GARDEN-008 — Erdős–Straus

WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Erdős–Straus is overlaid on the MuncyNautics frame: the seat names WHERE the problem lives in the frame, the species (S5 — The Lane / Carry) names WHAT KIND of owe its residual is, the forbidder is the executed witness — the paid lanes are the return schedule (periodic, permanent); the escapee must dodge every schedule at every modulus — density thinner than any power… — and the structured residual states exactly what remains open: the last lane: primes ≡ 1 (mod 24) — AND ENTRY 42 IDENTIFIES ITS SHAPE. The known identities cover residues 5, 7, 11, 13, 17, 19 and 23 mod 24, so the survivors are exactly the class {1}: seven of the eight reduced class… 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-008-RERUN-20260830

MN-CERT-GARDEN-008-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED)

GARDEN-008

Erdős–Straus

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

S5 — The Lane / Carry

reciprocate

4/n paid in three coenergy entries (unit fractions = the reciprocal register)

the paid lanes are the return schedule (periodic, permanent); the escapee must dodge every schedule at every modulus — density thinner than any power

4/n = 1/x + 1/y + 1/z — existence audited per n

the reciprocal register kept: 4/n paid in three coenergy entries on periodic return schedules per modulus; survivors exactly primes ≡ 1 (mod 24) — a covering system ONE class short (Σ1/ord = 1.361111 measured on the closed Sierpiński cover to copy)

the last lane: primes ≡ 1 (mod 24) — AND ENTRY 42 IDENTIFIES ITS SHAPE. The known identities cover residues 5, 7, 11, 13, 17, 19 and 23 mod 24, so the survivors are exactly the class {1}: seven of the eight reduced classes tiled, a deficit of exactly 1/8. That is A COVERING SYSTEM ONE CLASS SHORT — structurally the same object as Sierpiński’s, where the covering CLOSES and thereby forces compositeness. So the owe is not “find a proof” but “close a covering”, and entry 42 exhibits a closed one to copy, with tiling condition Σ1/ord ≥ 1 measured at 1.361111. What Erdős–Straus lacks is the eighth generator, not the method

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