The wave island

The wave island is the range of very light masses of conjugate matter χ, roughly 3×10⁻¹⁹ eV to 10⁻⁴ eV, in which each quantum state of a dark-matter halo holds so many quanta that the halo behaves as a classical wave field rather than as a gas of particles. There the gated attraction can act collectively: as the waves scatter off one another, it moves their power into narrow ranges of momentum, so that a halo condenses into streams and dense cores. Debt 3 computed how fast this happens and asked what fixes the strength of the coupling. If the gated channel also makes the cores of dwarf galaxies (Scenario A), condensation is mandatory in the faintest galaxies and drains their dark matter, which observation excludes. If the coupling is free (Scenario B), streams become an adjustable option rather than a prediction. The light mass has one further consequence: the field can be produced by misalignment, as axions are.

Stands: the gated condensation rate Γ_self, Scenario B, quarantined, relic abundance by misalignment · Died: Scenario A and the ultra-faint-dwarf endpoint · Open: folded sections on calibrating the rate’s coefficient c and rows 1 and 2 in wave language, neither itemized in #11 §14 · Superseded: a folded section on Debt 3a’s cubic suppression

Map#

The wave island is the branch that the classicality theorem leaves open: the coupling needed for collective behavior is reached only where χ is a wave. There, in the words of notes/debt3a-stream-stability.md, “the collective sector is reborn in field language. The halo is an incoherent wave field; the gated attraction drives condensation in k-space — power flowing into narrow-momentum streams”. The notes write the island’s upper edge as “≲ meV” (3a), “≲ 0.1 meV” (3b) and 10⁻⁴ eV (3c and the lab notebook’s addendum v0.2). This section uses 3c’s range, “roughly 3×10⁻¹⁹ eV ≲ m ≲ 10⁻⁴ eV with Scenario-B couplings”, which closed Debt 3; its lower edge is the bound on fuzzy dark matter that also closed Scenario A’s light-mass branch. Every page below is a claim of the program, drawn from notes/debt3b-wave-island.md and notes/debt3c-ufd-endpoint.md (the Debt-3 calc notes) and summarized in checkpoint #11 §9 (ii), tagged [D + T]. None is machine-checked. The established wave physics they build on is in wave dark matter.

  • The gated condensation rate Γ_self comes first, because everything after it compares against it. The page sets out the wave-kinetic mechanism the rate rests on [T], the coupling and halo quantities it is built from, and the result, Γ_self ≈ c g²ρ² min(σ, v*)⁴/(m³σ⁶) with c = O(5–15), in its gate-open and gate-narrow forms: a power-law suppression (v*/σ)⁴ where particles show an exponential one. It then gives the two corollaries, the island discriminant and the gravitational floor, and the race against orbital stirring that frames both scenarios. Folded sections hold Debt 3a’s superseded cubic estimate and two open items, the calibration of c against Levkov–Panin–Tkachev simulations and the restatement of prediction rows 1 and 2 for waves.
  • Obituary: Scenario A and the ultra-faint-dwarf endpoint follows the first answer to what fixes the coupling: the gated channel makes the cores of classical dwarfs, by analogy with self-interacting dark matter. The page gives the environment table in which streams lose everywhere except in ultra-faint dwarfs, the test against Segue 1 (a rate ratio of about 660 and a condensation time of about 1.5×10⁴ yr), the critical mass and its two branches, the mass drain by repeated collapse and the light-mass branch excluded in advance, the robustness checks, and what the kill took with it.
  • Scenario B: tunable streams (quarantined) is the other answer: the cores come from elsewhere and the coupling is free. The page sets out the window for streams in terms of the mean-field parameter X, ten orders of magnitude wide at m = 0.1 meV with Milky Way numbers, explains why a tunable consequence is a degeneration flag in Lakatos’s sense, and records an unresolved conflict over its fuzzy-dark-matter option.
  • Relic abundance by misalignment on the wave island closes the section with a consequence of the light mass rather than of the gate: a field this light, coupled only through gravity and its own self-interaction, is produced by misalignment, which removes the lab notebook’s relic-abundance problem on this branch. The 5.4 : 1 ratio of dark to ordinary matter stays open.

Boundaries#