BIG-BANG NUCLEOSYNTHESIS FROM HQIV NETWORK WEIGHTS: LOCK-IN η, EPOCH LADDER, AND INTEGRATED WITNESSES IN THE LEAN LIBRARY

This is the eighth paper in the HQIV preprint series and the fifth Tier-2 closure note. It establishes what the BBN Lean stack formally proves about primordial light-element abundances once lock-in baryon-to-photon ratio η, nucleon masses, and composite-trace binding energies are already fixed by upstream witnesses.

At the imported lock-in value η_paper = 6.10 × 10^{-10}, the faithful stoichiometric integrator (mirrored in Lean) yields:

• Y_p ≈ 0.24422 (within the Cooke-style observed band)
• D/H ≈ 2.51185 × 10^{-5} (within ~0.5σ of the Coc et al. semi-analytic anchor)
• ³He/H ≈ 1.012 × 10^{-5}
• ⁷Li/H ≈ 2.536 × 10^{-10} (pre-astrophysical depletion; inside the broad Spite-plateau envelope)

These readouts are generated from valley counts, Boltzmann weights, and cluster binding Q values on the same 8 × 8 so(8) network used for nucleon binding, combined with a dynamic C₂ lapse clock and stoichiometric synthesis-window integration. No BBN-specific fit of η or nuclear parameters is performed.

Machine-checked Lean vital bundles certify:

• Network vital readout (positivity, η identity, cluster-binding alignment)
• Epoch vital readout (shell-ladder ordering)
• Integrated Y_p witness (within 1% of freeze-out partition)
• Full BBN vital readout (umbrella certificate)

The same local-curvature slot equations and outside modulators are reused from the companion nucleon-binding and baryogenesis papers; only the epoch witness ξ(T) changes. Comparison-layer results (Coc et al. semi-analytics, observational anchors) are recorded explicitly and are never used as inputs.

Reproducibility All numerical witnesses are regenerated by the scripts in the accompanying scripts.zip bundle (primary entry point: hqiv_bbn_integrator.py). Machine-checked proofs live in the public HQIV Lean 4 repository. Data exports (bbn_integrator.json, bbn_paper_tables.json, bbn_witnesses.json) are included.