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This note documents a precise rational identity in the HR biface-genesis branch of bigravity.

May 8, 2026Open Access

BPB/MBE HR Rational Branch: Exact a0 = cH0/5 Priority Technical Note

Key Points

This note documents a precise rational identity in the HR biface-genesis branch of bigravity.
Identified the binomial HR cosmological potential V_g^F(y) and its parameters including β0, β1, β2, β3, and y_t.
Calculated structural acceleration scale a0^HR and compared it with the source-locked HAL corpus value.
Provided technical note and audit scripts in Python, JSON, and Markdown formats.
The branch yields V_g^F(y_t)=81/100 leading to the calculated value of ΔΩ=81/500.
Established Ω_perm=81/125 and s_HR=4/5, resulting in 1−s_HR=1/5.
Differentiated the exact structural acceleration scale a0^HR as cH0/5 from HAL corpus value 1−s_surv,0.

Abstract

This priority technical note records an exact rational identity in the BPB/MBE biface-genesis branch of ghost-free Hassan–Rosen bigravity. For the binomial HR cosmological potential VgF (y) =β0+3β1 y+3β2 y²+β3 y³ with β0=459/500, β1=-27/100, β2=3/5, β3=-1 and yₜ=3/10, the branch gives VgF (yₜ) =81/100, ΔΩ=81/500, Ωₚerm=β0+β1=81/125, sHR=Ωₚerm/VgF (yₜ) =4/5, and therefore 1−sHR=1/5. The corresponding exact structural acceleration scale is a0HR=cH0/5. The note explicitly distinguishes this rational HR branch value from the source-locked HAL corpus value 1−sₛurv, 0=0. 2043075602291394. The package includes the technical note, LaTeX source, exact Python audit script, JSON/Markdown audit outputs, and hostile-review guardrails.

BPB/MBE HR Rational Branch: Exact a0 = cH0/5 Priority Technical Note

Key Points

Abstract

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