{"as_of":"2026-08-18T10:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a58b0c01decbc64c3306951f82da1db5b361ea638bb6439d934ca27f01a20db1","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T14:56:51.483097Z","state":"measured"},{"denominator":45,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":45,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2512.19332/citation-record","integrity":"/paper/2512.19332/integrity","json":"/paper/2512.19332/citation-record.json","paper":"/paper/2512.19332"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T14:56:51.142857Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.142857Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:1e3479f4630d3c9fdcb2409caa063c1cb4fc9b8c4c5088a23b29293d51d367f4","observation_id":"544c5bed-1c5d-4a64-a5c1-8867bb7a47dc","resolution":{"observed_at":"2026-08-03T14:56:51.142857Z","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":"2026-08-03T14:56:51.155372Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.155372Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:e5c7dfa1c031de7a89560001539ea23ce14d918c0d3b4a26b23ca442e021512f","observation_id":"31f1391b-e91c-4215-a052-728ecad791f7","resolution":{"observed_at":"2026-08-03T14:56:51.155372Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4230/lipics.icalp.2019.104","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)","work_id":"2cd0909b-61de-4340-ae31-57e6d54e21e5","year":2019},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.161729Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:e0a02b0ceb4fcc82a2e942ae3b9a309556b9b51d7a3def05c22b4e5706e0969f","observation_id":"85448cd0-9aee-4fc1-b565-1bf31c852624","resolution":{"observed_at":"2026-08-03T14:59:08.241111Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-03T14:56:51.167989Z","title":"Kostylev, Mikaël Monet, Jorge Pérez, Juan L","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.167989Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:a7b181a54f95f539d388893db133c3fae5ed002ac6fbea7850e590451c366ea4","observation_id":"e4c2e2cf-e659-472d-84e1-13033bd8ff9b","resolution":{"observed_at":"2026-08-03T14:56:51.167989Z","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":"2026-08-03T14:56:51.173266Z","title":"Lin, and Peter T","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.173266Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:ca721e5444fb52be275161712dfba7947cb1f5ddc52d8b2bbe5bb6c5ec5f0db7","observation_id":"54d6a1be-67ee-40ba-9020-ac27a6472e27","resolution":{"observed_at":"2026-08-03T14:56:51.173266Z","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":"2026-08-03T14:56:51.179335Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.179335Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:456cfd79ae58876e9a9559591f3f623883505098bfec2f3e511b6e165a1882bc","observation_id":"875fc4e7-1f2f-4ff3-8391-11575dc8e7ee","resolution":{"observed_at":"2026-08-03T14:56:51.179335Z","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":"2026-08-03T14:56:51.184944Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.184944Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:ce33893957f7c97ce4c672be3b721b21d4928c633127fe7e89ca5486a7d22d30","observation_id":"7b9ff6ff-2dc3-42ac-ab27-395abe0a9828","resolution":{"observed_at":"2026-08-03T14:56:51.184944Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-03T14:56:51.192004Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.192004Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:2072f14d4f8fc39d72df86503e44901b8b48a24a077dac451c8001fbc7eaf823","observation_id":"2c00f566-6acb-43e6-bddc-cef31c76061a","resolution":{"observed_at":"2026-08-03T14:56:51.192004Z","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":"2026-08-03T14:56:51.199562Z","title":"2004.Approximation by algebraic numbers","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.199562Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:241ed7244920eedce41c778b05b824c11a7f5abb907db8c320f293827e95925b","observation_id":"9374e8c0-ec4c-4c3e-b8dc-0d02bd34d07b","resolution":{"observed_at":"2026-08-03T14:56:51.199562Z","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":"2026-08-03T14:56:51.205619Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.205619Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:ce6bf2cce61c254ae499429c9bb1219f089ce856c5e51196d2ee692e2eedd562","observation_id":"03d3157f-2bb9-494d-ab33-7566fb6d43eb","resolution":{"observed_at":"2026-08-03T14:56:51.205619Z","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":"2026-08-03T14:56:51.211591Z","title":"Consens and Alberto O","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.211591Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:326a9fa33f7fab31508bac36c496f7cece7ec3829058dc555c112125ffe0abe9","observation_id":"bafd9baa-d385-4252-a9c3-ecacf037fd25","resolution":{"observed_at":"2026-08-03T14:56:51.211591Z","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":"2026-08-03T14:56:51.219930Z","title":"Cruz, Alberto O","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.219930Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:0353f65f83a40491763be9f3fee6d795fde5940de6300986bc2c02b886aa65ba","observation_id":"7f22f904-cb59-4253-9814-8ce71aca2519","resolution":{"observed_at":"2026-08-03T14:56:51.219930Z","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":"2026-08-03T14:56:51.229857Z","title":"Dannert and Erich Grädel","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.229857Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:3474457141639f801a036945ecee7f5a296b6cd1f266d6aeee2b7b3e62e92c7f","observation_id":"31e5f3a0-3bad-45e3-9bc3-41cec6210fba","resolution":{"observed_at":"2026-08-03T14:56:51.229857Z","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":"10.4230/lipics.icdt.2024.22","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)","work_id":"004bb335-5e0a-4040-8c18-8ef03ada7681","year":2024},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.236474Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:91e051188f42e5564a761feec6015d03942d01eb2559fe4e4792f0bb2f219a97","observation_id":"5d753645-e8ae-48a5-8455-d4cd6792824a","resolution":{"observed_at":"2026-08-03T14:59:07.850105Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4230/lipics.icdt.2020.9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)","work_id":"ef93bc16-68e5-4ad8-be62-4fdea4f3c66c","year":2020},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.246712Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:616e1d8e6cccd6207d295874f440e9290c11823abbde94608d5635ccece478a7","observation_id":"ba4f36da-5df6-42e7-874c-0d76d38b84f7","resolution":{"observed_at":"2026-08-03T14:59:07.549783Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.24963/kr.2020/38","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Krishna, Wim Martens, Matthias Niewerth, and Tina Trautner","venue":null,"work_id":"100ec85e-a3c5-49ce-9244-e00713b06ac9","year":2020},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.251973Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:c3cc3fdba4dc65c5565b79233282e41e0488647c4cbb897a341be0448fa5ab56","observation_id":"a34c753c-1110-4c2e-b722-28bde62d6d4a","resolution":{"observed_at":"2026-08-03T14:59:07.217115Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.46298/lmcs-21(1:21)2025","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Logical Methods in Computer Science","work_id":"16391dab-3c07-4498-b91a-63ddfc2c5f59","year":2025},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.258760Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:c5daa312da8fd900460af8b38e01cde58af049124a4ff9b8c448073de920f808","observation_id":"b818065c-ac90-4613-8f76-96f09110fc5f","resolution":{"observed_at":"2026-08-03T14:59:06.895655Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1145/3725237","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Proceedings of the ACM on Management of Data","work_id":"26e345b9-a8f0-4e22-83fe-669a7a2425a6","year":2025},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.264491Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:570230b1dd2034228a72e694b5f5bdcf1806ec5fcddb2dc507cbebe13e2901f6","observation_id":"71a04472-fb26-48ef-b7fd-d66fcc98314b","resolution":{"observed_at":"2026-08-03T14:59:06.596526Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-03T14:56:51.273727Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.273727Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:3a746f0fe9f03287cb17d5791662ff26f33aa54b33c09029465447d96e6a0ce2","observation_id":"8062175c-f1ec-4445-af36-c2984c3fd761","resolution":{"observed_at":"2026-08-03T14:56:51.273727Z","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":"10.4230/lipics.icdt.2023.1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"arXiv (Cornell University)","work_id":"5c7e8e1a-c0ab-4ec1-8a7e-81db6ffccef0","year":2023},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.278580Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:9f06f180d63df041bc56e8054c61b38e0e16d29c19d9d989c17cb6ba8588e6a1","observation_id":"c4cfee07-c9ba-43a9-b972-d52dbfa68bb1","resolution":{"observed_at":"2026-08-03T14:59:06.324478Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-03T14:56:51.288072Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.288072Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:ce3969a25c137bac26f0c4862160649983204a61748b2e207e0dad44e4e2a961","observation_id":"ea0a3a7b-e1de-4b10-a973-8fbe8c51b325","resolution":{"observed_at":"2026-08-03T14:56:51.288072Z","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":"10.1016/j.jcss.2013.01.008","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Freydenberger and Nicole Schweikardt","venue":"Journal of Computer and System Sciences","work_id":"236261fc-4193-48fb-bb1c-fb62f8dbbe8d","year":2013},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.293244Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:7b9aa79f3e910b8d5c92fea9ba547643ae4ba2c23afe5798aef70008ccfcb9c3","observation_id":"df28f459-09a2-402a-bac6-8faea6b7fcbe","resolution":{"observed_at":"2026-08-03T14:59:06.125116Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-03T14:56:51.300139Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.300139Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:10d45f57d8f1fdde9df7f0e36b3d168e402b8556e93d19e049dd278cf119d202","observation_id":"a3ed07ca-a768-4739-8449-365e9c3c4998","resolution":{"observed_at":"2026-08-03T14:56:51.300139Z","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":"10.1007/978-3-031-11321-5_2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Lecture notes in computer science","work_id":"b3a2c7ea-ae95-4544-864f-34e38ac8d24d","year":2022},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.308442Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:40a81fe221441c8f0228e8f806488533f9d58d657b608b309d89879beef88b70","observation_id":"95375eed-4122-4cc4-a0dc-00c68d1f9fcc","resolution":{"observed_at":"2026-08-03T14:59:05.831062Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-03T14:56:51.316342Z","title":"Schoenholz, Patrick F","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.316342Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:45d2f310022da5a1f9f1f59d7304cecdaf7eb07c901f55b19cc60166a91053f4","observation_id":"a5176046-0104-4e51-af49-bf84cbb65e17","resolution":{"observed_at":"2026-08-03T14:56:51.316342Z","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":"2026-08-03T14:56:51.326593Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.326593Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:1f81a2e540f719a07ce3b309f1e80ae4bd00247d39ab22012955cc25e57e69b1","observation_id":"d55d2d2f-c77c-430a-adc3-f6e17dc41615","resolution":{"observed_at":"2026-08-03T14:56:51.326593Z","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":"2026-08-03T14:56:51.336040Z","title":"Hamilton, Zhitao Ying, and Jure Leskovec","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.336040Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:20a13a101ea00fb6bc67c8f5436fe54ca1433b0cd8a2bb9215041300fe34231d","observation_id":"cb38a018-0ca3-41aa-9bdd-eccd070cba57","resolution":{"observed_at":"2026-08-03T14:56:51.336040Z","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":"2026-08-03T14:56:51.344682Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.344682Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:6bdeb885e8ff48c914101aec37d8fed2d60a902a2fa236b47862ff0d02f6a098","observation_id":"0109412e-6ac3-4859-8976-374bb7ab921b","resolution":{"observed_at":"2026-08-03T14:56:51.344682Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.06091","last_updated":"2025-08-08T07:35:35Z","snapshot_observed_at":"2026-08-05T22:59:40.825824Z","submitted_at":"2025-08-08T07:35:35Z","title":"Aggregate-Combine-Readout GNNs Are More Expressive Than Logic C2","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.06091","snapshot_observed_at":"2026-08-03T14:56:51.351646Z","title":"Hauke and Przemyslaw Andrzej Walega","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.351646Z"},"links":{"cited_paper":"/paper/2508.06091","citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:3a162915bb27352c2a7292550bba160cf29aff8c9ec93aab28cee4d5f15cde49","observation_id":"7dbb5153-ed82-4f56-b7af-3f3fe5105f46","resolution":{"observed_at":"2026-08-03T14:56:51.351646Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.04661","last_updated":"2024-05-08T04:34:47Z","snapshot_observed_at":"2026-08-16T15:17:24.620615Z","submitted_at":"2023-07-10T15:59:09Z","title":"On the power of graph neural networks and the role of the activation function","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.04661","snapshot_observed_at":"2026-08-03T14:56:51.357521Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.357521Z"},"links":{"cited_paper":"/paper/2307.04661","citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:5ef1de4a921f47547b72e9ad63218409a437735bcfbf6678f65c03aa32f20ae4","observation_id":"87f7d12a-b28d-4955-b5a4-4b1def9ca5cf","resolution":{"observed_at":"2026-08-03T14:56:51.357521Z","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":"2026-08-03T14:56:51.364576Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.364576Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:f4113fd74b7473e449d57d02a87e53c904528a348ffda8e2414e271933a34174","observation_id":"3c20d715-b883-435f-af24-c59a4052868f","resolution":{"observed_at":"2026-08-03T14:56:51.364576Z","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":"2026-08-03T14:56:51.370685Z","title":"Kipf and Max Welling","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.370685Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:679a1ca155ae8554707af9ac5ac5d4f5fdecdcf46d969018489ed9c0f82d57ef","observation_id":"c53de951-b471-401f-8b4b-1a806138e28e","resolution":{"observed_at":"2026-08-03T14:56:51.370685Z","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":"2026-08-03T14:56:51.384163Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.384163Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:6d55534204696e656dfbbbc659db0fb6ecf332a79916c4380db79c36cfbced7a","observation_id":"b97fb67e-65f4-4a06-a1fb-c2851887a38c","resolution":{"observed_at":"2026-08-03T14:56:51.384163Z","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":"2026-08-03T14:56:51.390671Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.390671Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:a482196f9fa4367a7c421a146cba1af2dfa4480fe7b97ede3ad53419ca35aa21","observation_id":"e692896d-0b9d-4894-bdc7-7e451bd25452","resolution":{"observed_at":"2026-08-03T14:56:51.390671Z","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":"2026-08-03T14:56:51.398111Z","title":"Mendelzon and Peter T","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.398111Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:37d5cae7d4c629c7fd35aa073636e263ba870df95d84350cf38c47b419d7dca3","observation_id":"97f3a0b2-78da-44c0-a7c3-0deba27bf000","resolution":{"observed_at":"2026-08-03T14:56:51.398111Z","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":"2026-08-03T14:56:51.407958Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.407958Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:08eed7be3a968c39d08cdd4ea4c391840452d6a519bacfec325cdbe455a39852","observation_id":"fa7fa9ab-0124-4c4e-9fb1-a31f2505f31d","resolution":{"observed_at":"2026-08-03T14:56:51.407958Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.19173","last_updated":"2025-03-31T00:46:30Z","snapshot_observed_at":"2026-08-16T12:47:10.669057Z","submitted_at":"2025-03-24T21:52:05Z","title":"Graph neural networks extrapolate out-of-distribution for shortest paths","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.19173","snapshot_observed_at":"2026-08-03T14:56:51.415954Z","title":"Nerem, Samantha Chen, Sanjoy Dasgupta, and Yusu Wang","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.415954Z"},"links":{"cited_paper":"/paper/2503.19173","citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:c4a524bc42bfbb9a119572fed8b5f1485ea59abd7a2a14249154e16a173ab6c9","observation_id":"31762b2e-888b-4041-a65a-71a94bc597ee","resolution":{"observed_at":"2026-08-03T14:56:51.415954Z","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":"2026-08-03T14:56:51.422279Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.422279Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:00fd760240258ff5fb5fbc685f9ee1711ccccbaf695cdab90d9e398aa141bf3d","observation_id":"c3a43cfd-0856-446b-9468-f95e364ab01a","resolution":{"observed_at":"2026-08-03T14:56:51.422279Z","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":"2026-08-03T14:56:51.428467Z","title":"Reutter, Miguel Romero, and Moshe Y","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.428467Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:530e08e043da7437299b31a9a91732dbdb4974325405d3bfd81914cae9fb9a8b","observation_id":"016cf1c0-80ef-4a22-afcd-fe937d5f8f46","resolution":{"observed_at":"2026-08-03T14:56:51.428467Z","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":"2026-08-03T14:56:51.436223Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.436223Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:4850d1ba7dc215fe3a6e6e966b69066db8f2fb0b2cebf478964c9f945327fe22","observation_id":"bbf657c3-91dc-4de7-9a87-937362eaa381","resolution":{"observed_at":"2026-08-03T14:56:51.436223Z","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":"2026-08-03T14:56:51.443315Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.443315Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:fbdba447d16a37a7de728dbfecd7eda2cff5b91d61dea9a9f8fc5f9ededfcf2b","observation_id":"6b3a05a9-1717-4707-aa8b-e995b108aff2","resolution":{"observed_at":"2026-08-03T14:56:51.443315Z","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":"2026-08-03T14:56:51.454155Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.454155Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:c4af139743785ba50a448b95537c1a78c445f1f85b99ff48e9b6d65da32c2f8f","observation_id":"d8a0f78f-d701-4486-aac1-54b259a0062d","resolution":{"observed_at":"2026-08-03T14:56:51.454155Z","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":"2026-08-03T14:56:51.461014Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.461014Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:ca9a99e6392298f9ff61e3cf36e8cf2c5a3244e1a33a26de37822d50fdec9b47","observation_id":"be2cb2f2-7b7a-4e5f-aaac-6fe68c95beef","resolution":{"observed_at":"2026-08-03T14:56:51.461014Z","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":"2026-08-03T14:56:51.470077Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.470077Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:658d76d54db4a9b083f9106a6807a39f7a7bf23e180597deb270150453db7e57","observation_id":"8bc2eac5-5767-4c78-8d71-45682d96d936","resolution":{"observed_at":"2026-08-03T14:56:51.470077Z","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":"2026-08-03T14:56:51.483097Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-03T14:56:51.483097Z"},"links":{"citing_paper":"/paper/2512.19332"},"observation_digest":"sha256:03727bb297cadb505709200f7c98263341edcb05cca75b5c20311c80ee9d176c","observation_id":"a6665bfe-e390-4368-a905-004e6e843b87","resolution":{"observed_at":"2026-08-03T14:56:51.483097Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.19332","last_updated":"2026-05-26T10:39:23Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-11T18:51:51.191068Z","submitted_at":"2025-12-22T12:27:36Z","title":"A Logical View of GNN-Style Computation and the Role of Activation Functions"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":34,"verified_exact":9,"verified_fuzzy":0},"total_outbound_references":45},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2512.19332."}