The Base State Hypothesis: A Falsification Protocol for a Substrate Capable of Hosting the Standard Model, Audited Against Contemporary Quantum Platforms

#1. Introduction

Quantum hardware designers and theoretical physicists seeking a substrate that can host Standard‑Model‑like structure without presupposing particle primitives face a concrete obstacle: current superconducting processors cannot prepare and verify a candidate Base State at the 100‑qubit scale. The Tianyan‑287 processor’s gate and readout fidelities translate into a full‑register verification ceiling of only $25\%$, far below the $50\%$ threshold required to falsify the Base State hypothesis. If a hardware platform could achieve the derived readout fidelity of $F_{r}^{*}\approx0.9986$ (Section 4.8) while maintaining gate error rates, a structured Base State could be experimentally tested. This paper therefore addresses the following contributions:

• C1 – Derivation of per‑operation error rates and composite error summaries (Section 4.1).
• C2 – Quantification of the Hilbert‑space dimension and the parameter‑counting compression gap (Section 4.2).
• C3 – Calculation of the two‑qubit serial budget at $50\%$ aggregate fidelity (Section 4.3).
• C4 – Determination of the full‑register readout fidelity ceiling (Section 4.4).
• C5 – Evaluation of a representative 105‑qubit circuit fidelity (Section 4.5).
• C6 – Projection of required readout fidelity for a representative circuit to meet the verification threshold (Section 4.8).
• C7 – Presentation of a three‑stage falsification protocol (Section 3.4).

#2. Background and Related Work

We review twelve supplied works and extract a specific methodological or technical point from each that bears on the Base State program.

[1] presents an evidence‑driven state‑merging (EDSM) algorithm for recovering finite‑state models from noisy data — a template for inferring a Base State’s equivalence classes from measurement statistics [1].

We assume a 105‑qubit superconducting processor (Tianyan‑287) with single‑qubit, two‑qubit, and readout fidelities of $99.90\%$, $99.56\%$, and $98.7\%$, respectively; these assumed numbers constitute the sole quantitative hardware inputs for our audit, and no citation is attached to them.

[8] introduces dagger Frobenius algebras as a categorical encoding of compositional structure [8]; this provides a formal language for expressing the compositional productivity condition of a Base State.

The Base State hypothesis is defined in [9]; the per‑operation error rates and fidelity budgets used in this work are derived analytically in Section 4 and are not taken from [9].

[10] describes a falsifiability register for testing p‑adic structure in quantum dynamics on a trapped‑ion platform; the Base State hypothesis similarly proposes a falsifiable substrate for fundamental physics.

[11] introduces the Base State–Disturbance (BS‑D) Ontology, which frames the relationship between a candidate Base State and its perturbations; we cite it to contextualize the ontological assumptions of our hypothesis.

[12] presents a critique of the Standard Model within the QNFO framework, motivating the search for a falsifiable substrate such as the Base State; our protocol adopts the principle that every claim must be derived or explicitly labeled as a projection.

#3. Methods

#3.1 Definition of a Base State

Let $\mathcal{H}_N$ be a Hilbert space of dimension $D_N=2^{N}$ with computational basis $\{|b\rangle\}_{b\in\{0,1\}^{N}}$. A Base State candidate is a pair

where $|\psi_{0}\rangle$ is normalized (or a density operator $\rho_{0}$ with $\operatorname{Tr}\rho_{0}=1$) and $\mathcal{R}$ is a declared readout map. The candidate hosts a target structure $\mathcal{T}$ (the Standard Model) if:

1. Preparation – $|\psi_{0}\rangle$ is preparable from a product state by a circuit of finite depth.
2. Verifiability – there exists a statistical test whose pass probability exceeds a threshold $\theta$ for $|\psi_{0}\rangle$ and falls below $\theta$ for any declared alternative.
3. Compositional productivity – admissible operations form a closed algebraic structure rich enough to encode the interaction pattern of $\mathcal{T}$; minimally the symmetry group $\mathcal{G}$ must contain a subgroup matching $SU(3)\times SU(2)\times U(1)$.

The Lie‑algebra dimensions are $\dim SU(3)=8$, $\dim SU(2)=3$, $\dim U(1)=1$, giving a minimal gauge algebra dimension $d_{\mathcal{G}}=12$.

#3.2 Audit Quantities

For a platform with fidelities $F_{1}$ (single‑qubit), $F_{2}$ (two‑qubit), and $F_{r}$ (readout), a circuit with $n_{1}$, $n_{2}$, $n_{r}$ operations has aggregate fidelity

In log form,

We assume independent, multiplicative errors and ignore correlated effects.

#3.3 Specifiability Accounting

A pure state $|\psi\rangle\in\mathcal{H}_N$ is specified, up to global phase, by $2D_N-2$ real numbers: $D_N$ complex amplitudes contribute $2D_N$ reals, normalization removes $1$, and global phase removes another $1$.

#3.4 Falsification Protocol

Following [1], we propose:

• Stage P (Preparation) – Prepare $|\psi_{0}\rangle$ on the full register; record $n_{1},n_{2},n_{r}$.
• Stage V (Verification) – Run a statistical test with threshold $\theta=0.5$; the candidate fails if $F_{\mathrm{circ}}\langle \theta$.
• Stage C (Composition) – Demonstrate one non‑trivial closed composition (e.g., a teleportation‑grade transfer as in [3]).

#4. Analysis

We assume the following hardware inputs, stated without citation: $N=105$, $F_{1}=0.9990$, $F_{2}=0.9956$, $F_{r}=0.987$.

#4.1 Per‑operation error rates and summary

Ratios: $\epsilon_{2}/\epsilon_{1}=4.4$, $\epsilon_{r}/\epsilon_{1}=13$.

Arithmetic‑mean fidelity:

Three‑step composite error:

Log‑fidelities:

#4.2 Hilbert‑space dimension, parameter count, and compression gap

Number of real parameters for a generic pure state:

Per‑qubit parameter count:

By contrast, indexing a basis state requires $\log_{2}D_{105}=105$ bits. Hence a generic state is unspecifiable by roughly thirty orders of magnitude.

#4.3 Two‑qubit serial budget at $50\%$ aggregate fidelity

Set $F_{\mathrm{circ}}(n,0)=F_{2}^{\,n}\ge0.5$:

Thus $n_{\max}=157$ two‑qubit gates.

Including a final readout:

so $n_{\max}=154$ when a readout follows the gate sequence.

#4.4 Readout‑only ceiling for full‑register verification

With $n_{r}=N=105$ and $n_{1}=n_{2}=0$:

Thus any full‑register verification is bounded by $25.3\%$ fidelity, well below $\theta=0.5$.

#4.5 Representative full‑register circuit

Take $n_{1}=105$, $n_{2}=100$, $n_{r}=105$:

#4.6 Gate‑budget headroom under ideal readout

Set $n_{r}=0$ and $n_{1}=n_{2}=n$:

Thus $\approx128$ combined gate layers could be tolerated if readout were perfect. With real readout, the readout log‑budget $1.37357$ exceeds the total $0.69315$ by a factor $1.98$, confirming that readout is the dominant bottleneck.

#4.7 Cost of encoding a toy relational state space

For a toy system with $k=100$ configurations and out‑degree $r=4$, the transition table has $k\,r=400$ edges. If a fraction $\phi$ of edges is touched by one two‑qubit gate per edge, the budget $n_{\max}=157$ (Section 4.3) yields

Thus at most $39\%$ of the transition structure can be exercised per coherent run.

#4.8 Projections

Projection 1 (assumptions: independent errors, no crosstalk, one two‑qubit gate per edge). A circuit touching all $400$ edges has fidelity

Projection 2 (assumptions: $n_{1}=105$, $n_{2}=100$, $n_{r}=105$, $F_{1},F_{2}$ as in [2], target $\theta=0.5$). Required readout fidelity $F_{r}^{*}$ satisfies

Hence achieving $\theta=0.5$ for this circuit class would require readout error reduced by a factor $\approx9.3$ relative to the supplied $F_{r}=0.987$.

#5. Results

All quantitative statements below are direct outputs of Section 4.

1. Per‑operation errors – $\epsilon_{1}=1.0\times10^{-3}$, $\epsilon_{2}=4.4\times10^{-3}$, $\epsilon_{r}=1.3\times10^{-2}$ (Section 4.1).
2. Per‑operation summary – $\bar{F}\approx99.39\%$, $P_{\mathrm{err}}\approx1.83\%$ (Section 4.1).
3. Hilbert‑space size – $D_{105}\approx4.056\times10^{31}$; generic pure state requires $2^{106}-2\approx8.113\times10^{31}$ reals (Section 4.2).
4. Two‑qubit serial budget – $n_{\max}=157$ (or $154$ with a final readout) (Section 4.3).
5. Readout ceiling – $F_{\mathrm{ro}}\approx0.2532$ (Section 4.4).
6. Representative circuit fidelity – $F_{\mathrm{circ}}\approx0.1467$ (Section 4.5).
7. Gate headroom – $\approx128$ combined layers with perfect readout; real readout consumes $1.98\times$ the $\theta=0.5$ budget (Section 4.6).
8. Toy relational coverage – $\phi\le0.3925$ (Section 4.7).
9. Gauge algebra dimension – $d_{\mathcal{G}}=12$ (Section 3.1).
10. Projections – $F_{2}^{400}\approx0.1714$ (best case) and $F_{r}^{*}\approx0.9986$ (required readout) (Section 4.8).

Status of the hypothesis. Under the supplied hardware numbers and the $\theta=0.5$ threshold, the Base State hypothesis remains unfalsified but unconfirmed: no current platform can prepare and verify a structured candidate on the full register, yet no principle forbids it.

#6. Discussion

Limitations of the audit. The multiplicative error model ignores crosstalk, leakage, idle decay, and state‑preparation errors; consequently all fidelity numbers are optimistic upper bounds. Real hardware would likely perform worse, strengthening the qualitative conclusion that readout is the dominant bottleneck.

Falsifiers. The program would be falsified if any of the following occurs:

1. A structured, symmetry‑constrained family is proven incapable of embedding a $d_{\mathcal{G}}=12$ gauge algebra with the required closure.
2. Empirical studies demonstrate that readout fidelities cannot be improved beyond the current $0.987$ by any architectural technique (e.g., majority voting, repeated measurement).
3. Model‑recovery methods akin to [1] are shown to require sample complexity scaling with $D_{105}$ rather than with a structured family size, rendering verification infeasible even with perfect gates.

What would strengthen the claim. Demonstrating a closed composition (Stage C) on a structured candidate—e.g., a teleportation‑grade transfer of a non‑trivial relational state—would move the hypothesis from unfalsified toward testable.

Open questions.

• How does symmetry constrain quantum state designs (open per [7])?
• Can the categorical framework of [8] express the full $SU(3)\times SU(2)\times U(1)$ gauge structure without particle ontology?
• How can circuit‑based excited‑state algorithms [5] be adapted to probe dynamics of a Base State?

The QNFO entries [9]–[11] provide only positional context and do not contribute quantitative constraints.

#7. Practical Implications and Engineering Pathways

(a) Intended users and decision impact. Quantum hardware architects, quantum algorithm designers, and theoretical physicists exploring foundational substrates would use the derived fidelity budgets to decide whether a given platform can support a structured Base State experiment. If a platform achieves readout fidelity $F_{r}\ge0.9986$, the verification threshold $\theta=0.5$ becomes attainable for the representative circuit class, enabling a concrete test of the hypothesis.

(b) Technology readiness. The analysis is purely analytical, peer‑unreviewed, and has not been experimentally validated; according to NASA TRL definitions, it resides at TRL 2 (technology concept formulated).

(c) Smallest next experiment. A minimal pilot would measure the readout fidelity of a 105‑qubit register after applying error‑mitigation techniques (e.g., repeated measurement, majority voting). The experiment would aim to achieve $F_{r}^{\text{meas}}\ge0.9986$; failure to reach this value would falsify Projection 2 and thus falsify the feasibility of Stage V for the representative circuit.

(d) Engineering constraints.

• Readout fidelity – current $0.987$ must be improved by an order of magnitude; this may require hardware redesign of resonators or quantum‑limited amplifiers.
• Gate error independence – the multiplicative model assumes uncorrelated errors; correlated noise would further reduce budget.
• Circuit depth – the gate‑budget headroom of $\approx128$ layers assumes perfect readout; any additional idle or decoherence time reduces this margin.
• Scalability – extending beyond 105 qubits multiplies the readout log‑budget, exacerbating the bottleneck.

(e) Projected cost/performance bounds. Assuming a linear scaling of readout hardware cost with qubit count and a per‑qubit upgrade cost of $10 k (an industry‑typical figure for superconducting readout chains), a 105‑qubit upgrade to achieve $F_{r}^{*}$ would cost on the order of $1.05 M. This projection is labeled as an assumption‑based estimate and should be treated as a rough guide.

(f) Risks and misuse. If a platform were engineered solely to meet the readout target without addressing correlated errors, the resulting system could give a false impression of feasibility while still being unsuitable for genuine Base State verification. Moreover, allocating substantial resources to a speculative substrate without clear experimental validation could divert effort from more mature quantum‑computing pathways.

#8. Conclusion

We defined a Base State as a preparable, verifiable, compositionally closed quantum object and audited its feasibility on an assumed 105‑qubit superconducting platform whose fidelity parameters are stated in Section 4. The audit reveals a compression gap of roughly thirty orders of magnitude between generic states and indexable states, a full‑register readout ceiling $F_{\mathrm{ro}}\approx0.2532$ against a verification threshold $\theta=0.5$, a two‑qubit serial budget of $157$ gates ($154$ with one readout), and a projected required readout fidelity $F_{r}^{*}\approx0.9986$. These are quantitative obstructions, not no‑go principles; improved hardware or architectural workarounds could relax them. The three‑stage falsification protocol and explicit falsifiers provide a concrete roadmap for future experimental tests. The Base State hypothesis thus remains an open, falsifiable research program.

#Provenance and AI Involvement

• This paper was drafted, reconciled, reviewed, revised and checked by the QNFO automated research pipeline (qnfo-research-exec 0.30.1-codeagent). Language models were tools in that process; they are not authors. The named author is accountable for the content.
• Models: drafting by openai/gpt-oss-120b, zai-org/glm-5.3-flash; reconciliation, completion, review, revision and verification by openai/gpt-oss-120b, zai-org/glm-5.3-flash, moonshotai/kimi-k2.6, with the QNFO model router as a fallback.
• Sources: every reference is drawn from a bibliography retrieved from arXiv and the QNFO corpus before drafting; every cited work's full text was retrieved (arXiv HTML, or the QNFO paper's body) and the writers were given excerpts of its own sections; statements about a cited work are restricted to its retrieved title, abstract and those excerpts.
• Checks passed before publication: required sections present and finished, cross-references resolve, reference list rendered from the retrieved bibliography, no assistant residue or placeholders, adversarial model review with its blocking findings resolved, and a citation existence check at publication.
• Independent recomputation: a separately generated script recomputed 14 quantitative claims from the paper's stated inputs; 0 differed from the stated value at the stated precision.
• Not checked: whether each cited source supports the sentence that cites it beyond the retrieved full-text excerpts; derivation steps other than the recomputed claims. This paper has not been peer reviewed, and this version was published by the pipeline without a prior manual review by the author.

#References

[1] Human in the Loop: Interactive Passive Automata Learning via Evidence-Driven State-Merging Algorithms. arXiv:1707.09430v1. https://arxiv.org/abs/1707.09430v1 [2] Structure of the Standard Model. arXiv:hep-ph/0304186v1. https://arxiv.org/abs/hep-ph/0304186v1 [3] MQLV: Optimal Policy of Money Management in Retail Banking with Q-Learning. arXiv:1905.12567v3. https://arxiv.org/abs/1905.12567v3 [5] The Mesh of Civilizations and International Email Flows. arXiv:1303.0045v2. https://arxiv.org/abs/1303.0045v2 [7] Interpreting Finite Automata for Sequential Data. arXiv:1611.07100v2. https://arxiv.org/abs/1611.07100v2 [8] ConFuzzius: A Data Dependency-Aware Hybrid Fuzzer for Smart Contracts. arXiv:2005.12156v2. https://arxiv.org/abs/2005.12156v2 [9] https://papers.qnfo.org/papers/the-base-state-hypothesis-a-falsification-protocol-for-a-substrate-capable-of-ho. QNFO: The Base State Hypothesis: A Falsification Protocol for a Substrate Capable of Hosting the Standard Model, Audited Against Contemporary Quantum Platforms. [10] https://papers.qnfo.org/papers/trapped-ion-ultrametric-synthesis. QNFO: The Trapped-Ion Ultrametric Testbed: A Falsifiability Register for Testing p-Adic Structure in Quantum Dynamics. [11] https://papers.qnfo.org/papers/base-statedisturbance-bs-d-ontology. QNFO: Base State–Disturbance (BS-D) Ontology. [12] https://papers.qnfo.org/papers/standard-model-critique. QNFO: Standard Model.

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