Scale and Boundary Candidates in CAELIX
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2026
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| _version_ | 1866901208445222912 |
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| author | Ball, Alan |
| author_facet | Ball, Alan |
| contents | <p><strong>Scale and Boundary Candidates in <a title="CAELIX - Constructive Algorithmics for Emergent Lattice Interaction eXperiments" href="https://caelix.co.uk/" target="_blank" rel="noopener">CAELIX</a> </strong>is a working note on two low-energy boundary candidates in the <a title="CAELIX - Constructive Algorithmics for Emergent Lattice Interaction eXperiments" href="https://caelix.co.uk/" target="_blank" rel="noopener">CAELIX</a> framework: the fine structure constant α and the Higgs vacuum expectation value.</p> <p>The note does not claim a closed derivation of the full scale problem. Its purpose is narrower and more architectural. It argues that <a title="CAELIX - Constructive Algorithmics for Emergent Lattice Interaction eXperiments" href="https://caelix.co.uk/" target="_blank" rel="noopener">CAELIX</a> requires two distinct but structurally linked meanings of scale: Burden and Resolution.</p> <p>The burden ladder concerns the computation required to sustain and propagate a motif on the substrate. The resolution ladder concerns how deeply a probe forces internal structure into view.</p> <p>Within that split architecture, the low-energy fine structure candidate is treated as a junction quantity:</p> <p> </p> <p>α⁻¹ = 4π³ + π² + π − 1/3315</p> <p> </p> <p>The scaffold 4π³ + π² + π is read as belonging to the long-wavelength side of the resolution ladder, while the modifier 1/(3 × 5 × 13 × 17) is read as a burden-side bookkeeping term inherited from the substrate.</p> <p>The Higgs vacuum expectation value is treated as a second boundary candidate:</p> <p> </p> <p>v ∼ M_Pl / 243⁷</p> <p> </p> <p>Its role in the note is not to close the hierarchy problem, but to show why the electroweak scale also appears near the same unresolved interface between geometric scaffold, computational burden and scale selection.</p> <p>The leading running hypothesis advanced here is observation-cost running. On this view, the low-energy electromagnetic regime forms a broad infrared plateau. Running begins when probe resolution starts to penetrate charged burden structure. The measured running of α is then interpreted as the macroscopic signature of additional computation forced by deeper observation of charged lattice patterns.</p> <p>The note is explicitly provisional. It does not claim a full forward derivation of the coefficient pattern (4,1,1), a finished renormalisation law, exact threshold locations for the running of α, or a completed solution to the Higgs hierarchy problem. It is intended as a disciplined working architecture and as a guide for later computational and experimental tests.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19421875 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Scale and Boundary Candidates in CAELIX Ball, Alan CAELIX fine structure constant Higgs vacuum expectation value observation-cost running balanced ternary discrete lattice physics emergent physics scale hierarchy burden ladder resolution ladder electromagnetic coupling vacuum polarisation threshold penetration particle as pattern computational burden Mathematical physics Particle physics Quantum physics Theoretical physics Computational topology <p><strong>Scale and Boundary Candidates in <a title="CAELIX - Constructive Algorithmics for Emergent Lattice Interaction eXperiments" href="https://caelix.co.uk/" target="_blank" rel="noopener">CAELIX</a> </strong>is a working note on two low-energy boundary candidates in the <a title="CAELIX - Constructive Algorithmics for Emergent Lattice Interaction eXperiments" href="https://caelix.co.uk/" target="_blank" rel="noopener">CAELIX</a> framework: the fine structure constant α and the Higgs vacuum expectation value.</p> <p>The note does not claim a closed derivation of the full scale problem. Its purpose is narrower and more architectural. It argues that <a title="CAELIX - Constructive Algorithmics for Emergent Lattice Interaction eXperiments" href="https://caelix.co.uk/" target="_blank" rel="noopener">CAELIX</a> requires two distinct but structurally linked meanings of scale: Burden and Resolution.</p> <p>The burden ladder concerns the computation required to sustain and propagate a motif on the substrate. The resolution ladder concerns how deeply a probe forces internal structure into view.</p> <p>Within that split architecture, the low-energy fine structure candidate is treated as a junction quantity:</p> <p> </p> <p>α⁻¹ = 4π³ + π² + π − 1/3315</p> <p> </p> <p>The scaffold 4π³ + π² + π is read as belonging to the long-wavelength side of the resolution ladder, while the modifier 1/(3 × 5 × 13 × 17) is read as a burden-side bookkeeping term inherited from the substrate.</p> <p>The Higgs vacuum expectation value is treated as a second boundary candidate:</p> <p> </p> <p>v ∼ M_Pl / 243⁷</p> <p> </p> <p>Its role in the note is not to close the hierarchy problem, but to show why the electroweak scale also appears near the same unresolved interface between geometric scaffold, computational burden and scale selection.</p> <p>The leading running hypothesis advanced here is observation-cost running. On this view, the low-energy electromagnetic regime forms a broad infrared plateau. Running begins when probe resolution starts to penetrate charged burden structure. The measured running of α is then interpreted as the macroscopic signature of additional computation forced by deeper observation of charged lattice patterns.</p> <p>The note is explicitly provisional. It does not claim a full forward derivation of the coefficient pattern (4,1,1), a finished renormalisation law, exact threshold locations for the running of α, or a completed solution to the Higgs hierarchy problem. It is intended as a disciplined working architecture and as a guide for later computational and experimental tests.</p> |
| title | Scale and Boundary Candidates in CAELIX |
| topic | CAELIX fine structure constant Higgs vacuum expectation value observation-cost running balanced ternary discrete lattice physics emergent physics scale hierarchy burden ladder resolution ladder electromagnetic coupling vacuum polarisation threshold penetration particle as pattern computational burden Mathematical physics Particle physics Quantum physics Theoretical physics Computational topology |
| url | https://doi.org/10.5281/zenodo.19421875 |