A New Way to Cancel Out Empty-Space Energy

In the paper's words

The observed dark‑energy density ρ_Λ^rm obs≈10^-47 GeV⁴ is smaller than the naïve quantum‑field‑theoretic vacuum estimate by roughly 10¹20, a discrepancy that blocks predictive cosmology. Existing proposals retain the Archimedean real number field and invoke fine‑tuned counterterms. The present work fills the gap by exploiting the adelic product formula ∏_v|q|_v=1 for rational numbers q and the conjectured decay of the one‑loop vacuum energy density ρ_rm vac(p)∝ p^-k with k>0 for each prime p.

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

Numbers it reports

1. For the test mode $q=2$ we have $$ |2|_{\infty}=2,\qquad |2|_{2}=2^{-1}=0.5,\qquad |2|_{p}=1\;(p\neq2). $$ Thus $$ \prod_{v}|2|_{v}=2\times0.5\times\prod_{p\neq2}1=1 . \tag{13} $$ Interpreting the vacuum contribution of each mode as proportional to $|q|_{v}$, the real‑sector divergence $2$ is exactly cancelled by the $p=2$ contribution $0.5$, leaving a net factor $1$ for the mode.

   from 4.4 Net adelic vacuum energy

2. Following [8], we impose the matching condition $$ \omega_{0}= (p-1)\frac{\Lambda^{4}}{16\pi^{2}} . \tag{14} $$ For $p=3$: $$ \omega_{0}=2\frac{\Lambda^{4}}{16\pi^{2}}=\frac{\Lambda^{4}}{8\pi^{2}} . $$ Compute the numerical factor: $$ \frac{1}{8\pi^{2}} = \frac{1}{8\times9.869604401}= \frac{1}{78.95683521}=0.01266 . $$ Thus $$ \omega_{0}=0.01266\times10^{76}\,\text{GeV}^{4}=1.2665\times10^{74}\,\text{GeV}^{4}. \tag{15} $$ Expressed as a fraction of the naive vacuum energy (9): $$ \frac{\omega_{0}}{I_{\infty}} = \frac{0.01266}{0.00633257}=2.0 , $$ consistent with the factor $(p-1)=2$ in (14).

   from 4.5 Matching condition for $p=3$

3. 13) $\prod_{v}|2|_{v}=1$ Exact cancellation of the real factor $2$ by the $p=2$ factor $0.5$ Matching condition $\omega_{0}$ for $p=3$ (Eq.

   from 5. Results

4. Gate fidelity : Implementation of the non‑local tree connectivity requires high‑fidelity multi‑qudit gates; error rates above $10^{-3}$ could mask the tiny energy differences.

   from (d) Engineering Constraints

How it is done

1. We derive an explicit symbolic expression for the $p$‑adic one‑loop bubble integral with a $p$‑adic momentum cutoff, evaluate the adelic sum over all places using zeta‑regularisation, and perform a concrete arithmetic demonstration that the adelic product over all completions cancels the divergent real‑sector contribution for the rational mode $q=2$.

   from Abstract

2. Engineering pathway outlining the next quantum‑simulation experiment and the technology readiness assessment (Section 7).

   from 1. Introduction

3. Inequalities for $p$‑adic equiangular lines are established in [6], where the authors derive the bound $|n|^{2}\le |d|\max\{|n|,\gamma^{2}\}$ for a collection of $p$‑adic $\gamma$‑equiangular lines.

   from 2. Background and Related Work

4. Our analysis proceeds in three stages: $p$‑adic one‑loop bubble integral.

   from 3. Methods

What would falsify it

1. A single observation that would falsify the main claim is the detection of a non‑zero net vacuum energy contribution from a $p$‑adic mode that does not cancel the real contribution for a rational momentum $q$.

   from 6.2 Failure Modes and Falsifiability

2. Other potential failure modes include: Breakdown of the product formula in a physical context (e.g., if a physical observable depends on $|q|_{v}$ in a non‑multiplicative way).

   from 6.2 Failure Modes and Falsifiability

3. Discussion of the assumptions, failure modes, and falsifiability criteria (Section 6).

   from 1. Introduction

Where the claim stops

1. While the result is promising, it rests on several assumptions that can be experimentally probed via quantum‑simulation of $p$‑adic oscillators.

   from 8. Conclusion

2. Assuming a matching condition $\omega_{0}=(p-1)\Lambda^{4}/(16\pi^{2})$ with $p=3$, we obtain $\omega_{0}\approx1.27\times10^{-2}\Lambda^{4}$.

   from Abstract

3. If one assumes that the adelic regularisation leaves a residual of order $10^{-47}\,\text{GeV}^4$, the model can reproduce the observed dark‑energy density, but this residual is an input rather than a derived outcome.

   from Abstract

Where to read

1. Abstract193 words · 1 min
2. 1. Introduction327 words · 1 min
3. 2. Background and Related Work431 words · 2 min
4. 3. Methods223 words · 1 min
5. 4. Analysis413 words · 2 min
6. 5. Results129 words · 1 min
7. 6. Discussion313 words · 1 min
8. 7. Practical Implications and Engineering Pathways282 words · 1 min
9. 8. Conclusion149 words · 1 min
10. Provenance and AI Involvement225 words · 1 min