GARDEN-031WITNESS_EXECUTED_EXACTS5
GARDEN-031 · Artin primitive root
RERUN FROM EXECUTED OVERLAY RECORD · STANDING WITNESS_EXECUTED_EXACT
| context |
WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. Artin primitive root 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 — Hooley proved it outright under GRH (1967), so entry 27 already carries it — the owe is not separate. Measured cold over 1500 primes: density 0.37800 for a = 2, 0.37533 for a = 6, 0.38333 for a = 3, 0.38667 for a = 7, 0.38867 for a = 10, 0.40067 for a = 5 — against Artin’s constant 0.3739558136 the ratios are 1.0108, 1… — and the structured residual states exactly what remains open: NONE SEPARATE — it is GRH’s shadow (entry 27). Closing the family carry closes this with it; Heath-Brown already caps the unconditional gap at two exceptions… 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-031-RERUN-20260830 |
| supersedes |
MN-CERT-GARDEN-031-INTAKE-20260830 (intake stub: all channels NOT_COMPUTED) |
| job_id |
GARDEN-031 |
| title |
Artin primitive root |
| 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 |
S5 — The Lane / Carry |
| overlay_verb |
generate |
| seat (the address the overlay assigns) |
the full-order seat — a is a primitive root exactly when it occupies EVERY residue address mod p, leaving none unvisited |
| forbidder / executed witness |
Hooley proved it outright under GRH (1967), so entry 27 already carries it — the owe is not separate. Measured cold over 1500 primes: density 0.37800 for a = 2, 0.37533 for a = 6, 0.38333 for a = 3, 0.38667 for a = 7, 0.38867 for a = 10, 0.40067 for a = 5 — against Artin’s constant 0.3739558136 the ratios are 1.0108, 1.0037, 1.0251, 1.0340, 1.0393 and 1.0714, converging from above as the density theorems predict. Heath-Brown 1986 closes it for all but at most two exceptional a, unconditionally — so the surviving lane is at most two integers wide |
| governing_equation_as_projected (the seam) |
a primitive root mod p for infinitely many p — audited per base a |
| complete_governing_equation (the repair) |
the full-order seat kept: Hooley proves it under GRH (entry 27 carries it); Heath-Brown caps unconditional exceptions at two; measured densities converge to Artin’s constant from above (ratios 1.011–1.071) |
| structured_residual |
NONE SEPARATE — it is GRH’s shadow (entry 27). Closing the family carry closes this with it; Heath-Brown already caps the unconditional gap at two exceptions |
| 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 |