{"as_of":"2026-08-12T18:58:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:92c5ae23b529e50dda24e5772ede3c3890de228e63a60b697d95fd9b6a4e6957","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T12:07:18.425008Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"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/2412.14677/citation-record","integrity":"/paper/2412.14677/integrity","json":"/paper/2412.14677/citation-record.json","paper":"/paper/2412.14677"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:07:18.765539Z","title":"The idempotents that differ by signs are singled out by plus/minus signs","venue":null,"work_id":"e384626b-272f-42e3-b5f3-241a2a038320","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.337516Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:c39fd52de5aab848158d08f9596de0816cf2436ab001e7c654f3a49791f1dbca","observation_id":"f5e43f6c-5c68-40e1-826e-cec374300b24","resolution":{"observed_at":"2026-08-11T12:07:18.770495Z","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":"2026-08-11T12:07:18.783033Z","title":"Left ideal basis (otherwise projecto r, or spinor basis); 4","venue":null,"work_id":"100a7f01-eb78-4d5d-80b0-8bda9c4b8849","year":1998},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.330994Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:24a6424e713aeb9f1ad5b3394cdc0070a77ce06b5c88222baec4e8ddf7594797","observation_id":"b5ce039f-0999-4f01-96d9-b669661af02e","resolution":{"observed_at":"2026-08-11T12:07:18.787977Z","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":"2026-08-11T12:07:18.750368Z","title":"The number of elements, denoted as (1),(2) or (4), in the list of tw o-sided ideal determines a type of matrix rep: 1 ↔ R, 2 ↔ C, and 4 ↔ H, i.e","venue":null,"work_id":"3469021f-42da-4b3d-afd4-fe63ad4ba16b","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.341906Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:95a63fec7ff206afeb90ac93878fdad48c6fcacf723f90939fecf3340c55eabe","observation_id":"ae077934-3386-4cf0-bb27-0e918982889a","resolution":{"observed_at":"2026-08-11T12:07:18.755444Z","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":"2026-08-11T12:07:18.733494Z","title":"}P1 for the left ideal spinors I(P1)","venue":null,"work_id":"5640e6f0-96e0-4406-b394-78cdfd5394a4","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.346432Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:2b83594b44ec11e777f9f55c21a22bf2c379cf3766b2ab00d7d14088bff86001","observation_id":"eac49581-7bfe-4d5f-aab0-7d5b4f6e30fd","resolution":{"observed_at":"2026-08-11T12:07:18.740286Z","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":"2026-08-11T12:07:18.719395Z","title":"The matrix type and dimension is in agreement with the 8-periodicity table 1","venue":null,"work_id":"0af265ac-a9bf-441b-87c3-eae50603227f","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.350675Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:45d44605058c1cc39fdeb9ea8e70469dec890bffdb6b254f80604831d40dfd08","observation_id":"dd5fbc11-da8c-4ed0-9551-b0f4609661c4","resolution":{"observed_at":"2026-08-11T12:07:18.723709Z","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":"2026-08-11T12:07:18.705203Z","title":"In tables the spinor expressions for semisimple algebras includes two idempotents that are related by grade inversion (denoted by ÙPi)","venue":null,"work_id":"c73c536d-1f2d-4a0b-b01a-b0b14039c597","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.355374Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:24b30817d16b3cac29e0e2961cc17ff5465e4c337d8ffd72445a1860b60c608f","observation_id":"bb838118-2875-4c45-9c33-ea2161131166","resolution":{"observed_at":"2026-08-11T12:07:18.710465Z","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":"2026-08-11T12:07:18.689411Z","title":null,"venue":null,"work_id":"8f47dcae-6c8a-418c-8927-980ee540a3a9","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.359565Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:4d3ae9b78deefb69a50ae75c296f9f0823a4e926adefe3b003540976fb561bec","observation_id":"06aa910a-4661-432f-864e-9705cd76f72c","resolution":{"observed_at":"2026-08-11T12:07:18.693888Z","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":"2026-08-11T12:07:18.676677Z","title":null,"venue":null,"work_id":"53c5f86a-5406-406f-9078-ef9fa4a6c93e","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.364069Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:1941c8cf40811e2294590c8a3e2596ee4635313cea3c6a6cda8a97894a46a738","observation_id":"5ee84b22-653e-408a-8e05-61bd8d4bf0cf","resolution":{"observed_at":"2026-08-11T12:07:18.680901Z","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":"2026-08-11T12:07:18.663271Z","title":null,"venue":null,"work_id":"410bfcbf-f070-488f-9cb4-2fb2b9d894b3","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.368802Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:7626f4d29ffa50fc0082a6676e67b2f2c750c364d8808022e93c43c64c4bab58","observation_id":"6ba44a7d-dd9c-47a7-a8dd-1b5e3e4cb283","resolution":{"observed_at":"2026-08-11T12:07:18.667468Z","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":"2026-08-11T12:07:18.649044Z","title":null,"venue":null,"work_id":"347fb3e6-fefe-4a97-b645-f94e9998b27d","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.372610Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:0df1adca75f682ad6df8e721da7e8becd8ac075f5a00a3114b8f672220ee1a59","observation_id":"a2a89f11-ad31-4196-b93d-6caa0e53c607","resolution":{"observed_at":"2026-08-11T12:07:18.653504Z","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":"2026-08-11T12:07:18.634521Z","title":null,"venue":null,"work_id":"fc38dbaf-1f6b-47d4-a0a8-39768da7d4dc","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.376329Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:039f216a8d32e879db97415d83334841a24ad9b2966328ea141ca67dbe32f4e7","observation_id":"2787db90-aa8e-466a-a7f7-45b07998bc6f","resolution":{"observed_at":"2026-08-11T12:07:18.638640Z","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":"2026-08-11T12:07:18.621459Z","title":null,"venue":null,"work_id":"f0fb8720-95ec-49cf-8e3f-4d8b9adea9eb","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.380176Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:a142be1daf3e55438a30e4836b3aed9bec4973a62cfb076e0e0af54ce78cc1f2","observation_id":"cc6d01f3-ca3d-40ce-878d-fe676f239ccc","resolution":{"observed_at":"2026-08-11T12:07:18.625712Z","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":"2026-08-11T12:07:18.606754Z","title":null,"venue":null,"work_id":"978c0413-3ac8-4749-a010-7e10110c18a2","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.383753Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:d16bd912a30c3f35d74e18154d83e7513e7abb272a7e1166da504e42cbb0253e","observation_id":"080329f1-5edd-4654-a4f0-a13d73b3747f","resolution":{"observed_at":"2026-08-11T12:07:18.611040Z","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":"2026-08-11T12:07:18.594085Z","title":null,"venue":null,"work_id":"bf61d465-1776-48ed-9ef4-cd4903726a5d","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.387985Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:87236778230357a4ead8ed98206b601fc64a7d5e00635a9f3448c984cadbc77a","observation_id":"23937cec-c12d-4d79-8e81-a2eba0d8a0d0","resolution":{"observed_at":"2026-08-11T12:07:18.598401Z","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":"2026-08-11T12:07:18.581180Z","title":null,"venue":null,"work_id":"45d965a5-eda5-40d4-96e4-4c79c6f96d58","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.391694Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:23e9a0f0cf7133a812d0ea0f6002961095651927102f3f39eab4ca2765d1a89d","observation_id":"6f5b8eda-bdae-461f-a63a-112425cfc201","resolution":{"observed_at":"2026-08-11T12:07:18.585768Z","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":"2026-08-11T12:07:18.566212Z","title":"Example of construction of the real spinor data table for Cl 2,2 algebra","venue":null,"work_id":"a89dc355-b442-497b-9bfa-834419154c89","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.395900Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:2a5dbd7d55afa2904dac3a3651cc6d6b7d922192317327c322078825471b2864","observation_id":"9d520321-9bd7-4e86-b4a3-f5ed8ef30b86","resolution":{"observed_at":"2026-08-11T12:07:18.571025Z","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":"2026-08-11T12:07:18.553232Z","title":null,"venue":null,"work_id":"da9e42e8-bf35-4f26-a04f-3956b989eeb0","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.400166Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:6f1761c7039d335f2ea0c18f59e1637b08d480f1b7208e1c76cd3ed2e9c47611","observation_id":"9bb0eca1-e5db-4a17-8e76-527ef4e6ffc2","resolution":{"observed_at":"2026-08-11T12:07:18.557849Z","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":"2026-08-11T12:07:18.539248Z","title":"Find a list of two-sided ideal (division ring) K by multiplying the obtained left ideal elements by same idempotent from left, K = P S = P {Cl 2,2}P","venue":null,"work_id":"cd7575fe-aadb-4e7a-8f59-b6a8a1b408a2","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.404189Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:7f642f05a31984809c437b86a681415ef39d3e3f416c83139683404409b5a690","observation_id":"2db217f4-f0ac-489a-b1aa-c0a8c3d1d5e8","resolution":{"observed_at":"2026-08-11T12:07:18.544137Z","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":"2026-08-11T12:07:18.523970Z","title":null,"venue":null,"work_id":"d5d4ad11-7319-4df7-8cae-5141bfe1dde3","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.408281Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:0d55c7c7c6bc4112b35976f19d5869ec41d479fe764ae247e21cad6e9415e871","observation_id":"9923b126-1242-4b86-828d-a73a98c8fdb9","resolution":{"observed_at":"2026-08-11T12:07:18.529253Z","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":"2026-08-11T12:07:18.509968Z","title":"Once the four-component ideal basis S = {S(1), S (2), S (3), S (4)} is determined one can compute a matrix rep of basis vectors in algebraic spinor bas is","venue":null,"work_id":"eb2c1991-0aa2-4f84-a2e5-4eafc397396e","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.412033Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:3a7ea88aac5eb1f99b617a51e0071153e53a13d9d6edcc897d47e1f59a08924e","observation_id":"b8f7f160-1177-4420-9882-3c0923e4ec37","resolution":{"observed_at":"2026-08-11T12:07:18.514688Z","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":"2026-08-11T12:07:18.496130Z","title":null,"venue":null,"work_id":"6303801f-fdff-4ade-a1f1-938a6d29a263","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.416048Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:7e65b9d9618863de5503d03d20a0b26bed5b7a0eba28854844e2891f217d4429","observation_id":"039c768d-80c1-4d2e-9706-ea2932900088","resolution":{"observed_at":"2026-08-11T12:07:18.500850Z","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":"2026-08-11T12:07:18.483054Z","title":"In the matrix form the general MV spinor can be expanded in the ide al basis as ˆΨ = s1E11 + s2E21 + s3E31 + s4E41","venue":null,"work_id":"446a475a-e01b-4f38-8396-7d3a1739b964","year":null},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.420386Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:6d837573c29d599460f61b43071256fc939dee39a5d42d47b6ef44164cf227e0","observation_id":"333f2861-df27-46af-9099-f50c3a3aa55d","resolution":{"observed_at":"2026-08-11T12:07:18.487566Z","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":"2026-08-11T12:07:18.460817Z","title":"The results of the example are summarized in Table VI ( Cl 2,2 algebra)","venue":null,"work_id":"23756811-b05c-4263-b371-e1b5497547a2","year":1998},"citing_paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:18.425008Z"},"links":{"citing_paper":"/paper/2412.14677"},"observation_digest":"sha256:8fcb9cd274a53494e5aa1b9ba0a01c56948397078fd7a62e5f649e4d9abd9366","observation_id":"46cb9343-a14d-4705-ad10-94b07a0ce83f","resolution":{"observed_at":"2026-08-11T12:07:18.469413Z","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"}}],"paper":{"arxiv_id":"2412.14677","last_updated":"2024-12-19T09:30:46Z","latest_version":1,"primary_category":"math-ph","snapshot_observed_at":"2026-08-11T17:59:31.756987Z","submitted_at":"2024-12-19T09:30:46Z","title":"Clifford geometric algebra: Real and complex spinor data tables"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":0,"verified_fuzzy":11},"total_outbound_references":23},"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 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2412.14677."}