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2026
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| Acceso en línea: | https://doi.org/10.5281/zenodo.18950168 |
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| _version_ | 1866901779669581824 |
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| author | Bénard, J_T |
| author_facet | Bénard, J_T |
| contents | <h1><span lang="en-GB">Abstract</span></h1> <p><span lang="en-GB">We formulate the hypothesis that </span><span lang="en-GB"><strong>Z₁₂₀ = Z₃ × Z₅ × Z₈</strong></span><span lang="en-GB"> is a universal invariant of biological timing. The three factors have independent biological origins: Z₃ from the rotary mechanism of ATP synthase (Boyer 1997), Z₅ from the five substages of meiotic prophase I and from the cardinal identity |Z₁₆ \ {e}| = 15 = 3×5, and Z₈ from the Bott periodicity residue in the Clifford tower Cl⁺(3). Their product 120 = 3×5×8 appears simultaneously as: (i) the denominator of the spectral invariant </span>η<span lang="en-GB"> = 49/120 of the Dirac operator on T²/Z₁₆; (ii) the lifespan in days of the erythrocyte; (iii) the number of degrees in each step of the ATP synthase </span>γ<span lang="en-GB">-rotation; (iv) the period of the Rule 150/105 cellular automaton on a ring of size N=120. The hypothesis predicts that biological processes governed by Z₃ symmetry will manifest characteristic timescales that are multiples of 40 = lcm(8,5) = 120/3. We identify the collagen triple helix as the critical test case and propose a falsifiable research program.</span></p> <p lang="en-GB"> </p> <p><span lang="en-GB"><strong>Keywords: </strong></span><span lang="en-GB">Z₁₂₀, biological periodicity, ATP synthase, erythrocyte, spectral invariant, T144, orbifold, Clifford algebra, universality hypothesis</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18950168 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Z₁₂₀ = Z₃ × Z₅ × Z₈ : Invariant universel des cycles biologiques Bénard, J_T <h1><span lang="en-GB">Abstract</span></h1> <p><span lang="en-GB">We formulate the hypothesis that </span><span lang="en-GB"><strong>Z₁₂₀ = Z₃ × Z₅ × Z₈</strong></span><span lang="en-GB"> is a universal invariant of biological timing. The three factors have independent biological origins: Z₃ from the rotary mechanism of ATP synthase (Boyer 1997), Z₅ from the five substages of meiotic prophase I and from the cardinal identity |Z₁₆ \ {e}| = 15 = 3×5, and Z₈ from the Bott periodicity residue in the Clifford tower Cl⁺(3). Their product 120 = 3×5×8 appears simultaneously as: (i) the denominator of the spectral invariant </span>η<span lang="en-GB"> = 49/120 of the Dirac operator on T²/Z₁₆; (ii) the lifespan in days of the erythrocyte; (iii) the number of degrees in each step of the ATP synthase </span>γ<span lang="en-GB">-rotation; (iv) the period of the Rule 150/105 cellular automaton on a ring of size N=120. The hypothesis predicts that biological processes governed by Z₃ symmetry will manifest characteristic timescales that are multiples of 40 = lcm(8,5) = 120/3. We identify the collagen triple helix as the critical test case and propose a falsifiable research program.</span></p> <p lang="en-GB"> </p> <p><span lang="en-GB"><strong>Keywords: </strong></span><span lang="en-GB">Z₁₂₀, biological periodicity, ATP synthase, erythrocyte, spectral invariant, T144, orbifold, Clifford algebra, universality hypothesis</span></p> |
| title | Z₁₂₀ = Z₃ × Z₅ × Z₈ : Invariant universel des cycles biologiques |
| url | https://doi.org/10.5281/zenodo.18950168 |