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Auteur principal:	De Jesus, Elias
Format:	Recurso digital
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Publié:	Zenodo 2026
Sujets:	Tellegen budget, dual partition, AM–GM–HM inequality, Lorentz factor, budget halving, coherence corridor, binary black holes, power means, aggregated reconstruction
Accès en ligne:	https://doi.org/10.5281/zenodo.19417533
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For a conserved binary partition a + b = 1 with Thales altitude h = √ab and Lorentz factor γ = 1/(2h), the Tellegen budget h2 + χ2/4 = 1/4 constrains the total information capacity of a single partition to 1/4 [1]. We prove that the maximum of the doubly contracted gap GM − HM = (γ − 1)/(2γ2) is exactly 1/8, attained uniquely at γ = 2. This establishes the Dual Tellegen Budget: the maximum information that can be stored in the inter-layer coupling between two adjacent levels of the AM–GM–HM hierarchy is exactly half the single- partition Tellegen budget. At γ = 2: the upper-layer gap is AM − GM = 1/4 (one Tellegen unit), the lower-layer gap is GM − HM = 1/8 (one Dual Tellegen unit), and the total gap is AM − HM = 3/8. The upper-to-lower ratio is exactly 2. At γ = 2, the coupling power is h2 = 1/16, while the lower-layer gap is GM − HM = 1/8 = 2h2: the Dual Tellegen budget is twice the coupling power at this point. We test the budget halving principle—the conjecture that each successive nesting level of the power mean hierarchy halves the available budget—by computing the maxima of adjacent power-mean gaps Mp − Mp−1 on a + b = 1 for p = 0, −1, −2, −3, −4. The halving is exact for Levels 0–2 (the AM–GM–HM triad: maxima 1/2, 1/4, 1/8) and breaks at Level 3, where the maximum of HM − M−2 is approximately 0.0467, not 1/16 = 0.0625. The Level 3 maximum occurs at γ ≈ 1.33, R ≈ 1.77—just above the nominal corridor ceiling 7/4 = 1.75. Empirical tests on 4,149 binary black hole simulations from the SXS catalog confirm: (i) the γ = 2 state appears in the GW150914 time-resolved merger at t ≈ +0.03 s with GM − HM = 0.12498 ≈ 1/8; (ii) stellar spectral models cluster near γ = 2 at T ≈ 30,000 K (ionizing partition) and T ≈ 35,000 K (UV partition); (iii) three NANOGrav pulsars sit at γ ≈ 2 with GM − HM ≈ 0.124; and (iv) the reconstruction principle from aggregated scalar geometry predicts that each additional gap measurement should add independent information, which is confirmed: the second gap (GM–HM) adds 14.8% to radiated-energy prediction beyond γ alone, while the third gap (HM–M−2) adds only 0.1% globally but improves prediction by 270% specifically within the corridor.

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