fix(cauchy): slow divergers truncate honestly — valve arms below cycle_cutoff_time and watches the loop floor

[ofloveandhate]

Finishes the Cauchy divergent-path truncation arc: slowly-diverging paths (fractional-order blowup, e.g. x = t^(-1/2) from x²t−1) now truncate honestly at the security valve instead of crawling to the tracker's far-larger thresholds. Measured on a t^(-1/3) diverger before this work: ~117k extra steps over 3 more decades of |t| at up to 70 digits of precision.

Two composing pieces, each necessary and neither sufficient:

1. Arm the valve below cycle_cutoff_time (B1's CycleTimeCutoff semantics, manual E.5.9)

A slow diverger carries significant pole mass at every radius, so it is never pole-mass-in-zone and the security valve never armed — the divergence bailout was unreachable for exactly the paths that need it. Below the cutoff the valve now arms unconditionally. Applied to the valve ONLY, deliberately not to acceptance: forcing the zone there would re-open the junk-success hole (a Laurent pole's stationary finite mean would be accepted once below the cutoff); pole junk still runs to its honest non-Success terminal. A genuinely convergent path's mean has long stabilized by the cutoff, so arming cannot reintroduce the cyclic-6 false truncations.

2. The valve watches the loop FLOOR, not just the mean

Arming alone was proven insufficient by the (deliberately red) regression test: the valve watched the Cauchy MEAN, and around a closed loop the branches of t^(-p/q) cancel — the mean sits near 0 while every loop sample has norm ~r^(-p/q). Mean-watching is structurally blind to fractional-pole divergers.

The watched quantity is now the stronger of the extrapolated endpoint's dehomogenized norm (still the earliest signal for a clean infinite endpoint) and the loop floor — the minimum dehomogenized norm over the Cauchy loop samples. The floor exceeds max_norm only when the entire loop is beyond it. This is safe where watching samples directly was not (any single sample transiently spiking truncated finite cyclic-6 paths, 156 → 153, which is why sample-watching was removed): a transient spike lifts the max, never the min.

Tests

• slow_diverger_hits_security_max_norm_below_cycle_cutoff (previously red by design): the x²t−1 diverger now returns SecurityMaxNormReached promptly instead of dying at the tracker's threshold after ~12 decades of |t|.
• Full endgame suite (412 cases) and the complete ctest battery green — cyclic-6 keeps all its solutions.

🤖 Generated with Claude Code