GARDEN-023WITNESS_EXECUTED_EXACTS4
GARDEN-023 · Zaremba
RERUN FROM EXECUTED OVERLAY RECORD · STANDING WITNESS_EXECUTED_EXACT
| context |
WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Zaremba is overlaid on the MuncyNautics frame: the seat names WHERE the problem lives in the frame, the species (S4 — The Pointwise) names WHAT KIND of owe its residual is, the forbidder is the executed witness — the tame registry has dimension 0.9839 (nearly full); BK/Huang prove density one; an orphan census is permanent silence against growing covering multiplicity… — and the structured residual states exactly what remains open: pointwise discharge: density one → every q. AND ENTRY 9 (LONELY RUNNER) IS THE SAME BOUND IN A DIFFERENT LATTICE. Lonely Runner guarantees a gap ≥ 1/(n+1) for n runners; Zaremba guarantees |x − p/q| ≥ 1/((K+2)q²) for par… 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-023-RERUN-20260830 |
| supersedes |
MN-CERT-GARDEN-023-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED) |
| job_id |
GARDEN-023 |
| title |
Zaremba |
| 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 |
S4 — The Pointwise |
| overlay_verb |
ladder |
| seat (the address the overlay assigns) |
the bounded reciprocal ladder A = 5 — the Gauss map is A5’s arm run as dynamics |
| forbidder / executed witness |
the tame registry has dimension 0.9839 (nearly full); BK/Huang prove density one; an orphan census is permanent silence against growing covering multiplicity |
| governing_equation_as_projected (the seam) |
∀q ∃p/q with partial quotients ≤ 5 — audited per denominator |
| complete_governing_equation (the repair) |
the bounded reciprocal ladder kept as A5’s arm run as dynamics (Gauss map): tame registry dimension 0.9839, BK/Huang density one; |x − p/q| ≥ 1/((K+2)q²) — the Lonely-Runner bound in the continued-fraction lattice |
| structured_residual |
pointwise discharge: density one → every q. AND ENTRY 9 (LONELY RUNNER) IS THE SAME BOUND IN A DIFFERENT LATTICE. Lonely Runner guarantees a gap ≥ 1/(n+1) for n runners; Zaremba guarantees |x − p/q| ≥ 1/((K+2)q²) for partial quotients bounded by K. Same form — one over a count, plus a constant — with Lonely Runner counting RUNNERS and Zaremba counting PARTIAL QUOTIENTS. Verified cold at q ≤ 8: √3 has K = 2, bound 3.906×10⁻³, measured 0.017765; φ has K = 1, bound 5.208×10⁻³, measured 0.006966; √2 has K = 2, bound 3.906×10⁻³, measured 0.014214; π has K = 292, bound 5.315×10⁻⁵, measured 0.001264 — the bound holds in every case, and π’s huge quotient is exactly why it is a poor detuning target. So A ZAREMBA-GOOD NUMBER IS A LONELY RUNNER IN THE CONTINUED-FRACTION LATTICE: bounded quotients is bounded runner count is a guaranteed gap. The two entries share one discharge |
| 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 |