A canonical map, then a measurable diamond.
The ideal apparatus map fixes the action scale, energy scale and clock. A four-link component test checks reciprocal matter dynamics and local Gauss balance.
The apparatus-to-model map.
For each physical flux–charge pair, choose scales Φ₀ and Q₀ with a common product Φ₀Q₀=S₀. If the retained apparatus Hamiltonian is E₀ times the target Hamiltonian, the model clock is τ=tE₀/S₀. Invertible readout gains alone do not establish this canonical structure or dynamics.
| Physical record | Model coordinate | Required property |
|---|---|---|
| Link flux Φ, signed charge Q | θ=Φ/Φ₀; E=Q/Q₀; U=exp(iθ) | Independent angle and signed momentum; periodic coupling |
| First matter flux–charge pair | ψ=(Φ/Φ₀+iQ/Q₀)/√2 | Complex bracket −i in model units |
| Second matter flux–charge pair | w=(Φ/Φ₀−iQ/Q₀)/√2 | Complex bracket +i; w is the conjugated canonical second species |
| Calibrated action S₀ and energy E₀ | t₀=S₀/E₀ in seconds | All channel action products agree within a bounded mismatch |
The two species can use ordinary canonical hardware pairs. The reversed complex convention supplies the second species sign. The normalized model electric variable is not automatically a laboratory Maxwell field, and its Gauss generator is not yet an identified electric-charge law.
One instrumented incidence diamond.
Nodes are 0, 01, 02 and 012. Links follow the two downward paths from face 012 to vertex 0. Their incidence signs are b=(−1,1,−1,−1); the cycle is c=(1,1,−1,−1). The graph has four nodes, four links and one loop.
Record 24 state coordinates plus eight outputs measuring the complex couplings independently. A computed exp(iθ) always has unit modulus; it cannot validate the actual coupling. Record clocks, applied sources, feedback, probe disturbance and joint calibration uncertainty.
For isolated gauge-field calibration, the loop phase satisfies φ″=−4aκ sin φ. Its finite-amplitude period follows an elliptic integral, so a finite-amplitude measurement must use that prediction rather than its linear limit.
Seven condition families with discriminating controls.
| Condition | Measured signature |
|---|---|
| A · Signed rotor response | Constant electric cycle kick; loop phase slope 4ε |
| B · Plaquette response | Finite-amplitude pendulum; compare with plaquette coupling disabled |
| C · Reciprocal matter dynamics | Electric acceleration −b, both continuity laws and conserved Gauss values |
| D · Relative equilibrium and kick | Opposite matter phase rotation, loop holonomy −1, then predicted cycle-kick response |
| E · Known source | One-species radial loss produces the specified local source and trace return |
| F · Changed local frame | Equal invariant histories, correctly transformed raw trajectories |
| G · Blinded faults | Wrong species sign gives initial Gauss slope (2,−2,0,0); disabled electric response gives (−2,2,0,0) |
The proposed component coefficients are a=1, κ=1/16, μ=0 and g=1, with g=0 for calibration. They are declared component values. The diamond is not an invariant subsystem carrying the full tetrahedral trapping theorem.
A concrete proposed measurement rule.
CD-1 proposes 20 independent preparations per condition, randomized and blinded, with model sample interval at most 1/1000 and horizon 8π. Physical time and sample rate are chosen after t₀ calibration. These counts are an initial design, not a power calculation.
Engineering targets are 1/100 in the declared dimensionless state, source, Gauss, coupling and energy decision channels, with channel action mismatch at most 1/1000. Use the exact bounds and prefix rules in the protocol; these targets do not replace the earlier endpoint theorem tolerances.
Supply at least 99% joint coverage for every quantity used in a run’s decision. Missing calibration, unresolved controls, saturation, missing channels or unbounded reconstruction/solver error yields HOLD. A sampled residual does not establish a continuous-time bound without an intersample certificate. Weak trajectory agreement alone does not establish the SDW absolute defect path or energy-work bounds.
The next physical return is an actual Hamiltonian/actuator design, calibrated action and energy scales, attainable error allocation, validated reconstruction and attributable non-constructor review. No experiment has been executed.
Dataset watch.
A weekly watch checks for improved experimental gauge-simulator releases on Monday mornings in Chicago time. It prioritizes raw phase/electric/matter records, closed loops, source tests and calibration. It sends updates only for meaningful new releases. The watch does not publish changes or contact researchers.
Read the published-dataset audit →