{"as_of":"2026-08-14T23:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e7ef83a133d6582d96c84df78780d34180b41d8f711a497213b1cbe932797248","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":"2026-08-14T06:32:32.682623+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:fabe808523a51f1277d3b8051dc54b00267974596c0b6746fc35ecca4c53ecb9","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:d527660f11a08ce6b167f40f8f06ac706f95a626aa2f285a26ab04a766666701","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:a25de1e588e24db981746b330fc331aef03e16042ae5c94b45cc03ba76e33b6c","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:f2d52b030b83c833fda6037b068414089a5b30da4907459e4006fff5f1623294","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:ea4a1785a224197e9062593f52ee50f59830b846699f9991b824f77c4a20af46","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:6f162f51fbe123fe05ef846e6476c22f1ed942eddc7d38bfaf1c4ad3cfb2943c","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:66d819963a048c4fab291501cdf5b327f7f8e77dc029d4221fa8054818226e8e","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:bbdc624e8388fa977f1a754f9a8e044326aa840ce2285f5fafdf1dad895f545d","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:1e5eab253ff5070155d718c34d0cf6cab7e3f2d22d458d437137474446e7e17d","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:2e7c2c3f6a4f94ccf159f763cc78b216b1e48f9afeb916875148c94767b831db","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:6911e52fc8772ce3e8ff3c9e15d77fc0ef09b94678551826ba77ec411956590b","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:1908a73a3aef49dc9f2d9b603a6844da01653636666797f1ef0b0ac4e094987f","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:c67b2555c07a817681d43e33719ff51088985e09de92e5e9c0a11d137696fe90","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:4a60f643d887fd36182bfad16ec7c6ac26e99c06e339fe7689f040943264d25a","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:9a6ba8e4e44c9789c79c21de365209a7917dcb58c88d42ebfbb6cf80c6159570","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:2ac6454a1ed0aedaa720cd6d0e22f509ab946299fd3208c1dcb6d40b830c562c","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"sha256:104a1ac00635c4006ae9661b689ac7f917bd79ca47ce1ff1687eac8e06cd9e90","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:dfe019b6cd236c748da86c40e6a36df9458df390d2cf32999f717dac4b4d7330","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:ca8a87a0fbfb204d65837375bd99242f7f9ec7cf15910002a164bd3fc6ab1bfa","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:c323ab65d7f62b5431d78fe4923882a1ca0bd203f6416711b8e53997b6323f7a","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:c4497706591fe88765e9d2bb09098570fcca1ab61862f2987e86e42cef9ebc8b","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:bc606153e35cf3fff8684c7b3c96cf2b4c85c233b8b18cfdbd340285b6257562","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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:b202161a91c9fd0d28b13e4aa6db1bbf8e5c3a0e61147d5b87708e46d14390a9","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2412.14677."}