feat: deploy Kalpana RIF O(1) Studio with Needle-in-a-Haystack benchmarks, layer architecture, and Swagger API

app.js

@@ -151,9 +151,9 @@ async function handleUserChat() {
 
   if (!response || response === `According to our **Kalpana O(1) Holographic Memory Matrix**:\n\n> *"${groundedFact}"*\n\n`) {
     if (pLower.includes('o(1)') || pLower.includes('kv cache') || pLower.includes('kalpana') || pLower.includes('rif')) {
-      response += `### ⚡ Kalpana O(1) Memory vs. Standard KV Caching\n\n- **Standard KV Cache:** Scales linearly $O(N)$ with sequence length, requiring **384 GB VRAM** for a 3M token context.\n- **Kalpana RIF:** Replaces tensor concatenation with continuous wave interference, maintaining a strictly constant **6.00 MB memory footprint** across all context horizons.\n- **Unit Economics:** Reduces context hosting costs from **$432/user/mo** down to **$0.22/user/mo** on a single A100 GPU!`;
+      response += `### ⚡ Kalpana O(1) Memory vs. Standard KV Caching\n\n- **Standard KV Cache:** Scales linearly O(N) with sequence length, requiring **384 GB VRAM** for a 3M token context.\n- **Kalpana RIF:** Replaces tensor concatenation with continuous wave interference, maintaining a strictly constant **6.00 MB memory footprint** across all context horizons.\n- **Unit Economics:** Reduces context hosting costs from **$432/user/mo** down to **$0.22/user/mo** on a single A100 GPU!`;
     } else if (pLower.includes('sky is blue') || pLower.includes('sky blue')) {
-      response += `### 🌌 Why the Sky is Blue (Rayleigh Scattering)\n\nSunlight reaches Earth's atmosphere and is scattered in all directions by gases ($N_2, O_2$). Because blue light travels as smaller, shorter waves (~400 nm), it scatters roughly **10 times more efficiently** than longer red waves ($I \\propto 1/\\lambda^4$). The human eye's cone cells are also sensitive to blue, making the sky appear azure blue!`;
+      response += `### 🌌 Why the Sky is Blue (Rayleigh Scattering)\n\nSunlight reaches Earth's atmosphere and is scattered in all directions by gases (Nitrogen and Oxygen). Because blue light travels as smaller, shorter waves (~400 nm), it scatters roughly **10 times more efficiently** than longer red waves (inversely proportional to the 4th power of wavelength). The human eye's cone cells are also sensitive to blue, making the sky appear azure blue!`;
     } else {
       try {
         const clean = prompt

index.html

@@ -103,7 +103,7 @@
                   <span class="bubble-badge">Qwen2.5-0.5B + RIF</span>
                 </div>
                 <div class="bubble-body">
-                  Hello! 👋 I am **Kalpana AI**, operating on our **$O(1)$ Resonant Interference Field (RIF)** continuous memory matrix with a strictly invariant **6.00 MB RAM footprint**.
+                  Hello! 👋 I am **Kalpana AI**, operating on our **O(1) Resonant Interference Field (RIF)** continuous memory matrix with a strictly invariant **6.00 MB RAM footprint**.
                   
                   How can I help you today?
                   - Ask complex science, physics, math, sports, or engineering questions
@@ -364,14 +364,14 @@
             <div class="diagram-container">
               <div class="diagram-block block-input">
                 <div class="block-title">1. Input Tokens & Embeddings</div>
-                <div class="block-desc">Incoming prompt tokens $[x_1, x_2, \dots, x_t]$ mapped to token vectors $\mathbf{v}_t \in \mathbb{R}^{4096}$</div>
+                <div class="block-desc">Incoming prompt tokens (x1, x2, ... xt) encoded into continuous dimensional embedding vectors.</div>
               </div>
 
               <div class="diagram-arrow">▼</div>
 
               <div class="diagram-block block-transformer">
-                <div class="block-title">2. Transformer Hidden Layer Stack ($L = 0 \dots 31$)</div>
-                <div class="block-desc">Every layer contains Multi-Head Self Attention (32 parallel heads). Each head projects Query ($Q_t$), Key ($K_t$), and Value ($V_t$).</div>
+                <div class="block-title">2. Transformer Hidden Layer Stack (Layers 00 to 31)</div>
+                <div class="block-desc">Every layer contains Multi-Head Self Attention (32 parallel heads). Each head projects Query (Q), Key (K), and Value (V) attention vectors.</div>
 
                 <!-- Inner Interception Layer -->
                 <div class="rif-interception-box">
@@ -380,7 +380,7 @@
                   <div class="interception-grid">
                     <div class="sub-block">
                       <strong>Standard Transformers KV:</strong>
-                      <code>torch.cat([Buffer_{t-1}, K_t], dim=-2)</code>
+                      <code>torch.cat([Previous_Cache, New_Key_Tokens], dim=-2)</code>
                       <span class="val-rose">❌ Linear O(N) Unbounded VRAM</span>
                     </div>
                     <div class="sub-block">
@@ -469,7 +469,7 @@
 self.key_cache[layer_idx] = torch.cat([self.key_cache[layer_idx], key_states], dim=-2)
 self.value_cache[layer_idx] = torch.cat([self.value_cache[layer_idx], value_states], dim=-2)</code></pre>
                 <div style="font-size: 0.8rem; color: var(--red); margin-top: 0.5rem; font-weight: 600;">
-                  Memory Shape: <code>[batch, heads, seq_len, head_dim]</code> ➔ Grows continuously with every token ($O(N)$).
+                  Memory Shape: <code>[batch, heads, seq_len, head_dim]</code> ➔ Grows continuously with every token (O(N) Growth).
                 </div>
               </div>
 
@@ -485,7 +485,7 @@ def update(self, key_states, value_states, layer_idx):
     self.val_rif.write(t, value_states)
     return self.key_rif.batch_reconstruct(t_range), self.val_rif.batch_reconstruct(t_range)</code></pre>
                 <div style="font-size: 0.8rem; color: var(--green); margin-top: 0.5rem; font-weight: 600;">
-                  Memory Shape: <code>[batch, heads, bands, head_dim]</code> ➔ Strictly Constant ($O(1)$).
+                  Memory Shape: <code>[batch, heads, bands, head_dim]</code> ➔ Strictly Constant (O(1)).
                 </div>
               </div>
             </div>