You find a better result. Four measures improve, the required safety margin holds, and the calculations check out. Should the previous candidate disappear from your shortlist?
In our experiment, keeping it was the right decision. The new candidate used a more complicated waveform and had a higher peak. Whether it was preferable depended on which constraints the next stage of the research would impose.
8DB, our omnimodal database, retained both candidates with their exact parameters, evidence and relationships. Its native lattice operations let us compare them under different sets of requirements. The result was a more useful answer than one overall score: this candidate improves the four targeted bounds; that one remains an alternative when peak and complexity also matter.
One small problem, examined closely
The experiment studied six oscillatory loop shapes at one fixed reference profile, motivated by a component of a forced Navier–Stokes construction. A loop had to preserve specified averages and satisfy a common margin of 0.1. Its shape also affected mathematical bounds used to assess the construction.
Think of these as several engineering constraints on the same design. A reduction in one bound can be useful, but it does not automatically improve every later stage.
Our reference waveform combined a sine with a third harmonic at ratio 1/9. A candidate adding a signed fifth harmonic retained the target margin and improved all four targeted bounds:
| Mathematical quantity | Change from the 1/9 reference |
|---|---|
| First inverse-phase shear derivative bound | About 6.79% lower |
| Second inverse-phase shear derivative bound | About 13.12% lower |
| Normalized B-primitive bound | About 0.10% lower |
| Normalized A-primitive bound | At least 1.138% lower |
| Squared peak amplitude | About 1.65–2.11% higher |
| Nonzero harmonics | Three instead of two |
These are mathematical bounds for matched fixed-profile candidates, rather than runtime or database-throughput measurements. Both candidates meet the same margin requirement. The final two rows explain why the earlier shape remains relevant: a later stage may place tighter limits on peak amplitude or prefer the simpler waveform.
Signed fifth-harmonic candidate versus the 1/9 reference at the same fixed profile and margin 0.1. Marks show certified ratio intervals; some are narrower than a pixel. Harmonic count is exactly 3 versus 2. This is a comparison of mathematical quantities, not throughput.
Four-bound comparison: the reference is dominated. Include peak and harmonic count: both remain alternatives.
Change the question without losing the evidence
A frontier is the set of candidates that remain unbeaten across the measures you have selected. One candidate can remove another from that frontier only when it is at least as good on every selected measure and better on at least one.
In this experiment, 8DB uses conservative comparisons between certified intervals. Overlapping bounds remain incomparable. The system does not invent an improvement from rounding.
With the four targeted bounds selected, the fifth-harmonic candidate removes the 1/9 reference from the frontier. Add peak and harmonic count, and the reference returns. Its evidence has stayed in the store throughout; changing the decision criteria changes the comparison.
The implementation connects several native capabilities. A stored GeoQL parameter chart orders the six declared candidates for evaluation. Interval and polynomial checks establish the numerical bounds. Lattice operations compute the competing frontiers. Typed links connect the completed experiments to their original plans and source records.
Each mechanism has a specific job. The geometric ordering schedules work; it does not certify the mathematics or prove that the chosen order is optimal.
Make the comparison checkable
Interval analysis supplies a way to reason with enclosing bounds rather than treating a rounded estimate as an exact answer. Here, polynomial certificates cover the declared phase domain, so a sampled plot is not the source of the upper bounds.
A separate exact-rational checker reconstructs the calculations from the rational waveform coefficients. On September 18, we reran that checker against the retained result: all six candidates passed, covering 968 scalar enclosures and 54 complete cells. It also rejected all 37 deliberately altered inputs in its finite test suite, including changes to coefficients, coverage and frontier membership.
That rerun checks the exported mathematics and comparison records. The historical native integration test separately exercised persistence and reopening. Neither check establishes an improved full Navier–Stokes proof. The next research step is to determine whether the local gains remain useful when parameter variation and the larger construction's remaining conditions are included.
Keep what the next decision may need
The practical value is continuity. A result, its conditions, the alternatives and the next question can remain connected as the investigation changes direction.
An investigation budget is another reason to preserve useful alternatives. Once measured, preparation time, memory and total computation cost can sit beside answer quality in the decision. A more elaborate result may be worthwhile; retaining a simpler adequate option keeps that choice visible.
This complements our work on tracking conclusions when evidence changes and retaining research across experiments. Here, the question is which alternatives should remain available before a final decision has been made.
If your team compares designs across several constraints, bring us one decision and the measures that matter. We can explore how to preserve the candidates, their evidence and the conditions that change your shortlist. Contact 8Braid.
Method scope: six declared waveforms at a fixed ideal profile, with exact rational parameters and whole-phase certificates. The 37 rejection tests are a finite control suite, not a general security guarantee. Numerical certificates and source associations do not confer Lean or Comparator proof status on this experiment.
Evidence scope Fixed-profile certified bounds · Exact-rational audit rerun September 18 · Native lattice comparison. Explore the evidence.
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