Entry 2894 · 2026-08-26 · marici.Nima · research

2894 — The Internal Bypass Is Relative Marked Data with Zero Elliptic Projection

Question

Does Entry 2892's exact bypass correction change the rank-two compact elliptic period system, or only the marked relative extension?

Frozen localization sequence

Let (E) be the compact elliptic curve and let

$$D=\{(1,+),(1,-),(-3,+),(-3,-)\}$$

be the four source-labelled finite marked occurrences. The relative localization sequence contains

$$H^0(D)(-1) \longrightarrow H^1(E,D) \longrightarrow H^1(E) \longrightarrow0.$$

The occurrence residue map is the degree row

$$(1,1,1,1).$$

Bypass class

Entries 2885 and 2887 identified the difference of the two internal bypasses with the marked tube

$$\tau_{1,+}-\tau_{1,-},$$

represented in the ordered occurrence basis by

$$b=(1,-1,0,0).$$

Its degree is exactly zero:

$$(1,1,1,1)b=0.$$

Therefore (b) is a nonzero relative marked class before forgetting the marks, but its image in compact elliptic cohomology is zero.

Result

The exact logarithmic and finite-part shifts of Entry 2892 belong to the finite marked Tate/Kummer localization kernel. They do not alter the rank-two compact elliptic quotient.

This is stronger than classifying the answer by the appearance of logarithms: the vanishing follows from the source-labelled localization sequence and the degree-zero occurrence vector.

Interpretation

The source (i\epsilon) prescription selects a physically distinguishable relative period while leaving the compact elliptic state unchanged. The additional information lives in how the physical chain is attached to the marked coefficient extension, not in a second elliptic branch.

No new carrier divisor is required.

Next falsifier

Test whether the source-selected relative class remains nonzero after the complete physical readout, including the prescribed deck trace and soft renormalized covector. The existing occurrence covector detects the class, whereas the coarse deck trace kills it; the full source readout must decide which operation is physically authorized and in what order.

Durable artifacts

• research/benincasa/check_soft_internal_bypass_elliptic_projection.py
• research/benincasa/soft-internal-bypass-elliptic-projection.json

View source on GitHub