{"as_of":"2026-08-12T07:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fb7a7970816bc6fc8f6ea6aae19f1edc6b06a8ddc01f169f43b3be65b0ca8f46","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:42:42.403930Z","state":"measured"},{"denominator":33,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":33,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2507.07976/citation-record","integrity":"/paper/2507.07976/integrity","json":"/paper/2507.07976/citation-record.json","paper":"/paper/2507.07976"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:42:50.354632Z","title":"Aguiar and S","venue":null,"work_id":"ce8c326e-7e1e-49dc-8f0d-58dfde23e47d","year":2017},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:37.599741Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:9277a896444c1fb4f02d8c55942f60954bc3049c3c1bb657674a0e2aa7aeb2ad","observation_id":"00a735a9-bab6-437c-a10d-5abb08ba71a3","resolution":{"observed_at":"2026-08-06T18:42:50.491919Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:50.043572Z","title":null,"venue":null,"work_id":"a26d32b4-036c-4d0c-8d90-52faa5f10f71","year":2003},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:37.638912Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:1b056d0d2015ceaabb09e0ec8a74f0c0b8e7c935837803b8f9f64b153e10dda7","observation_id":"2faa1535-7acd-48b4-8c38-9b41f0354230","resolution":{"observed_at":"2026-08-06T18:42:50.184932Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:49.805242Z","title":null,"venue":null,"work_id":"6a12d884-cf00-4eba-9326-b53d5de71da1","year":1988},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:37.694874Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:16a8ac9a618b74ecd67c97c311e7b9c99f7a6a9108c8cbb809801b141d6f0df2","observation_id":"4f9523e0-7863-4c02-81ec-46bf2f93f6b8","resolution":{"observed_at":"2026-08-06T18:42:49.902819Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:49.520554Z","title":null,"venue":null,"work_id":"79098f06-3fa1-4c3b-bc55-9f1ee1e817ed","year":1989},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:37.759762Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:2f00f5bb3f10f8bb5e3333bf652de03b5031ea8f31d2c010a14ce89887ff05a8","observation_id":"732e0b7e-384e-4b54-8e36-b8a918be6ea5","resolution":{"observed_at":"2026-08-06T18:42:49.656188Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:49.262721Z","title":"Birkhoff and R","venue":null,"work_id":"98416047-a8f7-4df3-b017-4d5f01aa3a2e","year":1956},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:37.886370Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:5f83e3bea155c3b37f9da408fee0f33de2d5abdd53f1a965de8c17f32b7c90f4","observation_id":"f87a1f88-b421-49ac-9826-f63b72d04b9d","resolution":{"observed_at":"2026-08-06T18:42:49.378225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:48.961233Z","title":"Bochnak, M","venue":null,"work_id":"db6d3768-203a-435c-9484-59656182bd4f","year":1998},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:37.995738Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:fc3297f74d8ff718e64408c80d497dd1015075fc3c003d30e0476ff921dc2eff","observation_id":"ced247f4-88a6-4e63-8fa0-e5cd9980b209","resolution":{"observed_at":"2026-08-06T18:42:49.124901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:48.706429Z","title":"Br¨ ocker","venue":null,"work_id":"3294c1a8-c48e-43ed-924f-800f417644ec","year":1988},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:38.121795Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:11d76c36fa46d2dd285a989318771cd196260aa0a92fe98d335479440d77f19b","observation_id":"ab64fb0b-cc11-4d5b-8177-74e8dd0524a7","resolution":{"observed_at":"2026-08-06T18:42:48.819352Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:48.503896Z","title":null,"venue":null,"work_id":"b055b87a-f317-49d8-a5cf-8d342b80ea43","year":1988},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:38.288259Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:03fb04ed74e2c2bdc8e3d3375e6052887ceee43c9113c18175338c2f094a9a67","observation_id":"da56465b-eb8b-4a7a-88b1-10cac802c6bd","resolution":{"observed_at":"2026-08-06T18:42:48.597170Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:48.238154Z","title":"de Boor, K","venue":null,"work_id":"98241392-f881-4bed-ac68-8ba85d3210aa","year":1993},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:38.355238Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:ab9691dc273fe2c7ded8aae7e5f9c76168e2b43e00560db0e0e0a6505002d991","observation_id":"0aafaf6e-1091-4ae9-ab5a-82bbbb79a2c8","resolution":{"observed_at":"2026-08-06T18:42:48.364545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:48.010489Z","title":null,"venue":null,"work_id":"059b9f5f-e523-4947-a4f7-91c521c7d78a","year":1989},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:38.455131Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:35e83f5f503494f703f381d4ab462471e4700e66955a229630e7387d21ece233","observation_id":"774f0d07-5b12-468b-9065-cd1ef12a1b25","resolution":{"observed_at":"2026-08-06T18:42:48.125393Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:47.783536Z","title":null,"venue":null,"work_id":"0b0280a8-7881-4c96-b494-393c5510d9f9","year":2010},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:38.587091Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:1781ea5649f4692b96ea5fd3c3720ed53061f2c73afd1c17222b3d58c199780b","observation_id":"52ca786a-1550-4b52-83ac-af43a0ff1084","resolution":{"observed_at":"2026-08-06T18:42:47.894759Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:47.571061Z","title":"DiPasquale and F","venue":null,"work_id":"ce680fc9-5292-4859-b85f-8f9bba9268a9","year":2020},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:38.717473Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:4c8b67f3ffdab4bf898762a0b64013d7d2dbdf76ebbb9913898e10524cc2e9f0","observation_id":"22cd0220-3b31-4911-a907-3c029507d3e0","resolution":{"observed_at":"2026-08-06T18:42:47.672182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:47.292748Z","title":"DiPasquale, F","venue":null,"work_id":"e9dc23e9-7efe-4e3f-9b7c-9a71631aa3c0","year":2017},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:38.865686Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:6fae86bc9ab16d8f222e2d4f00bbd77a388a040e412643eaaa60a7c6dac038aa","observation_id":"eeca06ed-6b06-4654-8bb9-ec0f26e5bdb7","resolution":{"observed_at":"2026-08-06T18:42:47.429137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:38.968475Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:38.968475Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:4344e50e5d2e44a039d73243bdb2636e2e5d1a8b6973b9911489e267d4d9cd0d","observation_id":"14ab59cd-d173-4980-8efe-321cafe32525","resolution":{"observed_at":"2026-08-06T18:42:38.968475Z","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":"2026-08-06T18:42:47.044080Z","title":"Henriksen and J","venue":null,"work_id":"692811b6-39a3-4fc2-966a-df4128efe9e9","year":1962},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:39.114113Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:a2f446e87f0feaa34e7802b9d6228721aa5855e516eff10cd072b4b2ba4d966b","observation_id":"3af33cbf-d29f-4117-8f45-0b022fb9363e","resolution":{"observed_at":"2026-08-06T18:42:47.168161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:46.731137Z","title":null,"venue":null,"work_id":"fc58f651-3e15-4932-8b41-f46db89dc941","year":1955},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:39.274967Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:7c04a6d908cfb9221a101bf0bf094491c2ab9c1c4f214bfabcf5c07e6e68fd46","observation_id":"9de59516-b918-4115-a5a7-27bf8645423e","resolution":{"observed_at":"2026-08-06T18:42:46.860026Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.09624","last_updated":"2024-08-19T00:56:44Z","snapshot_observed_at":"2026-07-06T19:02:11.267510Z","submitted_at":"2024-08-19T00:56:44Z","title":"Attention is a smoothed cubic spline","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.09624","snapshot_observed_at":"2026-08-06T18:42:39.402921Z","title":"Lai, L.-H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:39.402921Z"},"links":{"cited_paper":"/paper/2408.09624","citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:11427a66bf96328dbfd2279d8bdb40b035801a5b64e9592ed1630d26348f2c01","observation_id":"3ecffe69-52db-4b94-b579-a19911882c7e","resolution":{"observed_at":"2026-08-06T18:42:39.402921Z","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":"2026-08-06T18:42:46.487189Z","title":"Lapenta and I","venue":null,"work_id":"2d437fb3-07aa-4b4a-9fbf-c0b801391c00","year":2015},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:39.512486Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:128412c00b34d839e2e403dc089704abe7618ba766f5592ed40c4b3da368b5ca","observation_id":"d8a2e491-1c1c-407b-b832-e4ccdb009b53","resolution":{"observed_at":"2026-08-06T18:42:46.618343Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:46.263845Z","title":"Lucas, J","venue":null,"work_id":"26fdd868-f889-428b-bbc4-e46eb767ab1c","year":2012},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:39.917584Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:aa409f9a31ac909a3aef2815fede4f8576b9847d01966c64c2808d94b7fd9564","observation_id":"cba0478e-815f-4ff1-b13d-cd659688a3b6","resolution":{"observed_at":"2026-08-06T18:42:46.361640Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:46.022850Z","title":"Lucas, J","venue":null,"work_id":"d1757fb9-0e64-4148-87d3-3a1917815ed9","year":2009},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:40.787706Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:9b13904368237ceb4667eb4165f6bd122d0ed7c1d27523fe2e9fe1b70f69fa98","observation_id":"1f1ed511-49f8-41da-b1db-fc4768ee33b3","resolution":{"observed_at":"2026-08-06T18:42:46.142853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:45.736513Z","title":"Lucas, D","venue":null,"work_id":"f64d767d-bf70-4216-a92d-a5436bd36823","year":2015},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:40.910362Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:f74e1f9d68f5a2ffbd2ee092dc1813f2f59cce9b1a61879274ceeaedcb9f862d","observation_id":"e69e85f1-96ad-44a6-921c-9eae101131f1","resolution":{"observed_at":"2026-08-06T18:42:45.858136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:45.478427Z","title":null,"venue":null,"work_id":"f043df42-f306-461b-9950-0e90055cb6f9","year":1989},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:41.025926Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:21ebc8190364bfec79645ea52c8c2649d1203a11a00a0d9db1ab17752277bdd0","observation_id":"ea39ad45-63f0-4139-b200-f03d3ea0f69b","resolution":{"observed_at":"2026-08-06T18:42:45.589392Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:45.188888Z","title":null,"venue":null,"work_id":"070d6010-6181-477f-9af9-056486caa958","year":2011},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:41.191606Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:e7dd471863e72b491c36561c3f39967249920bb77234143fcb07228a1c4890b5","observation_id":"e5688b59-599a-4da8-ba17-0753ad47ead1","resolution":{"observed_at":"2026-08-06T18:42:45.319893Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:44.969558Z","title":null,"venue":null,"work_id":"49f350ad-b01a-4f21-b7a0-3e506aeb4ece","year":1984},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:41.291440Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:ac0cb46dcad49207d04a52a0e39ae7adcfc504ccc298823c8a0bb493429b01c9","observation_id":"a180833a-429a-4e21-8279-1bbdfb03fa59","resolution":{"observed_at":"2026-08-06T18:42:45.065158Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:44.596337Z","title":null,"venue":null,"work_id":"255d1cd3-39e5-49d8-9681-c98a3f971ed5","year":2007},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:41.429887Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:93999292cb0fae8d9e7bebf96986f13a71a690610ca63d9421d820726621f55c","observation_id":"c4e299c8-242f-4d72-9f8d-927555de84f3","resolution":{"observed_at":"2026-08-06T18:42:44.801141Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:44.340840Z","title":"Marshall","venue":null,"work_id":"7be39d6b-3bdb-4ab7-9c51-341fd2340527","year":1992},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:41.529080Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:f71e737f1d3a9162a844322d4ca04158e239480e35f81022ae2c1ef31e39fa0b","observation_id":"946f6128-14c0-4789-a39e-7dfaabad34b5","resolution":{"observed_at":"2026-08-06T18:42:44.477524Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:44.077743Z","title":"Matouˇ sek.Lectures on discrete geometry, volume 212 of Graduate Texts in Mathematics","venue":null,"work_id":"9d4c3462-82ad-43aa-9303-3d189bfea6f7","year":2002},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:41.659657Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:4f11ea2b2d8f7d84028574584a2275ef519f1f2542eff73ffab5b9b09f36c790","observation_id":"41a0355e-e79d-47eb-ae02-5e6068f6ad54","resolution":{"observed_at":"2026-08-06T18:42:44.229360Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:43.721366Z","title":"Ovchinnikov","venue":null,"work_id":"fae227d6-f554-47c7-af37-d56e874125c0","year":2002},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:41.769325Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:adbb1cafaae3bacf999ce4eebf864665be9d02fbe4e82910ac8e8fea335f5c58","observation_id":"1d0c13cf-a4ae-4179-a746-d4581ba84d2d","resolution":{"observed_at":"2026-08-06T18:42:43.900467Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:43.463109Z","title":"Plaumann","venue":null,"work_id":"352c58ba-ffca-4631-a444-598ad09d42dc","year":2012},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:41.879595Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:bfede6fef47fc842ce5e6a577e81f897f5eedace020fb4dd266441774d2e1ca8","observation_id":"2349e566-c49f-4070-b7e7-0ec4c7be133c","resolution":{"observed_at":"2026-08-06T18:42:43.579291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:43.280882Z","title":"Shekhtman and T","venue":null,"work_id":"1887d6dc-3c49-49ca-9e40-941a5b0ab6a2","year":2022},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:42.029121Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:dc3b0ee0eedac6075af158a7b76d1799b392641231a533effb4f763d0bd28bd3","observation_id":"06b43c92-ce9a-45f0-8641-18dc657a459c","resolution":{"observed_at":"2026-08-06T18:42:43.378097Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:43.042955Z","title":"Stoer and C","venue":null,"work_id":"492dc0c1-c84f-4a0c-8369-7b5b09c04fbe","year":2012},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:42.179301Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:791da2c2daa0ef3d50ab2da5e8c06d58228c24c27e46b0f3367862acd8484216","observation_id":"db2333ba-57dd-45fd-b051-051ffb98381b","resolution":{"observed_at":"2026-08-06T18:42:43.145484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:42.813551Z","title":null,"venue":null,"work_id":"8db10d1f-2da7-400a-9e7c-5c3bd47f1fe1","year":2010},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:42.269417Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:675b583231ff4522cc64665ec2f16c0aa312857e7de8ef38eeabef39d36259e1","observation_id":"77de3c02-4bd1-474b-bd91-b24167cb5459","resolution":{"observed_at":"2026-08-06T18:42:42.912160Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T18:42:42.559377Z","title":null,"venue":null,"work_id":"6fc777a7-bc5e-48c2-96a6-4e4a702f287c","year":2001},"citing_paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T18:42:42.403930Z"},"links":{"citing_paper":"/paper/2507.07976"},"observation_digest":"sha256:e01dc3fc1c66c7153f7760657fa667e03b849868213cd81e52d340bbf4694d84","observation_id":"27b4a8b6-f545-44b6-91ac-40e47411b38f","resolution":{"observed_at":"2026-08-06T18:42:42.667138Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.07976","last_updated":"2025-07-16T21:32:40Z","latest_version":2,"primary_category":"math.AG","snapshot_observed_at":"2026-08-12T03:17:27.773443Z","submitted_at":"2025-07-10T17:53:21Z","title":"Pierce-Birkhoff conjecture is true for splines"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":0,"verified_fuzzy":18},"total_outbound_references":33},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2507.07976."}