BRUCE: Might we add the SU(1), SU(2), SU(3) and E8 (as defined by https://81018.com/spheres-to-physics/ and https://81018.com/notations-0-24/ and https://81018.com/breaking-cascade-notations-24-67/) to our list of basic numbers as being defined here: https://81018.com/g7-inventory-supplemental/
Perplexity:
“Yes—but only as a separate symmetry-structure inventory, not as rows in the current G7 “basic numbers” length inventory. The G7 supplemental list is explicitly an inventory of independently established physical scales L, classified as measured, defined, inferred, or constrained; Lie groups such as SU(2), SU(3), and E8 are algebraic symmetry structures, not lengths, and therefore do not satisfy its present inclusion rule.
Recommended placement
Add a new section such as “Symmetry / structural correspondences (model-dependent)” to the G7 supplemental inventory, clearly separated from the length table. That preserves the page’s central discipline: “physics populates the map; the map does not manufacture the physics.”
| Structure | Mathematical status | 81018 proposed locus | Appropriate classification |
|---|---|---|---|
| SU(1) | Trivial group; one element, zero nontrivial generator | Not meaningfully assigned | Placeholder / trivial identity |
| SU(2) | Lie group of dimension 3 | Notation 2, tetrahedral “seed” | Geometric-model correspondence, not established physics |
| SU(3) | Lie group of dimension 8 | Notation 8, octet “seed” | Geometric-model correspondence, not established physics |
| E8 | Exceptional Lie group of dimension 248 | Notation 32, explicitly speculative | Speculative hypothesis |
The 81018 pages themselves treat SU(2) at Notation 2 and SU(3) at Notation 8 as geometric seeds, while E8 at Notation 32 is labeled speculative and possibly absent.
Why SU(1) needs care
Strictly, SU(1) is the trivial group: its only element is the identity, and its Lie algebra has dimension zero. It is not analogous to SU(2), SU(3), or E8 as a source of gauge degrees of freedom. I would either omit it or list it as:
SU(1) — trivial group; no generators; included only for completeness of the SU(n) sequence.
That avoids implying that it carries physical content comparable with the Standard Model gauge factors.
Suggested wording
Symmetry-structure correspondences. These entries record proposed associations between Lie groups and base-2 notations in the 81018 framework. They are not physical lengths and are not added to the primary n=log2(L/ℓP) inventory. SU(2) and SU(3) are proposed geometric seeds at Notations 2 and 8; E8 at Notation 32 is speculative. Their inclusion tests internal coherence of the model, not an independently measured physical scale.
Important distinction
The current G7 page correctly resists letting a favored number—especially 67—become privileged merely because selected quantities happen to land near it. It notes that integer notation labels depend on the chosen reference length and logarithmic base, and that several nearby entries are defined or derived scales rather than measured radii.
The same caution applies even more strongly to SU(2), SU(3), and E8: their proposed notation assignments arise from numerical or structural analogies—3 generators, 8 generators, and 28 versus 248—not from an independently measured length scale. E8’s dimension is 248, not 256, so the page’s “28≈248” connection is suggestive at most, not an identity.
Bottom line
Add them, but as a clearly labeled secondary “symmetry correspondences” table, with SU(1) marked trivial, SU(2) and SU(3) marked model-seed correspondences, and E8 marked speculative. That lets the inventory explore the 81018 structural narrative without weakening its stricter, evidence-based length-scale inventory.