GARDEN-035WITNESS_EXECUTED_EXACTS3
GARDEN-035 · Hilbert’s Tenth over ℚ
RERUN FROM EXECUTED OVERLAY RECORD · STANDING WITNESS_EXECUTED_EXACT
| context |
WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Hilbert’s Tenth over ℚ is overlaid on the MuncyNautics frame: the seat names WHERE the problem lives in the frame, the species (S3 — The Span) names WHAT KIND of owe its residual is, the forbidder is the executed witness — Matiyasevich–Robinson–Davis–Putnam settled it over ℤ (undecidable, 1970), and the rational case remains open in the opposite direction from most conjectures here — a NEGATIVE answer is expected. Koenigsmann 2010 showed ℤ is universally definable in ℚ, which brings the rational case within one quantifier of the integer … — and the structured residual states exactly what remains open: the definability step — whether ℤ is DIOPHANTINE in ℚ (existentially definable), not merely universally. This is the one entry in the Codex where MN predicts the conjecture FAILS, and says so… 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-035-RERUN-20260830 |
| supersedes |
MN-CERT-GARDEN-035-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED) |
| job_id |
GARDEN-035 |
| title |
Hilbert’s Tenth over ℚ |
| 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 |
S3 — The Span |
| overlay_verb |
decide |
| seat (the address the overlay assigns) |
the rational base again — whether Diophantine solvability over ℚ is decidable; the frame’s issuing rule asks whether every address can be ADJUDICATED, not merely issued |
| forbidder / executed witness |
Matiyasevich–Robinson–Davis–Putnam settled it over ℤ (undecidable, 1970), and the rational case remains open in the opposite direction from most conjectures here — a NEGATIVE answer is expected. Koenigsmann 2010 showed ℤ is universally definable in ℚ, which brings the rational case within one quantifier of the integer case. The frame reads this as a boundary marker rather than a target: an undecidable register is one where the books cannot be audited in finite time, which the Law permits |
| governing_equation_as_projected (the seam) |
a decision procedure for Diophantine solvability over ℚ — sought |
| complete_governing_equation (the repair) |
the adjudication register kept: MRDP closes ℤ (undecidable); Koenigsmann puts ℤ universally definable in ℚ — one quantifier from the integer case; MN reads an undecidable register as a lawful boundary and PREDICTS THE CONJECTURE FAILS (the one such entry) |
| structured_residual |
the definability step — whether ℤ is DIOPHANTINE in ℚ (existentially definable), not merely universally. This is the one entry in the Codex where MN predicts the conjecture FAILS, and says so |
| 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 |