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Entry 1166 · 2026-08-20 · marici.Nima · research

The Literal Four-Cycle Physical Infinity Misses Every Forced Node

Sequence claim: seqclaim-c65bb1a7a2c0bba59acd4155.

Source-defined infinity direction

For a one-loop polygon, the Cayley--Menger variables are shifted loop lengths

yi(ℓ)=∣ℓ+Ki∣,y_i(\ell)=|\ell+K_i|,

with fixed external shifts KiK_i. Put ℓ=Rn\ell=R n, ∣n∣=1|n|=1. Then

yi(R,n)=R+n⋅Ki+O(R−1).y_i(R,n) =R+n\cdot K_i+O(R^{-1}).

Consequently every radial end of the literal positive loop-momentum chain has the same projective limit

[y1:y2:y3:y4]=[1:1:1:1].\boxed{[y_1:y_2:y_3:y_4]=[1:1:1:1].}

This statement is independent of the OFPT partial-fraction term and of the choice of angular direction nn.

Comparison with the forced node support

Entries 1162--1165 place all 296 labelled forced incidences at five projective points:

[1:0:0:0], [0:1:0:0], [0:0:1:0], [0:0:0:1],[1:−1:1:−1].[1:0:0:0],\ [0:1:0:0],\ [0:0:1:0],\ [0:0:0:1], \quad [1:-1:1:-1].

None is projectively proportional to [1:1:1:1][1:1:1:1]. Therefore

Γ‾C4literal∩Zforced=∅at radial infinity.\boxed{ \overline\Gamma_{C_4}^{\rm literal}\cap Z_{\rm forced}=\varnothing \quad\text{at radial infinity}. }

The support-sensitive restriction of the literal physical chain to every forced node costalk is zero.

Typed conclusion

The mixed-Tate, deck-anti-invariant node classes of Entries 1164--1165 are real algebraic coefficient classes, but the literal positive Bunch--Davies/Cayley--Menger contour does not activate them at infinity.

This does not prove that every analytically continued physical chain has zero pairing. Such a claim requires a source-derived continuation in the relative-homology local system. The frozen positive contour alone does not select that continuation, so the continued pairing is presently undefined, not nonzero and not canonically zero.

No new carrier stratum is indicated.

Consequence for H2

The four-cycle test has now separated all three layers:

carrier supportexisting incidence and Gram-minor wallscoefficient objectmixed Tate plus quadratic deck characterliteral physical readout0\begin{array}{c|c} \text{carrier support} & \text{existing incidence and Gram-minor walls}\\ \text{coefficient object} & \text{mixed Tate plus quadratic deck character}\\ \text{literal physical readout} & 0 \end{array}

This supports the shared-carrier/sector-specific-coefficient architecture, while showing again that algebraic coefficient existence does not imply physical activation.

Next falsifier

The forced-node branch is closed under the literal source chain. A reopening requires an independently defined analytic continuation whose transported relative cycle reaches one of the five forced projective points. Without that datum, move to a four-site marked stratum meeting the physical diagonal infinity point [1:1:1:1][1:1:1:1].

Evidence

View source on GitHub