{"as_of":"2026-08-08T05:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9a9fbe7fdbfc34e6c3199f0a62a20fbbc6f8efa7555c73e7aab751fb06bb0f3b","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:49:29.921659Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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/2506.07111/citation-record","integrity":"/paper/2506.07111/integrity","json":"/paper/2506.07111/citation-record.json","paper":"/paper/2506.07111"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:35.308473Z","title":"Efendiev, T","venue":null,"work_id":"4c63ec4a-3616-499a-a7a5-a8493606e040","year":2009},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:26.335290Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:8fb4c02720ed1f2ba8f61495113ab531339ea940f4e78fe43136b6f9b2a8139d","observation_id":"b264326d-c472-4502-b1d7-2ceaa668a8a0","resolution":{"observed_at":"2026-08-07T05:49:35.407299Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:35.076687Z","title":null,"venue":null,"work_id":"a2440077-fec9-41f2-a685-cf71fd8ad72a","year":2008},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:26.398911Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:d536249028f3920c1bcadcf7cead2db7a3e0a170eaa7a210f3b86b5d0763ac7b","observation_id":"870ce99d-80ab-4161-beb2-8deee5981bd6","resolution":{"observed_at":"2026-08-07T05:49:35.190409Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:34.772024Z","title":"Steinhauser, Computational Multiscale Modeling of Fluids and Solids, Springer, 2017","venue":null,"work_id":"4b5c7c21-8c04-4439-a99f-00eb628b34df","year":2017},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:26.502991Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:72a18aa928ab4de4af646f80d668e0fa7aea2d8ed5cea7edd381a049ddd1416d","observation_id":"dd4c6217-51aa-4193-b1dc-8e237e94705e","resolution":{"observed_at":"2026-08-07T05:49:34.960430Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:34.549382Z","title":null,"venue":null,"work_id":"34af9e53-a25f-40b7-a2c7-a6f2ea233b5b","year":2012},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:26.641402Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:96e3adde7463a48d18ffcdefaa16080933f1e2be9d0a899adbbc91772ffefaa3","observation_id":"70c89ad3-7f7e-479b-8cc2-9bdb34c65cb4","resolution":{"observed_at":"2026-08-07T05:49:34.649838Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:34.309179Z","title":"Bensoussan, J.-L","venue":null,"work_id":"c224e4ff-3121-4899-b7b5-c30389146160","year":2011},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:26.757268Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:b4cd0b97f3c47b6b206b96bc8288d809fe22ceeac0fe0853c9ba1ce57d918c48","observation_id":"a09595b1-5445-4882-961b-6b589df729d0","resolution":{"observed_at":"2026-08-07T05:49:34.404450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:34.060540Z","title":null,"venue":null,"work_id":"de59a399-3e50-43b7-b019-97f1f45298f5","year":1999},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:26.886581Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:3550f74172d0a64f736841fee806275d69e3c30a62314d66cdf22789d41d38b3","observation_id":"3cd196e5-d735-42ca-a231-b57f98f84b03","resolution":{"observed_at":"2026-08-07T05:49:34.172266Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:33.911112Z","title":null,"venue":null,"work_id":"58fc3aa0-8669-4168-8f6b-1b5b4826b8c4","year":2022},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:27.035978Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:91c999fef6bf82f4051a92582edaf1a0053d55b949331a2bfb3bf4485f32985a","observation_id":"17291962-3e78-4fd7-8636-6332de1cb4fe","resolution":{"observed_at":"2026-08-07T05:49:33.978840Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:33.637874Z","title":null,"venue":null,"work_id":"7288bc3e-10cc-46ef-b5dd-f36c7e928a0f","year":1998},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:27.219180Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:b5f395293a8a6a1492a62853d201960a657079df6ab5f675f865220466e4d320","observation_id":"1c99b893-68f7-489d-9885-5a647c541182","resolution":{"observed_at":"2026-08-07T05:49:33.807421Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:27.346104Z","title":"Linz, Analytical and Numerical Methods for Volterra Equations, SIAM, 1985","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:27.346104Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:a1bf7382e84066f088d8f0385ab7407f51c497d30305d4a8e944c57ee9fd6bce","observation_id":"72573cce-7240-42dd-a532-a368be2256ff","resolution":{"observed_at":"2026-08-07T05:49:27.346104Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:33.398980Z","title":null,"venue":null,"work_id":"3fbb987d-f0b6-43d4-bf08-7236e25f1d5b","year":2022},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:27.480113Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:777518418f35a1a6b6f8e8aa20272736693d92136694ffad41ec99ac223bb5a8","observation_id":"fe43229d-673a-4a11-af14-401fcbd0a835","resolution":{"observed_at":"2026-08-07T05:49:33.556685Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:27.652802Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:27.652802Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:c02ead7398725febcaf5ba99f5fac2a88d9faaeefc1ef71c5c90d522f9f1d33f","observation_id":"9b388ace-bd59-4927-aa48-2a7cddf3114a","resolution":{"observed_at":"2026-08-07T05:49:27.652802Z","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":"2026-08-07T05:49:27.789440Z","title":"Braess, Nonlinear Approximation Theory, Springer, Berlin, Heidelberg, 1986","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:27.789440Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:e2a3587a7c7c8fa4164ed4cd3202ce558bbff850967fd2b19141eadb743f3062","observation_id":"a1632f26-e6fb-46dd-ae4b-6352fe4e3500","resolution":{"observed_at":"2026-08-07T05:49:27.789440Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:33.200961Z","title":"Beylkin, L","venue":null,"work_id":"c64347f9-5028-44cb-96e9-68baba74cf6e","year":2005},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:27.920382Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:cb42d5f79578e9622fa6553e5f241a86fbc9c9bc6bfccef906cbf37490a9e6be","observation_id":"6304bfa5-8952-4c7a-8917-3c13a41c94fc","resolution":{"observed_at":"2026-08-07T05:49:33.270390Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:32.938659Z","title":"Hornung (Ed.), Homogenization and Porous Media, Springer Science & Business Media, 1997","venue":null,"work_id":"bb5a6725-9bdf-4423-a151-8c99bd2d4810","year":1997},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:28.062781Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:1094719e1fd92d091ce38adcfbd315d85ab839b08dafc752edc093be6a2fd89c","observation_id":"9125053f-f5c2-4116-9174-79ed801d65dc","resolution":{"observed_at":"2026-08-07T05:49:33.077975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:32.742733Z","title":"Knabner, L","venue":null,"work_id":"07de9c13-b732-4e8f-a3f0-3d86c028c436","year":2003},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:28.240939Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:fab873c4f7883bd3742b71aa41195a7163578509a5bb8fcb056be1fbad0fab52","observation_id":"c6fe191b-157c-408c-8c93-069c968d7ab2","resolution":{"observed_at":"2026-08-07T05:49:32.861114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:32.493631Z","title":"Quarteroni, A","venue":null,"work_id":"9b63f736-7079-43c7-9c1d-6d7936a8bcdb","year":1994},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:28.452515Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:464a6fb048aa5341debb7f296022734ef511e42b0d6f3000c9b2764a1a7630ab","observation_id":"91fcbd44-8604-46e0-a657-09802075c745","resolution":{"observed_at":"2026-08-07T05:49:32.611654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:32.253844Z","title":null,"venue":null,"work_id":"290e50cb-4706-4886-830b-fd37407c657f","year":2008},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:28.624241Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:ebaef842bc1730bc1214bf01aa1354f6ee544aea68e501c945b8534ee39159db","observation_id":"008992b8-f32b-4098-9790-7fda1c6a4612","resolution":{"observed_at":"2026-08-07T05:49:32.346413Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:28.778447Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:28.778447Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:55f551854808e74286bcb2dd80c4e67d64ffae48ff661bd97ffcb152f4610eb9","observation_id":"4a542f07-8f7a-4dd0-96b5-69c7b55ad8ec","resolution":{"observed_at":"2026-08-07T05:49:28.778447Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:31.966892Z","title":"McLean, V","venue":null,"work_id":"1efbe30f-8777-46cb-ba5a-7fd26bb6314f","year":1993},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:28.944135Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:4486fb1eae51a3a697572c2c06d3c6fe7bb7f2945cb78683a13550a885712c7c","observation_id":"7d8d637d-a93f-47c1-aba3-8827fc4638e0","resolution":{"observed_at":"2026-08-07T05:49:32.102026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:31.644391Z","title":"McLean, V","venue":null,"work_id":"ba210c09-8061-474e-b1c0-5bf66d2f5a73","year":1996},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:29.123775Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:667b48818b2c4af56edd10bdedd81101eaf4aa479e5cdafc2aac6cd44bf79d07","observation_id":"a272de04-3f0b-413d-acc4-a87f9221682e","resolution":{"observed_at":"2026-08-07T05:49:31.790285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:29.275799Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:29.275799Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:7c3ff03689c166acc2f11a13e39b2d824b227a0f6100a88f9f05ef4a10da9473","observation_id":"678e04c2-2491-453f-9c10-8eb8041b83aa","resolution":{"observed_at":"2026-08-07T05:49:29.275799Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:31.351758Z","title":"Halanay, On the asymptotic behavior of the solutions of an integro-differential equation, Journal of Mathematical Analysis and Applications 10 (2) (1965) 319–324","venue":null,"work_id":"b4b0caaa-b1b5-4138-be43-f4eeb454840a","year":1965},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:29.427401Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:5b47b2aea98e8e5458e32ba342a7c9c384396b2edc5e67a34f203bca61aa0195","observation_id":"1fc64b5f-56a3-4d67-bf32-cb198211920d","resolution":{"observed_at":"2026-08-07T05:49:31.496558Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:31.096955Z","title":"Saad, Numerical Methods for Large Eigenvalue Problems: Revised Edition, SIAM, 2011","venue":null,"work_id":"d09e0a30-083f-4e16-8895-8d02812a6da4","year":2011},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:29.568337Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:54bed5c7c9b7315adb8180041f9ae75b93ee1ee391f65f1b1f5d366c1b335f91","observation_id":"5d90292d-ba3f-4efc-bef2-bc53acc110c3","resolution":{"observed_at":"2026-08-07T05:49:31.199419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:30.791159Z","title":null,"venue":null,"work_id":"ac3ffc80-7d41-4267-8c85-b02f8271e7ec","year":2002},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:29.664119Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:051a31e87be5864595ec0cc4b78254a47e777285b3f3312c179a70565101e9e9","observation_id":"3f26c111-5bee-4042-a35e-788ff5328e47","resolution":{"observed_at":"2026-08-07T05:49:30.893765Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:30.512563Z","title":"Geuzaine, J.-F","venue":null,"work_id":"3103024a-3471-4ee9-a990-ddaa6655451b","year":2009},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:29.796973Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:0abacb24a4712f41ea5ce766c8bddc02a7fc99f361d67ee3c8a8bbd7f4fea17f","observation_id":"25fc4c21-36bc-4985-9e43-1159bc916096","resolution":{"observed_at":"2026-08-07T05:49:30.629296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:49:30.071232Z","title":"Alnæs, J","venue":null,"work_id":"80ebd266-e3fa-497d-8f35-c75662f4b71b","year":null},"citing_paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T05:49:29.921659Z"},"links":{"citing_paper":"/paper/2506.07111"},"observation_digest":"sha256:f98dd722aa0a320152d5d8d81054203e262b0e2e896ee4ec69e54986b0bbfffd","observation_id":"fc412ee2-79b1-4dce-8752-7b1d0149d583","resolution":{"observed_at":"2026-08-07T05:49:30.358419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.07111","last_updated":"2025-06-08T12:43:59Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-07T05:39:44.424610Z","submitted_at":"2025-06-08T12:43:59Z","title":"Computational homogenization of parabolic equations with memory effects for a periodic heterogeneous medium"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":0,"verified_fuzzy":13},"total_outbound_references":26},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2506.07111."}