GARDEN-043WITNESS_EXECUTED_EXACTS1
GARDEN-043 · Fermat primes
RERUN FROM EXECUTED OVERLAY RECORD · STANDING WITNESS_EXECUTED_EXACT
| context |
WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Fermat primes 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 rare conjecture asserting a FINITE census rather than an infinite one, which makes it the frame's mirror case: F₅ = 4294967297 = 641 × 6700417 (Euler 1732), and every F_n from 5 to 32 tested is composite with no prime found beyond 65537. The heuristic is the frame's own: the expected number of further Fermat primes… — and the structured residual states exactly what remains open: the exclusion — no proof that any single F_n is composite in general, let alone all. And a caution the Codex should carry: the same convergent-sum heuristic that predicts finiteness here predicts INFINITUDE for Mersenne,… 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. |
|---|---|
| schema |
MN-RECOVERY-CERTIFICATE-1.1 |
| certificate_id |
MN-CERT-GARDEN-043-RERUN-20260830 |
| supersedes |
MN-CERT-GARDEN-043-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED) |
| job_id |
GARDEN-043 |
| title |
Fermat primes |
| author |
Derrick E. Muncy |
| method |
MuncyNautics Seam Recovery Method v1.0 · Overlay Codex executed record |
| source_records |
The Overlay Codex (44 problems) · overlay-data.js (project record) · Overlay Codex, Annals format |
| species |
S1 — The Ceiling |
| overlay_verb |
issue |
| seat (the address the overlay assigns) |
the closed census — F_n = 2^(2ⁿ)+1, with exactly five seats issued (n = 0 to 4: 3, 5, 17, 257, 65537) and the conjecture that no sixth exists |
| forbidder / executed witness |
the rare conjecture asserting a FINITE census rather than an infinite one, which makes it the frame's mirror case: F₅ = 4294967297 = 641 × 6700417 (Euler 1732), and every F_n from 5 to 32 tested is composite with no prime found beyond 65537. The heuristic is the frame's own: the expected number of further Fermat primes is Σ 1/(2ⁿ ln 2) over n ≥ 5, a convergent sum totalling under 0.1 — so the census is expected to be closed, and expectation-of-a-convergent-sum is exactly the Brun structure from entry 41 |
| governing_equation_as_projected (the seam) |
F_n = 2^{2ⁿ} + 1 prime for some n ≥ 5? — audited by search
|
| complete_governing_equation (the repair) |
the closed census kept with its convergent expectation: Σ 1/(2ⁿ ln 2) over n ≥ 5 totals < 0.1 — census expected closed at five seats; F₅ = 641×6700417 (Euler); the heuristic is a lens, not a law (it predicts the OPPOSITE for Mersenne) |
| structured_residual |
the exclusion — no proof that any single F_n is composite in general, let alone all. And a caution the Codex should carry: the same convergent-sum heuristic that predicts finiteness here predicts INFINITUDE for Mersenne, so the heuristic is a lens, not a law |
| correction_rule |
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. |
| phase_retained |
True — seat, verb, and species carried; no bare-magnitude reduction performed |
| precision |
Measured figures in the witness computed cold in double precision on the session record; classification exact (no numeric claim promoted beyond its precision) |
| falsifier |
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 |
| standing |
WITNESS_EXECUTED_EXACT |
| promotion_authority |
YELLOW — the residual is a named open step; no GREEN issued on an open owe |
| honesty_state |
SUPPORTED |
| generated_utc |
2026-08-31T03:05:49.533Z |