Part I : Trans-Generational Continuity of Dark Matter and Dark Energy / Part II : terminal universe and the chorus trigger for the Big Bang / Part III: The Universe's Memory — Closure, Contraction, and Rebirth / Part IV: The Universe's Information — Horizons, Transport, and Continuity / Part Zero: Entropy Extremization and Structure in Self-Gravitating Systems

Version 4. 2 Part Zero: A Minimal Framework for Self-Gravitating Systems This work proposes a minimal framework in which self-gravitating systems are described by an entropy extremization condition rather than global entropy maximization. The approach leads to non-uniform but stable macroscopic configurations characterized by observable quantities such as density and velocity dispersion. A simple variational formulation connects these quantities and yields a scaling relation between them. While preliminary, the framework suggests a structural interpretation of effective sources that is compatible with gravitational dynamics. Possible extensions, including connections to cosmological components, are left for future work. Abstract Part Zero Self-gravitating systems exhibit persistent structure despite expectations ofhomogenization under entropy maximization. We propose that such systems are morenaturally described by an entropy extremization condition rather than global entropymaximization. The resulting configurations admit non-uniform density and velocitydispersion profiles. By linking the variational formulation to observable quantities, weobtain a scaling relation between velocity dispersion and density. This framework providesa consistent structural interpretation of effective sources compatible with gravitationalfield equations. Part I We call it dark matter because we cannot see it, and dark energy becausewe do not understand it. Both names reflect our limitations rather than thenature of the things themselves. This paper proposes that what isconventionally termed dark matter is more precisely Fundamental Matter (FM) — the basic form of matter, interacting solely through gravity — andthat what is conventionally termed dark energy is more preciselyFundamental Energy (FE) — the basic expansive property of space, symmetric to gravity. We propose that what is conventionally termed dark matter is moreprecisely Fundamental Matter (FM) — the basic form of matter, interactingsolely through gravity — and that dark energy is more preciselyFundamental Energy (FE) — the basic expansive property of space, symmetric to gravity. Both are entropic invariants: FM occupies themaximum entropy state available to gravity-only matter; FE has zeroentropy as a uniform property of space. This entropic inertness is thestructural reason why FM and FE persist across cosmological transitionswhile ordinary matter does not. The cosmological constant problemdissolves once vacuum energy (matter sector, extractable via Hawkingradiation) and FE (spatial property, not extractable) are recognised ascategorically distinct — reducing the 10¹²² discrepancy to a boundarycondition, not a fine-tuning problem. Baryonic asymmetry emerges as astructural consequence of the inherited inhomogeneous FM distribution. The fine structure constant α is derived from the FM/FE energy inventory asa fixed-point relation, recovering the observed value to seven significantfigures. The framework makes falsifiable predictions testable with JWST, Euclid, DESI, and LISA. Part II Part I established that Fundamental Matter (FM) and Fundamental Energy (FE) persist across cosmological generations while ordinary matter (OM) cycles through black holes via Hawking radiation. Part II extends thisframework to the terminal state of the universe. We propose that the finaluniverse — in which all OM has been converted to FM and only a singleclass of black holes remains — satisfies two distinct trigger conditions thattogether initiate a new Big Bang: a geometric condition, in which externalFE volume exceeds internal volume, and a thermodynamic condition, inwhich black hole entropy converges on horizon entropy. These twoconditions constitute a chorus trigger: they need not arrive simultaneously, but both must be met. We further propose that our universe is the firstcosmological generation (n = 0), and derive that OM depletion reachescompletion within approximately 4 generational cycles under f = 0. 844, derived from the observed OM fraction. The framework requires no inflatonfield, no external fine-tuning, and no appeal to structures beyond FM, FE, and classical thermodynamics. Fine-tuning is not imposed from outside —each generation, the universe converges upon its own constants throughthe self-referential structure of FM, FE, and α. Part III The terminal universe satisfies two conditions — geometric andthermodynamic — that together constitute the Chorus Trigger. Whatfollows is the mechanism by which the universe closes, contracts, and opens again. We propose that Fundamental Energy (FE), identified as the Hawking quantum vacuum at the cosmologicalhorizon, undergoes pair production at the de Sitter boundary; atthe cosmological horizon, pair production manifests vacuumproperties (matter and antimatter), converting to FM state —which then enters the trans-horizon layer, a physicallyinaccessible but physically real space admitting only gravity-only matter. Following the Chorus Trigger, this trans-horizon FMundergoes Horizon Equivalent Exchange (HEX): FM traverses thecosmological horizon inward — material state preserved, noentropic exchange — returning to Domain 1. As trans-horizon FMreturns, the accessible FE volume shrinks. The de Sitter horizoncontracts. The approximately 18 causally isolated terminal blackholes — one per de Sitter bubble, N = (Rₒbs / RdS) ³ ≈ 18 —converge toward a black-hole-dominated asymptotic terminalconfiguration. The Big Bang is not an explosion into externalspace. It is an inward event — an entropic seeding phasetransition into pre-existing, pre-defined space between theterminal black-hole-dominated state and the contracting cosmichorizon. The universe closes upon itself, and opens again. Thisis the universe's memory. Part IV Two Languages, One UniverseWhat is conserved, and how it is carried — these are not thesame question, but they share the same answer. The thermody-namic argument traces what persists across the cosmologicaltransition. The information-theoretic argument traces themechanism by which it is delivered. The two formalisms are in-dependent in their language and mutually compatible in theirconclusions. Together they describe a universe that does notforget. > **What is the minimal information structure from which geom-etry, entropy, and cosmological vacuum emerge? **> We propose it is FM — Fundamental Matter. The argument un-folds below. One proposition anchors everything that follows: > **There is one ledger. ** The black hole event horizon andthe cosmological horizon do not maintain separate accounts —they are two faces of the same boundary, governed by the samerelation: S = A / 4Gℏ. FM moves within this unified ledger asthe sole carrier that traverses both boundaries without en-tropic mediation. Once this is established, the rest is not achoice. It follows.