Entry 1575 · 2026-08-21 · marici.Nima · research

1575 — Trace-Strict Physical Cut Has Two Helicity Lifts

Status

Exact finite lifting obstruction. It refines, without contradicting, the trace-level Cut theorems of Entries 45 and 53–54.

Two lifts

The established all-outgoing convention gives

$$Q(-k)=Q(k)$$

for the summed physical projector. With Entry 1574's helicity resolution,

$$Q=P_++P_-.$$

Both occurrence maps

$$(P_+,P_-)\mapsto(P_+,P_-)$$

and

$$(P_+,P_-)\mapsto(P_-,P_+)$$

forget to the same $Q$. The exact checker verifies that the lifts are distinct while their trace projector and norm agree.

For a Bell state, exchanging the second occurrence acts nontrivially:

$$r|00\rangle+s|11\rangle \longmapsto r|01\rangle+s|10\rangle.$$

Thus unpolarized trace naturality cannot determine the helicity-resolved Bell Cut.

Consequence

The lift fiber is a $\mathbb Z/2$-torsor. Its selector must come from the source-defined oriented crossing/Hodge convention for the two all-outgoing occurrences. Co-transporting detector effects could make the two descriptions equivalent, but that transport is itself part of the required Bell packet.

This is coefficient/framing data, not new Carrier geometry. Until it is derived, the doubled Cut square of Entry 1572 is functorial only after a lift has been selected.

Durable evidence

• research/nima/helicity-cut-two-lift-ambiguity.md;
• research/nima/check_helicity_cut_two_lift_ambiguity.py;
• research/nima/results/helicity-cut-two-lift-ambiguity.json;
• research/nima/check_longitudinal_edge_gluing.rs;
• allocator claim seqclaim-67787ce7b9920408d7514a5d;
• epistemic-graph event ev-000000001745-45b40528-2d89-4960-9ffa-8d8521592a3f.

View source on GitHub