{"as_of":"2026-08-11T20:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b3cdbe82ec940c23ebff07d1b2d727631e8a23c1dc00501418c7e4427ed00e64","coverage":[{"denominator":5,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T18:17:17.533246Z","state":"measured"},{"denominator":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T18:16:37.464490Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-06-30T21:35:04.231563Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.14868","snapshot_observed_at":"2026-08-05T18:16:37.464490Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2508.14866","last_updated":"2025-08-20T17:29:03Z","snapshot_observed_at":"2026-08-05T18:16:35.087388Z","submitted_at":"2025-08-20T17:29:03Z","title":"Abundance Diagnostics from Slitless Imaging Spectrometer: A Proof-of-Concept for MaGIXS-2","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T18:16:37.464490Z"},"links":{"cited_paper":"/paper/2508.14868","citing_paper":"/paper/2508.14866"},"observation_digest":"sha256:d0bb1184a35032441efb5c2132f3a61c57eb80e74f972c70143a92f3c2bb1fd3","observation_id":"3219fba8-8b13-47c1-94dc-4a02f4d12f4e","resolution":{"observed_at":"2026-08-05T18:16:37.464490Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"cited_work":{"arxiv_id":"2508.14868","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.14868","snapshot_observed_at":"2026-06-30T21:35:04.231563Z","title":"Critical trajectories in kinetic geometry","venue":null,"work_id":"c57a59a9-d526-4b2b-8d69-ffb02496adeb","year":2025},"citing_paper":{"arxiv_id":"2605.13582","last_updated":"2026-06-01T13:42:04Z","snapshot_observed_at":"2026-08-08T03:11:38.359634Z","submitted_at":"2026-05-13T14:15:24Z","title":"Transfer of regularity by kinetic mollification along critical trajectories","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-14T17:58:51.517366Z"},"links":{"cited_paper":"/paper/2508.14868","citing_paper":"/paper/2605.13582"},"observation_digest":"sha256:797b169e91f2b839f0ac5d0e50a595b1abc2160a0e7804b78df57a8cef3c3052","observation_id":"5e346c4f-67b5-4620-b979-9fcb181c6f58","resolution":{"observed_at":"2026-05-14T17:59:22.027516Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"cited_work":{"arxiv_id":"2508.14868","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.14868","snapshot_observed_at":"2026-06-30T21:35:04.231563Z","title":"Critical trajectories in kinetic geometry","venue":null,"work_id":"c57a59a9-d526-4b2b-8d69-ffb02496adeb","year":2025},"citing_paper":{"arxiv_id":"2605.13582","last_updated":"2026-06-01T13:42:04Z","snapshot_observed_at":"2026-08-08T03:11:38.359634Z","submitted_at":"2026-05-13T14:15:24Z","title":"Transfer of regularity by kinetic mollification along critical trajectories","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-30T21:33:39.906787Z"},"links":{"cited_paper":"/paper/2508.14868","citing_paper":"/paper/2605.13582"},"observation_digest":"sha256:758697e267390821ca9c4b85e27566963609279cd1dfcc2c3c55627f6d5519a6","observation_id":"3d836c95-7def-4346-9276-df8572c16991","resolution":{"observed_at":"2026-06-30T21:35:04.233699Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"cited_work":{"arxiv_id":"2508.14868","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.14868","snapshot_observed_at":"2026-06-30T21:35:04.231563Z","title":"Critical trajectories in kinetic geometry","venue":null,"work_id":"c57a59a9-d526-4b2b-8d69-ffb02496adeb","year":2025},"citing_paper":{"arxiv_id":"2605.21080","last_updated":"2026-05-20T12:16:12Z","snapshot_observed_at":"2026-08-08T08:55:20.502387Z","submitted_at":"2026-05-20T12:16:12Z","title":"On the kinetic $p$-Laplace equation with nonlocal diffusion","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-21T03:22:22.290450Z"},"links":{"cited_paper":"/paper/2508.14868","citing_paper":"/paper/2605.21080"},"observation_digest":"sha256:c8ac80e7cc1720d06f67eb6341ffb174f75979e5b74096f38d8fb788c9ea26fa","observation_id":"e17d8f3b-9361-4133-8c94-5ae707b26345","resolution":{"observed_at":"2026-05-21T03:23:55.759894Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2508.14868/citation-record","integrity":"/paper/2508.14868/integrity","json":"/paper/2508.14868/citation-record.json","paper":"/paper/2508.14868"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T18:17:18.320594Z","title":"Dixmier, Position relative de deux vari´ et´ es lin´ eaires ferm´ ees dans un espace de Hilbert, Revue Sci","venue":null,"work_id":"eb92f341-9675-48db-8138-cd44eb609b9d","year":1948},"citing_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T18:17:17.236680Z"},"links":{"citing_paper":"/paper/2508.14868"},"observation_digest":"sha256:2570f3e17bdadc908b2c2815abfe15c82143b36263752cef9acd294cedd20c98","observation_id":"3c607f14-75e9-490f-88eb-5ea5119f9e76","resolution":{"observed_at":"2026-08-05T18:17:18.392988Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T18:17:18.173428Z","title":"Halmos, Two subspaces, Trans","venue":null,"work_id":"d5e19797-d861-49f4-b2fa-26d249602055","year":1969},"citing_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T18:17:17.305120Z"},"links":{"citing_paper":"/paper/2508.14868"},"observation_digest":"sha256:aaacbfcc5ebb06dadebfe9b86e682c0fa684f09bfcecd88fe073a30d5e8ebb14","observation_id":"5ee59935-b8f2-461e-bd4e-7029f0d28351","resolution":{"observed_at":"2026-08-05T18:17:18.248387Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T18:17:17.962798Z","title":"Porta; L","venue":null,"work_id":"78ce4e6a-a9d3-46f9-93e6-c7aa4cf45c38","year":1987},"citing_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T18:17:17.389162Z"},"links":{"citing_paper":"/paper/2508.14868"},"observation_digest":"sha256:22c2aea1bc26b4d9f8b39c663a559cb55f0f5a77e71f05e983a14c006169d9f1","observation_id":"c9ab02e1-5faf-4011-b98b-d88b7064fee1","resolution":{"observed_at":"2026-08-05T18:17:18.075876Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.12984","last_updated":"2025-08-14T11:14:21Z","snapshot_observed_at":"2026-07-06T15:30:37.936757Z","submitted_at":"2023-05-22T12:44:26Z","title":"The matched projections of idempotents on Hilbert $C^*$-modules","version":4},"cited_work":{"arxiv_id":"2305.12984","doi":null,"metadata_source":"pith","pith_arxiv_id":"2305.12984","snapshot_observed_at":"2026-08-05T18:17:17.646803Z","title":"The matched projections of idempotents on Hilbert $C^*$-modules","venue":"math.OA","work_id":"abd6b35e-9838-4493-a8dd-ea2e2feb8bb8","year":2023},"citing_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T18:17:17.450542Z"},"links":{"cited_paper":"/paper/2305.12984","citing_paper":"/paper/2508.14868"},"observation_digest":"sha256:3af0ce47f25f2de430139be22cd09b05c526721852a8bf7a7b3caefc19ca0a3c","observation_id":"353930f3-828a-4456-8046-43373a491b43","resolution":{"observed_at":"2026-08-05T18:17:17.685647Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T18:17:17.818683Z","title":null,"venue":null,"work_id":"9db9c5fd-9a35-4e17-ae93-90f9fe20eb42","year":2025},"citing_paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T18:17:17.533246Z"},"links":{"citing_paper":"/paper/2508.14868"},"observation_digest":"sha256:611d8c2cdcf1baee54fd0e87f6db421ae3e128e0708e4b62fba9c2df636fa31e","observation_id":"51920ff9-4480-4d79-a041-df23227877de","resolution":{"observed_at":"2026-08-05T18:17:17.886420Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.14868","last_updated":"2025-08-20T17:30:39Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-09T20:47:04.708064Z","submitted_at":"2025-08-20T17:30:39Z","title":"Critical trajectories in kinetic geometry"},"reference_resolution":{"displayed":5,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":1,"verified_fuzzy":3},"total_outbound_references":5},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 5 of 5 outbound references and 4 inbound Pith citation observations for arXiv:2508.14868."}