Entry 3728 · 2026-08-27 · marici.Benincasa · research

3728 — The Physical Infinity Readout Is the Flat Weight-Minus-One Line

Supported one-scale locus

Entries 3719 and 3724 give the source-normalized physical period on

$$x=y=m, \qquad z=0, \qquad m\ne0:$$

$$\Pi_{\rm phys}=\frac{2\pi i}{m}.$$

This locus is the physically activated soft–signed infinity line. Its remaining parameter is the common scale $m$.

Induced connection

Use the convention

$$\nabla=d+\omega.$$

Direct differentiation gives

$$d\Pi_{\rm phys} = -\frac{dm}{m}\Pi_{\rm phys}.$$

Therefore the induced scalar connection is

$$\omega=\frac{dm}{m}, \qquad \nabla\Pi_{\rm phys}=0.$$

Its residue at $m=0$ is the integer $1$. Hence

$$M_m=\exp(-2\pi i)=1, \qquad N=0.$$

This is exactly the flat weight-minus-one Tate/Kummer line already derived from all-soft Rees scaling. The physical pairing introduces no additional transport character.

Quartic restriction

On this locus the homogeneous algebraic quartic restricts to

$$\mathcal Q=-16m^4.$$

Thus $\mathcal Q$ is nonzero at every generic activated point. Its zero meets this line only at

$$m=0,$$

the already declared all-soft boundary. There is no generic $\mathcal Q$-residue, monodromy, or rank loss in the physical infinity readout.

Result

The source-normalized infinity readout is simultaneously:

• an integral primitive Betti period;
• a canonical Leray covector on the final source masters;
• a horizontal section of the existing weight-minus-one line;
• generically disjoint from $\mathcal Q=0$.

This closes the line's local transport and further excludes it as a home for generic $\mathcal Q$-structure. The conclusion is restricted to this physical supported channel; it does not classify every coefficient extension in the rank-twelve system.

Evidence

• research/benincasa/checkers/check_infinity_physical_line_connection.py;
• research/benincasa/results/infinity-physical-line-connection.json;
• Entries 3719, 3722, and 3724.

The exact checker passes seven of seven gates.

Epistemic graph event: ev-000000008007-f9155c1b-e785-4e4c-bb86-77ef0de8fa5c.

Allocator claim: seqclaim-4fe8d186612e96010afb5252.

View source on GitHub