| _version_ | 1866901371366670336 |
|---|---|
| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <p>For a conserved binary partition a + b = 1 with Thales altitude h = √ab and Lorentz<br>factor γ = 1/(2h), the Tellegen budget h2 + χ2/4 = 1/4 constrains the total information<br>capacity of a single partition to 1/4 [1]. We prove that the maximum of the doubly contracted<br>gap GM − HM = (γ − 1)/(2γ2) is exactly 1/8, attained uniquely at γ = 2. This establishes<br>the Dual Tellegen Budget: the maximum information that can be stored in the inter-layer<br>coupling between two adjacent levels of the AM–GM–HM hierarchy is exactly half the single-<br>partition Tellegen budget.<br>At γ = 2: the upper-layer gap is AM − GM = 1/4 (one Tellegen unit), the lower-layer<br>gap is GM − HM = 1/8 (one Dual Tellegen unit), and the total gap is AM − HM = 3/8.<br>The upper-to-lower ratio is exactly 2. At γ = 2, the coupling power is h2 = 1/16, while the<br>lower-layer gap is GM − HM = 1/8 = 2h2: the Dual Tellegen budget is twice the coupling<br>power at this point.<br>We test the budget halving principle—the conjecture that each successive nesting level<br>of the power mean hierarchy halves the available budget—by computing the maxima of<br>adjacent power-mean gaps Mp − Mp−1 on a + b = 1 for p = 0, −1, −2, −3, −4. The halving is<br>exact for Levels 0–2 (the AM–GM–HM triad: maxima 1/2, 1/4, 1/8) and breaks at Level 3,<br>where the maximum of HM − M−2 is approximately 0.0467, not 1/16 = 0.0625. The Level 3<br>maximum occurs at γ ≈ 1.33, R ≈ 1.77—just above the nominal corridor ceiling 7/4 = 1.75.<br>Empirical tests on 4,149 binary black hole simulations from the SXS catalog confirm:<br>(i) the γ = 2 state appears in the GW150914 time-resolved merger at t ≈ +0.03 s with<br>GM − HM = 0.12498 ≈ 1/8; (ii) stellar spectral models cluster near γ = 2 at T ≈ 30,000 K<br>(ionizing partition) and T ≈ 35,000 K (UV partition); (iii) three NANOGrav pulsars sit<br>at γ ≈ 2 with GM − HM ≈ 0.124; and (iv) the reconstruction principle from aggregated<br>scalar geometry predicts that each additional gap measurement should add independent<br>information, which is confirmed: the second gap (GM–HM) adds 14.8% to radiated-energy<br>prediction beyond γ alone, while the third gap (HM–M−2) adds only 0.1% globally but<br>improves prediction by 270% specifically within the corridor.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19417533 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Dual Tellegen Budget: Maximum Inter-Layer Transfer at γ = 2 and the Budget Halving Principle De Jesus, Elias Tellegen budget, dual partition, AM–GM–HM inequality, Lorentz factor, budget halving, coherence corridor, binary black holes, power means, aggregated reconstruction <p>For a conserved binary partition a + b = 1 with Thales altitude h = √ab and Lorentz<br>factor γ = 1/(2h), the Tellegen budget h2 + χ2/4 = 1/4 constrains the total information<br>capacity of a single partition to 1/4 [1]. We prove that the maximum of the doubly contracted<br>gap GM − HM = (γ − 1)/(2γ2) is exactly 1/8, attained uniquely at γ = 2. This establishes<br>the Dual Tellegen Budget: the maximum information that can be stored in the inter-layer<br>coupling between two adjacent levels of the AM–GM–HM hierarchy is exactly half the single-<br>partition Tellegen budget.<br>At γ = 2: the upper-layer gap is AM − GM = 1/4 (one Tellegen unit), the lower-layer<br>gap is GM − HM = 1/8 (one Dual Tellegen unit), and the total gap is AM − HM = 3/8.<br>The upper-to-lower ratio is exactly 2. At γ = 2, the coupling power is h2 = 1/16, while the<br>lower-layer gap is GM − HM = 1/8 = 2h2: the Dual Tellegen budget is twice the coupling<br>power at this point.<br>We test the budget halving principle—the conjecture that each successive nesting level<br>of the power mean hierarchy halves the available budget—by computing the maxima of<br>adjacent power-mean gaps Mp − Mp−1 on a + b = 1 for p = 0, −1, −2, −3, −4. The halving is<br>exact for Levels 0–2 (the AM–GM–HM triad: maxima 1/2, 1/4, 1/8) and breaks at Level 3,<br>where the maximum of HM − M−2 is approximately 0.0467, not 1/16 = 0.0625. The Level 3<br>maximum occurs at γ ≈ 1.33, R ≈ 1.77—just above the nominal corridor ceiling 7/4 = 1.75.<br>Empirical tests on 4,149 binary black hole simulations from the SXS catalog confirm:<br>(i) the γ = 2 state appears in the GW150914 time-resolved merger at t ≈ +0.03 s with<br>GM − HM = 0.12498 ≈ 1/8; (ii) stellar spectral models cluster near γ = 2 at T ≈ 30,000 K<br>(ionizing partition) and T ≈ 35,000 K (UV partition); (iii) three NANOGrav pulsars sit<br>at γ ≈ 2 with GM − HM ≈ 0.124; and (iv) the reconstruction principle from aggregated<br>scalar geometry predicts that each additional gap measurement should add independent<br>information, which is confirmed: the second gap (GM–HM) adds 14.8% to radiated-energy<br>prediction beyond γ alone, while the third gap (HM–M−2) adds only 0.1% globally but<br>improves prediction by 270% specifically within the corridor.</p> |
| title | The Dual Tellegen Budget: Maximum Inter-Layer Transfer at γ = 2 and the Budget Halving Principle |
| topic | Tellegen budget, dual partition, AM–GM–HM inequality, Lorentz factor, budget halving, coherence corridor, binary black holes, power means, aggregated reconstruction |
| url | https://doi.org/10.5281/zenodo.19417533 |