What question did this study set out to answer?

This research aims to extend the Nico sector model to include the alpha-chain, examining the implications for the carbon-oxygen ratio in early star-forming galaxies.

June 8, 2026Open Access

Paper CCLXXV: Carbon-to-Oxygen from the kappa=0->kappa=-1 Boundary -- Extending the Nico Isobaric Sector to the alpha-Chain, a Hard C/O Ceiling of Unity, and the z=6.625 Test (LAP1-B)

Key Points

This research aims to extend the Nico sector model to include the alpha-chain, examining the implications for the carbon-oxygen ratio in early star-forming galaxies.
Extends the Nico sector model to the alpha-chain by analyzing the carbon-burning step.
Tests predictions against the chemical composition of the LAP1-B galaxy at redshift z=6.625.
Evaluates the kappa-crossing behavior in relation to C/O ratios and elemental abundances.
Log(C/O)=-0.07(+0.16/-0.24) in LAP1-B aligns with the predicted ceiling; deviation below -0.25 falsifies the model.
C/O ratios approach a hard ceiling of 1 for the alpha-channel; predictions indicate a positive correlation with [Ni/Fe] excess.
The model asserts that C/O cannot exceed 1, bounding the behavior of stellar nucleosynthesis mechanisms.

Abstract

The Nico sector (Paper CLIX) derives Fe-group anomalies (10-20% Ni/Fe CCSN overproduction, presolar grain delta (61Ni/58Ni), Mn/Ni tension) from isobaric Co->Ni transmutation at the kappa=0->kappa=-1 G2-permutohedron boundary via the H- square-face sector with the zero-parameter cross-term sqrt6/28. That sector is Fe-group only. We extend it to the light alpha-chain. The alpha particle (4He, four nucleons) is a quaternion unit (dim H=4) ; 12C=3 alpha closes on the three imaginary quaternion axes i, j, k (the same transverse triad carrying sigmaT2*= (1/2) ³ in CCXLVII/CCLXVIII), while 16O=4 alpha requires also closing the longitudinal real axis. The carbon-burning step 12C (a, g) 16O is one additional valve-gated kappa-crossing carrying the canonical Fano coefficient sigmaₑ7=1/2, so the steady-state ratio is C/O= (1-p) /p=1 (p=1/2): a hard ceiling, log (C/O) ->0, in the pristine metal-free limit, declining toward solar (C/O=0. 55, Nₑff=1. 50 crossings) as enrichment adds crossings. Test: LAP1-B at z=6. 625 (Nakajima et al. 2026, Nature 653), the most chemically primitive star-forming galaxy known (12+log O/H=6. 31, 4. 2e-3 solar), has log (C/O) =-0. 07 (+0. 16/-0. 24), sitting on the predicted ceiling at 0. 44 sigma, on the CEMP/UFD locus above the ordinary trend. Predictions: P1 hard ceiling C/O>1 needs a separate channel) ; P2 the C/O (N) relation approaches the ceiling asymptotically at lowest O/H; P3 LAP1-B log (C/O) =0. 00, falsified if tightened below ~-0. 25; P4 cross-sector -- C/O elevation correlates positively with the CLIX Ni/Fe excess in the same population (same boundary, same event), a link absent from standard yields. Honest scope: load-bearing assumption is that 12C (a, g) 16O is one valve-gated crossing at exactly 1/2 (sensitivity: +-0. 05 in p moves log C/O by ~0. 09 dex) ; the channel cannot reach C/O>>1; LAP1-B's hard ionizing field (stellar-SED) is outside this abundance law; single data point at large uncertainty (CIV/OIII=4. 2+-1. 8). Zero free parameters (sigmaₑ7=1/2 reused). Framework count: 276 numbered papers. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10. 5281/zenodo. 19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M. D. , University of Minnesota. ORCID: 0000-0002-1143-941X.

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