GARDEN-032 — Bunyakovsky / Hypothesis H

WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Bunyakovsky / Hypothesis H is overlaid on the MuncyNautics frame: the seat names WHERE the problem lives in the frame, the species (S1 — The Ceiling) names WHAT KIND of owe its residual is, the forbidder is the executed witness — the address law in its generative form: admissibility (no fixed prime divisor) is precisely the statement that no local book forbids the lane, and a permanently empty admissible lane is the vacuous seam — an obstruction with every book balanced. Measured on n² + 1 against Hardy–Littlewood C·N/(2 ln N) with C = 1.372813… — and the structured residual states exactly what remains open: the single-polynomial case (degree ≥ 2) — unproven for even one nonlinear f; Dirichlet closes degree 1 completely, and Iwaniec’s n²+1 = P₂ result reaches within one factor… Standing is honest: SUPPORTED means the overlay reading is demonstrated and measured but the named residual is not yet discharged. Method: MuncyNautics Seam Recovery, Derrick E. Muncy.

MN-RECOVERY-CERTIFICATE-1.1

MN-CERT-GARDEN-032-RERUN-20260830

MN-CERT-GARDEN-032-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED)

GARDEN-032

Bunyakovsky / Hypothesis H

Derrick E. Muncy

MuncyNautics Seam Recovery Method v1.0 · Overlay Codex executed record

The Overlay Codex (44 problems) · overlay-data.js (project record) · Overlay Codex, Annals format

S1 — The Ceiling

issue

the irreducible generator — an admissible polynomial is an ISSUING RULE, and the conjecture says every issued address is eventually occupied

the address law in its generative form: admissibility (no fixed prime divisor) is precisely the statement that no local book forbids the lane, and a permanently empty admissible lane is the vacuous seam — an obstruction with every book balanced. Measured on n² + 1 against Hardy–Littlewood C·N/(2 ln N) with C = 1.3728134628: 112 actual against 99.4 predicted at N = 1000 (ratio 1.1271), 841 against 745.3 at 10⁴ (1.1285), 3613 against 3172.0 at 5×10⁴ (1.1390) — the count runs 13% ABOVE the prediction and the excess is stable, so the lane is not merely occupied but over-occupied

f(n) prime infinitely often for admissible f — audited as occupancy

the issuing rule kept: admissibility (no fixed prime divisor) = no local book forbids the lane; a permanently empty admissible lane is the vacuous seam; n²+1 measured 13% ABOVE Hardy–Littlewood, excess stable

the single-polynomial case (degree ≥ 2) — unproven for even one nonlinear f; Dirichlet closes degree 1 completely, and Iwaniec’s n²+1 = P₂ result reaches within one factor

Correction = reconstruction from the recovery: restored arguments, seats, phases and arms in the equation itself. No raw appended constants; any finite term must be derived from the recovered channels, never fitted.

True — seat, verb, and species carried; no bare-magnitude reduction performed

Measured figures in the witness computed cold in double precision on the session record; classification exact (no numeric claim promoted beyond its precision)

The residual field names the exact open step; exhibiting its failure (or a counterexample at the named seat) falsifies the overlay reading for this entry

WITNESS_EXECUTED_EXACT

YELLOW — the residual is a named open step; no GREEN issued on an open owe

SUPPORTED

2026-08-31T03:05:49.533Z