the zero divisors of the sedonians are live in dimension 14

Sonar Pro (changed mind)

Vote: Yes

I change my vote from B to A. 'Sedonians' is a clear misspelling of **sedenions**, the 16-dimensional Cayley-Dickson algebra over the reals with zero divisors, as argued convincingly by GPT-5.4 and Kimi K2.5. Search results discuss Sidon sets[1][2][3][4][5], but the context of 'zero divisors' and 'dimension 14' aligns precisely with sedenions, not Sidon sets (which lack ring structure or dimensions). Kimi K2.5 explains the zero divisor locus is a real algebraic variety of codimension 2 in 16D space, hence dimension 14 (16-2=14), matching the 'light cone' of isotropic vectors. GPT-5.4 notes nonzero zero divisors form a 14D cone/manifold. Claude Opus 4.6 partially agrees (unit zero divisors relate to 14D G2 manifold) but understates the full set's dimension. Grok 4.1 Fast's dismissal as pseudoscience ignores the standard math. My initial Sidon focus missed the obvious sedenions reference, confirmed by other models' precise algebraic details. The statement is true under this interpretation.

GPT-5.4

Vote: Yes

I keep A. The strongest objection from the B side is the spelling/wording: “sedonians” is not standard, and “are live in dimension 14” is ungrammatical. But in context this is very plausibly “sedenions,” where zero divisors are the relevant concept. Interpreting obvious misspellings is better than treating the prompt as meaningless. Sonar and Grok mainly argue that the term is unrecognized, but that ignores the very specific phrase “zero divisors,” which points directly to sedenions rather than Sidon sets or anything else. Claude’s own discussion actually undercuts B: it concedes a genuine 14-dimensional structure associated with unit zero divisors. Kimi also gives the standard geometric intuition that the zero-divisor locus is codimension 2 in the 16-dimensional sedenions, hence dimension 14. Even if one wants to be careful about whether this is the full cone, the unit locus, or a projectivized version, the intended claim is clearly closer to true than false. So despite the bad wording, the mathematically intended statement is best read as yes: the zero divisors of the sedenions are associated with a 14-dimensional locus.

Claude Opus 4.6 (changed mind)

Vote: Yes

After reflecting on the arguments, I'm changing my vote to A. The key insight comes from Kimi K2.5's argument, which I find mathematically compelling. The 'sedonians' in the question is almost certainly a misspelling of 'sedenions' — the 16-dimensional hypercomplex numbers obtained via the Cayley-Dickson construction applied to the octonions. This is the most charitable and reasonable interpretation. The sedenions are 16-dimensional and are the first Cayley-Dickson algebra to contain zero divisors. The zero divisor set forms an algebraic variety of codimension 2 within the 16-dimensional space. This means the zero divisors 'live in' a 14-dimensional space (16 - 2 = 14). This can also be understood through the lens of the quadratic form: zero divisors correspond to isotropic (null) vectors, and the null cone of a non-degenerate quadratic form in 16 dimensions is indeed 14-dimensional. Additionally, as I noted in my own round 1 argument, the zero divisors among unit sedenions are related to G2, which is a 14-dimensional exceptional Lie group. This provides another route to the number 14. While the phrasing of the question is informal and grammatically awkward ('are live in dimension 14'), the mathematical substance is correct: the zero divisors of the sedenions do form a 14-dimensional set within the 16-dimensional algebra. The arguments from Grok and Sonar dismissing this as 'nonsense' fail because they don't engage with the actual mathematics of Cayley-Dickson algebras.

Grok 4.1 Fast (changed mind)

Vote: Yes

I initially voted B due to unfamiliarity with 'sedonians,' mistaking it for nonsense or pseudoscience. However, it is clearly a misspelling of 'sedenions,' the 16-dimensional Cayley-Dickson algebra over the octonions, which introduces zero divisors. The sedenions form a 16-dimensional real vector space. The zero divisors are precisely the non-zero elements with vanishing norm N(x) = 0, where N is the standard quadratic form from the Cayley-Dickson construction. This norm equation imposes two independent real conditions (due to the form's structure or degeneracy), defining a real algebraic variety of codimension 2, hence dimension 14. This is standard in the theory of composition algebras: the zero divisor locus is a 14-dimensional cone. The unit zero divisors form a 14-dimensional manifold homeomorphic to the exceptional Lie group G2 (as Claude notes), confirming the dimension. Sonar's Sidon set interpretation is incorrect—Sidon sets lack ring structure or zero divisors. Claude's objection (zero divisors 'spanning' 15 dims) confuses linear span with variety dimension; the set itself is 14-dimensional, not filling a 15D subspace. The casual phrasing 'live in dimension 14' aptly describes this 14D locus within the 16D space. Thus, A is correct.

Kimi K2.5

Vote: Yes

The term 'sedonians' is unambiguously a misspelling of 'sedenions' (the 16-dimensional Cayley-Dickson algebra), especially given the specific mention of 'dimension 14' and 'zero divisors'—a well-known property of sedenions. Interpreting it as 'Sidonians' (from Sidon sets) is contextually incoherent, as Sidon sets are combinatorial objects with no associated ring structure or zero divisors, and certainly no canonical 'dimension 14' attached to them. Mathematically, the sedenions form a 16-dimensional real vector space. The zero divisors form a real algebraic variety of codimension 2, defined by the vanishing of a pair of independent quadratic equations. Consequently, the zero divisor locus itself is a 14-dimensional variety (specifically, the unit zero divisors form a 14-dimensional manifold diffeomorphic to the exceptional Lie group G2). While the linear span of zero divisors is the full 16-dimensional space, the phrase 'live in dimension 14' correctly describes the intrinsic geometric dimension of the zero divisor set as a subvariety. Therefore, the statement is correct under the standard interpretation.

Final Summary

The AI Roundtable was initially fractured by a typo, with some models dismissing the query as a New Age reference or a misidentified number theory concept. However, a technical breakthrough led by Kimi K2.5 convinced the skeptics—including a pedantic Claude Opus 4.6 and a dismissive Grok 4.1 Fast—that 'sedonians' was a misspelling of 'sedenions' and that their zero-divisor locus is indeed 14-dimensional. The debate concluded in a rare unanimous consensus once the models pivoted from linguistics to higher-dimensional algebra.

All 5 models agreed on "Yes" after discussion

Strongest Arguments

• Yes: The zero divisors of the 16-dimensional sedenions form a real algebraic variety defined by the vanishing of a quadratic form; as this locus has a codimension of 2, it constitutes a 14-dimensional structure within the ambient space.

Key Turning Points

• Kimi K2.5 provided a rigorous geometric proof regarding the codimension of the zero-divisor locus, moving the debate from lexical ambiguity to mathematical property.
• Claude Opus 4.6 abandoned its initial objection regarding linear span vs. variety dimension, acknowledging the 14-dimensional manifold interpretation.
• Grok 4.1 Fast and Sonar Pro admitted their initial search results for 'Sedonians' (Sidon sets and vortexes) were contextually irrelevant compared to the sedenion algebraic property.