diff --git a/README.md b/README.md
index 10b8d7894af3435c9b659bcb4bce8da7ccc15efd..e15217f450c30641a76cf4cbeac436bbce6059c2 100644
--- a/README.md
+++ b/README.md
@@ -1,10 +1,28 @@
 ---
-title: Angular Separation Vit Demo
-emoji: 📊
-colorFrom: yellow
-colorTo: yellow
+title: v1(W_O) is not identifiable
+emoji: 🎛️
+colorFrom: purple
+colorTo: red
 sdk: static
 pinned: false
+license: apache-2.0
 ---
 
-Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference
+# The dominant direction of $W_O$ is not identifiable
+
+Interactive demo (precomputed gallery, static) for *"Same function,
+different pruning: the dominant direction of $W_O$ under free, soft,
+and hard intervention"*.
+
+Code: <https://github.com/mmunozpl/angular-separation-vit>
+Results: <https://huggingface.co/datasets/ManPla/angular-separation-vit-results>
+Checkpoints: <https://huggingface.co/ManPla/angular-separation-vit-checkpoints>
+DOI: [10.5281/zenodo.21630535](https://doi.org/10.5281/zenodo.21630535)
+
+Browse 72 precomputed combinations (12 layers × 3 gauge strengths ×
+2 random seeds), all from the real ViT-B/16 seed-42 base checkpoint
+(anchor column of the paper), showing that a value-output gauge
+transformation moves each head's dominant weight direction $v_1(W_O)$
+at will —even flipping which pair of heads looks "most redundant"—
+while the OV circuit $W_v W_O$, the only quantity the model's function
+actually depends on, stays fixed to machine precision.
diff --git a/datos.json b/datos.json
new file mode 100644
index 0000000000000000000000000000000000000000..eb0033fcf37d7591de5ad6742035c890203e8c84
--- /dev/null
+++ b/datos.json
@@ -0,0 +1,1226 @@
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+  "mismo_par": false
+ }
+}
\ No newline at end of file
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diff --git a/index.html b/index.html
index b0c4b3666032a737f3903db53e6a8a9272483e28..5cdc6c9372a2ca8dd5bbcb8f75c01c1940ff002f 100644
--- a/index.html
+++ b/index.html
@@ -1,19 +1,188 @@
 <!doctype html>
-<html>
-	<head>
-		<meta charset="utf-8" />
-		<meta name="viewport" content="width=device-width" />
-		<title>My static Space</title>
-		<link rel="stylesheet" href="style.css" />
-	</head>
-	<body>
-		<div class="card">
-			<h1>Welcome to your static Space!</h1>
-			<p>You can modify this app directly by editing <i>index.html</i> in the Files and versions tab.</p>
-			<p>
-				Also don't forget to check the
-				<a href="https://huggingface.co/docs/hub/spaces" target="_blank">Spaces documentation</a>.
-			</p>
-		</div>
-	</body>
+<html lang="es">
+<head>
+<meta charset="utf-8">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<title>v1(W_O) no es identificable</title>
+<style>
+  :root { color-scheme: light dark; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto,
+      Helvetica, Arial, sans-serif;
+    max-width: 880px;
+    margin: 2rem auto;
+    padding: 0 1.2rem;
+    line-height: 1.55;
+  }
+  h1 { font-size: 1.5rem; }
+  .links a { margin-right: 1rem; }
+  .controles {
+    display: flex;
+    flex-wrap: wrap;
+    gap: 1.2rem;
+    margin: 1.5rem 0;
+    padding: 1rem;
+    border: 1px solid #8884;
+    border-radius: 10px;
+  }
+  .controles label {
+    display: flex;
+    flex-direction: column;
+    font-size: 0.85rem;
+    font-weight: 600;
+    gap: 0.3rem;
+  }
+  select {
+    font-size: 1rem;
+    padding: 0.3rem 0.5rem;
+  }
+  #imagen {
+    width: 100%;
+    border-radius: 10px;
+    border: 1px solid #8884;
+  }
+  table { border-collapse: collapse; margin: 1rem 0; }
+  td, th { padding: 0.35rem 0.8rem; border: 1px solid #8886; text-align: left; }
+  .veredicto {
+    padding: 1rem;
+    border-radius: 10px;
+    margin-top: 1rem;
+    font-size: 1.05rem;
+  }
+  .distinto { background: color-mix(in srgb, orangered 15%, transparent); }
+  .igual { background: color-mix(in srgb, seagreen 15%, transparent); }
+  code { font-size: 0.95em; }
+</style>
+</head>
+<body>
+
+<h1>La dirección dominante de <em>W<sub>O</sub></em> no es identificable</h1>
+
+<p>Demo de <em>"Same function, different pruning: the dominant
+direction of W<sub>O</sub> under free, soft, and hard
+intervention"</em>. Una práctica habitual para podar o interpretar
+cabezas de atención lee el primer vector singular de la proyección de
+salida, <code>v1(W_O)</code>, como la "dirección representativa" de
+cada cabeza. Este trabajo muestra que esa dirección <strong>no está
+determinada por la función</strong>: existe una libertad de gauge
+<code>W_v &rarr; W_v R,  W_O &rarr; R⁻¹ W_O</code> que deja la salida
+—y el circuito <code>W_v W_O</code>— exactamente intactos, pero mueve
+<code>v1(W_O)</code> a voluntad.</p>
+
+<p>Los ejemplos de abajo usan pesos reales de ViT-B/16 (semilla 42, la
+columna ancla del paper), precalculados para 12 capas × 3 fuerzas de
+gauge × 2 semillas aleatorias (72 combinaciones). Elige una
+combinación y compara cuánto se mueve la dirección de peso frente a
+cuánto se mueve la función.</p>
+
+<div class="controles">
+  <label>Capa
+    <select id="capa"></select>
+  </label>
+  <label>Fuerza del gauge
+    <select id="fuerza">
+      <option value="suave">Suave (R cerca de la identidad)</option>
+      <option value="media" selected>Media</option>
+      <option value="fuerte">Fuerte (R muy distinto de la identidad)</option>
+    </select>
+  </label>
+  <label>Intento (semilla)
+    <select id="semilla">
+      <option value="1" selected>Intento 1</option>
+      <option value="2">Intento 2</option>
+    </select>
+  </label>
+</div>
+
+<img id="imagen" src="" alt="matrices de redundancia antes/después del gauge">
+
+<table id="tabla-metricas">
+  <tr><th>Cantidad</th><th>Valor</th></tr>
+  <tr><td>Deriva de v1(W_O) (dirección de peso)</td><td id="deriva-v1"></td></tr>
+  <tr><td>Deriva del circuito OV (la función)</td><td id="deriva-circ"></td></tr>
+</table>
+
+<div id="veredicto" class="veredicto"></div>
+
+<p class="links">
+  <a href="https://github.com/mmunozpl/angular-separation-vit">Código (GitHub)</a>
+  <a href="https://huggingface.co/datasets/ManPla/angular-separation-vit-results">Resultados (HF)</a>
+  <a href="https://huggingface.co/ManPla/angular-separation-vit-checkpoints">Checkpoints (HF)</a>
+  <a href="https://doi.org/10.5281/zenodo.21630535">DOI del código</a>
+</p>
+
+<script>
+let DATOS = null;
+
+async function cargarDatos() {
+  const resp = await fetch("datos.json");
+  DATOS = await resp.json();
+}
+
+function poblarCapas() {
+  const sel = document.getElementById("capa");
+  for (let i = 0; i < 12; i++) {
+    const opt = document.createElement("option");
+    opt.value = i;
+    opt.textContent = `Capa ${i}`;
+    if (i === 3) opt.selected = true;
+    sel.appendChild(opt);
+  }
+}
+
+function actualizar() {
+  const capa = document.getElementById("capa").value;
+  const fuerza = document.getElementById("fuerza").value;
+  const semilla = document.getElementById("semilla").value;
+  const clave = `L${capa}_${fuerza}_s${semilla}`;
+  const d = DATOS[clave];
+  if (!d) return;
+
+  document.getElementById("imagen").src = d.img;
+  document.getElementById("deriva-v1").textContent = d.deriva_v1.toFixed(3);
+  document.getElementById("deriva-circ").textContent =
+    d.deriva_circ.toExponential(2);
+
+  const [i0, j0, c0] = d.par_antes;
+  const [i1, j1, c1] = d.par_despues;
+  const veredicto = document.getElementById("veredicto");
+  const pct = Math.round(d.deriva_v1 * 100);
+
+  let html = `<p>La dirección de peso se ha movido un
+    <strong>${pct}%</strong> de la escala posible, mientras que el
+    circuito —lo único que la red realmente calcula— se mantiene
+    <strong>${d.ordenes_magnitud} órdenes de magnitud</strong> por
+    debajo: la misma función, exactamente.</p>
+    <p><strong>Par de cabezas más "redundante" según los pesos:</strong><br>
+    Antes del gauge: cabezas <strong>${i0}</strong> y <strong>${j0}</strong>
+    (|cos| = ${c0})<br>
+    Después del gauge: cabezas <strong>${i1}</strong> y <strong>${j1}</strong>
+    (|cos| = ${c1})</p>`;
+
+  if (d.mismo_par) {
+    veredicto.className = "veredicto igual";
+    html += `<p>✅ Es el mismo par esta vez — prueba otra capa o otro
+      intento; con gauges genéricos suele cambiar.</p>`;
+  } else {
+    veredicto.className = "veredicto distinto";
+    html += `<p>🔀 ¡Es un par distinto! Un modelo funcionalmente
+      idéntico —mismos outputs, mismo circuito OV— decidiría podar
+      otras cabezas. La redundancia que los pesos muestran es, en
+      parte, una elección arbitraria de coordenadas, no una propiedad
+      de la función.</p>`;
+  }
+  veredicto.innerHTML = html;
+}
+
+(async () => {
+  poblarCapas();
+  await cargarDatos();
+  actualizar();
+  for (const id of ["capa", "fuerza", "semilla"]) {
+    document.getElementById(id).addEventListener("change", actualizar);
+  }
+})();
+</script>
+
+</body>
 </html>