GARDEN-024 — Lehmer

WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Lehmer is overlaid on the MuncyNautics frame: the seat names WHERE the problem lives in the frame, the species (S7 — The Floor) names WHAT KIND of owe its residual is, the forbidder is the executed witness — the minimal excitation IS the Law’s lifted inverse-conjugate pair (Salem); Smyth floors the non-self-paired sector at the plastic number; Dobrowolski prices the crack; no M ∈ (1, 1.17628) ever found… — and the structured residual states exactly what remains open: the self-paired (Salem) floor — the YM mass-gap species at the arithmetic place. AND ENTRY 3 (COLLATZ) IS THE SAME OBJECT WITH THE SIGN REVERSED. Both are log-sum floors: Lehmer needs Σlog|root| bounded away from 0 FROM … 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-024-RERUN-20260830

MN-CERT-GARDEN-024-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED)

GARDEN-024

Lehmer

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

S7 — The Floor

gap

the carrier vacuum (Kronecker: M = 1 ⟺ cyclotomic) and the lifted pair α·1/α

the minimal excitation IS the Law’s lifted inverse-conjugate pair (Salem); Smyth floors the non-self-paired sector at the plastic number; Dobrowolski prices the crack; no M ∈ (1, 1.17628) ever found

M(α) > 1 + δ for non-cyclotomic α? — the measure audited as magnitude

the lifted pair α·1/α kept (Salem = self-paired sector): Kronecker closes M = 1 exactly at cyclotomic; Smyth floors the non-self-paired sector at the plastic number; the owe is a log-sum floor — Σ ln|root| bounded away from 0, the mass-gap species

the self-paired (Salem) floor — the YM mass-gap species at the arithmetic place. AND ENTRY 3 (COLLATZ) IS THE SAME OBJECT WITH THE SIGN REVERSED. Both are log-sum floors: Lehmer needs Σlog|root| bounded away from 0 FROM ABOVE (no measure creeping down to 1), Collatz needs the orbit’s log-drift bounded away from 0 FROM BELOW (no orbit creeping up to non-descent). Measured: the Collatz per-step drift is log3 − 2log2 = −0.143841, a multiplicative analogue of exp(drift) = 0.866025, against Lehmer’s smallest known measure 1.176281 with log 0.162358. The two gaps to zero are 0.143841 and 0.162358, a ratio of 0.885951. HONEST NOTE: that numerical closeness is suggestive, not structural — what IS structural is that both owes read “this log-sum cannot reach zero”, the mass-gap species stated twice with opposite orientation. A floor theorem for either orientation is a floor theorem for the species

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