AV: fix the high-SNR empty-live-volume crash and report the collapse; add the extrinsic zoom box

[oshaughnessy-junior]

Two backports from rift_O4d, both measured on rift_O4c itself rather than inferred.

1. The crash (000cf79b)

On a loud, well-localized source the extrinsic-export ILE dies with

===> FAILED ANALYSIS <====
zero-size array to reduction operation CUPY_CUB_MAX which has no identity
Probable reasons: SEOB nyquist or starting frequency limit or signal duration

The stated reason is wrong -- the generic handler attributes any exception to waveform
generation -- and the failure is not GPU-specific; the host path fails identically.

Mechanism. A double-precision exp of a lnL more than ~745 nats below the peak underflows
to zero, so at high amplitude almost every cold draw over the extrinsic prior comes back
-inf and the live set starts with a handful of members. With few live points and one
dominant weight, prob_stop_thr saturates at max(lkl) (every other weight has underflowed,
so the discard_prob quantile IS the top sample) while lkl_stop_thr falls back to the
smallest. The resulting threshold is applied downstream as a strict lkl > thr, so each cycle
discards at least one point regardless of merit; the live set ratchets to one, then to zero,
and the next reduction is over an empty array.

Fix. Clamp the threshold strictly below the largest live value (np.nextafter), so it can
never discard the whole live volume, and raise a named LiveVolumeCollapse rather than letting
a reduction fail. In a healthy run len(lkl) >> nsel and lkl_stop_thr is the nsel-th
largest, far below the max, so the clamp never engages.

Measured on rift_O4c at rho_net = 146.8, 12 replicates, cold production config:

tree	crashed	exported
4a8703f3 (this branch's base)	12/12	0
with the clamp	0/12	12

The collapse report ships with the clamp, deliberately

The clamp alone would be a downgrade in one respect. A run that used to crash now completes
and exports -- at eff_samp=1.00, fairdraw=1, a one-sample "posterior". Unreported, that
trades a silent THINNING (a crashed export writes nothing and is visibly missing from the
count) for a silent CONTAMINATION (a degenerate export looks ordinary to CIP). So the branch
also carries the [AV COLLAPSE] report: ~40 additive lines after the integration loop, read
by no sampling decision. It fires on either of two geometric conditions -- the final live set
holding no more points than the dimension (it cannot span the space, let alone describe a
posterior in it), or Kish ESS < 2 (fewer than two effective samples is one sample) -- and
prints the ESS and the live-set size. Pareto k-hat is deliberately not used as a gate: it
exceeds its nominal 0.70 threshold even in the healthy runs on this problem (the converged
rho=51.4 replicates measure 0.819-1.605), so it would have false-flagged good exports. ESS
separates the regimes with an order of magnitude and nothing in between (16.3-34.3 healthy
vs 1.0-2.0 collapsed).

Inert where the integral already converges

The gate for a frozen production line. Same host, same GPU, sequential, 20 replicates each
at rho_net = 51.4, comparing distributions (seed-matching cannot work across code versions:
the clamp changes the sequence of threshold decisions, so the sample stream diverges):

	baseline	patched	test
fully converged	13/20	15/20	Fisher p = 0.73
fairdraw distribution	median 8, mean 6.45	median 8, mean 6.65	Mann-Whitney p = 0.63
crashed	0/20	0/20

No detectable change in behaviour. The patched arm flags 2/20 as collapsed; the baseline has
an exact equivalent it does not flag (fairdraw=1, eff_samp=1.11), so those are the same
event reported, not a behaviour change.

Worth noting from that control: 3 of 20 baseline runs at rho=51.4 came back at fairdraw <= 2
(eff_samp 1.1-2.0). The collapse is not a switch that flips above rho ~ 72; it is a tail that
exists at moderate amplitude and grows. Today those runs are exported unflagged.

2. The extrinsic zoom box (ca9c4249)

rift_O4c has no --limit-* options at all, so this brings the feature in its already-fixed
form (rift_O4d PR #58 plus its GPU-safety follow-up) rather than introducing the defect and
repairing it. --limit-{right-ascension,declination,inclination,psi} restrict extrinsic
sampling AND prior. The transforms:

• declination -- the sampled variable under --declination-cosine-sampler is sin(dec)
  (closures do dec = pi/2 - arccos(z)), so [lo,hi] -> [sin lo, sin hi], order preserved;
• inclination -- the sampled variable is cos(iota), and cos is decreasing on [0,pi], so
  the order swaps: [lo,hi] -> [cos hi, cos lo].

Prior mass is identical under both parameterizations, so lnZ is unchanged for the same
physical box. Tests cover both transforms, clipping, empty/inverted ranges raising, reduction
to the legacy samplers at full range, and end-to-end integrate agreement; the inclination
order-swap test is mutation-tested (flipping the reverse flag fails it). A run with no limit
given is bit-identical.

While porting, rift_O4c was found to carry the same latent bug the O4d branch fixed: the
scalar time-marginalized closure passed the raw sampled inclination (i.e. cos iota under
the cosine sampler) as an angle, while dec was converted correctly in the same loop. Fixed.

Known limitation, carried across deliberately: --internal-sky-network-coordinates plus a
sky box is a hard error, because an equatorial box selects the wrong patch of a rotated frame.
That forecloses 2-IFO boxing, where the ring is narrow in the NETWORK frame -- the right fix is
to interpret the limits in that frame. Follow-up work, not attempted here.

Scope

The clamp stops exports from vanishing; it does not make the loudest events correct. At
rho ~ 147 the patched exports are degenerate one-sample draws -- now flagged rather than
silent. Boxing converges for rho <~ 100. Above that, measurements on rift_O4d put standalone
AV ~15 nats high in lnZ against an AV+GMM portfolio with a comparable peak search, so the
portfolio is the answer there; that is separate work (see PR #168 for the fair-draw backend it
needs on this branch).

Validation harness, all measurements and the reproduce commands:
RIFT_roboto_paper/analyses/extrinsic_collapse_demo/ (run/O4C_INERT_CONTROL_2026-08-13.md,
run/O4C_PORT_STATUS_2026-08-11.md).

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