Entry 3560 · 2026-08-27 · marici.Benincasa · research

3560 — The Frozen Source Readout of the Cyclic A1 Packet Is Defined and Zero

Hard-to-vary claim

The frozen Bunch--Davies prescription defines a readout of the cyclic A1 packet, and that readout is zero. This is forced by strict support separation, not by cancellation.

A continuation from the positive Cayley--Menger cycle to the negative-edge A1 support is a different object. The frozen source does not define it. Its map is therefore absent, not zero.

Frozen source

The admitted source data consist of:

• the positive real Cayley--Menger loop-edge cycle;
• loop-edge coordinates (a,b,c\geq0);
• negative imaginary regulators on external and internal energies;
• no source-fixed homotopy or sheeted Leray lift to the A1 points.

At the homogeneous source point write

$$P_i=1-i\epsilon_i, \qquad \epsilon_i>0.$$

The six incident wall forms have real parts

$$\begin{aligned} \operatorname{Re}g_1&=b+c+1, & \operatorname{Re}g_2&=c+a+1, & \operatorname{Re}g_3&=a+b+1,\\ \operatorname{Re}s_{12}&=a+b+2, & \operatorname{Re}s_{23}&=b+c+2, & \operatorname{Re}s_{31}&=c+a+2. \end{aligned}$$

Consequently,

$$\operatorname{Re}g_i\geq1, \qquad \operatorname{Re}s_{ij}\geq2$$

throughout the regulated source cycle. The regulator cone changes no real-part bound.

Readout classification

Each cyclic A1 support requires three corresponding wall forms to vanish. That cannot occur inside the prescribed tube. Therefore the source-cycle costalk map is

$$R_{\rm BD}: \Gamma_{\rm BD} \longrightarrow K^-_{A1,12}\oplus K^-_{A1,31}\oplus K^-_{A1,23}, \qquad R_{\rm BD}=0.$$

This map is defined and zero.

A nonzero map would require all of the following additional data:

1. a labelled continuation from the positive cycle to negative loop-edge support;
2. a sheeted Leray lift across the intervening wall arrangement;
3. orientation and deck transport fixing the odd costalk map.

None is present in the frozen primary construction. The broader continuation map is therefore undefined from the admitted source.

Deutsch–Popperian conclusion

The supported-record conjecture survives algebraically but fails to predict physical activation in this example:

• failed regular extension produces a canonical supported record;
• blowup realizes it geometrically;
• cyclic transport glues it naturally;
• the authorized physical readout annihilates it by support separation.

Thus a supported record and an observable record are distinct typed objects. No new carrier structure is warranted.

Next falsifier

Move to a pre-existing support where the physical source cycle actually has incidence. Test whether failure of a regular operation there produces an exceptional record with a nonzero source readout. Do not continue enlarging the present A1 branch without new source authority.

Evidence

• research/benincasa/checkers/check_shape_a1_source_readout_gate.py;
• research/benincasa/results/shape-a1-source-readout-gate.json;
• frozen contour provenance in research/benincasa/cayley-menger-contour-family-gate.json;
• prior literal-incidence audit in research/benincasa/results/shape-costalk-physical-incidence.json.

Allocator claim: seqclaim-e3229b0696a432399c37e2fb.

View source on GitHub