Toroidal Black Holes II E = mc3, 5D Continuous Poloidal Winding, Mass–Energy Packaging, and the Dimensional Signature of c
Abstract
Part II of the Toroidal Black Hole (TBH) programme develops a continuous-winding account of the Obscura transition. The central proposal is that a collapsing toroidal configuration does not merely capture light: it captures and reorganises the complete incoming mass–energy content, including matter, radiation, and field excitations. A single poloidal circulation progressively wraps this content into a layered interior. Each completed traversal increments a hypermechanical layer counter; above a critical activation condition, the hidden spatial coordinate χ becomes dynamically accessible. The resulting 4 + 1 sector is then related to the observable 3 + 1 sector by a projection map.
The second contribution is a sector-indexed dimensional ladder. Its visible rung is the familiar E2 = m2c2. The proposed hypermechanical rung is written E3 = m3c3H, where cH is the characteristic scale of the hidden sector. This is not introduced as a replacement for the measured relation in our sector. Rather, it is a conjectured level-native generator whose relation to observable energy must be supplied by an explicit projection map. The index n = Ds − 1 is motivated by the dimension of the directional sphere SDs−1 in a sector with Ds spatial dimensions; this geometric correspondence motivates the ladder but does not, by itself, derive the law En ∝ mncn.
The third contribution makes the relation between layer accumulation and operational time explicit. A hypermechanical layer invariant Jn = Enτn is defined at each level, while the conversion from that invariant to a coordinate increment ∆χ is assigned to a projection functional Πχ. This separates an intrinsic level quantity from its observable coordinate representation and avoids silently identifying unlike sector-native quantities.
The paper also revisits conditional predictions associated with the working closure R/r = π: Ωm = 1/π, ΩΛ = 1 − 1/π, a circulation threshold βcrit = 1/π under a stated Reynolds-number closure, and a projected secondary-layer radius ratio r1/r0 = 1−1/π. These are model hypotheses, not established consequences of TBH geometry. Agreement with a cosmological parameter value is not treated as validation; current DESI DR2 analyses and their data-combination dependence are explicitly noted. Each major conjecture is paired with a numerical, observational, or logical falsification condition. The framework remains speculative and is presented as a structured programme for derivation and testing.
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BibTeX
@misc{kleschev2026toroidal,
title = {{Toroidal Black Holes II E = mc3, 5D Continuous Poloidal Winding, Mass–Energy Packaging, and the Dimensional Signature of c}},
author = {Anton Kleschev},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23599143},
url = {https://zenodo.org/records/23599143},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Toroidal Black Holes II E = mc3, 5D Continuous Poloidal Winding, Mass–Energy Packaging, and the Dimensional Signature of c
AU - Anton Kleschev
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23599143
UR - https://zenodo.org/records/23599143
AB - Part II of the Toroidal Black Hole (TBH) programme develops a continuous-winding account of the Obscura transition. The central proposal is that a collapsing toroidal configuration does not merely capture light: it captures and reorganises the complete incoming mass–energy content, including matter, radiation, and field excitations. A single poloidal circulation progressively wraps this content into a layered interior. Each completed traversal increments a hypermechanical layer counter; above a critical activation condition, the hidden spatial coordinate χ becomes dynamically accessible. The resulting 4 + 1 sector is then related to the observable 3 + 1 sector by a projection map. The second contribution is a sector-indexed dimensional ladder. Its visible rung is the familiar E2 = m2c2. The proposed hypermechanical rung is written E3 = m3c3H, where cH is the characteristic scale of the hidden sector. This is not introduced as a replacement for the measured relation in our sector. Rather, it is a conjectured level-native generator whose relation to observable energy must be supplied by an explicit projection map. The index n = Ds − 1 is motivated by the dimension of the directional sphere SDs−1 in a sector with Ds spatial dimensions; this geometric correspondence motivates the ladder but does not, by itself, derive the law En ∝ mncn. The third contribution makes the relation between layer accumulation and operational time explicit. A hypermechanical layer invariant Jn = Enτn is defined at each level, while the conversion from that invariant to a coordinate increment ∆χ is assigned to a projection functional Πχ. This separates an intrinsic level quantity from its observable coordinate representation and avoids silently identifying unlike sector-native quantities. The paper also revisits conditional predictions associated with the working closure R/r = π: Ωm = 1/π, ΩΛ = 1 − 1/π, a circulation threshold βcrit = 1/π under a stated Reynolds-number closure, and a projected secondary-layer radius ratio r1/r0 = 1−1/π. These are model hypotheses, not established consequences of TBH geometry. Agreement with a cosmological parameter value is not treated as validation; current DESI DR2 analyses and their data-combination dependence are explicitly noted. Each major conjecture is paired with a numerical, observational, or logical falsification condition. The framework remains speculative and is presented as a structured programme for derivation and testing.
ER -