48df-a200-64de0757277e","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Souplet, Q","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:38d577a5aa3d99d1f732d8fed21ddfc661b9bc9a797dac4bf33786fa6d972e82","observation_id":"45c78aee-6cf1-454d-9854-06912d9c1f70","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:e71e3aa33c1c1db1fb3604bf3b19137625ef5e9166696c16f638ec6811c8d2da","observation_id":"9f3a8afb-d5f8-40ca-b419-7383bcc1fed9","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:18f71bdeeccdeb14a7bc3629b4534632c4a350c45404e403c3ebde8d17e54f15","observation_id":"5a3756ea-c737-49bb-ad49-a43fba153ede","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:64e74a4e9aa4e1b7084a558a59aa59bebce45c0f015ed77c8f507b195837b3e2","observation_id":"64e30a57-c19e-4a9b-958a-e9a2d6cd18c6","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:6c1b719211894f4e74785ab0242e0f6c741586b3ef4cb8af7f53c9e647bd06be","observation_id":"d257a27c-a14e-4421-9c7c-4db659738f8e","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:999ca937929ce4f9a0fb81b1cfebb3253900bf461c30cf1a481aa72c4226e1d9","observation_id":"4e175125-a47c-44b2-817f-ef69354c1b60","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.11933","last_updated":"2026-05-12T10:45:09Z","snapshot_observed_at":"2026-07-06T23:23:39.723268Z","submitted_at":"2026-05-12T10:45:09Z","title":"On the existence and nonexistence of global solutions of the semilinear heat equation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.11933","snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Zhang and Z","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"cited_paper":"/paper/2605.11933","citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:cfebab6880595f7f7ddef7f5d24141d6db1e050ec895bd7f677f13f7fb23d475","observation_id":"3b448c4f-65be-46a0-8b9a-e85a1402a55b","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Zhang, F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:e8e6d2a30895b29cd4c2f08cf40693512f20d4201af5b27269d54c24cd048591","observation_id":"b840415a-bbec-41bc-9922-620463cd7dd9","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T06:33:18.586775Z","title":"Zeng, The critical exponents for the quasi-linear parabolic equations with inhomogeneous terms,J","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-07-14T06:33:18.586775Z"},"links":{"citing_paper":"/paper/2607.11165"},"observation_digest":"sha256:451531f97b6018756159cd38555019fa546cd0153c29207e671726b3da2c63c0","observation_id":"1fb5f885-f48f-4f77-965d-6340abb8dedb","resolution":{"observed_at":"2026-07-14T06:33:18.586775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.11165","last_updated":"2026-07-13T07:01:52Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-07-16T23:19:14.089678Z","submitted_at":"2026-07-13T07:01:52Z","title":"Finite time blow-up for an inhomogeneous parabolic equation"},"reference_resolution":{"displayed":48,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":48,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":48},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2607.11165."}