What held, and what we killed
Approved is not governed. A claim counts here only when its artifact says so, and the losses get the same type size as the wins. Every figure below is rendered from a committed JSON file at build time.
Held up (2, and 0 with no gain)
Shu-Osher shock: log-derivative limiter sensor vs the best classical limiter (superbee)
+6.30% / +6.39% / +23.58% L2
Held-out runs (shift 10, shift 100, nx 800) at the threshold 5 tuned on the base case, where it scored +6.32%.
cfd_nnc_comprehensive.jsonLane-Emden n=3 solved in log space
7.7x fewer evals, 30x smaller error
Part of the step reduction comes from a max_step cap on the classical run.
tractability_benchmarks.json
Killed by our own runs (8)
Sod shock tube: the same limiter sensor
-26.13% L2 vs superbee
Best sensor setting L2 0.01180 against superbee 0.00935, after the exact solution gained its rarefaction fan. Reported, not hidden.
cfd_nnc_comprehensive.jsonBessel J0 in log space is more accurate
0.10x accuracy ratio
Below 1: the log-space run was less accurate.
tractability_benchmarks.jsonMixing schemes never lowers the spectral gap below the weakest one
9 counterexamples in 88 valid cases
Status in the artifact: REFUTED.
spectral_gap_boundary_moo.jsonCASCADE wins across many physics domains
10 "1/r" cases, 2 distinct outcomes
A synthetic toy benchmark: one 2-D problem relabelled per domain. Not citable.
cascade_21_simulation_results.jsonEvery Pareto solution beats Van Leer on the Sod tube
10 of 30 dominate
Optimizer: pymoo NSGA-II. GlobalMOO was not connected for this run.
shock_tube_dual_moo.jsonMeta-derivative schemes preserve Lorenz chaos
k = 0.3 collapses to a fixed point
The attractor is destroyed, not preserved.
chaos_corrected.jsonA unitary region in the quantum phase scan
0 of 1000 runs unitary
Norm drift never reached the unitarity tolerance in the historical nonunitary blend model (revision e06aaa4).
quantum_phase_corrected.jsonMeta-BDF handles stiff Robertson kinetics
4 of 5 Meta-BDF runs wrong
Max error above 0.1 for every k > 0; only k = 0, the classical limit, and plain BDF/LSODA are right.
robertson_stiff_ode.json
The CASCADE suite is a synthetic toy benchmark: one 2-D objective family relabelled per domain, scored by distance to the centre, which is not the singular point for every profile. The full table renders from its stored artifact. Each result names the optimizer that ran: mostly pymoo NSGA-II, with one historical GlobalMOO comparison (equal total budgets not verified) on the synergy page.
Every null, negative and retracted result
Kept on the site, in full, with the run that decided it. One line each, taken from the page.
Inconclusive
Cosmology grid test (H0/S8)
No configuration met the resolution criterion, but the sweep covered only part of its k range and used an H0 criterion no single H0 value can meet. It neither supports nor rules out the model.
/proof/negative-results
Control failed
k(L) scaling trend
In the synthetic 8-scale NSGA-II model, giving every scale the same admissible k range lowers the fit from R^2 = 0.7096 to R^2 = 0.4370, and the model's own linear-pattern test fails. The archived formula is not a validated physical lookup rule. (Formerly /cascade/k-lookup, which now redirects here.)
/results/multiscale
Retired
k(L) calculator
The former calculator extrapolated an eight-point synthetic fit to arbitrary problems, and a fresh common-bounds control fails it. The page now explains the retirement; the fit stays in the Python API for compatibility, marked as an unvalidated physical lookup.
/tools/calculator
Not physics results
CASCADE synthetic toy benchmark
One 2-D toy problem per profile, relabelled with domain names and scored by distance to the centre, which is the singular point only for some profiles. No physics model from those domains is evaluated.
/results/cascade
Negative
Chaos test: Lorenz attractor
No meta-calculus scheme in the stored run preserves chaos. The best-looking one, meta-0.3, settles on a fixed point of the Lorenz system.
/demos/chaos
Retracted
Consumer hardware benchmark
The earlier page presented a prescribed timestep as a discovered speedup. The script chooses that timestep in advance, so the step-count reduction is true by construction. It does not establish equal accuracy, stability or HPC equivalence.
/demos/consumer-hardware
Reclassified
GUD benchmark claims
The tracked artifact numerically checks bigeometric power-law identities and stores values from the archived k(L) formula. It contains no controlled speed benchmark and no independent physical-scale validation.
/proof/gud-benchmarks
Elementary
MOO invariance under NNC transforms
A Pareto front is unchanged exactly when each objective is mapped by a strictly increasing function. On strictly positive objectives, f^k qualifies only for k > 0; for k < 0 it reverses every dominance relation. An elementary order-theory fact, not a property specific to non-Newtonian calculus.
/theory/moo-invariance
Mixed outcomes
MOO-first experiments
Each experiment with its outcome: a tie, a correction, a failed control, a negative, a refutation, an invalid run and an inconclusive one.
/results/experiments
Failures
Failures and pivots
Claims that failed validation and the lessons learned, placed on the 12-year timeline.
/learn/lessons
Archive
Research archive
What was overclaimed, what the data actually shows, and what we learned.
/research/archive
Not supported under equal budgets
GlobalMOO June headline (99.4% lower chi-squared)
In the June 2026 run the two optimizers' budgets were not verified equal, and their objectives and scoring differed. A preregistered rerun at equal measured budgets (10 pairs x 200 evaluations, on the June problem with its optimum moved off the box centre) read inconclusive, Wilcoxon p = 0.105.
/globalmoo
Not established
Chart selection T1: is the chart effect real?
A chart effect on held-out HV is supported only for the log chart on problem a, and it is small (+0.000345, 0.84% of raw, Holm p 0.0365). The negative control is too imprecise to rule out a generic chart effect of that size, and "chart choice matters more than optimizer choice" is not established.
/research/chart-selection#t1
Not affordable
Chart selection T2: a pilot-based chart picker
The measured picker is reproducible, where CASCADE Phase A is not, but what it mostly picks is a domain restriction, not a chart. It is not affordable at this budget (427-607 evaluations against a 300-evaluation main run), and harmlessness is not established.
/research/chart-selection#t2
Inconclusive
Chart selection T3: aligned coordinate vs restricted domain
The only effect supported by the preregistered rule is the domain restriction on problem a (+0.000471, 1.14% of LF, Holm p 0.010). The stability-aligned coordinate is inconclusive on a and leans worse on b; a coordinate contribution is neither shown nor excluded.
/research/chart-selection#t3
Inconclusive
Chart selection T4: four more coordinate shapes
Across a power map, a piecewise-linear map, a Hermite map with the knot at u = 0.8 and a logistic map in log h, no stability-aligned coordinate on the full domain gave a detectable held-out HV gain at 20 seeds: 0 of 8 comparisons is a real effect, and none is excluded at the 1% margin. The coordinate effects are inconclusive, not excluded.
/research/chart-selection#t4
No effect
Chart selection T5: a zero-evaluation picker, tested prospectively
The picker costs 0 objective evaluations for its decision and almost always picks LR, the stability-restricted domain, wherever the problem has a limit. On the new problem d, LR - raw on held-out HV was "no effect" by the preregistered rule (median -0.00029, CI inside +-1% of raw, p 0.43). The rule tells which arm makes every step stable, not whether the restriction will help held-out HV.
/research/chart-selection#t5
Marginal
Chart selection T6: more seeds for the restriction
On 50 new optimizer seeds (21-70) with the same fixed datasets, the held-out gain on a is a real effect by the preregistered rule, but only barely: Holm p 0.0447, +0.000214 (0.52% of LF), and the bootstrap CI of the median difference includes 0. b and d are inconclusive.
/research/chart-selection#t6
No real effect
Chart selection T7: three new graph problems
On three new graph families, restricting h to [h_min, 0.98 h*(s)] showed no real effect on held-out HV at 300 evaluations: no effect on e, inconclusive on f and g. Across the six problems in the series, the held-out benefit is real only on a, and the unstable share does not order the effects (Spearman rho 0.086, n = 6, descriptive).
/research/chart-selection#t7
The checks that passed, with their controls, are in Proof and Results.