{"as_of":"2026-08-16T15:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fe26a528db32308ae4051155ec49efe3649087b81124ca007747e7ed5e2fab77","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:09:56.247203Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.04375/citation-record","integrity":"/paper/1908.04375/integrity","json":"/paper/1908.04375/citation-record.json","paper":"/paper/1908.04375"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:09:57.493510Z","title":"ABE, Combinatorics for small ideals on Pκλ, Mathematical Logic Quar- terly 43 (1997), 541-549","venue":null,"work_id":"62e0d1fc-52d3-4d19-87b0-a3c17fabb20f","year":1997},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:55.941061Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:cd19f57ed20b4920df188c0280c799322244a15c4ba1de5136a4180b58f0bcde","observation_id":"00aac4e9-6f28-4172-b2bb-447dcd8482dc","resolution":{"observed_at":"2026-08-14T14:09:57.504128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:57.464519Z","title":null,"venue":null,"work_id":"fc6ea28a-acb4-4e09-b4ee-06ce55acca40","year":1977},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:55.955638Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:9648c7ce2f9326349fa8591cc54b22419a3452d055f190da274a333e5695b688","observation_id":"09a0ad71-2b00-41b2-9c6c-bba7ffcc2c0c","resolution":{"observed_at":"2026-08-14T14:09:57.473153Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:57.440888Z","title":"BAUMGARTNER, Ineffability properties of cardinals II , in : Logic, Foundations of Mathematics and Computability Theorys (R","venue":null,"work_id":"4530fd31-03ea-4a64-a7b5-76373daac632","year":1977},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:55.962248Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:9bb0a2faa50e9f056452727c1cb4248f0ceb279107894d11c43b98b82463885d","observation_id":"f74d2e03-fba0-44a9-824d-f6a06e344441","resolution":{"observed_at":"2026-08-14T14:09:57.448255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:57.411429Z","title":"BOOS, Infinitary compactness without strong inaccessibility , Journal of Symbolic Logic 41 (1976), 33-38","venue":null,"work_id":"caa99e5e-0656-43be-a257-48b6b1c3b09c","year":1976},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:55.969242Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:e0d41383dfc478e10e0dd1be045c236f4dc8c4826df0dcd381a3cdefee1b148b","observation_id":"507573d2-d5e5-42b3-9bac-5ef257773ea0","resolution":{"observed_at":"2026-08-14T14:09:57.425321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:57.378720Z","title":null,"venue":null,"work_id":"073d47c1-aead-49a1-9845-893a6eb68e51","year":1985},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:55.977475Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:8475c4fdfff75a5fc8198ce9a20c3ef40b3cdc557542fda13ec3c9afe22c5e5a","observation_id":"a83de33e-fdaa-45cf-8f30-a775737e963b","resolution":{"observed_at":"2026-08-14T14:09:57.388900Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:57.352758Z","title":"CARR, Pκλ Partition relations , Fundamenta Mathematicae 128 (1987), 181-195","venue":null,"work_id":"c2750653-0d49-42e2-a765-ef39688aded2","year":1987},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:55.986906Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:3c2dba151a7c999019a655ee546540840b206fbcc3308d1e8ac8073386084683","observation_id":"dd62b1db-28c0-47f2-bb84-c102aa470211","resolution":{"observed_at":"2026-08-14T14:09:57.361263Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:55.997219Z","title":"CUMMINGS, M","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:55.997219Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:4fa8686e0b25c72cb3700fd26b55a74fcb33c108357fcba1b9adec0dcae811d5","observation_id":"d9467732-43b2-4029-937e-159a79b365b3","resolution":{"observed_at":"2026-08-14T14:09:55.997219Z","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":"2026-08-14T14:09:57.308284Z","title":"DI PRISCO and W.S","venue":null,"work_id":"c2eadc79-a0b2-46cb-b47a-a283d8aa518b","year":1980},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.008532Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:36b89a47f588356b5b3d828bba3f69477d6adf924da292045489cabb8f65d54d","observation_id":"3b46c62b-3281-40ef-9961-c83115e04a22","resolution":{"observed_at":"2026-08-14T14:09:57.316174Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:57.097629Z","title":"DONDER and P","venue":null,"work_id":"fbdff3cd-d091-4aa2-9d9b-664648488563","year":1993},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.016578Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:223ef556c30096fa61741b9dae8d03b9892f93fe697b3d61b4bc796da9891fe9","observation_id":"317ca77d-0202-4a50-b3fd-14171509524d","resolution":{"observed_at":"2026-08-14T14:09:57.107672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:57.064472Z","title":"FONTANELLA, The strong tree property at successors of singular car- dinals, Journal of Symbolic Logic 79 (2014), 193-207","venue":null,"work_id":"49d42f63-6bb3-4598-9471-b2af00bf2ac0","year":2014},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.026231Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:6ef40ed237472b1ba13b00e0807377e926cacb11a647073525f9d30a0a37e9a1","observation_id":"d56ecb43-9b4e-4e47-8ac6-d512dc111864","resolution":{"observed_at":"2026-08-14T14:09:57.081491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:57.039597Z","title":"FONTANELLA and P","venue":null,"work_id":"8426856c-adcb-406e-bd7d-66c1dc997cad","year":2016},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.032780Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:a3369db47024fa3d524cb621c4a10908943a720e02212428e4ca20781b84166f","observation_id":"73c70a1c-f359-41b8-8ce8-2647a3a033c9","resolution":{"observed_at":"2026-08-14T14:09:57.046960Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.995776Z","title":"JOHNSON, Distributive ideals and partition relations , Journal of Symbolic Logic 51 (1986), 617-625","venue":null,"work_id":"b9fb4385-10f7-44f8-86a4-84e8444c32d7","year":1986},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.040644Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:84beaaabe03227aad403898c4152d1c25ff87a02f72e5e234749ea031037f5d4","observation_id":"1d5a671f-e31d-434f-bbda-3880c58e8b9c","resolution":{"observed_at":"2026-08-14T14:09:57.018363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.957212Z","title":"JOHNSON, Some partition relations for ideals on Pκλ, Acta Mathe- matica Hungarica 56 (1990), 269-282","venue":null,"work_id":"50ae117d-f096-44d8-b22b-37fb99d6a1bc","year":1990},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.048175Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:badc226393c111200c374e9e739e70cea82daaccb39679defab43d98bdfcca8a","observation_id":"b9d8eeed-7322-4a0e-8a7b-0524762d0e26","resolution":{"observed_at":"2026-08-14T14:09:56.970656Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.919929Z","title":"LANDVER, Singular Baire numbers and related topics , Ph.D","venue":null,"work_id":"1ced890b-84b9-4cab-a95b-4c08165251e3","year":1990},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.057187Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:ec8bb952f604f422d509cae8e1400c879edab1c80e10569a83c32b9db26d887a","observation_id":"c472f80d-d751-45d7-821f-ca427b64a0be","resolution":{"observed_at":"2026-08-14T14:09:56.929476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.892375Z","title":"MAGIDOR and S","venue":null,"work_id":"e06bf12f-6e6e-4c6a-af76-2c9582a4093c","year":1994},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.076054Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:98621cfd1c5f4bd35cd0806d1848bc704a93739ed88247ad7724dbbc7473847e","observation_id":"c3825218-033d-474a-ba5d-575b9df00f26","resolution":{"observed_at":"2026-08-14T14:09:56.901518Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.861600Z","title":"MATET, Partition relations for κ-normal ideals on Pκ (λ), Annals of Pure and Applied Logic 121 (2003), 89-111","venue":null,"work_id":"77762730-37a2-455c-88a2-44ca03cb8953","year":2003},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.083912Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:4285669e19afb87a7bde40a8040f0cc59941f280922c85d05cf771e58945b872","observation_id":"f3ca2a2b-ede4-46c2-ab3f-364d4adde8ee","resolution":{"observed_at":"2026-08-14T14:09:56.868343Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.826867Z","title":"MATET, Covering for category and combinatorics on Pκ (λ), Journal of the Mathematical Society of Japan 58 (2006), 153-181","venue":null,"work_id":"191a5a2b-49c3-44b7-9b87-fbfaed3a48fc","year":2006},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.091383Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:e459ae3c6579fdc4e298f01f63c26b92ba756b44a2083a85dee81ea7892c8ac6","observation_id":"8eb7c193-57b5-493f-abc0-4585fc0543b6","resolution":{"observed_at":"2026-08-14T14:09:56.839397Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.799892Z","title":"MATET, Weak square bracket partition relations for Pκ (λ), Journal of Symbolic Logic 73 (2008), 729-751","venue":null,"work_id":"e8aad7db-44b4-4b3c-b606-e49006b42327","year":2008},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.099649Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:0ef1bc4591f0a6b846e263fda523f58703f48573b8212d7b3f54e31719710995","observation_id":"de803b20-cde6-4056-8ad9-c4ebd37b565e","resolution":{"observed_at":"2026-08-14T14:09:56.808905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.770580Z","title":"MATET, Large cardinals and covering numbers , Fundamenta Mathe- maticae 205 (2009), 45-75","venue":null,"work_id":"6c0f5f56-db1b-41f2-a3b4-b33c4164a1b4","year":2009},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.107335Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:51fe8d1d90f22ca53c8694f72026685f887ab05a421599a6a6901b6813a3e103","observation_id":"bb7d441e-0cf4-4f90-9227-4ba8b4ac8830","resolution":{"observed_at":"2026-08-14T14:09:56.779986Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.114600Z","title":"MATET, Normal restrictions of the non-cofinal ideal on Pκ (λ), Funda- menta Mathematicae 221 (2013), 1-22","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.114600Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:8d50f8de2eb3dd79a507ce921022438ce851d0c6f8edd0825f60e21a5fcc3985","observation_id":"a6d3a740-290b-4297-9bad-2837c9f82ecf","resolution":{"observed_at":"2026-08-14T14:09:56.114600Z","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":"2026-08-14T14:09:56.714941Z","title":"MATET, Scales with various kinds of good points , Mathematical Logic Quarterly 64 (2018), 349-370","venue":null,"work_id":"3d1c6074-676a-4bea-8cf2-8352a70e6f0b","year":2018},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.123653Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:43c573e0f8ad2aa0966e2db28dd234e8f42d2e351d560575f72202cb6a730fc6","observation_id":"16c4ee66-02b3-41b2-8b28-99ffe482a318","resolution":{"observed_at":"2026-08-14T14:09:56.723176Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.683358Z","title":"MATET, Applications of pcf theory to the study of ideals on Pκ (λ), preprint","venue":null,"work_id":"958ed025-54ef-493a-84b4-7c9035e625d5","year":null},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.133362Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:e9294bfa4b8534556488944ff7adf08428b0a594e0ea6cd490708d7a4fd4b6ed","observation_id":"0e60d237-f018-4d5b-a9e8-544eccbc3bad","resolution":{"observed_at":"2026-08-14T14:09:56.692762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.649253Z","title":"MATET and C","venue":null,"work_id":"689008f0-cc47-4836-ba60-d93acbd25759","year":2005},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.139627Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:fa08f3f3907961da0506b7cec0cf44725340d6b84b4dc214c76f99046b24e698","observation_id":"e1a00463-77f4-4105-bb56-b626c1e51c8e","resolution":{"observed_at":"2026-08-14T14:09:56.656059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.623327Z","title":"MATET, C","venue":null,"work_id":"c9080209-2b8f-4697-a54b-6e31a6ce95ae","year":2003},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.146993Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:9c36dea0e9491ee70d66e6ca92cf51899c37c6069cd764159b1c2f6756c278d2","observation_id":"c00d22b8-6095-42d1-9ab2-fac4c30eca31","resolution":{"observed_at":"2026-08-14T14:09:56.630291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.595570Z","title":"MATET, C","venue":null,"work_id":"2698ffa7-6337-4d05-9096-7566b5769d42","year":2016},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.154175Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:01b5585396d1bb9e30e6a9066351bcbc18e7b1287766277ea84ee42db3804e99","observation_id":"676dad5a-6965-4e9e-b4d2-5761ff0ab241","resolution":{"observed_at":"2026-08-14T14:09:56.604127Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.570099Z","title":"MATET, A","venue":null,"work_id":"de753494-71b1-4a12-8683-cf36b2ddd3ac","year":2005},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.161695Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:48c43d3a711da84648b898b6424e1d0c3f2e57201360379fc33b1a1efba83ba5","observation_id":"0ac995fd-3674-4ad0-84f8-6aedc2b74d00","resolution":{"observed_at":"2026-08-14T14:09:56.578435Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.543023Z","title":"MATET and S","venue":null,"work_id":"36ab872c-932a-4eef-8c6f-266700f462dd","year":null},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.170872Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:887874110c3e4f2f441729e87f48f344c27aca7525128c25736eec46c9a661ff","observation_id":"2e9b33a3-5467-4197-a8dd-13e8bff17a44","resolution":{"observed_at":"2026-08-14T14:09:56.550201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.521581Z","title":"MENAS, On strong compactness and supercompactness , Annals of Mathematical Logic 7 (1974), 327-359","venue":null,"work_id":"78ca9124-9a93-45d0-937f-06018ae5c3e7","year":1974},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.178045Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:34806c8c184390b74a26d81272624e90e07a23daf817abeebc8c9dda6295f7f1","observation_id":"3d1158c8-5c31-447f-90a3-91011af6878a","resolution":{"observed_at":"2026-08-14T14:09:56.528306Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.499920Z","title":"NEEMAN, Aronszajn trees and the failure of the singular cardinal hy- pothesis, Journal of Mathematical Logic 9 (2009), 139-157","venue":null,"work_id":"ea678451-724b-4baf-9e06-827188a6eda4","year":2009},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.184233Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:e65dd3d79c26862c9c92edebdfad97dfa2813db46f6ccb5b770a3432daaa2bae","observation_id":"dfa4edb4-82df-4025-9a43-7c291d8d3d5c","resolution":{"observed_at":"2026-08-14T14:09:56.506772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.192328Z","title":"SHELAH, Cardinal Arithmetic , Oxford Logic Guides vol","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.192328Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:4476f0591a226c784f8f02b35d87a8c1b337eb736935af024113e8d65aaa761c","observation_id":"f69e16af-0349-4362-9d95-33561f3f82fe","resolution":{"observed_at":"2026-08-14T14:09:56.192328Z","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":"2026-08-14T14:09:56.200040Z","title":"SHELAH, The Generalized Continuum Hypothesis revisited , Israel Jour- nal of Mathematics 116 (2000), 285-321","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.200040Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:0c184590b119d11222350ee8c22d3ec2f6b41c980a4ef731c48e43827cb1a355","observation_id":"4cd1f6cc-5211-4500-a486-62ea753e5d44","resolution":{"observed_at":"2026-08-14T14:09:56.200040Z","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":"2026-08-14T14:09:56.440463Z","title":"SHIOYA, Partition properties for subsets of Pκλ, Fundamenta Mathe- maticae 161 (1999), 325-329","venue":null,"work_id":"c866b691-78cb-4f10-9054-1c9f82d70843","year":1999},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.207499Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:3408ee3bfd361357e133e94b1ede8ae33b44e4ab712404c878175bd079f65e1f","observation_id":"36f9528e-6133-4432-b270-26d05a9d3852","resolution":{"observed_at":"2026-08-14T14:09:56.449521Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.413297Z","title":"SOLOVAY, Strongly compact cardinals and the GCH , in : Proceedings of the Tarski Symposium, (L","venue":null,"work_id":"94ed5e11-7308-4e20-8442-58713ad79cbe","year":1974},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.215845Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:308c0b2cb8b9a1d288a8bdc706de7c234d392d02582bc84c7911bf9261c64444","observation_id":"50416442-b378-44ca-8a41-bd0c87f2841a","resolution":{"observed_at":"2026-08-14T14:09:56.420448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.390314Z","title":"SPECKER, Sur un probl` eme de Sikorski , Colloquium Mathematicum 2 (1951), 9-12","venue":null,"work_id":"c7f13ab9-609e-483d-aa8d-91d32042da0a","year":1951},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.224740Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:a1126e3a54ca19e6e27df3d064036436afcb2e5c93ef5e22cd229cc44e4859cb","observation_id":"231e758f-934d-41ff-818a-62958b4aee80","resolution":{"observed_at":"2026-08-14T14:09:56.397134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.364009Z","title":"USUBA, Ineffability of Pκλ for λ with small cofinality , Journal of the Mathematical Society of Japan 60 (2008), 935-954","venue":null,"work_id":"60fd9399-fa87-475d-8576-344163787b9a","year":2008},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.233362Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:e0ba8a631f88efa3cbd9058167e8ce826e0bab90a92e0c185e84e699c1d1a133","observation_id":"92f340ba-5ea9-4ee8-bde2-607f7bcf8aaf","resolution":{"observed_at":"2026-08-14T14:09:56.374077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.331187Z","title":"USUBA, Hierarchies of Ineffabilities , Mathematical Logic Quarterly 59 (2013), 230-237","venue":null,"work_id":"c092d01b-4666-456b-9eb8-063ccf7c1884","year":2013},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.240664Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:ccbb0ecc49cb9fe9ea97a91e30110cc805143eda181af2c85582699de71dc765","observation_id":"a3d7e224-01a8-441e-8725-cea3f2797509","resolution":{"observed_at":"2026-08-14T14:09:56.345463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:09:56.302063Z","title":"WEIß, The combinatorial essence of supercompactness , Annals of Pure and Applied Logic 163 (2012), 1710-1717","venue":null,"work_id":"6ee4dbdf-1dbb-44b5-acf9-99b152906cc8","year":2012},"citing_paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T14:09:56.247203Z"},"links":{"citing_paper":"/paper/1908.04375"},"observation_digest":"sha256:397a00d704a274d679fa7c2dc595d17e43cd32d8dc4cbc74564800f7e7c050c3","observation_id":"f248299c-71db-4118-9119-6c839b600e6c","resolution":{"observed_at":"2026-08-14T14:09:56.313778Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.04375","last_updated":"2019-08-12T20:46:00Z","latest_version":1,"primary_category":"math.LO","snapshot_observed_at":"2026-08-14T13:41:51.935403Z","submitted_at":"2019-08-12T20:46:00Z","title":"Piece selection and cardinal arithmetic"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":0,"verified_fuzzy":31},"total_outbound_references":37},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:1908.04375."}