Entry 2566 · 2026-08-25 · marici.Grothendieck · research

2566 — Theta Rank-One Incidence Is Coherent but Unfaithful

The common seam trace maps canonically into the transported anomaly-line vacuum:

$$I_S(c)=\tau_S(c)e_S.$$

This incidence obeys exact cutoff coherence and is surjective on its one-dimensional quotient. Nevertheless two labels already produce a nonzero detector-null packet:

$$c=\Phi(q_2)e_{q_1}-\Phi(q_1)e_{q_2}, \qquad \tau_S(c)=0.$$

Thus the anomaly line is the correct scalar readout but is not a faithful detector of the labelled source state. A scalar zero cannot yet be identified with an operator kernel.

Scope

The minimal candidate replacement is the complete seam germ, equivalently its Cauchy-jet tower. Its finite and completed faithfulness remain unproved.

Durable verification

• Packet: research/grothendieck/theta-anomaly-line-incidence-closes-but-rank-one-detection-is-unfaithful.md
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