Entropic Gravity on a Dark Superfluid: A Six-Manuscript Series (Papers I–V and the Letter)

A six-manuscript series deriving the Milgrom acceleration scale from the cosmological constant, with no adjustable parameters, by joining two published results: the Dorau–Much theorem (the semiclassical Einstein equations from quantum relative entropy; Phys. Rev. Lett. 136, 091602 (2026) ) and Berezhiani–Khoury superfluid dark matter (Phys. Rev. D 92, 103510 (2015) ). Assuming dark matter is a light boson that condenses in galactic halos, and adding two postulates — Einstein's fluctuation measure on the Dorau–Much entropy functional, and the entropy–area law on the condensate's own acoustic horizons — the series derives a₀ = c²√ (Λ/24π) = (1. 080 ± 0. 010) ×10⁻¹⁰ m s⁻² (4–11% below the empirical determinations), an emergent Newton constant that is counted rather than fitted, a dark-energy sector in which Λ is an integration constant and w = −1 a structural identity, the carrier's identity card (a 6–16 eV misalignment axion-like particle), and a zero-parameter galactic phenomenology package. The series is staked on a pre-registered falsification calendar headed by a frozen, single-fork Gaia DR4 wide-binary prediction — δṽ = 0. 12–0. 17, decided on 2026-12-02: a clean Newtonian outcome kills the proposal outright. Contents: • Paper I (flagship) — assumptions A1–A4; the a₀ law; the counted Gₚh; the separation theorem; dark energy; a critical assessment of the assumptions; the master results ledger N1–N19. • Paper II — a ceiling on distance-scaled achromatic noise in pulsar timing arrays: K₉₅ = 5. 6×10⁻¹³ s² kpc⁻¹ (a self-contained archival measurement). • Paper III — dark-matter phenomenology: the carrier identity card, the galactic scorecard, the wide-binary test, and the falsification calendar. • Paper IV — the quintic superfluid: exact black soliton, transverse Bogoliubov spectrum, branch-edge physics, and a laboratory analog of the emergent force law (self-contained quantum-fluids physics). • Paper V — the σ-resolved radial-acceleration relation from archival groups and clusters: the break exists, is not baryonic bookkeeping at or above group scale, and bounds the carrier mass near 8 eV. • Letter — the a₀ = c²√ (Λ/24π) result in PRL format. The analysis code and the frozen prediction ledgers (with embedded UTC timestamps and versioned revisions) are archived separately at DOI 10. 5281/zenodo. 21560680 and maintained at https: //github. com/MrJevrem/entropic-superfluid-gravity. Every quantitative claim in the manuscripts is tagged as assumption, inheritance, known input, match, or new result. This work was carried out with the help of Claude Fable 5, an AI research system built by Anthropic, which performed the derivations, wrote and executed the analysis code, and drafted the manuscripts; the human author directed the program and takes sole responsibility for the content. Current publication policies do not permit AI systems to hold authorship; each manuscript carries a contribution statement recording that co-authorship was intended. Version 2 (2026-07-25) extends the series with the quantum-foundations arc (derivation records D27–D32, ledger entries N20–N22): the Penrose–Onsager quantification of the carrier's post-virialization state; a mode-selection theorem deriving single-mode coherence from the convexity of the entropic equation of state (validated against the laboratory exchange-energy mechanism) ; the demonstration that the entropic interaction is its own condensation channel, with the ordering requirement ladder completing in microseconds against the rotating-lattice end state (one adverse finding — anomalously slow T = 0 ordering — recorded as a failed pre-registered criterion and repaired by the theory's native normal fraction) ; and two substrate consistency theorems showing the entropic functional's resolution is forced by the medium's own Bogoliubov regulator and the phonon's canonical structure is inherited from the microscopic field. Papers I and III are updated accordingly; Papers II and IV change only in a ledger-range footnote; Paper V and the Letter are unchanged. Contact: mr. marko. jevremovic@gmail. com