# Open problems — how to attack (or extend) Causal Symmetry

Each problem states what "done" looks like. Results in either direction are
progress; several of these are designed so that a negative answer falsifies a
named part of the framework.

## 1. The spinfoam transfer matrix (the decisive theory test)

**Problem.** Compute, from Lorentzian EPRL transition amplitudes for the
black-to-white geometry transition (cf. Christodoulou–D'Ambrosio,
arXiv:1801.03027), the effective 2×2 transfer matrix M_ij between boundary
spin-network states encoding a logical basis.

**Done =** report (i) the effective leakage angle cos²θ_eff = Tr(MM†)/2 and
(ii) whether M ≈ cosθ·V for a *fixed* unitary V (coherent restriction) or is
decohered. The null hypothesis to beat: average fidelity 1/dim(H_P)
(Supplement II §2). If amplitudes show no code-subspace preservation, WHO-1
fails and the framework dies at the microphysical level.

**Tools:** sl2cfoam-next-class amplitude numerics; HPC. This has not been
asked of existing amplitudes, and it is a publishable question independent of
this framework.

## 2. Γ(ω) from first principles

**Problem.** The near-horizon wall coupling Γ controls all echo phenomenology.
Three candidate scalings (Supplement III §3): dimension-counting
e^(S_mat−S_BH) ≈ e^(−10⁷⁷); dynamical funneling O(1); thermalized
1−e^(−ħω/k_B T_H) (Boltzmann). **Done =** any derivation, in any
quantum-gravity approach, that selects a scaling. Selecting (a) or (c)
eliminates the framework's distinctive GW signature; that is a fine outcome.

## 3. Fit the template to real events

**Problem.** The phase-coherent template (Supplements II–IV; `code/`) has
mass-, spin-, and Γ-dependence and a resonance comb at 1/Δt. **Done =** a
matched-filter or comb search over public LIGO/Virgo/KAGRA data with official
PSDs (PyCBC/bilby), reporting detection or Γ_min exclusion per event
(Supplement IV §4 gives the forecast machinery). Required ringdown SNRs:
≳12–18. Loud events at design sensitivity and beyond are the targets.

## 4. The Teukolsky barrier

**Problem.** The barrier reflectivity is computed here for Schwarzschild
(`code/rw_barrier.py`, unitarity 6×10⁻¹³). **Done =** the same table for Kerr
(s = −2 Teukolsky via Sasaki–Nakamura), validated against published values,
merged into the template. Mechanical but genuinely useful to the wider
echo-phenomenology community.

## 5. Sub-millimeter transient search (early branch)

**Problem.** If the black-to-white lifetime scales as M², primordial holes of
≈6×10²² kg complete their bounce today, emitting at λ ~ 0.1 mm. **Done =** a
feasibility study or archival search for sub-mm/THz transients with the
predicted spectral character (cf. Barrau–Rovelli, Phys. Lett. B 739, 405).

## 6. The Page fork, decided

**Problem.** Early transition (transfer replaces islands) vs. late transition
(islands purify; Planck-scale "thin bridge"). **Done =** either a lifetime
calculation trusted by the community (problem 1 feeds this), or an argument
that one branch is internally inconsistent. The framework survives on either
branch but tells a different story; its authors would rather know.

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*Also welcome: any demonstration that the WHO clauses (confinement,
legibility, funneling — manuscript §2) conflict with an established theorem.
Subadditivity-based objections should engage Supplement III §4, where the
island compatibility question is framed.*