Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T12:07:18.425008Z
Paper Citation Record · LEDGER
Clifford geometric algebra: Real and complex spinor data tables
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.
A citation records a reference. It does not transfer a finding from one paper to another.
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One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
23 of 23 outbound references displayed
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- unresolved12
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation f5e43f6c-5c68-40e1-826e-cec374300b24 · outbound
This paper cites The idempotents that differ by signs are singled out by plus/minus signs.
Clifford geometric algebra: Real and complex spinor data tables The idempotents that differ by signs are singled out by plus/minus signs
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.770495Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b5ce039f-0999-4f01-96d9-b669661af02e · outbound
This paper cites Left ideal basis (otherwise projecto r, or spinor basis); 4.
Clifford geometric algebra: Real and complex spinor data tables Left ideal basis (otherwise projecto r, or spinor basis); 4
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.787977Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ae077934-3386-4cf0-bb27-0e918982889a · outbound
This paper cites 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.
Clifford geometric algebra: Real and complex spinor data tables 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
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.755444Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation eac49581-7bfe-4d5f-aab0-7d5b4f6e30fd · outbound
This paper cites }P1 for the left ideal spinors I(P1).
Clifford geometric algebra: Real and complex spinor data tables }P1 for the left ideal spinors I(P1)
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.740286Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation dd5fbc11-da8c-4ed0-9551-b0f4609661c4 · outbound
This paper cites The matrix type and dimension is in agreement with the 8-periodicity table 1.
Clifford geometric algebra: Real and complex spinor data tables The matrix type and dimension is in agreement with the 8-periodicity table 1
Reference 5
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- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.723709Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation bb838118-2875-4c45-9c33-ea2161131166 · outbound
This paper cites In tables the spinor expressions for semisimple algebras includes two idempotents that are related by grade inversion (denoted by ÙPi).
Clifford geometric algebra: Real and complex spinor data tables In tables the spinor expressions for semisimple algebras includes two idempotents that are related by grade inversion (denoted by ÙPi)
Reference 6
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- raw_fallback, observed 2026-08-11T12:07:18.710465Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 06aa910a-4661-432f-864e-9705cd76f72c · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 7
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- unresolved
- raw_fallback, observed 2026-08-11T12:07:18.693888Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5ee84b22-653e-408a-8e05-61bd8d4bf0cf · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 8
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- raw_fallback, observed 2026-08-11T12:07:18.680901Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6ba44a7d-dd9c-47a7-a8dd-1b5e3e4cb283 · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 9
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- raw_fallback, observed 2026-08-11T12:07:18.667468Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a2a89f11-ad31-4196-b93d-6caa0e53c607 · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 10
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- raw_fallback, observed 2026-08-11T12:07:18.653504Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2787db90-aa8e-466a-a7f7-45b07998bc6f · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 11
- Resolution
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- raw_fallback, observed 2026-08-11T12:07:18.638640Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation cc6d01f3-ca3d-40ce-878d-fe676f239ccc · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 12
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- raw_fallback, observed 2026-08-11T12:07:18.625712Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 080329f1-5edd-4654-a4f0-a13d73b3747f · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 13
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- raw_fallback, observed 2026-08-11T12:07:18.611040Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 23937cec-c12d-4d79-8e81-a2eba0d8a0d0 · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 14
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- raw_fallback, observed 2026-08-11T12:07:18.598401Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6f5b8eda-bdae-461f-a63a-112425cfc201 · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:07:18.585768Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9d520321-9bd7-4e86-b4a3-f5ed8ef30b86 · outbound
This paper cites Example of construction of the real spinor data table for Cl 2,2 algebra.
Clifford geometric algebra: Real and complex spinor data tables Example of construction of the real spinor data table for Cl 2,2 algebra
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.571025Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9bb0eca1-e5db-4a17-8e76-527ef4e6ffc2 · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:07:18.557849Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2db217f4-f0ac-489a-b1aa-c0a8c3d1d5e8 · outbound
This paper cites 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.
Clifford geometric algebra: Real and complex spinor data tables 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
Reference 18
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- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.544137Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9923b126-1242-4b86-828d-a73a98c8fdb9 · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:07:18.529253Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b8f7f160-1177-4420-9882-3c0923e4ec37 · outbound
This paper cites 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.
Clifford geometric algebra: Real and complex spinor data tables 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
Reference 20
- Resolution
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- raw_fallback, observed 2026-08-11T12:07:18.514688Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 039c768d-80c1-4d2e-9706-ea2932900088 · outbound
This paper cites an unresolved cited work.
Clifford geometric algebra: Real and complex spinor data tables Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:07:18.500850Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 333f2861-df27-46af-9099-f50c3a3aa55d · outbound
This paper cites In the matrix form the general MV spinor can be expanded in the ide al basis as ˆΨ = s1E11 + s2E21 + s3E31 + s4E41.
Clifford geometric algebra: Real and complex spinor data tables In the matrix form the general MV spinor can be expanded in the ide al basis as ˆΨ = s1E11 + s2E21 + s3E31 + s4E41
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.487566Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 46cb9343-a14d-4705-ad10-94b07a0ce83f · outbound
This paper cites The results of the example are summarized in Table VI ( Cl 2,2 algebra).
Clifford geometric algebra: Real and complex spinor data tables The results of the example are summarized in Table VI ( Cl 2,2 algebra)
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:07:18.469413Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
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