The No-Singularity Theorem: Representational Exclusion of Infinite Curvature from Cadence Invariance
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2026
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| _version_ | 1866901781674459136 |
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| author | Beaupain, Michael John |
| author_facet | Beaupain, Michael John |
| contents | <p><strong>Description:</strong> Paper S excludes the classical Big Bang singularity from Light Frame Cadence Theory as a structural impossibility rather than a dynamical one. A1 (cadence invariance) fixes <span class="katex"><span class="katex-mathml">C0=1/c>0C_0 = 1/c > 0 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">1/</span><span class="mord mathnormal">c</span><span class="mrel">></span></span><span class="base"><span class="mord">0</span></span></span></span>; A2 (finite contract) bounds the mode load <span class="katex"><span class="katex-mathml">TD2+TS2+TR2≤C0−2\mathrm{TD}^2 + \mathrm{TS}^2 + \mathrm{TR}^2 \le C_0^{-2} </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathrm">TD</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mbin">+</span></span><span class="base"><span class="mord"><span class="mord mathrm">TS</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mbin">+</span></span><span class="base"><span class="mord"><span class="mord mathrm">TR</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mrel">≤</span></span><span class="base"><span class="mord"><span class="mord mathnormal">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">−2</span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span>. Together they force every mode load below <span class="katex"><span class="katex-mathml">cc </span><span class="katex-html"><span class="base"><span class="mord mathnormal">c</span></span></span></span>, so no representable configuration reaches infinite curvature. The singularity is not avoided by a bounce, phase transition, or smoothing mechanism — it is not a member of the representable configuration space. What replaces the singular epoch is a bounded breathing fabric with the CMB as representability boundary, redshift as accumulated representational cost, and closure dynamics at the contract ceiling. Compared with LQC, Penrose CCC, BGV theorem, and pre-Big-Bang / ekpyrotic scenarios; six falsification conditions stated. A secondary Light-Origin corollary (scoped framework-bounded) extends the exclusion to the concept of "beginning" as an ordered event within LFCT.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20269559 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The No-Singularity Theorem: Representational Exclusion of Infinite Curvature from Cadence Invariance Beaupain, Michael John LFCT, no-singularity theorem, initial singularity exclusion, cadence invariance, finite representational contract, bounded curvature, representability boundary, breathing fabric, CMB boundary readout, loop quantum cosmology, Penrose CCC, BGV theorem, Light-Origin corollary, zero free parameters <p><strong>Description:</strong> Paper S excludes the classical Big Bang singularity from Light Frame Cadence Theory as a structural impossibility rather than a dynamical one. A1 (cadence invariance) fixes <span class="katex"><span class="katex-mathml">C0=1/c>0C_0 = 1/c > 0 </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">1/</span><span class="mord mathnormal">c</span><span class="mrel">></span></span><span class="base"><span class="mord">0</span></span></span></span>; A2 (finite contract) bounds the mode load <span class="katex"><span class="katex-mathml">TD2+TS2+TR2≤C0−2\mathrm{TD}^2 + \mathrm{TS}^2 + \mathrm{TR}^2 \le C_0^{-2} </span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathrm">TD</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mbin">+</span></span><span class="base"><span class="mord"><span class="mord mathrm">TS</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mbin">+</span></span><span class="base"><span class="mord"><span class="mord mathrm">TR</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span><span class="mrel">≤</span></span><span class="base"><span class="mord"><span class="mord mathnormal">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">−2</span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span>. Together they force every mode load below <span class="katex"><span class="katex-mathml">cc </span><span class="katex-html"><span class="base"><span class="mord mathnormal">c</span></span></span></span>, so no representable configuration reaches infinite curvature. The singularity is not avoided by a bounce, phase transition, or smoothing mechanism — it is not a member of the representable configuration space. What replaces the singular epoch is a bounded breathing fabric with the CMB as representability boundary, redshift as accumulated representational cost, and closure dynamics at the contract ceiling. Compared with LQC, Penrose CCC, BGV theorem, and pre-Big-Bang / ekpyrotic scenarios; six falsification conditions stated. A secondary Light-Origin corollary (scoped framework-bounded) extends the exclusion to the concept of "beginning" as an ordered event within LFCT.</p> |
| title | The No-Singularity Theorem: Representational Exclusion of Infinite Curvature from Cadence Invariance |
| topic | LFCT, no-singularity theorem, initial singularity exclusion, cadence invariance, finite representational contract, bounded curvature, representability boundary, breathing fabric, CMB boundary readout, loop quantum cosmology, Penrose CCC, BGV theorem, Light-Origin corollary, zero free parameters |
| url | https://doi.org/10.5281/zenodo.20269559 |