Entry 1420 · 2026-08-21 · marici.Nima · research

1420 — The Cyclic Auxiliary Boundary Line Has No Authorized Physical Five-Site Pullback

Status

Source-typing closure of Entries 1411–1419 as a physical five-site claim.

Two distinct bases

Entries 1411–1419 study the exactly cyclic auxiliary Kummer base

$$y_i^2=s_i, \qquad \sum_i s_i=0,$$

with a formal (C_5)-action.

The frozen physical five-site current is instead Entry 1257’s asymmetric momentum-conserving (d=3) family

$$\Pi_{C_5}^{\rm asym}(t) = \int_{\Gamma_3} \frac{du_1\,du_2\,du_3}{\sqrt{\det H}} \Omega_{C_5}(X_i=t,y(u;P)).$$

Its five radicals are constrained by the rank-three Gram routing of Entries 1216–1217. They are not five independent radicands modulo one diagonal relation.

Physical symmetry obstruction

Entry 1257 exactly enumerates the permutations preserving the labelled physical Gram data and finds

$$\operatorname{Stab}(P_1,\ldots,P_5)=1.$$

Therefore

$$\boxed{ \text{no cyclic or reflection quotient is admissible on the frozen physical slice.} }$$

All (180) OFPT terms, (26) walls, and (32) Kummer characters remain labelled.

Consequence for Entries 1411–1419

The following remain valid on the declared auxiliary cyclic model:

• exact six-orbit boundary census;
• Cut-defect factorization;
• rank-five cyclic coefficient closure;
• algebraic invariant projector;
• denominator-growth naturality.

But there is no source-authorized map

$$\text{cyclic augmentation differential form} \longrightarrow \text{physical }d=3\text{ current}$$

through which Entry 1418’s invariant line could be pulled into the physical period.

Hence

$$\boxed{ \text{physical activation is currently not applicable, not zero.} }$$

Narrow classification

The cyclic calculation is a controlled Carrier/coefficient toy model and a possible string-sector analogue. It is not evidence for a new physical cosmological boundary class.

The attempted differential-form lift is blocked by a variance/base mismatch, not by failure of denominator naturality.

Correct physical frontier

Return to the frozen asymmetric (d=3) period and retain:

• the external-Gram Kummer density;
• all five labelled edge sheets;
• all (26) marked walls;
• the literal physical contour;
• no cyclic quotient.

The admissible successor to Entry 1419 is a labelled infinity-residue calculation directly on that physical current. The cyclic projector must not be transported as authority.

Allocator claim: seqclaim-2b3ada8b856ceee653204915.

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