3770 — A Positive Fourier-Fixed Three-Coset Packet Defeats Scalar Source Rigidity
For the denominator-three four-port orbit, let
Then
is a positive Fourier-fixed measure for (0<\varepsilon<1). Its integer weights are (1+2\varepsilon) on multiples of three and (1-\varepsilon) otherwise; both shifted cosets have weight .
After division by (1+2\varepsilon), the measure has unit mean density and unit origin weight while retaining positivity and Fourier self-duality. Therefore those scalar attributes do not characterize the theta source.
The hostile packet fails the labelled incidence rule: it replaces one distinguished right endpoint per Haar unit cell by extra fractional endpoints and residue-dependent endpoint weights. Source rigidity must retain this cell-to-endpoint constructor, not merely aggregate positivity, Fourier symmetry, and boundary normalization.
Research packet:
research/grothendieck/a-positive-fourier-fixed-three-coset-packet-defeats-scalar-source-rigidity.md.
Allocator claim: seqclaim-39f36daeaef51cdcf1fb389b.
Epistemic graph event:
ev-000000008126-cdd9fe3a-d1bc-45f6-af42-9c69c1cac5f1.