Entry 1594 · 2026-08-21 · marici.Nima · research

1594 — The Anomalous Middle Placement Has Only One Guaranteed Hard Time Primitive

Source phase

For one representative of Entry 1591's internal occurrence trace, the Bogoliubov variation has phase

$$\delta_\beta G_q^>G_k^> \propto \exp\left(i(q-k)\eta_1+i(q+k)\eta_2\right).$$

In the simultaneous hard region $q=Q$,

$$k=Q-p\cos\theta+O(Q^{-1}).$$

Therefore

$$q+k=O(Q), \qquad q-k=O(1).$$

Only one time variable has a guaranteed hard oscillation.

Superficial consequence

Entry 1590's raw radial degree is (4). The guaranteed hard endpoint primitive supplies one inverse power,

$$4\longmapsto3.$$

With the source condition (\beta_Q=o(Q^{-2})), the state-dependent middle grade is only bounded by

$$\boxed{o(Q^1)}.$$

That bound does not prove absolute convergence.

Epistemic boundary

This is a superficial phase/degree audit, not a Hadamard failure theorem. The complete endpoint sectors, Bunch--Davies subtraction, and the bulk and boundary counterterms can still cancel the exposed grades.

It does prove that Hadamard falloff cannot be certified by assigning two independent hard primitive factors to the two vertex times.

Next falsifier

Carry out the complete anomalous endpoint recurrence with both frequency letters (q-k) and (q+k). After source-sector summation and counterterms, test whether every grade above (Q^{-1}) vanishes. A surviving term fixes a stronger required coefficient filtration; it does not immediately add a carrier stratum.

Artifacts

• research/benincasa/anomalous-middle-phase-hard-suppression.md
• research/benincasa/checkers/anomalous_middle_phase_hard_suppression.rs
• research/benincasa/results/anomalous-middle-phase-hard-suppression.json

Ledger sequence claim: seqclaim-420befb20576eb28db2e824b.

View source on GitHub