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, 7 insertions, 6 deletions

diff --git a/ep_run/lt_ep_train.py b/ep_run/lt_ep_train.py
index 9974bd8..4e7b8b1 100644
--- a/ep_run/lt_ep_train.py
+++ b/ep_run/lt_ep_train.py
@@ -229,9 +229,10 @@ def ep_step(blk, idx, y, T1, T2, eps, beta, jacreg=0.0, holo=0, hr=0.02, t1max=0
         for p, g in zip(blk.block, grr):
             if g is not None:
                 grads[id(p)] = g * lam if grads.get(id(p)) is None else grads[id(p)] + lam * g
-    if eigreg > 0:                                       # #2: leading-abscissa control (surgical, one-sided; alt to jacreg)
-        from eig_control import eig_penalty
-        ge, _om = eig_penalty(blk, zs, eigreg, eig_margin, blk.__dict__.setdefault('_eigcache', {}))
+    if eigreg > 0:                                       # #2 v2: TRUE leading map-eigenvalue control (aep 'spectral', soft one-sided)
+        from eig_control import spec_penalty              # (omega/numerical-abscissa version refuted 2026-07-03, eig_recheck)
+        ge, _rho, _mu = spec_penalty(blk, zs, eps, blk.c, eigreg, eig_margin,
+                                     blk.__dict__.setdefault('_eigcache', {}))
         for pid, g in ge.items():
             grads[pid] = g if grads.get(pid) is None else grads[pid] + g
     return grads, res
@@ -375,8 +376,8 @@ def main():
     ap.add_argument('--res_gate', type=float, default=0.0)     # validity gate: skip task grads above this res
     ap.add_argument('--wsd', type=float, default=0.0)          # WSD: hold peak lr, cosine-decay only the last wsd fraction
     ap.add_argument('--resreg', type=float, default=0.0)       # T1-residual penalty: defend z_T1 (cap ratio vs task grad); run res_gate=0
-    ap.add_argument('--eigreg', type=float, default=0.0)       # #2: leading-abscissa (numerical-abscissa) control — surgical alt to jacreg
-    ap.add_argument('--eig_margin', type=float, default=1.0)   # penalize omega(J_nc) above this (free-phase Hopf boundary ~ 1+c)
+    ap.add_argument('--eigreg', type=float, default=0.0)       # #2 v2: soft penalty on TRUE |lam|_lead(I+eps*J_F) — aep 'spectral' at C512
+    ap.add_argument('--eig_margin', type=float, default=0.995) # rho target: penalize |lam|_lead above this (<1 = contracting relaxation map)
     ap.add_argument('--diag_cos', type=int, default=0)         # #1: every N steps, log cos(EP grad, exact BPTT grad) + res
     ap.add_argument('--fingerprint', action='store_true')      # load --init_ckpt, print (res,cos,abscissa,val) fingerprint, exit
     ap.add_argument('--opt', choices=['adamw', 'lion', 'lionlars', 'sgdm', 'sgdsai'], default='adamw')
@@ -522,7 +523,7 @@ def main():
         from diag_cos import fingerprint
         fp = fingerprint(blk, cfg.T1, cfg.T2, cfg.eps, cfg.beta, cfg.holo, cfg.hr, cfg.t1max, cfg.res_est, cfg.t2sel)
         print(f"[fingerprint] ckpt={cfg.init_ckpt or 'scratch'} | res={fp['res']:.2e} cos(EP,BPTT)={fp['cos']:.4f} "
-              f"num_abscissa={fp['num_abscissa']:+.4f} val={fp['val']:.4f}", flush=True)
+              f"rho={fp['rho']:.5f} Re_mu={fp['mu_re']:+.4f} val={fp['val']:.4f}", flush=True)
         return
     for step in range(start_step, cfg.steps + 1):
         idx, y = get_batch('train', cfg.B, cfg.T)