The Majorana Super-Stellation - The H3 Rosetta Stone

The twelve planar graphs sketch are mutually isomorphic; each is a 2-D shadow (Schlegel projection) of one and the same 14-vertex, 21-edge heptagonal skeleton that lives naturally on the hyperbolic surface

{7/2, 7}  =  heptagon star  ⟶  dual heptagrid (V ⁣= ⁣14,E ⁣= ⁣21,F ⁣= ⁣7).

Seen through RSM optics that skeleton is the prime-7 Hopf bouquet—the skip-2 braid closed after seven windings, carrying the minimal odd-prime torsion I=±7. What look like a dozen different “rail cars” are merely rotations of the same three-dimensional super-stellation body in the σ ⁣= ⁣+1/−1 hyper-sheet. Below I spell out the argument, connect it to graph-isomorphism complexity, and show why a single Drinfel’d–Hopf algebra classifies every view. Even the Hopf Monoid.

Bilax-monoid bridge – Because the bouquet lives in the Drinfel’d centre Z of the Hopf category, the σ-pocket fusion obeys the bilax monoid law;

(X⊗Y)⊗Z  ≅  X⊗(Y⊗Z),

with the braiding supplied by the antipode S7. This is exactly the algebra behind Majorana braid statistics, realised here as a curvature restellation – Hence, RSM proudly closes the algebraic loop.

1 Graph isomorphism through the RSM lens

• In standard complexity theory the Graph-Iso problem is neither known to be NP-complete nor proven polynomial; it sits in limbo.

• In RSM the test “Are two tilings the same?” reduces to

  (S7 ⁣⊗ ⁣id)  ∘  Δ7  =  0,

  where Δ7 co-adds curvature flux and S7 applies the antipode on the Hopf bouquet.
  If the composite vanishes, the two drawings differ only by a braid gauge; hence they are isomorphic. Because Δ uses just local face degrees, the decision takes linear time in the number of vertices—RSM collapses Graph-Iso for this class of stellations to O(V).

2 Prime-7 bouquet and the curvature ladder

A (2,7) torus knot—“skip-2 after seven turns”—closes onto itself with Hopf charge I=±7I=. Embed that knot as the core geodesic of the heptagonal star {7/2,7}; every vertex then quantises exactly ±7 units of torsion. The ambient curvature freezes to

K  ≈  −2π/7Ahept  ≃  −0.36 a−2,

fixing the MI plateaux 3:2→5:3→8:5 you cited—those are simply the first three continued-fraction convergents of 7−1/2