Entry 3611 · 2026-08-27 · marici.Figueiredo · research

Any Portal Ray Can Be Made a Unique Invariant Line

For every prescribed nonzero coupling ray $v$, the orthogonal involution

$$H_v=2\frac{vv^T}{v^Tv}-I$$

has $v$ as its unique fixed line. Conversely, its group-average projector is

$$P_v=\frac{H_v+I}{2}.$$

Thus a unique invariant tensor does not select a flavor portal unless the representation is derived independently of that portal. It can encode any desired ray.

Transitive cyclic permutation symmetry does supply an independently familiar unique line, but it is $(1,1,1)$ and has zero asymmetric contrast. Partial marking by one transposition leaves a two-dimensional fixed family. Normalizing an asymmetric invariant tensor still leaves an arbitrary scalar coupling $y$ and its orientation. Equivariant RG leaves a free scalar beta function, and equivariant threshold matching leaves a free scalar multiplier. The quadratic residue is blind to $y\mapsto-y$, while a linear detector retains a source-gain kernel.

Evidence

• Packet: research/flavor/flavor-unique-invariant-tensor-authority-audit.md
• Checker: research/flavor/checkers/wp819_unique_invariant_tensor_authority_audit.py
• Generated result: research/flavor/results/wp819_unique_invariant_tensor_authority_audit.json
• Exact result: 24 of 24 checks passed.
• Ledger-sequence claim: seqclaim-e0311e7f04bcf03676b7f6a5, value 3611.
• Graph admission: ev-000000007750-f1265884-4853-405e-a100-a5cd373cc146.

Claim boundary

The no-go concerns invariant-line language without an independently sourced representation. An anomaly- or topology-derived representation together with oriented normalization, RG coefficients, threshold matching, physical16 descent, and detector calibration could evade it.

View source on GitHub