From 01828000438f5f2ac2520eca6b9f581f6b4bcad8 Mon Sep 17 00:00:00 2001
From: Dmitry <ada.dmitry@gmail.com>
Date: Sun, 17 May 2026 16:24:34 +0300
Subject: [PATCH 1/2] Implement trace functionality for Hopfield and Hamming
 networks; update Gemfile.lock and app.rb for new dependencies and features

---
 Gemfile.lock    |   6 +-
 app.rb          |  41 +++++++++-
 hamming.rb      |   2 +-
 trace.rb        |  18 +++++
 views/index.erb | 202 +++++++++++++++++++++++++++++++++++++++++++-----
 5 files changed, 242 insertions(+), 27 deletions(-)
 create mode 100644 trace.rb

diff --git a/Gemfile.lock b/Gemfile.lock
index 07c22c4..acc9dd9 100644
--- a/Gemfile.lock
+++ b/Gemfile.lock
@@ -6,7 +6,6 @@ GEM
     logger (1.7.0)
     multi_json (1.21.1)
     mustermann (3.1.1)
-    nio4r (2.7.5)
     nokogiri (1.19.3-aarch64-linux-gnu)
       racc (~> 1.4)
     nokogiri (1.19.3-aarch64-linux-musl)
@@ -23,8 +22,6 @@ GEM
       racc (~> 1.4)
     nokogiri (1.19.3-x86_64-linux-musl)
       racc (~> 1.4)
-    puma (8.0.1)
-      nio4r (~> 2.0)
     racc (1.8.1)
     rack (3.2.6)
     rack-protection (4.2.1)
@@ -60,6 +57,7 @@ GEM
       sinatra (= 4.2.1)
       tilt (~> 2.0)
     tilt (2.7.0)
+    webrick (1.9.2)
 
 PLATFORMS
   aarch64-linux-gnu
@@ -72,12 +70,12 @@ PLATFORMS
   x86_64-linux-musl
 
 DEPENDENCIES
-  puma
   rackup
   roo
   rubyXL
   sinatra
   sinatra-contrib
+  webrick
 
 BUNDLED WITH
    2.5.3
diff --git a/app.rb b/app.rb
index c7bb231..db494cd 100644
--- a/app.rb
+++ b/app.rb
@@ -4,11 +4,12 @@ require_relative 'loader'
 require_relative 'functions'
 require_relative 'hopfield'
 require_relative 'hamming'
+require_relative 'trace'
 
 EPS = 0.01
 
 set :bind,       '0.0.0.0'
-set :port,       4567
+set :port,       4568
 set :server,     'webrick'
 disable :protection
 set :host_authorization, { allow_if: ->(_env) { true } }
@@ -64,6 +65,44 @@ post '/recall_steps' do
   }.to_json
 end
 
+post '/recall_trace' do
+  content_type :json
+  noisy = JSON.parse(request.body.read)['vector'].map(&:to_f)
+
+  hopfield_steps = [noisy.map(&:to_i)]
+  hopfield_nets  = []
+  current = noisy.dup
+  MAX_HOPFIELD_ITER.times do
+    net = trace_hopfield_step(WEIGHTS, current)
+    nxt = net.map { |v| v >= 0 ? 1 : -1 }
+    changed = current.each_with_index.count { |v, i| v.to_i != nxt[i] }
+    hopfield_nets << { net: net.map { |v| v.round(3) }, changed: changed }
+    hopfield_steps << nxt
+    break if vectors_equal?(current, nxt)
+    current = nxt
+  end
+
+  eps_val = 0.9 / PATTERN_VECTORS.length
+  outputs = hamming_layer(PATTERN_VECTORS, noisy)
+  hamming_steps = [outputs.map { |v| v.round(2) }]
+  MAX_MAXNET_ITER.times do
+    nxt = maxnet_step(outputs, eps_val)
+    hamming_steps << nxt.map { |v| v.round(2) }
+    break if nxt.count { |v| v > 0 } <= 1
+    outputs = nxt
+  end
+  winner_idx = outputs.each_with_index.max_by { |v, _| v }[1]
+
+  {
+    hopfield_steps: hopfield_steps,
+    hopfield_nets:  hopfield_nets,
+    hamming_steps:  hamming_steps,
+    pattern_names:  PATTERN_NAMES,
+    hamming_winner: PATTERN_NAMES[winner_idx],
+    hamming_trace:  hamming_trace(PATTERN_VECTORS, noisy)
+  }.to_json
+end
+
 post '/recall' do
   content_type :json
   noisy = JSON.parse(request.body.read)['vector'].map(&:to_f)
diff --git a/hamming.rb b/hamming.rb
index 18544ff..12a6976 100644
--- a/hamming.rb
+++ b/hamming.rb
@@ -13,7 +13,7 @@ def maxnet_step(outputs, eps)
   end
 end
 
-MAX_MAXNET_ITER = 500
+MAX_MAXNET_ITER = 100
 
 def recall_hamming(pattern_vectors, input_vec)
   eps = 0.9 / pattern_vectors.length
diff --git a/trace.rb b/trace.rb
new file mode 100644
index 0000000..43e356f
--- /dev/null
+++ b/trace.rb
@@ -0,0 +1,18 @@
+def trace_hopfield_step(weights, vector)
+  n = vector.length
+  Array.new(n) { |i| n.times.sum { |j| weights[i][j] * vector[j] } }
+end
+
+def hamming_trace(pattern_vectors, input_vec)
+  n = input_vec.length
+  k = pattern_vectors.length
+  dots = pattern_vectors.map { |pv| pv.zip(input_vec).sum { |a, b| a * b } }
+  initial = dots.map { |dot| (dot.to_f + n) / 2.0 }
+  {
+    eps:             (0.9 / k).round(6),
+    k:               k,
+    n:               n,
+    dot_products:    dots,
+    initial_outputs: initial.map { |v| v.round(2) }
+  }
+end
diff --git a/views/index.erb b/views/index.erb
index 238a580..3fee0e1 100644
--- a/views/index.erb
+++ b/views/index.erb
@@ -3,6 +3,8 @@
 <head>
   <meta charset="UTF-8">
   <title>Сети Хопфилда и Хэмминга</title>
+  <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css">
+  <script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.js"></script>
   <style>
     * { box-sizing: border-box; margin: 0; padding: 0; }
 
@@ -184,6 +186,60 @@
 
     #results-section { display: none; }
 
+    #trace-panels {
+      display: flex;
+      gap: 1rem;
+      margin-top: 1.5rem;
+      flex-wrap: wrap;
+    }
+
+    .trace-panel {
+      flex: 1;
+      min-width: 220px;
+      background: #1e1e3a;
+      border: 1px solid #3a3a5a;
+      border-radius: 6px;
+      padding: 0.75rem 1rem;
+      font-size: 0.88rem;
+      color: #b0c4e8;
+      line-height: 1.8;
+      max-height: 420px;
+      overflow-y: auto;
+    }
+
+    .trace-panel-title {
+      font-family: monospace;
+      font-size: 0.75rem;
+      color: #8ab4f8;
+      text-transform: uppercase;
+      letter-spacing: 0.08em;
+      margin-bottom: 0.5rem;
+      border-bottom: 1px solid #3a3a5a;
+      padding-bottom: 0.3rem;
+    }
+
+    .trace-line {
+      font-family: monospace;
+      font-size: 0.82rem;
+      color: #888;
+      padding-left: 0.5rem;
+    }
+
+    .trace-header {
+      font-family: monospace;
+      font-size: 0.8rem;
+      color: #8ab4f8;
+      text-transform: uppercase;
+      letter-spacing: 0.05em;
+      margin-top: 0.5rem;
+    }
+
+    .trace-formula {
+      padding: 0.2rem 0;
+    }
+
+    .katex { color: #e8d8ff; }
+
     #loading {
       display: none;
       align-items: center;
@@ -241,6 +297,9 @@
       <span id="delay-label">300 мс</span>
     </span>
   </label>
+  <label class="step-toggle">
+    <input type="checkbox" id="formula-mode"> Показывать формулы вычислений
+  </label>
 
   <div class="recall-area">
     <div class="pattern-box">
@@ -252,6 +311,17 @@
       </div>
     </div>
 
+    <div id="trace-panels" style="display:none">
+      <div class="trace-panel">
+        <div class="trace-panel-title">Хопфилд</div>
+        <div id="trace-hopfield"></div>
+      </div>
+      <div class="trace-panel">
+        <div class="trace-panel-title">Хэмминг</div>
+        <div id="trace-hamming"></div>
+      </div>
+    </div>
+
     <div id="results-section">
       <div class="net-results">
         <div class="net-block">
@@ -290,15 +360,65 @@
     });
   });
 
-  const stepModeCheckbox = document.getElementById('step-mode');
-  const speedControl     = document.getElementById('speed-control');
-  const stepDelaySlider  = document.getElementById('step-delay');
-  const delayLabel       = document.getElementById('delay-label');
+  let currentRunId = 0;
+
+  const stepModeCheckbox    = document.getElementById('step-mode');
+  const formulaModeCheckbox = document.getElementById('formula-mode');
+  const speedControl        = document.getElementById('speed-control');
+  const stepDelaySlider     = document.getElementById('step-delay');
+  const delayLabel          = document.getElementById('delay-label');
 
   stepModeCheckbox.addEventListener('change', () => {
     speedControl.classList.toggle('visible', stepModeCheckbox.checked);
   });
 
+  function traceEl(panelId, className, content, isLatex = false) {
+    const panel = document.getElementById(panelId);
+    const el    = document.createElement('div');
+    el.className = className;
+    if (isLatex) {
+      el.innerHTML = katex.renderToString(content, { throwOnError: false, displayMode: false });
+    } else {
+      el.textContent = content;
+    }
+    panel.appendChild(el);
+    panel.scrollTop = panel.scrollHeight;
+  }
+
+  const hfLine    = (text) => traceEl('trace-hopfield', 'trace-line', text);
+  const hfFormula = (tex)  => traceEl('trace-hopfield', 'trace-formula', tex, true);
+  const hmLine    = (text) => traceEl('trace-hamming',  'trace-line', text);
+  const hmFormula = (tex)  => traceEl('trace-hamming',  'trace-formula', tex, true);
+
+  function clearTrace() {
+    document.getElementById('trace-hopfield').innerHTML = '';
+    document.getElementById('trace-hamming').innerHTML  = '';
+    document.getElementById('trace-panels').style.display = 'none';
+  }
+
+  function buildTrace(data) {
+    document.getElementById('trace-panels').style.display = 'flex';
+    const names = data.pattern_names;
+    const t     = data.hamming_trace;
+
+    hfFormula(String.raw`\operatorname{net}_i = \sum_{j} W_{ij} \cdot x_j \qquad x_i = \operatorname{sgn}(\operatorname{net}_i)`);
+    data.hopfield_nets.forEach((nd, i) => {
+      const mark = nd.changed === 0 ? '  ← сошлось' : '';
+      hfLine(`шаг ${i + 1}: изменено ${nd.changed}/64${mark}`);
+    });
+
+    hmFormula(String.raw`y_k = \frac{\mathbf{x} \cdot \mathbf{p}_k + n}{2}`);
+    const layer = names.map((n, i) => `${n}\\!=\\!${t.initial_outputs[i]}`).join(',\\;');
+    hmFormula(String.raw`\text{слой: }\;` + layer);
+    hmFormula(String.raw`\varepsilon = \tfrac{0.9}{K} = \tfrac{0.9}{${t.k}} = ${t.eps}`);
+    hmFormula(String.raw`y_i(t{+}1) = \max\!\left(0,\; y_i(t) - \varepsilon\!\sum_{j \neq i} y_j(t)\right)`);
+    data.hamming_steps.slice(1).forEach((step, i) => {
+      const vals = names.map((n, j) => `${n}\\!=\\!${step[j]}`).join(',\\;');
+      hmFormula(`\\text{iter ${i + 1}: }\\;` + vals);
+    });
+    hmFormula(String.raw`\Rightarrow \text{победитель: } \mathbf{` + data.hamming_winner + `}`);
+  }
+
   stepDelaySlider.addEventListener('input', () => {
     delayLabel.textContent = stepDelaySlider.value + ' мс';
   });
@@ -308,12 +428,17 @@
       .map(c => parseFloat(c.dataset.val));
   }
 
+  function hideResults() {
+    document.getElementById('results-section').style.display = 'none';
+    clearTrace();
+  }
+
   function clearGrid() {
     document.querySelectorAll('#input-grid .cell').forEach(c => {
       c.dataset.val = '-1';
       c.className = 'cell interactive off';
     });
-    document.getElementById('results-section').style.display = 'none';
+    hideResults();
   }
 
   function randomNoise() {
@@ -322,7 +447,7 @@
       c.dataset.val = v;
       c.className = 'cell interactive ' + (v === '1' ? 'on' : 'off');
     });
-    document.getElementById('results-section').style.display = 'none';
+    hideResults();
   }
 
   function vectorsEqual(a, b) {
@@ -357,17 +482,23 @@
     });
   }
 
-  async function showSteps(data) {
-    const delay  = parseInt(stepDelaySlider.value);
-    const cells  = [...document.querySelectorAll('#output-grid .cell')];
-    const names  = data.pattern_names;
+  async function showSteps(data, runId) {
+    const delay      = parseInt(stepDelaySlider.value);
+    const cells      = [...document.querySelectorAll('#output-grid .cell')];
+    const names      = data.pattern_names;
+    const showTrace  = formulaModeCheckbox.checked && data.hopfield_nets;
 
     document.getElementById('results-section').style.display = 'block';
     document.getElementById('hamming-answer').textContent = '—';
     document.getElementById('hamming-label').textContent = '';
     document.getElementById('hopfield-label').textContent = '';
 
-    // Инициализируем бары
+    if (showTrace) {
+      clearTrace();
+      document.getElementById('trace-panels').style.display = 'flex';
+      hfFormula(String.raw`\operatorname{net}_i = \sum_{j} W_{ij} \cdot x_j \qquad x_i = \operatorname{sgn}(\operatorname{net}_i)`);
+    }
+
     renderBars(names, data.hamming_steps[0]);
 
     const hfSteps = data.hopfield_steps;
@@ -379,16 +510,34 @@
         renderGrid(cells, hfSteps[i]);
         document.getElementById('hopfield-step').textContent =
           i === 0 ? 'Шаг 0 — входной вектор' : `Шаг ${i} из ${hfSteps.length - 1}`;
+        if (showTrace && i > 0 && data.hopfield_nets[i - 1]) {
+          const nd   = data.hopfield_nets[i - 1];
+          const mark = nd.changed === 0 ? '  ← сошлось' : '';
+          hfLine(`шаг ${i}: изменено ${nd.changed}/64${mark}`);
+        }
       }
       if (i < hmSteps.length) {
         renderBars(names, hmSteps[i]);
         document.getElementById('hamming-step').textContent =
           i === 0 ? 'Шаг 0 — слой Хэмминга' : `Итерация MAXNET ${i} из ${hmSteps.length - 1}`;
+        if (showTrace) {
+          const t = data.hamming_trace;
+          if (i === 0) {
+            hmFormula(String.raw`y_k = \frac{\mathbf{x} \cdot \mathbf{p}_k + n}{2}`);
+            const layer = names.map((n, j) => `${n}\\!=\\!${t.initial_outputs[j]}`).join(',\\;');
+            hmFormula(String.raw`\text{слой: }\;` + layer);
+            hmFormula(String.raw`\varepsilon = \tfrac{0.9}{${t.k}} = ${t.eps}`);
+            hmFormula(String.raw`y_i(t{+}1) = \max\!\left(0,\; y_i(t) - \varepsilon\!\sum_{j \neq i} y_j(t)\right)`);
+          } else {
+            const vals = names.map((n, j) => `${n}\\!=\\!${hmSteps[i][j]}`).join(',\\;');
+            hmFormula(`\\text{iter ${i}: }\\;` + vals);
+          }
+        }
       }
       await sleep(delay);
+      if (runId !== currentRunId) return;
     }
 
-    // Итог Хопфилд
     const hfFinal = hfSteps[hfSteps.length - 1];
     document.getElementById('hopfield-step').textContent =
       `Завершено за ${hfSteps.length - 1} шаг(ов)`;
@@ -397,13 +546,13 @@
     hfLabel.textContent = hfMatch ? `Совпадает с эталоном: ${hfMatch}` : 'Не совпадает ни с одним эталоном';
     hfLabel.className = 'status-label ' + (hfMatch ? 'yes' : 'no');
 
-    // Итог Хэмминг
     document.getElementById('hamming-step').textContent =
       `Завершено за ${hmSteps.length - 1} итерац(ий)`;
     document.getElementById('hamming-answer').textContent = data.hamming_winner;
     const hmLabel = document.getElementById('hamming-label');
     hmLabel.textContent = `Ближайший эталон: ${data.hamming_winner}`;
     hmLabel.className = 'status-label yes';
+    if (showTrace) hmFormula(String.raw`\Rightarrow \text{победитель: } \mathbf{` + data.hamming_winner + `}`);
   }
 
   function showResult(data) {
@@ -418,24 +567,32 @@
     hfLabel.textContent = hfMatch ? `Совпадает с эталоном: ${hfMatch}` : 'Не совпадает ни с одним эталоном';
     hfLabel.className = 'status-label ' + (hfMatch ? 'yes' : 'no');
 
-    document.getElementById('hamming-answer').textContent = data.hamming;
+    document.getElementById('hamming-answer').textContent = data.hamming_winner || data.hamming;
     const hmLabel = document.getElementById('hamming-label');
-    hmLabel.textContent = `Ближайший эталон: ${data.hamming}`;
+    hmLabel.textContent = `Ближайший эталон: ${data.hamming_winner || data.hamming}`;
     hmLabel.className = 'status-label yes';
 
-    // Скрываем бары в обычном режиме
     document.getElementById('maxnet-bars').innerHTML = '';
-
     document.getElementById('results-section').style.display = 'block';
+
+    if (data.hopfield_nets && data.hopfield_nets.length) {
+      clearTrace();
+      buildTrace(data);
+    }
   }
 
   async function recall() {
-    const vector   = getInputVector();
-    const stepMode = stepModeCheckbox.checked;
-    const endpoint = stepMode ? '/recall_steps' : '/recall';
+    const runId       = ++currentRunId;
+    const vector      = getInputVector();
+    const stepMode    = stepModeCheckbox.checked;
+    const formulaMode = formulaModeCheckbox.checked;
+    const endpoint    = formulaMode ? '/recall_trace'
+                      : stepMode   ? '/recall_steps'
+                                   : '/recall';
 
     document.getElementById('loading').style.display = 'flex';
     document.getElementById('results-section').style.display = 'none';
+    clearTrace();
 
     try {
       const resp = await fetch(endpoint, {
@@ -443,11 +600,12 @@
         headers: { 'Content-Type': 'application/json' },
         body: JSON.stringify({ vector })
       });
+      if (runId !== currentRunId) return;
       const data = await resp.json();
       document.getElementById('loading').style.display = 'none';
 
       if (stepMode) {
-        await showSteps(data);
+        await showSteps(data, runId);
       } else {
         showResult(data);
       }
@@ -459,4 +617,6 @@
 </script>
 
 </body>
+<footer style="margin-top:3rem; font-size:0.75rem; color:#666; text-align:center;">
+  &copy; Develop by Antipenko D.A. for MIAD - 2026
 </html>
-- 
2.52.0


From 8f85c0adbc1117ea7f02395538106104273a6a5d Mon Sep 17 00:00:00 2001
From: Dmitry <ada.dmitry@gmail.com>
Date: Sun, 17 May 2026 17:21:58 +0300
Subject: [PATCH 2/2] Fix port configuration and update Hamming network logic;
 enhance index view formulas and add deployment workflow

---
 .gitea/workflows/deploy.yml | 21 ++++++++++++++++++++
 app.rb                      |  6 +++---
 hamming.rb                  |  2 +-
 loader.rb                   |  2 ++
 views/index.erb             | 38 +++++++++++++++++++++----------------
 5 files changed, 49 insertions(+), 20 deletions(-)
 create mode 100644 .gitea/workflows/deploy.yml

diff --git a/.gitea/workflows/deploy.yml b/.gitea/workflows/deploy.yml
new file mode 100644
index 0000000..5256d23
--- /dev/null
+++ b/.gitea/workflows/deploy.yml
@@ -0,0 +1,21 @@
+name: Build and Push
+
+on:
+  push:
+    branches: [main]
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+
+      - name: Login to registry
+        run: |
+          echo "${{ secrets.REGISTRY_PASSWORD }}" | \
+          docker login git.ada-dev.ru -u ${{ secrets.REGISTRY_USER }} --password-stdin
+
+      - name: Build and push
+        run: |
+          docker build -t git.ada-dev.ru/ada/${{ gitea.repository }}:latest .
+          docker push git.ada-dev.ru/ada/${{ gitea.repository }}:latest
\ No newline at end of file
diff --git a/app.rb b/app.rb
index db494cd..107af7e 100644
--- a/app.rb
+++ b/app.rb
@@ -9,7 +9,7 @@ require_relative 'trace'
 EPS = 0.01
 
 set :bind,       '0.0.0.0'
-set :port,       4568
+set :port,       4567
 set :server,     'webrick'
 disable :protection
 set :host_authorization, { allow_if: ->(_env) { true } }
@@ -51,7 +51,7 @@ post '/recall_steps' do
   MAX_MAXNET_ITER.times do
     nxt = maxnet_step(outputs, eps)
     hamming_steps << nxt.map { |v| v.round(2) }
-    break if nxt.count { |v| v > 0 } <= 1
+    break if nxt.count { |v| v > 1e-9 } <= 1
     outputs = nxt
   end
 
@@ -88,7 +88,7 @@ post '/recall_trace' do
   MAX_MAXNET_ITER.times do
     nxt = maxnet_step(outputs, eps_val)
     hamming_steps << nxt.map { |v| v.round(2) }
-    break if nxt.count { |v| v > 0 } <= 1
+    break if nxt.count { |v| v > 1e-9 } <= 1
     outputs = nxt
   end
   winner_idx = outputs.each_with_index.max_by { |v, _| v }[1]
diff --git a/hamming.rb b/hamming.rb
index 12a6976..1545e3d 100644
--- a/hamming.rb
+++ b/hamming.rb
@@ -21,7 +21,7 @@ def recall_hamming(pattern_vectors, input_vec)
   outputs = hamming_layer(pattern_vectors, input_vec)
   MAX_MAXNET_ITER.times do
     next_out = maxnet_step(outputs, eps)
-    return next_out.each_with_index.max_by { |v, _| v }[1] if next_out.count { |v| v > 0 } <= 1
+    return next_out.each_with_index.max_by { |v, _| v }[1] if next_out.count { |v| v > 1e-9 } <= 1
     outputs = next_out
   end
 
diff --git a/loader.rb b/loader.rb
index 045e88e..da71b29 100644
--- a/loader.rb
+++ b/loader.rb
@@ -1,4 +1,6 @@
 require 'roo'
+require 'zip'
+Zip.warn_invalid_date = false
 
 def load_patterns(file)
   xlsx = Roo::Spreadsheet.open(file)
diff --git a/views/index.erb b/views/index.erb
index 3fee0e1..f1e0311 100644
--- a/views/index.erb
+++ b/views/index.erb
@@ -401,20 +401,23 @@
     const names = data.pattern_names;
     const t     = data.hamming_trace;
 
-    hfFormula(String.raw`\operatorname{net}_i = \sum_{j} W_{ij} \cdot x_j \qquad x_i = \operatorname{sgn}(\operatorname{net}_i)`);
+    hfFormula(String.raw`s_j(p{+}1) = \sum_{i=0}^{n-1} w_{ij}\,y_i(p)`);
+    hfFormula(String.raw`y_j(p{+}1) = f\!\left[s_j(p{+}1)\right], \quad f(s)=\begin{cases}1&s\geq0\\-1&s<0\end{cases}`);
     data.hopfield_nets.forEach((nd, i) => {
       const mark = nd.changed === 0 ? '  ← сошлось' : '';
-      hfLine(`шаг ${i + 1}: изменено ${nd.changed}/64${mark}`);
+      hfLine(`p=${i + 1}: изменено ${nd.changed}/64${mark}`);
     });
 
-    hmFormula(String.raw`y_k = \frac{\mathbf{x} \cdot \mathbf{p}_k + n}{2}`);
+    hmFormula(String.raw`w_{ik} = \tfrac{x_i^k}{2}, \quad T_k = \tfrac{n}{2}`);
+    hmFormula(String.raw`y_j^{(1)} = \sum_{i=0}^{n-1} w_{ij}\,x_i + T_j`);
     const layer = names.map((n, i) => `${n}\\!=\\!${t.initial_outputs[i]}`).join(',\\;');
-    hmFormula(String.raw`\text{слой: }\;` + layer);
-    hmFormula(String.raw`\varepsilon = \tfrac{0.9}{K} = \tfrac{0.9}{${t.k}} = ${t.eps}`);
-    hmFormula(String.raw`y_i(t{+}1) = \max\!\left(0,\; y_i(t) - \varepsilon\!\sum_{j \neq i} y_j(t)\right)`);
+    hmFormula(String.raw`y_j^{(2)}(0) = y_j^{(1)}:\;` + layer);
+    hmFormula(String.raw`0 < \varepsilon < \tfrac{1}{m},\quad \varepsilon = \tfrac{0.9}{${t.k}} = ${t.eps}`);
+    hmFormula(String.raw`s_j^{(2)}(p{+}1) = y_j^{(2)}(p) - \varepsilon\!\sum_{k \neq j} y_k^{(2)}(p)`);
+    hmFormula(String.raw`y_j^{(2)}(p{+}1) = f\!\left[s_j^{(2)}(p{+}1)\right]`);
     data.hamming_steps.slice(1).forEach((step, i) => {
       const vals = names.map((n, j) => `${n}\\!=\\!${step[j]}`).join(',\\;');
-      hmFormula(`\\text{iter ${i + 1}: }\\;` + vals);
+      hmFormula(`p=${i + 1}:\\; y^{(2)} = [\\;` + vals + `\\;]`);
     });
     hmFormula(String.raw`\Rightarrow \text{победитель: } \mathbf{` + data.hamming_winner + `}`);
   }
@@ -496,7 +499,8 @@
     if (showTrace) {
       clearTrace();
       document.getElementById('trace-panels').style.display = 'flex';
-      hfFormula(String.raw`\operatorname{net}_i = \sum_{j} W_{ij} \cdot x_j \qquad x_i = \operatorname{sgn}(\operatorname{net}_i)`);
+      hfFormula(String.raw`s_j(p{+}1) = \sum_{i=0}^{n-1} w_{ij}\,y_i(p)`);
+      hfFormula(String.raw`y_j(p{+}1) = f\!\left[s_j(p{+}1)\right], \quad f(s)=\begin{cases}1&s\geq0\\-1&s<0\end{cases}`);
     }
 
     renderBars(names, data.hamming_steps[0]);
@@ -513,7 +517,7 @@
         if (showTrace && i > 0 && data.hopfield_nets[i - 1]) {
           const nd   = data.hopfield_nets[i - 1];
           const mark = nd.changed === 0 ? '  ← сошлось' : '';
-          hfLine(`шаг ${i}: изменено ${nd.changed}/64${mark}`);
+          hfLine(`p=${i}: изменено ${nd.changed}/64${mark}`);
         }
       }
       if (i < hmSteps.length) {
@@ -523,14 +527,16 @@
         if (showTrace) {
           const t = data.hamming_trace;
           if (i === 0) {
-            hmFormula(String.raw`y_k = \frac{\mathbf{x} \cdot \mathbf{p}_k + n}{2}`);
+            hmFormula(String.raw`w_{ik} = \tfrac{x_i^k}{2}, \quad T_k = \tfrac{n}{2}`);
+            hmFormula(String.raw`y_j^{(1)} = \sum_{i=0}^{n-1} w_{ij}\,x_i + T_j`);
             const layer = names.map((n, j) => `${n}\\!=\\!${t.initial_outputs[j]}`).join(',\\;');
-            hmFormula(String.raw`\text{слой: }\;` + layer);
-            hmFormula(String.raw`\varepsilon = \tfrac{0.9}{${t.k}} = ${t.eps}`);
-            hmFormula(String.raw`y_i(t{+}1) = \max\!\left(0,\; y_i(t) - \varepsilon\!\sum_{j \neq i} y_j(t)\right)`);
+            hmFormula(String.raw`y_j^{(2)}(0) = y_j^{(1)}:\;` + layer);
+            hmFormula(String.raw`0 < \varepsilon < \tfrac{1}{m},\quad \varepsilon = \tfrac{0.9}{${t.k}} = ${t.eps}`);
+            hmFormula(String.raw`s_j^{(2)}(p{+}1) = y_j^{(2)}(p) - \varepsilon\!\sum_{k \neq j} y_k^{(2)}(p)`);
+            hmFormula(String.raw`y_j^{(2)}(p{+}1) = f\!\left[s_j^{(2)}(p{+}1)\right]`);
           } else {
             const vals = names.map((n, j) => `${n}\\!=\\!${hmSteps[i][j]}`).join(',\\;');
-            hmFormula(`\\text{iter ${i}: }\\;` + vals);
+            hmFormula(`p=${i}:\\; y^{(2)} = [\\;` + vals + `\\;]`);
           }
         }
       }
@@ -552,7 +558,7 @@
     const hmLabel = document.getElementById('hamming-label');
     hmLabel.textContent = `Ближайший эталон: ${data.hamming_winner}`;
     hmLabel.className = 'status-label yes';
-    if (showTrace) hmFormula(String.raw`\Rightarrow \text{победитель: } \mathbf{` + data.hamming_winner + `}`);
+    if (showTrace) hmFormula(String.raw`\Rightarrow \text{победитель (}\,y_j^{(2)}\text{ max):}\;\mathbf{` + data.hamming_winner + `}`);
   }
 
   function showResult(data) {
@@ -618,5 +624,5 @@
 
 </body>
 <footer style="margin-top:3rem; font-size:0.75rem; color:#666; text-align:center;">
-  &copy; Develop by Antipenko D.A. for MIAD - 2026
+  &copy; Created by Antipenko D.A. for MIAD - 2026
 </html>
-- 
2.52.0