A Channel-Resolved Energy Tensor as the Source of Gravity: Structure, Minimum-Length Regularization, Exact Gauge Coupling Unification, and Falsifiable Predictions

We write the source of the Einstein equation as a two-point, channel-resolved tensor whose internal indices label the four interactions of the matter Lagrangian: electromagnetic, strong, weak and Yukawa. Requiring every Standard Model particle to occupy exactly one slot forces rank four, giving 35 internal slots of which three vanish by gauge invariance. The partition is checked against g* = 106.75, a check that caught a three-degree-of-freedom double count. The Higgs mechanism becomes an exact transfer between slots, and metric contraction gives 32 equations of state separating Higgs-generated from QCD-generated mass. Because a single Newton constant multiplies the whole sum, the contracted Bianchi identity forbids differences between channel couplings. In the operator formulation the transfer rate is a commutator, so the sum rule follows from antisymmetry, and the functional-independence step becomes a decidable rank condition rather than an assumption. The conclusion is that the couplings are equal, the common part being a redefinition of G. The minimum length is derived, not postulated. Spacetime is a complex of rigid edges, two-dimensional cells carrying curvature as a deficit angle, and link nodes. Two independent conditions fix the scale and agree with a margin of 1.18, giving |QS| = 1.6651 Planck lengths. The cell shape is also derived: holography requires four cells at every node and one bit per cell requires equal areas, and of the seventeen flat vertex configurations only the square tiling satisfies both. In four dimensions the block is therefore a tesseract, not a simplex, since a rigid equilateral simplicial complex admits no flat configuration at all. The field equation on the complex varies the area rather than the dihedral angle. Varying the angle admits no vacuum solution; varying the area lets the Schlaefli identity remove the angle terms and gives the Regge form of Einstein's equation, with flat space as the vacuum solution. On a small complex the resulting constraints commute and physical states exist, where the angle variation gives an anomaly and none. The geometry is quantum: the area spectrum is discrete, an Immirzi-like parameter follows from the one-bit condition rather than being tuned, a single cell is in genuine superposition, and the classical limit is recovered because the spread of a typical state falls as one over root N. The construction is finite within a cutoff at 1.889 Planck masses, which is not the same as ultraviolet completeness. The earlier smeared-source implementation, and the no-go theorem that forced it, are withdrawn and replaced. One-loop coupling unification follows from two vector-like SU(2) triplets and a colour octet; the same triplets mediate the type-III seesaw, and standard thermal leptogenesis succeeds without resonance, with gauge annihilation included and suppressing the efficiency by only 7.6%. The framework has two bounded parameters. The sharpest experimental proposal is a channel-separated equivalence-principle test. Surveying all 280,840 three-pair combinations of sixteen materials, about one in twelve is well conditioned, so the separation is generic rather than a special design. We show that such a test bounds the coupling of QCD-generated mass as a whole rather than the trace anomaly alone, since the anomaly share and the absorbed remainder are exactly proportional, and we survey why pulsars, clocks, lunar laser ranging, atom interferometry and antimatter each fail to substitute. We also report negative results: six routes to deriving the tensor-to-scalar ratio all fail, and a survey of flavour mechanisms closes the predictive modular case. Claims tested and withdrawn are listed explicitly, including several withdrawn in this revision.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-25
DOI
https://doi.org/10.5281/zenodo.21871552
Primary Topic
International Science and Diplomacy
Type
preprint
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preprint

A Channel-Resolved Energy Tensor as the Source of Gravity: Structure, Minimum-Length Regularization, Exact Gauge Coupling Unification, and Falsifiable Predictions

Dr Sharanagouda N Patil, Naphatsakorn Suriyawong
Zenodo (CERN European Organization for Nuclear Research)
International Science and Diplomacy
preprint

A Channel-Resolved Energy Tensor as the Source of Gravity: Structure, Minimum-Length Regularization, Exact Gauge Coupling Unification, and Falsifiable Predictions

Dr Sharanagouda N Patil, Naphatsakorn Suriyawong
preprint en

Abstract

We write the source of the Einstein equation as a two-point, channel-resolved tensor whose internal indices label the four interactions of the matter Lagrangian: electromagnetic, strong, weak and Yukawa. Requiring every Standard Model particle to occupy exactly one slot forces rank four, giving 35 internal slots of which three vanish by gauge invariance. The partition is checked against g* = 106.75, a check that caught a three-degree-of-freedom double count. The Higgs mechanism becomes an exact transfer between slots, and metric contraction gives 32 equations of state separating Higgs-generated from QCD-generated mass. Because a single Newton constant multiplies the whole sum, the contracted Bianchi identity forbids differences between channel couplings. In the operator formulation the transfer rate is a commutator, so the sum rule follows from antisymmetry, and the functional-independence step becomes a decidable rank condition rather than an assumption. The conclusion is that the couplings are equal, the common part being a redefinition of G. The minimum length is derived, not postulated. Spacetime is a complex of rigid edges, two-dimensional cells carrying curvature as a deficit angle, and link nodes. Two independent conditions fix the scale and agree with a margin of 1.18, giving |QS| = 1.6651 Planck lengths. The cell shape is also derived: holography requires four cells at every node and one bit per cell requires equal areas, and of the seventeen flat vertex configurations only the square tiling satisfies both. In four dimensions the block is therefore a tesseract, not a simplex, since a rigid equilateral simplicial complex admits no flat configuration at all. The field equation on the complex varies the area rather than the dihedral angle. Varying the angle admits no vacuum solution; varying the area lets the Schlaefli identity remove the angle terms and gives the Regge form of Einstein's equation, with flat space as the vacuum solution. On a small complex the resulting constraints commute and physical states exist, where the angle variation gives an anomaly and none. The geometry is quantum: the area spectrum is discrete, an Immirzi-like parameter follows from the one-bit condition rather than being tuned, a single cell is in genuine superposition, and the classical limit is recovered because the spread of a typical state falls as one over root N. The construction is finite within a cutoff at 1.889 Planck masses, which is not the same as ultraviolet completeness. The earlier smeared-source implementation, and the no-go theorem that forced it, are withdrawn and replaced. One-loop coupling unification follows from two vector-like SU(2) triplets and a colour octet; the same triplets mediate the type-III seesaw, and standard thermal leptogenesis succeeds without resonance, with gauge annihilation included and suppressing the efficiency by only 7.6%. The framework has two bounded parameters. The sharpest experimental proposal is a channel-separated equivalence-principle test. Surveying all 280,840 three-pair combinations of sixteen materials, about one in twelve is well conditioned, so the separation is generic rather than a special design. We show that such a test bounds the coupling of QCD-generated mass as a whole rather than the trace anomaly alone, since the anomaly share and the absorbed remainder are exactly proportional, and we survey why pulsars, clocks, lunar laser ranging, atom interferometry and antimatter each fail to substitute. We also report negative results: six routes to deriving the tensor-to-scalar ratio all fail, and a survey of flavour mechanisms closes the predictive modular case. Claims tested and withdrawn are listed explicitly, including several withdrawn in this revision.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
International Science and Diplomacy
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