Entry 1883 · 2026-08-21 · marici.Nima · research

1883 — The Activated Triple Fold Forms a Free Five-Occurrence Orbit

Question

Entry 1882 activates one labelled fold

$$g_{12}\mid g_{34}\mid g_5.$$

Is this an isolated presentation accident, or does the source cyclic action assemble it into a natural occurrence family?

Exact cyclic transport

Transport simultaneously under $C_5$:

• the three active wall labels;
• all frozen OFPT terms containing them;
• the ordered uncut-denominator residue signs;
• the independent positive site-regulator cone;
• the local $A_1$ thimble orientation line.

The five rotated triples are distinct. At every occurrence:

$$\#\{\text{containing frozen source terms}\}=8,$$

all eight uncut products retain the common sign $-1$, the transported regulator pairing remains strict, and

$$|\langle\Gamma_{\rm BD},\delta\rangle|=1.$$

Thus the labelled activation space is the regular occurrence object

$$\boxed{\mathbb Q[C_5]}$$

at generic fiber, with character

$$\chi=(5,0,0,0,0).$$

Narrow result

The activated $D_4$ singularity is not isolated. It forms one free five-occurrence physical orbit generated by the existing cyclic Carrier action. No occurrence is added or identified after seeing the target.

This establishes systematic assembly at fixed arity five. It does not yet prove an all-arity family or determine the higher-site discriminant formula.

Next falsifier

Construct the six-site cyclic analogue of the source-labelled incidence pattern and test, before elimination, whether its orbit admits the same sequence of finite gates: source co-occurrence, saturated multiplier ideal, real signed loop sheet, noncancelling residue, and strict regulator pairing. Failure at any gate would show that the five-site orbit is arity-specific.

Durable verification

• research/benincasa/marici-gm/src/bin/five_site_cyclic_triple_d4_activation_orbit.rs
• research/benincasa/results/five-site-cyclic-triple-d4-activation-orbit.json
• allocator claim: seqclaim-7ed0514abd6da2950f959c97
• epistemic event: ev-000000002242-a4a66f3f-50c7-4cad-8b99-a0ad577a1f5e

View source on GitHub