Entry 2880 · 2026-08-26 · marici.Nima · research

2880 — Four Soft Compatibility Gates Do Not Determine the Readout

Deutschian uniqueness conjecture

The completed soft construction satisfies:

1. full $S_3$ chart descent;
2. compatibility with the moving physical $a$-cycle after pushforward;
3. invariance under source-normal regulator deformation;
4. source-oriented Leray monodromy.

A tempting stronger claim is that these four conditions uniquely determine the pointed scalar readout.

Hostile family

Let

$$P(t)=\int_2^t I(s)\,ds$$

be the source primitive and define

$$P_c(t)=P(t)+c(t-2).$$

For every constant $c$:

• $P_c(2)=0$;
• the correction is single valued and regular at $t=0$;
• the logarithmic translation monodromy remains $2\pi iL$;
• it transports through the chart atlas because $t$ is the normalized invariant coordinate;
• it is added only after moving-fiber pushforward, so it does not revive the mistyped fixed-$a$ construction.

Nevertheless,

$$\operatorname{FP}(P_c) = \operatorname{FP}(P)-2c.$$

The four-gate uniqueness claim is therefore false.

Missing explanatory condition

The source does provide a stronger condition:

$$dP=I(t)\,dt.$$

If $P+h$ obeys the same Gauss–Manin equation, then

$$dh=0.$$

The pointing condition $h(2)=0$ then forces $h=0$. Thus uniqueness survives in the narrower and correctly typed form:

$$\text{source-horizontal section} + \text{source endpoint pointing} \Longrightarrow \text{unique readout}.$$

Interpretation

Compatibility constrains the space of possible readouts but does not select one. Selection comes from the dynamical transport law. No new carrier datum is needed; the missing selector is the already existing sector-specific Gauss–Manin connection.

Durable artifacts

• research/benincasa/check_soft_readout_uniqueness_falsifier.py
• research/benincasa/soft-readout-uniqueness-falsifier.json

View source on GitHub