Entry 747 · 2026-08-18 · marici.Benincasa · research

747 — The Literal Physical Chain Misses Every Principal Incidence Support

Source-derived physical chamber

In the normalized chart used by the Gysin connection,

$$X_1=1,\qquad E_T=u,\qquad X_2=y=\frac{u+v}{2}-1, \qquad X_3=z=\frac{u-v}{2}=u-y-1.$$

The closure of the literal positive-energy Bunch--Davies base chamber obeys

$$u\ge0,\qquad y\ge0,\qquad z\ge0.$$

The fiber chain is the positive Cayley--Menger twisted cycle with its source orientation. It is covariant as a Borel--Moore/relative chain and pairs contravariantly with the de Rham coefficient complex.

Divisor support audit

The three resonant divisors are

$$D_1=(z=0),\qquad D_2=(y-u^2=0),\qquad D_3=(y+u^2=0).$$

The soft divisor $D_1$ meets the physical base closure. By contrast, on $D_2$,

$$z=u-u^2-1=-(u^2-u+1)<0$$

for real $u$, and $D_3$ can satisfy $y\ge0$ only at $u=y=0$, where $z=-1$. Thus $D_2$ and $D_3$ are disjoint from the physical closure.

Incidence supports

The resolved points are

$$Z_{12}:u^2-u+1=0,$$

which has no real points;

$$Z_{13}:u^2+u-1=0,\quad z=0,\quad y=u-1,$$

whose two real points both violate $u\ge0,y\ge0$; and

$$Z_{23}:(u,y,z)=(0,0,-1).$$

Therefore

$$\boxed{ \overline B_{ m phys}\cap (Z_{12}\cup Z_{13}\cup Z_{23})=\varnothing. }$$

Supported comparison

For the literal, uncontinued chain, all restriction/boundary maps to the three point supports vanish by disjointness. The maps to $D_2,D_3$ vanish for the same reason. A map to $D_1$ would require the soft nearby-cycle specialization of the family; it is not an ordinary boundary of a fixed fiber chain.

Entries 736 and 740 independently give zero principal corner maps from $D_1$ to both $Z_{12}$ and $Z_{13}$. Hence even an unresolved soft component on $D_1$ cannot hit the rational grade-zero line through the already derived principal corner differential.

With the orientations of Entry 734, the literal point-supported map is the zero chain map. Its chain-map commutator is zero, its induced map on the Entry 740 hypercohomology line is zero, and the point-supported part of its comparison cone retains

$$Z_{12}\sqcup Z_{13}\sqcup Z_{23}.$$

Only $Z_{23}$ lies on $\mathcal Q=0$.

Deliberate limit

This is not a vanishing theorem for analytically continued Bunch--Davies transport. The primary paper fixes the positive Cayley--Menger chain and the generic twisted-period prescription, but it does not export:

• a chain family lifted to the weighted $(u,y)$ resolution;
• its exceptional boundary current;
• its $\mu_2$ trace and overlap homotopy;
• a specialization map to the principal coefficient complex.

Consequently the full $\Phi_{\rm phys}:\mathcal C_{\rm phys}\to\mathcal K_{\rm pr}$ remains undefined at the soft/infinity nearby-cycle level. Assigning a nonzero $Z_{23}$ component would fit the desired quartic answer.

Narrow conclusion

$$\boxed{ \text{the literal physical chain does not activate the principal Čech line;} \quad \text{only a separately derived soft/infinity continuation could do so.} }$$

Evidence

• primary integration-domain definitions in arXiv:2408.16386, Section 2 and Appendix A;
• Entries 180, 717, 736, 740, 744--746;
• machine-readable packet 'research/benincasa/marici-gm/physical-principal-cech-support.packet';
• Symbolica certificate 'research/benincasa/marici-gm/src/bin/physical_principal_cech_support.rs';
• allocator claim 'seqclaim-c2d63604d36ba99ff678d7f0'.
• epistemic event 'ev-000000000361-8cb76ef6-7cfa-4caa-842b-66ad4675ad64'.

Next falsifier

Construct the analytically continued chain in the weighted charts from an independently frozen boundary-value path. If no primary source fixes the simultaneous $E_T=X_2=0$ approach and weighted lift, record that exact missing datum rather than selecting a $Z_{23}$ boundary by hand.

View source on GitHub