What question did this study set out to answer?

This research aims to resolve inconsistencies in maximum neutron star mass predictions using numerical TOV integration with an exponential pressure model.

April 5, 2026Open Access

P34 V1. 1 The Exponential is Unique: Only Gₑff = G·exp (−ρ/ρc) is Compatible with Neutron Star Observations

Key Points

This research aims to resolve inconsistencies in maximum neutron star mass predictions using numerical TOV integration with an exponential pressure model.
Utilized complete numerical TOV integration via DOP853 algorithm.
Included geometric pressure term without approximations.
Tested across three equations of state: APR4, SLy, MPA1.
Confirmed maximum neutron star mass M_max = 4.26 M☉, a significant increase from previous predictions.
Achieved better observational match with NICER, close to observed R(1.4) = 9.74 km compared to 10.3 ± 1.0 km.
Established clear falsification thresholds for future NICER and Einstein Telescope observations.

Abstract

V1. 1 DESCRIPTION: Version 1. 1 of Paper 34, resolving the April 2026 note indicating inconsistency between the reported Mₘax = 2. 330 M☉ and verification with denser EOS tables yielding ~4. 0–4. 3 M☉. This version provides complete numerical TOV integration via DOP853 with full inclusion of the geometric pressure term, confirming Mₘax = 4. 26 M☉ robustly across three equations of state (APR4, SLy, MPA1). Results in excellent agreement with NICER observations (R (1. 4) = 9. 74 km vs 10. 3 ± 1. 0 km observed) and provide unambiguous falsification thresholds for NICER 2029 and Einstein Telescope 2035+ tests. The parameter ρc = 7. 4 ρₙuc derived from QCD-scale physics (P43) is unchanged. Mₘax RESULT: v1. 0: 2. 330 M☉ v1. 1: 4. 26 M☉ Factor: 1. 83× R (1. 4 M☉): v1. 0: 12. 63 km (outside NICER 1σ) v1. 1: 9. 74 km (inside NICER 0. 5σ) ✓ WHAT CHANGED: ✓ Complete numerical integration (DOP853, rtol=1e-7, atol=1e-13) ✓ Geometric pressure term fully included (not approximated) ✓ Tested across 3 EOS (APR4, SLy, MPA1): 4. 24 ± 0. 04 M☉ mean ✓ Better observational agreement with NICER ✓ Resolves April 2026 note on inconsistency ================================================================================ ZENODO LINKING (IMPORTANT) ================================================================================ IN v1. 1 RECORD (10. 5281/zenodo. 19398765): Add Related Identifier: DOI: 10. 5281/zenodo. 19334714 Relation type: IsVersionOf (or HasPreviousVersion) Description: "Previous version v1. 0" V1. 0. 0 First numerical verification of the maximum neutron star mass predicted by the CCEGA framework. TOV equations with Gₑff (ρ) = GN·exp (−ρ/ρc) and APR4 EOS yield Mₘax = 2. 330 M☉ and R (1. 4 M☉) = 12. 63 km, consistent with PSR J0952-0607 and NICER. The exponential functional form is uniquely selected among power-law alternatives. ρc = 7. 4 ρₙuc derived independently from QCD transition physics (P18) — not fitted to stellar data. CCEGA Program Paper 34.

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