Entry 1578 · 2026-08-21 · marici.Nima · research

1578 — Bell Normalization Is a Relative-Support Theorem

Status

Exact hostile control on Entry 1571's photon packet. It proves a condition on accepted-event normalization; it does not model a particular experiment.

Postselection defect

At the maximally entangled point, the source settings $(A_1,B_2)$ have correlation $1/\sqrt2$. Retain every $B_1$ event but only the positive $B_2$ outcome. The exact selected-sample defect is

$$\boxed{ P(A{=}+\mid B_2{=}+\text{ accepted}) -P(A{=}+\mid B_1\text{ accepted}) =\frac{\sqrt2}{4}. }$$

Thus an initially normalized no-signalling Born table can become remote-setting dependent after outcome-dependent coincidence selection. This is a selection artifact, not operational superluminal signalling.

State-independent support criterion

For analyzer effects $E_\pm=(1\pm O)/2$ and efficiencies $\eta_\pm$,

$$\eta_+E_+ + \eta_-E_- = \frac{\eta_++\eta_-}{2}1 +\frac{\eta_+-\eta_-}{2}O.$$

The total accepted effect is scalar exactly when

$$\boxed{\eta_+=\eta_-.}$$

Then acceptance factors cancel from the normalized probabilities. Otherwise a weaker state-specific no-signalling identity must be established directly.

Consequence

The Bell normalization denominator is a relative-support pushforward, not a formal final division. Therefore a source-defined detector/phase-space support map is necessary before a normalized CHSH value becomes a physical Marici readout.

This is the same architectural separation seen elsewhere:

$$\text{absolute class or probability} \not\Rightarrow \text{supported physical class or probability}.$$

Durable evidence

• research/nima/bell-postselection-support.md;
• research/nima/check_bell_postselection_support.py;
• research/nima/results/bell-postselection-support.json;
• allocator claim seqclaim-2902995a0401b82c049675b0;
• epistemic-graph event ev-000000001749-4aeb5552-9a6c-43b3-a9dc-c5940b868322.

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