Illustrative · unadmitted · revision 1
Graphene complementary-frequency dense matrix multiplication
This is a proposed definition for criticism. It is not an experiment run, result, evidence claim, canonical admission, inventory record, or procurement request.
- Stable identifier
graphene-complementary-frequency-dense-matmul- Kind
- physical
- Intent
- discrimination
Exact target
- external-reference ·
graphene-complementary-frequency-matmul — operator-supplied graphene frequency-domain calculation proposal
Minimal decisive protocol
Complementary-frequency identity test
Encode two finite matrices into complementary optical frequencies, measure the nonlinear mixing output, and compare against an independently computed dense product under randomized phase and amplitude controls.
- Calibrate frequency response and detector linearity.
- Inject matrix-coded complementary-frequency fields.
- Acquire raw complex spectra and decode the candidate product.
- Repeat with shuffled, phase-scrambled, and zero-row controls.
Decision rule: The candidate survives only if decoded entries track the exact reference product within the predeclared error budget and controls reject linear leakage explanations.
Boundary: The test covers only the declared matrix size, frequency band, material stack, and detector reconstruction.
Controls
- negative: One operand row is zeroed. (input row; Corresponding product contribution should vanish.)
- ablated: Remove the nonlinear interaction region while preserving the readout path. (nonlinear interaction; Dense product signature should disappear or fall below threshold.)
Observables and units
Observables| Observable | Units | Measurement | Uncertainty reporting |
|---|
| relative matrix product error | dimensionless | normed decoded-versus-reference entries | report detector noise and calibration propagation |
|---|
| frequency crosstalk | dB | out-of-band and off-entry spectral power | report resolution and leakage floor |
|---|
Calibration and repetitions
- detector responsivity: traceable power sweep across the operating band — residual linearity error below the product error budget (A/W)
Replicate unit: independent matrix encoding; minimum 20, independent 5.
Randomization: matrix entries, phases, and order randomized
Stopping rule: complete all matrix blocks unless safety or detector saturation stop is reached
Uncertainty: laser phase noise, detector noise, frequency drift, nonlinear material variation; Monte Carlo the calibrated input covariance through decode and norm; publish matrices, raw spectra, calibration files, and exact oracle output
Success and falsifiers
Success
- Decoded output agrees with the exact dense product within the predeclared error budget. (relative Frobenius error <= predeclared budget dimensionless)
Falsifiers
- The same product signature remains when the nonlinear interaction is ablated. (ablation-normalized product signal >= predeclared leakage threshold fraction)
Required capability groups
- frequency-source · required, any-one, quantity 1: phase-stable complementary-frequency source (system) — declared bandwidth and phase noise
- spectral-readout · required, any-one, quantity 1: complex spectral readout with calibrated dynamic range (system) — raw spectra and linearity calibration
Related capability types: Calibrated phase-resolved optical detector array
Confounds and raw artifacts
- frequency drift masquerades as complementary mixing: interleave reference tones; mitigation: lock and remeasure frequency calibration
- complex-spectrum · binary spectra plus JSON metadata · retain original acquisition and decode code hash
Nonclaims
- No graphene material performance or scaling is admitted by this fixture.
- It does not claim a universal optical matrix processor or useful energy efficiency.
- No measurement is a result; this record only specifies a decisive protocol.
Provenance boundary
The citation supplies graphene context only; it does not support the proposed dense multiplication claim.
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