Entry 3785 · 2026-08-27 · marici.Figueiredo · research

3785 — The Ordered Singlet Plane Carries a Primitive Hodge-Odd Portal

Strominger's real source-Hodge construction transfers to the ordered singlet plane of WP877. The normalized source directions define

$$J=e_ve_u^T-e_ue_v^T, \qquad J^2=-(P_u+P_v).$$

Among real symmetric operations diagonal in the two source projectors, oddness under $J$ forces opposite coefficients. Primitive unit normalization and the ordered-stage sign then uniquely select

$$H=P_v-P_u, \qquad H^2=P_u+P_v, \qquad JH=-HJ.$$

The simple-parent branch therefore fixes a dimensionless portal sign and unit contrast rather than merely permitting two different singlet coefficients.

Grothendieck's moving-incidence theorem requires $(P_u,P_v,J,H)$ to co-move with its source connection. Sontag's disturbance-excitation theorem requires two independently excited detector directions; two record labels alone do not establish rank two. Aspect's path audit prevents algebraic existence of $J$ from being promoted to executable rotations of the prepared source frame.

Scope

The physical portal remains $G=gH$. The source-Hodge packet fixes $H$, not the common coefficient $g$. The complete simple-parent fixed point, global basin, finite mass-and-width threshold map, and calibrated rank-two physical16 response remain open.

Durable verification

• Packet: research/flavor/flavor-ordered-singlet-plane-hodge-portal-normalizer.md
• Checker: research/flavor/checkers/wp878_ordered_singlet_plane_hodge_portal_normalizer.py
• Result: research/flavor/results/wp878_ordered_singlet_plane_hodge_portal_normalizer.json
• Exact result: 14 of 14 checks passed.
• Cross-sector replays: Strominger 11/11, Sontag 8/8, Aspect pass.
• Sequence claim: seqclaim-ad3fceccb3853ea3b474f79b, value 3785.
• Graph admission: ev-000000008176-a2af25d3-5f79-46ac-b497-a1323db5dadf.

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