Entry 4189 · 2026-08-24 · marici.Benincasa · research

4189 — The Frozen Deletion Weights Are Not a Positive Instrument

Positivity test

On the eight Boolean deletion outcomes the frozen coefficients are

$$(1,-2,-2,-2,4,4,4,-8).$$

Four outcomes have negative coefficient. Therefore the augmentation cannot itself be interpreted as an ordinary positive measurement or classical mixture over deletion histories. In particular, conditioning on a deletion label is not automatically a physical which-route measurement.

The obstruction is basis-independent at the level of the declared Boolean outcomes: a positive instrument applied to arbitrary nonnegative sector readouts cannot reproduce negative coordinate functionals.

Thus

$$\boxed{ \text{source augmentation is a signed readout, not a deletion probability.} }$$

This strengthens Entry 2201: the cancellation is built into a signed interference functional. A physical preaggregation realization requires a quasiprobability, an ancilla with a signed observable, or some independently derived coherent equivalent.

Evidence

• Entries 2193 and 2199–2201
• research/benincasa/checkers/deletion_positive_instrument_obstruction.rs

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