diff --git a/competitions/trace_the_ace/V139_PRECOMMIT.md b/competitions/trace_the_ace/V139_PRECOMMIT.md
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+# V139 precommit — Component-specific applicability
+
+## Controller continuation
+V138 closed the generic two-literal *whole-V135* gating language under its frozen admission rule, but all four meta-folds independently selected the same interaction family: `support_log <= q80 AND prior_disp > q20`, with ~64% coverage. The selector improved overall LL slightly versus full V135 and beat the equal-capacity shuffled selector, but only 2/4 folds beat V135.
+
+## Residual
+The joint geometry is stable, but applying it to the entire V135 operator may discard the independently useful V75+RELATED composition outside the region.
+
+## Diagnosis
+Primary: component applicability. Secondary: composition representation. This is not a new generic router search.
+
+## Strongest rival
+The V138 interaction is incidental selection structure; component-specific application will not improve full V135 and any gain will be matched by a random same-coverage prior mask.
+
+## K(rho)
+An admissible intervention must:
+1. retain exact V97 fallback for unsupported objectives;
+2. retain V75+RELATED composition on supported rows outside the prior region;
+3. use the full V75+RELATED+objective-prior stack only inside the fixed V138-derived region;
+4. use no target labels at inference;
+5. beat full V135 on cross-fitted session-held-out predictions;
+6. beat a matched-coverage random prior-activation control.
+
+## Frozen operator
+For each outer fold, define thresholds from outer-training runtime fields only:
+- `support_log <= training q80`
+- `prior_disp > training q20`
+
+Supported outer rows satisfying both receive the full V135 stack. Other supported rows receive the composition-only V75+RELATED stack. Unsupported rows receive exact V97.
+
+No threshold search, no alternative conjunction, no tree/router, no post-result tuning.
+
+## Control
+Within each untouched outer fold, randomly permute the binary prior-activation mask across supported rows, preserving the exact number of prior-enabled rows. Apply full V135 on the shuffled mask and composition-only elsewhere. Fixed seed 20260823.
+
+## Action table
+PROMOTE_COMPONENT_LAW if:
+- incremental gain vs full V135 >= 0.0005;
+- advantage vs matched random control >= 0.0005;
+- >=3/4 folds beat V135;
+- all folds non-regress vs V97.
+
+RETAIN_COMPONENT_SIGNAL if incremental gain > 0, control advantage >= 0.0002, and >=3/4 folds beat V135.
+
+Otherwise CLOSE_COMPONENT_APPLICABILITY_HYPOTHESIS.
+
+## Epistemic status
+V139 is a second-generation mechanism test induced by V138 on the same 35,072-row corpus. Even a pass is not final untouched admission; it must subsequently survive competition-shaped/runtime verification.
+
+## Retention
+The run saves OOF predictions for V97, composition-only, full V135, V139, and matched random control so future tests do not need to rebuild the full transcript matrices merely to analyze this component law.
diff --git a/competitions/trace_the_ace/v139_component_applicability.py b/competitions/trace_the_ace/v139_component_applicability.py
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+++ b/competitions/trace_the_ace/v139_component_applicability.py
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+#!/usr/bin/env python3
+"""V139: component-specific applicability induced by V138.
+
+The whole-V135 two-literal gate was not admitted, but all V138 meta-folds selected
+support_log<=q80 AND prior_disp>q20. V139 asks whether that geometry belongs only
+to the objective-prior component. Composition-only is retained everywhere else.
+"""
+from __future__ import annotations
+import argparse,json,time
+from pathlib import Path
+import numpy as np
+from sklearn.model_selection import GroupKFold
+from sklearn.metrics import log_loss
+
+from v75_canonical_trajectory import load_training,SEED
+from v71_mastery_events import load_transcript
+from v85_evidence_state import build_v75
+from v94_related_control import segmented_control,build_control
+from v135_nested_supported_stack import components,feats,fit_stack,EPS,logit
+
+RNG_SEED=20260823
+SUPPORT_Q=.80
+DISP_Q=.20
+
+def main(a):
+    t0=time.time(); f=load_training(a.features,a.labels).reset_index(drop=True)
+    y=f.target.to_numpy(int); support=f.learning_objective.astype(str).to_numpy(); sessions=f.session_id.astype(str).to_numpy()
+    obj=(f.learning_objective_id if 'learning_objective_id' in f else f.learning_objective).astype(str).to_numpy()
+    print('ROWS',len(f),'SESSIONS',len(np.unique(sessions)),'OBJECTIVES',len(np.unique(obj)),flush=True)
+    cache={}; us=np.unique(sessions)
+    for j,sid in enumerate(us,1):
+        cache[str(sid)]=load_transcript(a.transcripts/f'{sid}.csv')
+        if j%2500==0: print('TRANSCRIPTS',j,'/',len(us),'elapsed',round(time.time()-t0,1),flush=True)
+    X75=build_v75(f,cache); print('V75',X75.shape,X75.nnz,'elapsed',round(time.time()-t0,1),flush=True)
+    rt=[];rz=[]
+    for i,r in f.iterrows():
+        text,z=segmented_control(cache[str(r.session_id)],str(r.learning_objective),'related'); rt.append(text);rz.append(z)
+        if (i+1)%5000==0: print('RELATED_ROWS',i+1,'elapsed',round(time.time()-t0,1),flush=True)
+    Xr=build_control(rt,rz); print('RELATED',Xr.shape,Xr.nnz,'elapsed',round(time.time()-t0,1),flush=True)
+
+    n=len(y); P0=np.zeros(n);P1=np.zeros(n);P2=np.zeros(n);PG=np.zeros(n);PC=np.zeros(n);GM=np.zeros(n,bool)
+    folds=[]; rng=np.random.default_rng(RNG_SEED)
+    outer=list(GroupKFold(4).split(np.zeros(n),y,sessions))
+    for k,(tr,va) in enumerate(outer,1):
+        q0,o75,orr,opp,oc,oseen=components(X75,Xr,y,tr,va,support)
+        ig=sessions[tr]; inner=list(GroupKFold(3).split(np.zeros(len(tr)),y[tr],ig))
+        ip75=np.zeros(len(tr));ipr=np.zeros(len(tr));ipp=np.zeros(len(tr));ic=np.zeros(len(tr));iseen=np.zeros(len(tr),bool)
+        for ltr,lva in inner:
+            atr=tr[ltr];ava=tr[lva]
+            _,a75,ar,ap,ac,aseen=components(X75,Xr,y,atr,ava,support)
+            ip75[lva]=a75;ipr[lva]=ar;ipp[lva]=ap;ic[lva]=ac;iseen[lva]=aseen
+        fitmask=iseen
+        m1=fit_stack(feats(ip75[fitmask],ipr[fitmask],ipp[fitmask],ic[fitmask],False),y[tr][fitmask])
+        m2=fit_stack(feats(ip75[fitmask],ipr[fitmask],ipp[fitmask],ic[fitmask],True),y[tr][fitmask])
+        q1=q0.copy();q2=q0.copy()
+        if oseen.any():
+            q1[oseen]=np.clip(m1.predict_proba(feats(o75[oseen],orr[oseen],opp[oseen],oc[oseen],False))[:,1],EPS,1-EPS)
+            q2[oseen]=np.clip(m2.predict_proba(feats(o75[oseen],orr[oseen],opp[oseen],oc[oseen],True))[:,1],EPS,1-EPS)
+
+        # Frozen V138-derived component region. Thresholds come only from outer-training inner-OOF fields.
+        train_support=np.log1p(ic[fitmask])
+        train_disp=np.abs(logit(ipp[fitmask])-logit(ip75[fitmask]))
+        sth=float(np.quantile(train_support,SUPPORT_Q)); dth=float(np.quantile(train_disp,DISP_Q))
+        outer_support=np.log1p(oc); outer_disp=np.abs(logit(opp)-logit(o75))
+        gm=oseen & (outer_support<=sth) & (outer_disp>dth)
+        qg=q1.copy(); qg[gm]=q2[gm]
+
+        # Matched-coverage random prior activation among supported rows.
+        sup_idx=np.flatnonzero(oseen); n_on=int(gm.sum()); cm=np.zeros(len(va),bool)
+        if n_on>0:
+            chosen=rng.choice(sup_idx,size=n_on,replace=False); cm[chosen]=True
+        qc=q1.copy(); qc[cm]=q2[cm]
+
+        P0[va]=q0;P1[va]=q1;P2[va]=q2;PG[va]=qg;PC[va]=qc;GM[va]=gm
+        fr={'fold':k,'rows':int(len(va)),'supported_fraction':float(oseen.mean()),'prior_coverage':float(gm.mean()),
+            'support_q80_threshold':sth,'prior_disp_q20_threshold':dth,
+            'v97_ll':float(log_loss(y[va],q0)),'composition_ll':float(log_loss(y[va],q1)),
+            'full_v135_ll':float(log_loss(y[va],q2)),'component_ll':float(log_loss(y[va],qg)),
+            'random_control_ll':float(log_loss(y[va],qc))}
+        folds.append(fr);print('FOLD',json.dumps(fr),flush=True)
+
+    l0=float(log_loss(y,P0));l1=float(log_loss(y,P1));l2=float(log_loss(y,P2));lg=float(log_loss(y,PG));lc=float(log_loss(y,PC))
+    inc=l2-lg; causal=lc-lg; all_nonreg=all(r['component_ll']<=r['v97_ll']+1e-12 for r in folds); beats=sum(r['component_ll']<r['full_v135_ll'] for r in folds)
+    if inc>=.0005 and causal>=.0005 and beats>=3 and all_nonreg:
+        verdict='PROMOTE_COMPONENT_LAW'; next_action='competition_shaped_runtime_verification'
+    elif inc>0 and causal>=.0002 and beats>=3:
+        verdict='RETAIN_COMPONENT_SIGNAL'; next_action='attack_then_untouched_verification'
+    else:
+        verdict='CLOSE_COMPONENT_APPLICABILITY_HYPOTHESIS'; next_action='zoom_out_beyond_current_composition_applicability'
+    out={'protocol':'V139_COMPONENT_APPLICABILITY','rows':int(n),
+      'controller':{'push':'full_v135','residual':'V138 stable support x prior-displacement geometry but whole-operator gate unadmitted',
+        'diagnosis':{'primary':'component_applicability','secondary':'composition_representation'},
+        'rival':'V138 interaction is incidental and matched random prior activation performs as well',
+        'K_effect':['retain_v97_unsupported','retain_composition_outside_prior_region','label_free_inference','beat_full_v135','beat_matched_random_control'],
+        'operator':'composition-only on supported rows except full V135 when support_log<=train_q80 and prior_disp>train_q20',
+        'control':'same-count random prior activation','epistemic_status':'second_generation_mechanism_test_not_final_admission'},
+      'v97_ll':l0,'composition_ll':l1,'composition_gain':l0-l1,'full_v135_ll':l2,'full_v135_gain':l0-l2,
+      'component_ll':lg,'component_gain':l0-lg,'incremental_vs_v135':inc,'random_control_ll':lc,'gain_vs_random_control':causal,
+      'prior_coverage':float(GM.mean()),'folds_beating_v135':int(beats),'all_fold_nonregression':bool(all_nonreg),'folds':folds,
+      'decision':{'verdict':verdict,'next_action':next_action},'elapsed_seconds':float(time.time()-t0)}
+    Path(a.out).write_text(json.dumps(out,indent=2));print('FINAL',json.dumps(out,indent=2),flush=True)
+    np.savez_compressed(a.oof,y=y,sessions=sessions,objectives=obj,support=support,p_v97=P0,p_comp=P1,p_v135=P2,p_component=PG,p_random=PC,prior_gate=GM)
+
+if __name__=='__main__':
+    p=argparse.ArgumentParser();p.add_argument('--features',type=Path,required=True);p.add_argument('--labels',type=Path,required=True);p.add_argument('--transcripts',type=Path,required=True);p.add_argument('--out',type=Path,default=Path('v139_component_applicability.json'));p.add_argument('--oof',type=Path,default=Path('v139_component_oof.npz'));main(p.parse_args())