Implement trace functionality for Hopfield and Hamming networks; update Gemfile.lock and app.rb for new dependencies and features

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)