Scalar-Derived Gauge Closure of the QDL–SO10–1 Benchmark: Explicit Threshold Blocks, Dynkin-Index Accounting, and the v0.3 Closure Test
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2026
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| _version_ | 1866901498669039616 |
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| author | Bourassa, James D. |
| author_facet | Bourassa, James D. |
| contents | <p>The QDL-SO10-1 grand-unification sequence defines a closure-first SO(10)-compatible benchmark within the Quantized Dimensional Ledger (QDL) program. Papers #1-#3 established the initial benchmark trilogy: a fixed SO(10)-compatible benchmark, its low-energy phenomenology, and a stress-test / robustness audit. Paper #5 began the executable hardening sequence by revising the gauge-closure target to inverse alpha_U = 44.501718, corresponding to alpha_U = 0.022471, and by converting the remaining Pati-Salam channel splittings into calibrated high-scale threshold targets.</p> <p>This paper supplies the v0.3 scalar-threshold hardening layer. The derivation is explicitly block-level: it proves that the calibrated v0.2 offset vector lies in a declared Dynkin-index threshold span, but it does not yet constitute a full component-by-component SO(10) scalar census. Three aggregate threshold blocks are introduced with traceless Dynkin-index splitting vectors d4 = (12, -6, -6), dL = (-6, 12, -6), and dR = (-6, -6, 12), equivalently corresponding to aggregate Dynkin-index blocks S4 = (18, 0, 0), SL = (0, 18, 0), and SR = (0, 0, 18) after common-shift subtraction.</p> <p>Using the high-scale threshold formula lambda_i = -(1 / 12 pi) times the sum over threshold blocks of S_i times ln(M_a / M_U), with M_U = 1.00 x 10^16 GeV, the v0.3 solution is ln r4 = 2.689679, ln rL = -1.989712, and ln rR = -0.699967. The corresponding threshold masses are M4 = 1.472695 x 10^17 GeV, ML = 1.367348 x 10^15 GeV, and MR = 4.966016 x 10^15 GeV. The derived threshold vector is (-1.284227, 0.950018, 0.334210), with RMS threshold residual below 10^-12 at displayed precision.</p> <p>The result advances QDL-SO10-1 from calibrated executable gauge closure to block-level scalar-derived gauge closure. It is a proof-of-principle scalar-threshold derivation layer, not the final microscopic scalar-sector completion. The next burden is a full component-level SO(10) to Pati-Salam to Standard Model scalar census and QDL admissibility verification.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19798837 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Scalar-Derived Gauge Closure of the QDL–SO10–1 Benchmark: Explicit Threshold Blocks, Dynkin-Index Accounting, and the v0.3 Closure Test Bourassa, James D. Quantized Dimensional Ledger QDL–SO10–1 SO(10) Pati–Salam grand unification scalar thresholds gauge coupling unification Dynkin indices threshold matching executable benchmark structural admissibility scalar-derived closure threshold blocks <p>The QDL-SO10-1 grand-unification sequence defines a closure-first SO(10)-compatible benchmark within the Quantized Dimensional Ledger (QDL) program. Papers #1-#3 established the initial benchmark trilogy: a fixed SO(10)-compatible benchmark, its low-energy phenomenology, and a stress-test / robustness audit. Paper #5 began the executable hardening sequence by revising the gauge-closure target to inverse alpha_U = 44.501718, corresponding to alpha_U = 0.022471, and by converting the remaining Pati-Salam channel splittings into calibrated high-scale threshold targets.</p> <p>This paper supplies the v0.3 scalar-threshold hardening layer. The derivation is explicitly block-level: it proves that the calibrated v0.2 offset vector lies in a declared Dynkin-index threshold span, but it does not yet constitute a full component-by-component SO(10) scalar census. Three aggregate threshold blocks are introduced with traceless Dynkin-index splitting vectors d4 = (12, -6, -6), dL = (-6, 12, -6), and dR = (-6, -6, 12), equivalently corresponding to aggregate Dynkin-index blocks S4 = (18, 0, 0), SL = (0, 18, 0), and SR = (0, 0, 18) after common-shift subtraction.</p> <p>Using the high-scale threshold formula lambda_i = -(1 / 12 pi) times the sum over threshold blocks of S_i times ln(M_a / M_U), with M_U = 1.00 x 10^16 GeV, the v0.3 solution is ln r4 = 2.689679, ln rL = -1.989712, and ln rR = -0.699967. The corresponding threshold masses are M4 = 1.472695 x 10^17 GeV, ML = 1.367348 x 10^15 GeV, and MR = 4.966016 x 10^15 GeV. The derived threshold vector is (-1.284227, 0.950018, 0.334210), with RMS threshold residual below 10^-12 at displayed precision.</p> <p>The result advances QDL-SO10-1 from calibrated executable gauge closure to block-level scalar-derived gauge closure. It is a proof-of-principle scalar-threshold derivation layer, not the final microscopic scalar-sector completion. The next burden is a full component-level SO(10) to Pati-Salam to Standard Model scalar census and QDL admissibility verification.</p> |
| title | Scalar-Derived Gauge Closure of the QDL–SO10–1 Benchmark: Explicit Threshold Blocks, Dynkin-Index Accounting, and the v0.3 Closure Test |
| topic | Quantized Dimensional Ledger QDL–SO10–1 SO(10) Pati–Salam grand unification scalar thresholds gauge coupling unification Dynkin indices threshold matching executable benchmark structural admissibility scalar-derived closure threshold blocks |
| url | https://doi.org/10.5281/zenodo.19798837 |