omega/norm-family refuted as stability signal; fingerprint story retracted; eigreg v2 = true map-eigenvalue (spec_penalty)HEADmaster

- eig_control: fix plain-PI bug (shifted PI for lambda_max of indefinite Sym);
  add lead_rho + spec_penalty (soft one-sided cap on |lam|(I+eps*J_F), 2-D
  Rayleigh-Ritz, matvec-only) — aep 'spectral' ported. eig_penalty demoted to
  diagnostic.
- eig_recheck.py (Lanczos audit): omega=+5..+13 on ALL operators incl the
  stablest (s2000 +12.8 while true alpha=-0.02); gap omega-alpha~10; old
  'warm -10.14 vs scratch +1.11' numbers were PI-mixture artifacts. RETRACTED.
- eig_v2_smoke/depth: v2 mechanics validated vs ARPACK; z_T1 readings >1 are
  unconverged-state contamination (150: 1.009 -> 400/800: 0.997-0.999,
  mu=-0.02..-0.006 matching eig_probe); fixed-point top = BAND of slow modes.
- lt_ep_train: --eigreg now spec_penalty (--eig_margin 0.995 = rho target);
  --fingerprint reports rho/Re_mu instead of num_abscissa.
- ONBOARDING §4-7 + FINDINGS 2026-07-03: retraction + verdict (fundamental
  quantity = finite-horizon path LE / resreg axis; de-cliff via floss-ept;
  spec_penalty = measure-mode scalpel for a detaching Hopf pair).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn

1 files changed, 34 insertions, 0 deletions

diff --git a/ep_run/eig_recheck.log b/ep_run/eig_recheck.log
new file mode 100644
index 0000000..49cd2a9
--- /dev/null
+++ b/ep_run/eig_recheck.log
@@ -0,0 +1,34 @@
+/home/yurenh2/miniconda3/lib/python3.13/site-packages/torch/autograd/graph.py:865: UserWarning: Attempting to run cuBLAS, but there was no current CUDA context! Attempting to set the primary context... (Triggered internally at /pytorch/aten/src/ATen/cuda/CublasHandlePool.cpp:330.)
+  return Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass
+  [rand-init b0] lam_max=  +5.089 lam_min=  -5.024 oldPI=  -0.182 newPI=  +4.818 res=1.62e+01
+  [rand-init b1] lam_max=  +4.958 lam_min=  -4.928 oldPI=  -0.143 newPI=  +4.819 res=1.11e+01
+[rand-init] (random init) lam_max=+5.023 lam_min=-4.976 oldPI=-0.163 <-- oldPI tracked lam_MIN (bug live) newPI=+4.819 res=1.36e+01 val=8.4893
+
+  [s2000-warmsrc b0] lam_max= +12.349 lam_min= -15.432 oldPI=  -6.062 newPI= +12.121 res=2.58e+00
+  [s2000-warmsrc b1] lam_max= +13.334 lam_min= -15.816 oldPI=  -6.800 newPI= +13.303 res=2.72e+00
+[s2000-warmsrc] (step 1900 best 3.1321) lam_max=+12.841 lam_min=-15.624 oldPI=-6.431 <-- oldPI tracked lam_MIN (bug live) newPI=+12.712 res=2.65e+00 val=3.1028
+
+  [resreg-scratch b0] lam_max= +10.712 lam_min=  -9.901 oldPI=  +2.080 newPI= +10.408 res=6.64e+00
+  [resreg-scratch b1] lam_max= +10.576 lam_min=  -9.794 oldPI=  +0.714 newPI= +10.566 res=5.84e+00
+[resreg-scratch] (step 9200 best 2.2156) lam_max=+10.644 lam_min=-9.847 oldPI=+1.397 (oldPI ~ lam_max, bug latent) newPI=+10.487 res=6.24e+00 val=2.2380
+
+  [fast-adaptive b0] lam_max=  +7.474 lam_min=  -7.285 oldPI=  +2.351 newPI=  +7.470 res=1.56e+00
+  [fast-adaptive b1] lam_max=  +8.313 lam_min=  -7.637 oldPI=  +2.472 newPI=  +8.289 res=1.82e+00
+[fast-adaptive] (step 24400 best 2.1023) lam_max=+7.893 lam_min=-7.461 oldPI=+2.412 (oldPI ~ lam_max, bug latent) newPI=+7.879 res=1.69e+00 val=2.1817
+
+  [warm-fast-live b0] lam_max=  +8.360 lam_min=  -8.382 oldPI=  -0.852 newPI=  +8.216 res=3.32e+00
+  [warm-fast-live b1] lam_max=  +8.580 lam_min=  -8.044 oldPI=  +0.688 newPI=  +8.327 res=2.10e+00
+[warm-fast-live] (step 4900 best 2.3064) lam_max=+8.470 lam_min=-8.213 oldPI=-0.082 <-- oldPI tracked lam_MIN (bug live) newPI=+8.272 res=2.71e+00 val=2.3378
+
+  [self-restart-live b0] lam_max= +11.042 lam_min= -10.908 oldPI=  -0.257 newPI= +10.983 res=6.85e-01
+  [self-restart-live b1] lam_max= +10.305 lam_min= -10.332 oldPI=  +0.463 newPI= +10.079 res=1.33e+00
+[self-restart-live] (step 8600 best 2.3809) lam_max=+10.673 lam_min=-10.620 oldPI=+0.103 (oldPI ~ lam_max, bug latent) newPI=+10.531 res=1.01e+00 val=2.3913
+
+operator              lam_max  lam_min    oldPI    newPI       res     val
+rand-init              +5.023   -4.976   -0.163   +4.819  1.36e+01  8.4893   # random init
+s2000-warmsrc         +12.841  -15.624   -6.431  +12.712  2.65e+00  3.1028   # step 1900 best 3.1321
+resreg-scratch        +10.644   -9.847   +1.397  +10.487  6.24e+00  2.2380   # step 9200 best 2.2156
+fast-adaptive          +7.893   -7.461   +2.412   +7.879  1.69e+00  2.1817   # step 24400 best 2.1023
+warm-fast-live         +8.470   -8.213   -0.082   +8.272  2.71e+00  2.3378   # step 4900 best 2.3064
+self-restart-live     +10.673  -10.620   +0.103  +10.531  1.01e+00  2.3913   # step 8600 best 2.3809
+EIG_RECHECK_DONE