Protocol
A completion that cannot be squeezed is commentary. The test is conditional narrowing in systems whose remainder is partly readable. The papers order six empirical steps; this bench occupies the first four of Rank 1, in a fully specified analog. Shields 2026a, §7.
From analog to field. Nuclei are not required, and claiming an exact uranium instant tomorrow would be fraud: S_⊥ is not readable there.
First crossing of a specified surface or functional. Do not shop among POVMs until the ontology is fixed.
This bench. Event is the first passage of the crest coordinate q through q_exit = 1.35. No fitted rate, no collapse, no extra observable.
Open related viewUse a system whose background can be diagnosed: an optical trap with a controlled noise floor, a Josephson washboard with a characterized drive, a false-vacuum analog in a condensate, an attosecond barrier in a measured field.
This bench. Here the analog is numerical and fully characterized: biased well plus eight Fourier modes with definite phases. Given (q(0), p(0), {θ_k}), the ODE returns exactly one first-exit time, or none within cutoff.
Open related viewAn unstructured average over the remainder yields a waiting-time law whose rate is set by barrier data. This is the statistical-mechanics analogy made calculable.
This bench. Phases drawn uniformly on the 8-torus. 120 complete individuals, 120 exits. Mean T* ≈ 17.85, std ≈ 10.91. An exponential with the same mean is a guide, not a fitted law. KS against that exponential is poor, and that is allowed.
Open related viewMeasure a slice of S_⊥. Predict an interval I for T*. Increase the measured slice. I must shrink. If it does not, Rank 1 is wrong for that analog.
This bench. Hold one true individual. Reveal the first m phases; resample the rest. Var(T*) falls 77.15 → 0 as m goes 0 → 8. Mean absolute error against the true instant falls with it. A dummy 8-vector that never enters the ODE does not collapse. This is Axiom A6, the kill test.
Open related viewThe mark is written in the same field. No collapse. No external apparatus. The same ontology on both sides of the ‘measurement.’
This bench. Not computed here. The intended lift is the nonlinear wave equation of paper §6. The present drive is put in by hand; in a finished theory it must be the same field.
Open related viewOnly then ask whether two distant lumps can inherit correlated remainders from a common preparation without a nonlocal term in the field equation. That is Einstein’s hard problem. It is not the entrance examination.
This bench. Not posed. Contact with already catalogued quantum statistics is a graduation constraint, not an entrance examination written in Bell’s variables.
Open related viewHow the numbers on the bench were produced. Every constant is on Math; every pass rule is on Verify.
Step 1
S_coarse is the well, the mass, the initial (q, p), and the amplitude spectrum. S_⊥ is the eight-vector of Fourier phases θ_k ∈ [0, 2π).
Step 2
Classical RK4, Δt = 0.003, t_max = 90. No Langevin term, no random kick in the law. The only numbers that ever look random are unread phases sampled as a model of laboratory ignorance.
Step 3
T* = inf { t > 0 : q(t) ≥ 1.35 }, linearly interpolated inside the RK4 step that first crosses. If the crest never exits before cutoff, the run is a non-event. The frozen true individual exits at T* = 21.139786.
Step 4
H1 repeatability, H2 individuality, H3 statistical shadow, H4 conditional narrowing, H5 dummy control, H6 noisy readout. Pass criteria are listed on Verify and are not adjusted after seeing the numbers.
Step 5
Frozen JSON is the companion run (40 draws per m on A6). This bench re-implements the same ODE in the browser. Anyone can recompute the true T* and re-run A6 live.
The paper’s three required behaviors — individual T*, statistical shadow, variance collapse — plus two controls. Pass criteria were fixed before scoring.
| Test | Axiom | What is done | Pass / fail |
|---|---|---|---|
H1 Repeatability 2026a §5.1 | A2 | Integrate the same complete phase vector eight times. The law has no primitive chance, so the eight T* values must be identical up to floating-point identity. | Spread of the eight T* values is 0. Any integrator noise, hidden RNG, or stochastic term in the ODE. |
H2 Individuality 2026a §5.2 | A1, A4 | Draw 120 independent phase vectors uniformly on the 8-torus. Keep the well and amplitude spectrum fixed. Each complete remainder must move T*. | Distinct remainders produce a spread of T* (unique ratio 1; std > 0). All remainders collapse to one instant — the unread structure would not be doing any work. |
H3 Statistical shadow 2026a §5.3 | A5 | Histogram the unread ensemble. Overlay an exponential with the same mean as a guide, not a fitted law. Compute a KS statistic against that exponential only as a diagnostic. | Unread phases spread T*. Exponential shape is not required. KS p is allowed to be small. Only if unread phases do not spread T*. A poor exponential fit is not a failure. |
H4 Conditional narrowing 2026a §5.4 | A6 | Hold one true individual. For m = 0…8, treat the first m phases as known and resample the remaining 8−m uniformly. Forty independent draws per m in the frozen run. Record Var(T*) and mean absolute error against the true instant. | Var(T*) at m = 8 is strictly below Var(T*) at m = 0, and the curve falls toward the true instant. Reading more of the true remainder does not shrink the uncertainty. That kills Rank 1 for this analog. |
H5 Dummy control 2026a §5.4 | A6 control | Repeat the narrowing protocol against an 8-vector that is never fed to the ODE. Same sample sizes. The dummy is a readout of nothing. | Dummy variance does not collapse as m goes 0 → 8. Any generic ‘more numbers ⇒ tighter T*’ curve. Narrowing would then be an artifact of the plot, not of S_⊥. |
H6 Noisy readout 2026a §7 | diagnostic cost | Add Gaussian noise of width σ to the measured phases of the true individual. Predict T* from the dirty readout. Mean absolute error against the true instant must grow with σ. | MAE rises as the diagnostic of S_⊥ gets dirty. Prediction insensitive to phase noise would mean the bench is not actually using the remainder. |
Ranked by fidelity to Einstein’s field program rather than present popularity. Shields 2026a, §4 Table 1.
Rank 1
Fine lump profile plus a definite background-field realization (mode phases)
Classical threshold crossing in a driven nonlinear field
Must identify the background (geometry, residual radiation, vacuum as a real field)
This bench occupies Rank 1.
Rank 2
Crest location inside a guiding field
First crossing of a surface is unique
Guiding structure is extra furniture; Einstein judged Bohm too cheap
Borrowed event, declined architecture.
Rank 3
Planck-scale ontological microstate
Ontological states permute; an undecayed class maps to a decayed class at a definite step
T* exists in principle; no access path yet
Not a near-term analog.
Shields 2026a, §8. The companion adds the institutional warning: do not cash T* in as a contribution to quantum gravity. Shields 2026b, §4.