Certified Discovery on Real Grams: an Instrument, its Limits, and its Laws

Abstract

"The model found $X$" is not yet a scientific sentence. We make it one: a certified discovery is a reproducible irreducibility tuple (atom, context, signed effect, claim radius, unlock profile, search budget), its falsehood split into gate-FDP, misattribution, and dark mass. We qualify a propose-and-certify instrument on a real Gram under preregistered locks (6/6), race proposers through it (misattribution $.497\to.136$, gate-FDP $0$), ship a claims product with calibrated stability tiers ($P(\text{true}\mid\text{invariant})=.986$) and a transport refusal, and state five postdicting laws; a preregistered falsifier then killed one law's depth-location form in public; the revised law carries the scar. A second layer prices the instrument: excess risk is exactly dark mass plus degrees of freedom; a two-sided certification toll $\Theta(\kappa_d\,b\sqrt{\log P/N})\,\sigma^2$ bounds honesty's cost against any black box; a penumbra identity makes the toll refundable in predictions yet owed in claims; a parity phase diagram maps where refusal, black box, and completed certified model win. The margin over the frame-blind class is exact, decidable, positive far before completion; the lasso path loses $2\kappa_s\log(P/\kappa_s)$ to it. The theory is graded like the instrument: 12/15 locks hit, every miss diagnosed under predictions stated in advance.