GARDEN-012 — Brocard

WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Brocard is overlaid on the MuncyNautics frame: the seat names WHERE the problem lives in the frame, the species (S2 — The Address) names WHAT KIND of owe its residual is, the forbidder is the executed witness — maximal disjointness at exploding magnitude; Overholt: abc ⇒ finiteness; three coarse-lattice landings (4, 5, 7), then 10¹⁵ of silence tracking the convergent sum… — and the structured residual states exactly what remains open: the address law + finite-to-exact (record says three) — AND ENTRY 43 SUPPLIES THE HEURISTIC. Brocard has the Fermat structure, not the Mersenne one: the expected number of solutions is Σ P(n!+1 is a square) ≈ Σ 1/√(n!), … 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-012-RERUN-20260830

MN-CERT-GARDEN-012-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED)

GARDEN-012

Brocard

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

S2 — The Address

full census

n! + 1 = m² — the complete registry evicted by the unit, asked to imitate a square

maximal disjointness at exploding magnitude; Overholt: abc ⇒ finiteness; three coarse-lattice landings (4, 5, 7), then 10¹⁵ of silence tracking the convergent sum

n! + 1 = m² — solutions sought by search

the census kept with its convergent expectation: Σ P(n!+1 = □) ≈ Σ n!^{−1/2}, tail beyond n = 7 totals 7.39×10⁻³ — census expected closed at {4, 5, 7}; abc ⇒ finiteness (Overholt)

the address law + finite-to-exact (record says three) — AND ENTRY 43 SUPPLIES THE HEURISTIC. Brocard has the Fermat structure, not the Mersenne one: the expected number of solutions is Σ P(n!+1 is a square) ≈ Σ 1/√(n!), which CONVERGES, and the tail beyond the three known solutions (n = 4, 5, 7) totals 7.3863×10⁻³ from n ≥ 8 and 8.1865×10⁻¹⁰ from n ≥ 20. So the census is expected closed at three with tail probability under 1%. This is the same convergent-expectation argument that closes the Fermat census, arriving at an entry the Codex had filed under a different species — evidence the S1/S2 split is finer than the phenomenon

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