Beyond the Qubit, Part II: A Constructive Research Programme for Post-Particle Computation, with Quantified Instrument Budgets, a Fano-Scale Admissibility Gate, and Embodied-Verification Pathways

In the paper's words

Research programmes that frame computation as a circuit of qubits face a growing epistemic critique: the companion analysis argues that the qubit-gate-circuit model projects a particle ontology onto systems better described relationally and field-theoretically [9]. The specific gap is that critiques of the qubit model stop at diagnosis: they name no measurement standard to inherit, no error budget a successor must satisfy, and no embodied test protocol by which a successor formalism could be falsified. This paper supplies the constructive half of the answer.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. We strip the computational description to its minimal relational content and show that for $n = 50$ constituent units a pairwise relational parametrization carries $1225$ parameters against $2^{50} \approx 1.1259 \times 10^{15}$ Hilbert-space amplitudes, a compression factor of $9.19 \times 10^{11}$.

   from Abstract

2. We convert the NEXT-100 design target of $0.5$–$1\%$ FWHM energy resolution at the double-beta-decay energy of $^{136}\mathrm{Xe}$ [5] into a one-sigma admissibility band $\sigma_E/Q_{\beta\beta} \in [2.1233 \times 10^{-3},\ 4.2466 \times 10^{-3}]$, derive a root-sum-square error-composition rule (five independent stages at $10^{-2}$ each compose to $2.2361 \times 10^{-2}$ statistically versus $5 \times 10^{-2}$ worst-case), and derive a tracking-drift bound of $6.0 \times 10^{-2}$ m per minute under stated illustrative assumptions.

   from Abstract

3. The contributions of this paper are: A minimal relational parametrization of an $n$-unit computational description, with an explicit count showing $n(n-1)/2$ pairwise parameters against $2^n$ Hilbert-space amplitudes, yielding a compression factor of $9.19 \times 10^{11}$ at $n = 50$, with a memory projection of $18.014$ PB versus $1.96 \times 10^4$ bytes under a stated 16-byte-per-amplitude assumption (derived in Section 4.1, Result R1).

   from 1. Introduction

4. A derived drift-growth bound for anchored tracking in an embodied verification rig: random-walk accumulation of per-frame anchor error gives $\delta_{\mathrm{drift}} = \varepsilon_f \sqrt{N} = 6.0 \times 10^{-2}$ m over a one-minute session under stated illustrative assumptions, against $3.6$ m under a constant per-frame bias (Section 4.4, Result R4).

   from 1. Introduction

5. Derived latency, persistence, and tracking budgets for the embodied instrument: a single $90$ Hz frame consumes $55.6\%$ of an assumed $20$ ms motion-to-photon budget; one-frame persistence blurs a $360\ \mathrm{deg/s}$ head motion by $4.0^\circ$; inter-sample angular travel is $6.0^\circ$ at $60$ Hz versus $0.36^\circ$ at $1$ kHz, a factor of $16.7$ (Section 4.5, Results R5–R7).

   from 1. Introduction

6. The NEXT experiment entry describes Phase I of the NEXT-100 neutrinoless double-beta-decay experiment, anticipating an energy resolution nearing the Fano factor in xenon of $0.5$–$1\%$ FWHM at $Q_{\beta\beta,{}^{136}\mathrm{Xe}}$, with a time-projection-chamber design allowing tracking and identification of the double-end-blob feature of the decay signature [5].

   from 2. Background and Related Work

How it is done

1. The specific gap is that critiques of the qubit model stop at diagnosis: they name no measurement standard to inherit, no error budget a successor must satisfy, and no embodied test protocol by which a successor formalism could be falsified.

   from Abstract

2. If that diagnosis is right, the cost of continuing on the qubit path is not merely engineering effort on a contested abstraction but the absence of any prepared alternative: no accepted measurement standard to inherit, no error budget a successor must meet, and no test protocol that could falsify a candidate formalism.

   from 1. Introduction

3. The NEXT experiment entry describes Phase I of the NEXT-100 neutrinoless double-beta-decay experiment, anticipating an energy resolution nearing the Fano factor in xenon of $0.5$–$1\%$ FWHM at $Q_{\beta\beta,{}^{136}\mathrm{Xe}}$, with a time-projection-chamber design allowing tracking and identification of the double-end-blob feature of the decay signature [5].

   from 2. Background and Related Work

4. The method is constructive derivation plus protocol mapping, with no new data collection.

   from 3. Methods

What would falsify it

1. The specific gap is that critiques of the qubit model stop at diagnosis: they name no measurement standard to inherit, no error budget a successor must satisfy, and no embodied test protocol by which a successor formalism could be falsified.

   from Abstract

2. We then map immersive-interface capabilities [1], [2], [3], [4], [6], [7], [8] onto a verification protocol in which a human operator is the readout instrument, and size a falsification pilot at $63$ participants per group for $80\%$ power against a medium effect.

   from Abstract

3. If that diagnosis is right, the cost of continuing on the qubit path is not merely engineering effort on a contested abstraction but the absence of any prepared alternative: no accepted measurement standard to inherit, no error budget a successor must meet, and no test protocol that could falsify a candidate formalism.

   from 1. Introduction

Where the claim stops

1. The results convert a philosophical dispute into a set of numbers, but each number rests on assumptions that a critic can attack directly.

   from 6. Discussion

2. The $n(n-1)/2$ pairwise count assumes that pairwise relations are the minimal descriptive content — the stripping move of [9] — and the supplied summary of [9] states this framing without technical detail, so the assumption cannot be checked against the companion paper's text as supplied here.

   from 6. Discussion

3. The Gaussian-width assumption is also a modelling choice: the entry does not state that the resolution figure is Gaussian, and non-Gaussian resolution functions would change the FWHM-to-sigma conversion.

   from 6. Discussion

Where to read

1. Abstract262 words · 1 min
2. 1. Introduction825 words · 4 min
3. 2. Background and Related Work1,236 words · 5 min
4. 3. Methods666 words · 3 min
5. 4. Analysis1,441 words · 6 min
6. 5. Results399 words · 2 min
7. 6. Discussion994 words · 4 min
8. 7. Practical Implications and Engineering Pathways821 words · 4 min
9. 8. Conclusion258 words · 1 min
10. Provenance and AI Involvement197 words · 1 min