What runs 048–060 say together — order holds, magnitude misses; first-order models rank and correlations set values; the seal is the weakest link

What forced this note. The owner asked what the failures say collectively, rather than one at a time. Read together, runs 048–060 (thirteen runs: six confirmed, four falsified, two unanticipated, one withdrawn) show four patterns and one cross-cutting fact. Each is a claim about where to look and how to seal next, and each is testable against the runs that follow.

1. Order holds; magnitude misses. Every sealed prediction about an ordering held: the cut-count order of H, U, V (054), carpet A's placement (055), all eight exponents from one polynomial (058), the ranks of five elliptic curves (057). Nearly every prediction about a value missed: the 0.85 ratio (053), B's bracket (055), the polynomial's values (058), the corrected exponent (059), the square's bias bracket (059), the disc (060). An uncalibrated offset sits under every absolute number: the three-size estimator reads the square 0.01–0.02 low (056, 059), the one-block renormalization reads carpets 0.01–0.07 high (058). Consequence for sealing: seal orders, differences and signs; seal absolute values only after a run has measured the offset they carry.

2. First-order models rank; correlations set the values. The genuine falsifications share one shape. Run 050: the symmetry breaking lives in the frozen core, not in the group action. Run 053: cut size does not set the class; arrangement matters. Run 059: the one-block picture misses the correlation between neighbouring blocks. Run 060: the exponent is a cancellation across the whole zero set, not a few zeros near the fixed point. In each, a local, independent, single-factor model got the ordering and the interactions between parts carried the rest — the composition-defect (commutator) idea of P-047, appearing in two threads before it had a name. Stated as a bet: in this project, the next correction to any first-order model will be a correlation term, and it will change values, not orders.

3. The seal is the weakest link. Of the seven non-confirmed outcomes, at least four trace to the test's specification rather than the hypothesis: 049's grid step exceeded the width it measured; 053's falsifier was set too loose to catch a real gap; 055's bracket was narrower than the instrument resolves (056 measured it); 059 read a slope on the shoulder of the crossing curve. Only 048/050, 053's core claim and 060's disc were hypotheses that were simply wrong. Nothing reviewed a seal before compute. Remedy, adopted with this note (OPS.md, The one rule for runs): a separate agent that has not seen the design reads each seal before compute and answers two questions — can this test fail for a reason other than the hypothesis being wrong, and can it pass without the mechanism being present.

4. A passed clause is not a confirmed idea. Three times (053, 057, 060) a sealed threshold was met while the mechanism behind it was absent: a first-versus-last pair-slope comparison that passed on an oscillation; a share ≥ 0.5 that was really an overshoot above 1. A single threshold stands in for a mechanism and can be satisfied without it. Remedy: seal the mechanism's signature — monotone convergence, a sign pattern, a scaling — rather than one cut-off number.

Cross-cutting: exact objects never failed; estimators did. Minimum-cut counts, the crossing polynomials, the Euler products and the polynomial zeros were computed exactly and were never the source of an error. Every difficulty came from three-size fits, pair slopes and bootstrap brackets. Where the mathematics allows, compute the object exactly and use sampling as the check on it.

What would show this note is wrong. If runs from 061 on keep missing orderings while hitting values, pattern 1 is backwards. If a reviewed seal fails for a specification reason the review should have caught, the remedy in 3 is not enough. If the next first-order correction that works is not a correlation term, pattern 2 is a coincidence of these threads.