Papers · William Alexander Aldred

The Generation Map Has a Fixed Point: Inheritance Self-Consistency in Bounce Cosmologies

by William Alexander Aldred — Independent Researcher

Abstract

A bounce cosmology that hands content from one generation to the next contains a generation map: a rule taking the full state a parent hands down to the state with which the child begins. Like any map, it can be asked for its fixed points — the states that reproduce themselves. This paper assembles that map, for one such frame, from corpus objects, runs the audit on the full handed-down state rather than on any one-dimensional projection, and reports what it selects, what it leaves flat, and what it does not touch.

The handed-down state is five-component: an axis hats, a conversion parity σ, a polarization ξ = s/n, an abundance n₀, and a carrier mass m, with wall density, wall spin, wall number density, and bounce scale derived. A map built on a single coordinate — the level weight — is flat across a wide plateau and its crossing is degenerate. That flatness is a true property of the projection. It is not a grade of the full map.

Solved on the full state, the map has a discrete fixed component. The inherited abundance

n₀^* ∈ 3.6406×10⁻¹²,; 5.5182×10⁻¹²,; 1.0174×10⁻¹¹ eV³,

the three values corresponding to the record's three discrete parent-and-era readings, is a fixed quantity of the map: a level reproduces itself only if the abundance it carries is the abundance its own wall hands down. Under inheritance reading R1, in which offspring inherit number and spin proportionally, the result is polarization-invariant — the parent's wall content scales as ξ⁻³ and the child's dilution as ξ⁺³, and the two cancel identically. Under reading R2, in which the offspring's number is set by the flipped spin content it carries, the map additionally selects ξ = 1. The corpus asserts both rule-forms and prices their agreement only at fully polarized parents; it does not rank them where they differ. The R1/R2 fork is therefore carried here, labeled OPEN, and every conclusion is stated per reading or shown to hold under both.

The fixed state's bounce scale is derived at zero free parameters: amin/arₑf = 7.33×10⁻³³ on the Standard Model era readings and 1.03×10⁻³² on the single-species era reading.

The discipline is stated on page one: the fixed point fixes inheritance, not Λ. At the fixed abundance the bounce-carrying vacuum channel still misses its target by +29 dex — +29.24, +29.69, and +29.42 dex across the three readings, mass-blind across the plateau. No fixed point of the full map selects a mass, because the corpus's generation map has no mass component: masses do not pass between generations in this frame. The joint condition fences the mass to a slab, 0 < m lesssim 2.67 eV at the fixed abundance, and no further.

The exportable content is the method (§7): assemble the full state, distinguish components the map computes from components it merely carries and components it does not contain, solve componentwise, and grade flat directions as continua, not selections. The frame result is a house-grade result, journal-grade when the fork is ruled.

The program

• The Aldred Limit
• Two Bounds and an Integration Constant
• Supplementary Memos for “Two Bounds and an Integration Constant”
• The Constant Changes Address
• The Crossing Charges Nothing
• No Derivation in the Frame
• Static Defects Carry No Nieh–Yan Charge
• Creation Events Are Nieh–Yan Charged
• There Is No Twisted Vacuum
• Propagation Is Not Enough
• Axiom H
• One Flaw, Two Residues
• The ε_eff Turnover
• The Generation Map Has a Fixed Point (this page)
• Three Fences Any Λ Mechanism Must Pass