GARDEN-006 — Odd perfect

WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Odd perfect is overlaid on the MuncyNautics frame: the seat names WHERE the problem lives in the frame, the species (S6 — The Positivity) names WHAT KIND of owe its residual is, the forbidder is the executed witness — even perfects hold the address (Euclid–Euler = the honest pairing); an odd candidate is a forgery squeezed between rich census (≥10 addresses) and rigid Euler seam. THE EULER SHAPE IS THE FRAME’S OWN ASYMMETRY CLAUSE: any odd perfect N = p^a·m² with p ≡ a ≡ 1 (mod 4), so exactly ONE unpaired prime seat must carry the e… — and the structured residual states exactly what remains open: the span exclusion: the odd lattice misses the even seat — equivalently, the single unpaired Euler seat cannot balance a square. Species S6 because the missing step IS a positivity statement — and that is precisely why t… 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-006-RERUN-20260830

MN-CERT-GARDEN-006-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED)

GARDEN-006

Odd perfect

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

S6 — The Positivity

forbid

abundancy 2 — closure at the even prime’s own seat

even perfects hold the address (Euclid–Euler = the honest pairing); an odd candidate is a forgery squeezed between rich census (≥10 addresses) and rigid Euler seam. THE EULER SHAPE IS THE FRAME’S OWN ASYMMETRY CLAUSE: any odd perfect N = p^a·m² with p ≡ a ≡ 1 (mod 4), so exactly ONE unpaired prime seat must carry the entire closure while every other sits in a conjugate pair — and that single seat is precisely what cannot balance a square. Measured over odd n < 400,000 the closest approach from below is n = 33705 at σ(n)/n = 1.999465955, a deficiency of 5.3405×10⁻⁴: near-misses accumulate, the value is never attained. Ochem–Rao floor any candidate above 10¹⁵⁰⁰ with ≥101 prime factors counted with multiplicity

σ(n)/n = 2 sought among odd n — a magnitude equation

Euler’s shape kept as the frame’s asymmetry clause: N = p^a m², p ≡ a ≡ 1 (mod 4) — ONE unpaired prime seat must carry the whole closure against a square; measured closest approach 1.999465955 (deficiency 5.34×10⁻⁴), the value never attained

the span exclusion: the odd lattice misses the even seat — equivalently, the single unpaired Euler seat cannot balance a square. Species S6 because the missing step IS a positivity statement — and that is precisely why this entry sits in the paid bucket rather than an owing one: the positivity completion is part of the executed statement, so naming the step names the payment, not a further debt

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