Two‑page brief · Foundations of physics

WaveTree

A history‑conditioned geometric framework in which matter, dark matter, and dark energy are three regimes of one substrate — with one specific, falsifiable residual prediction, and the strongest objections stated by the authors themselves.

Carl Downs · Independent researcher · [email protected] · In collaboration with Anthropic's Claude · Version 1.0, July 2026 · Full treatise › · PDF


Central thesis — STP (Spacetime‑Past) dominance

Historical spacetime is the substrate of reality. What ΛCDM distinguishes as ordinary matter (~5%), dark matter (~27%), and dark energy (~68%) are three regimes of one history field ℋ — a functional over the causal past of each spacetime point — distinguished by the coherence with which ℋ has been written onto the advancing present. The Now is a spacelike Cauchy surface whose conditioning by its own past spreads at c; gravity, inertia, and the classical–quantum boundary receive geometric readings within the same picture, each consistent by construction with GR, the SM, and ΛCDM.

1Three regimes of one substrate

~5% Coherent‑mode ℋ History written into localized, records‑making structures on the Now: carries conserved charges, couples through the Standard Model. ≡ baryonic matter
~27% Textured‑mode ℋ The correlations of the causal past — clumping, halo‑forming, gravitationally active — not yet written into records. w ≈ 0. ≡ dark matter
~68% Smooth‑mode ℋ The substrate's ensemble mean ⟨ℋ⟩: spatially and temporally smooth. w ≈ −1, with a stated fork on evolving w that DESI‑era data will decide. ≡ dark energy

2The falsifiable prediction — stated as a residual

P3 — history‑linked halo residuals beyond assembly bias

ΛCDM already predicts halo–history correlations through assembly bias (concentration tracks formation epoch), so a bare age–profile correlation is not news — and the treatise says so. The WaveTree prediction: after the simulated ΛCDM expectation (assembly bias + baryonic feedback, with stellar M/L systematics forward‑modeled) is subtracted, a positive residual correlation between halo lensing profiles and stellar‑population history proxies remains. ΛCDM predicts the residual vanishes. Testable at DESI Y5 / Euclid / LSST stacked precision; the treatise specifies the pipeline, including the closure test on pure ΛCDM mocks. A convincing null strips the framework to an interpretive reading with no independent empirical content — a consequence the treatise accepts in print.

3The objections are part of the document

Stated and answered up front

"A universal Now is an ether" (answer: the CMB comoving frame, given dynamical significance only at cosmological scale; local Lorentz invariance exact). "Expansion is a rate, not a velocity" (answer: what spreads at c is the causal conditioning of each slice by the last — the growth of the domain of dependence).

Conceded, and repaired in print

"History‑dependent inertia violates equivalence‑principle tests" — correct; the framework now forbids it (drag fixed by invariant content alone; MICROSCOPE, ALPHA‑g). "The N‑particle wave function lives in configuration space" — conceded; the identification is claimed only for single excitations and decohered records. The claim‑audit appendix carries explicit red rows: readings the framework itself excludes.

4Where it sits in the literature

The treatise places itself explicitly against its neighbors: the growing block of Broad and Ellis (the past as real and accumulating — WaveTree makes it dynamical); Mach's principle rotated into time (inertia from a body's own causal past); Smolin's principle of precedence (law from accumulated history); Deser–Woodard non‑local gravity (causal‑past functionals on the RHS of Einstein's equations); Verlinde's emergent gravity (dark phenomena as substrate memory — the closest published cousin); Wheeler–Feynman and Feynman–Stueckelberg (advanced–retarded structure; antimatter as historic spacetime pulled forward); and the computational‑substrate programs of Wolfram and 't Hooft (the author is a computer scientist; the substrate instinct is acknowledged as native). It is disciplined where the literature bites: MOND's radial acceleration relation already bounds the rotation‑curve arm of P3, which is why lensing is primary.

5What is asked of the reader

  1. Read the anticipated‑objections section first (Section iii) — it was written to save you time, and two of its entries record errors made and corrected during drafting.
  2. Assess whether P3, as specified (Section 6 + Appendix C, with the assembly‑bias subtraction and closure test), is well‑posed against DESI/Euclid/LSST data.
  3. Judge whether the composition — one substrate, three regimes, history as source — merits further formal work (the treatise names its own open problems, including the missing Lagrangian and the descriptive taxonomy).

The author is a layperson; the treatise was prepared in collaboration with an AI system acting as subject‑matter translator, and it says so on its face. Criticism is the purpose of circulation.