This document is a sub-report of the Banya Framework Master Report.
Banya Framework Operation Report
Inventor: Han Hyukjin (bokkamsun@gmail.com)
Date: 2026-03-25
The Higgs boson was discovered at the LHC in 2012, but the Standard Model cannot explain why the Higgs self-coupling constant $\lambda_H$ is approximately 0.13. The Standard Model leaves $\lambda_H$ as a free parameter. Likewise, why $m_H \approx 125$ GeV and why the ratio to the top quark mass $m_t \approx 172$ GeV is $\approx 0.72$ remain unexplained. These three values are interrelated yet their origin is unknown.
Analogy: the room size (Higgs mass), pillar thickness (top mass), and wall thickness (self-coupling) of a building are fixed, but there is no blueprint explaining why these proportions.
Hit
D-24 error 0.16%, D-25 error 0.10% (0.7$\sigma$), D-37 error 0.73% (D-24, D-16 assumed). All three values determined by CAS numbers $7$ and $27=3^3$.
Observed: 0.1293, Error: 0.16%
$7$ = CAS complete value, $54 = 2 \times 27 = 2 \times 3^3$. The Higgs self-coupling is determined by the ratio of CAS numbers.
Observed: 125.25 GeV, Error: 0.10% (0.7$\sigma$)
Directly derived from D-24. Multiplying the vacuum expectation value $v = 246.22$ GeV by $\sqrt{7/27}$ yields the Higgs mass.
Derived: $\sqrt{14/27} = 0.7200$, Observed: $125.25/172.69 = 0.7253$, Error: 0.73% (D-24, D-16 assumed)
$14 = 2 \times 7$, $27 = 3^3$. The Higgs-top cost ratio is determined by CAS numbers.
This round uses the cost structure of CAS operations. In the Banya equation, the cost of the observer writing state (CAS) manifests as the Higgs self-coupling.
From the CAS cost structure, substitute complete value $7$ and lattice volume $3^3 = 27$ into physical coupling constants.
CAS complete value: 7 Lattice volume: 3^3 = 27 Dual-axis cost: 2 Vacuum expectation value: v = 246.22 GeV Higgs mass relation: m_H = v * sqrt(2 * lambda_H) Top quark mass: m_t = 172.69 GeV (observed)
From $\lambda_H = 7/54$, derive the Higgs mass and Higgs-top ratio.
All three derivations are determined solely by CAS complete value $7$ and lattice volume $27 = 3^3$. This shows the free parameters of the Higgs sector are inevitable consequences of the CAS cost structure.
The ratio $2\lambda_H = 7/27$ appears repeatedly. $7/27$ is the ratio of CAS complete value to 3D lattice volume, and it is the single ratio governing the entire Higgs sector.
| Item | Current State | Resolution Path |
|---|---|---|
| Direct $\lambda_H$ measurement | LHC Run 3 ongoing, precision not yet sufficient | Await HL-LHC results |
| D-37 ratio experimental verification | $m_H/m_t$ ratio precision needs improvement | Verifiable with improved $m_t$ precision measurement |
| Item | Result | Status |
|---|---|---|
| D-24: $\lambda_H = 7/54$ | $0.12963$, error $0.16\%$ | Hit |
| D-25: $m_H = v\sqrt{7/27}$ | $125.37$ GeV, error $0.10\%$ | Hit |
| D-37: $m_H/m_t = \sqrt{14/27}$ | Derived $0.7200$, Observed $0.7253$, error $0.73\%$ (D-24, D-16 assumed) | Hit |