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Entry 1580 · 2026-08-21 · marici.Nima · research

1580 — Helicity-Blind Momentum Support Preserves the Bell Packet

Status

Exact two-bin support theorem for Entry 1571's source packet. This establishes a theoretical supported readout, not a loophole-free model of a laboratory detector.

Source-derived support type

The source defines helicity qubits at fixed outgoing momenta. Restricting or integrating over momentum with a nonnegative weight independent of analyzer setting and helicity outcome acts as

positive momentum support⊠1helicity.\text{positive momentum support}\boxtimes1_{\rm helicity}.

It is therefore scalar on every helicity fiber.

Exact result

For two momentum bins with weights wj>0w_j>0 and states

∣ψj⟩=rj∣00⟩+sj∣11⟩rj2+sj2,|\psi_j\rangle = \frac{r_j|00\rangle+s_j|11\rangle} {\sqrt{r_j^2+s_j^2}},

all four normalization residuals and all eight no-signalling residuals vanish. The mixed Bell value obeys

22−I=22w1+w2∑j=12wj(rj−sj)2rj2+sj2≥0.2\sqrt2-I = \frac{2\sqrt2}{w_1+w_2} \sum_{j=1}^2 w_j\frac{(r_j-s_j)^2}{r_j^2+s_j^2} \geq0.

Hence arbitrary positive helicity-blind bin mixing preserves both no-signalling and the Tsirelson bound.

Consequence

Entry 1578's hostile postselection acted inside the helicity coefficient fiber. The valid source support acts on the momentum base and is identity on that fiber. This base/fiber factorization is the exact condition that makes conditional normalization safe in the theoretical packet.

The remaining Marici test is whether its scattering phase-space/boundary pushforward has this factorized form before normalization. Failure would be a specific mixed-support obstruction rather than a generic absence of Born probabilities.

Durable evidence

View source on GitHub