mirror of
https://github.com/allaunthefox/SilverSight.git
synced 2026-07-31 01:25:21 +00:00
allaun
07e9b32284
All 9 agents completed work across 10 docket items: 1. roundtrip-prover: Completed decodeColoring_encodeColoring proof via native_decide + fin_cases (16 cases, 0 sorries) 2. build-integrator: Registered SilverSight.PIST.CMYKColoringCore in lakefile 3. systems-reviewer: Cross-reference audit (results pending) 4. sidon-sofa-computer: Direction A design (A*(n,x) computation) 5. gerver-colorer: Direction B design (chromatic number of Gerver's sofa) 6. pipeline-builder: CMYK -> UnitDistCandidateGen pipeline design 7. crt-formalizer: 2D CRT Sidon theorem scaffolding 8. lemma-prover: Monotonicity lemma proofs 9. golden-perturber: Golden-angle perturbation for coloring search Infrastructure: MCP autoproof server with fill_sorry, check_proof, get_sorry_context tools connecting to phi4 on neon-64gb via Tailscale. Document: CONSERVATION_LAW_CORRECTION.md fixes the false inequality.
284 lines
10 KiB
Python
284 lines
10 KiB
Python
#!/usr/bin/env python3
|
|
"""crt_capacity_envelope.py — CRT Torus Braid DAG capacity envelope.
|
|
|
|
Explores how many Sidon states are reachable under the CRT Torus Embedding
|
|
for different strand counts (8, 12, 16) and label sets.
|
|
|
|
Accepts max_depth as a CLI argument (default: 50).
|
|
"""
|
|
|
|
import sys
|
|
import math
|
|
import json
|
|
import time
|
|
import hashlib
|
|
from pathlib import Path
|
|
from collections import Counter
|
|
|
|
REPO_ROOT = Path(__file__).resolve().parent.parent
|
|
ARTIFACTS_DIR = REPO_ROOT / ".openresearch" / "artifacts"
|
|
|
|
# ── Coprimality ──────────────────────────────────────────────────────────────
|
|
|
|
def gcd(a, b):
|
|
while b:
|
|
a, b = b, a % b
|
|
return a
|
|
|
|
def pairwise_coprime(moduli):
|
|
for i in range(len(moduli)):
|
|
for j in range(i + 1, len(moduli)):
|
|
if gcd(moduli[i], moduli[j]) != 1:
|
|
return False
|
|
return True
|
|
|
|
# ── CRT Torus Embedding ─────────────────────────────────────────────────────
|
|
|
|
def embed(labels, S, moduli):
|
|
n = len(moduli)
|
|
M = math.prod(moduli)
|
|
embedded = []
|
|
for a in labels:
|
|
row = []
|
|
for i in range(n):
|
|
if i == 0:
|
|
row.append(a % moduli[0])
|
|
else:
|
|
row.append((S - a) % moduli[i])
|
|
embedded.append(row)
|
|
return embedded, M
|
|
|
|
def egcd(a, b):
|
|
if b == 0:
|
|
return a, 1, 0
|
|
g, x, y = egcd(b, a % b)
|
|
return g, y, x - (a // b) * y
|
|
|
|
def modinv(a, m):
|
|
g, x, _ = egcd(a, m)
|
|
if g != 1:
|
|
return None
|
|
return x % m
|
|
|
|
def crt_reconstruct(residues, moduli):
|
|
M = 1
|
|
for m in moduli:
|
|
M *= m
|
|
x = 0
|
|
for r, m in zip(residues, moduli):
|
|
Mi = M // m
|
|
inv = modinv(Mi % m, m)
|
|
if inv is None:
|
|
return None
|
|
x = (x + r * Mi * inv) % M
|
|
return x
|
|
|
|
def crt_values(embedded, moduli):
|
|
return [crt_reconstruct(row, moduli) for row in embedded]
|
|
|
|
def sidon_check(embedded, moduli):
|
|
M = math.prod(moduli)
|
|
n = len(embedded)
|
|
total_pairs = n * (n + 1) // 2
|
|
vals = crt_values(embedded, moduli)
|
|
sums = []
|
|
for i in range(n):
|
|
for j in range(i, n):
|
|
sums.append((vals[i] + vals[j]) % M)
|
|
counts = Counter(sums)
|
|
collisions = sum(c - 1 for c in counts.values())
|
|
score = 1.0 - collisions / total_pairs
|
|
return {
|
|
"total_pairs": total_pairs,
|
|
"distinct_residues": len(counts),
|
|
"collisions": collisions,
|
|
"sidon_score": round(score, 6),
|
|
}
|
|
|
|
# ── Prime-aware modulus selection ────────────────────────────────────────────
|
|
|
|
def pick_stride_moduli(n, identity_base=3, first_reflection=101, min_gap=10):
|
|
moduli = [identity_base]
|
|
p = first_refinement = first_reflection
|
|
while len(moduli) < n:
|
|
if all(p % d != 0 for d in range(2, int(p ** 0.5) + 1)):
|
|
if p - moduli[-1] >= min_gap:
|
|
moduli.append(p)
|
|
p += 1
|
|
return moduli
|
|
|
|
# ── DAG Node ─────────────────────────────────────────────────────────────────
|
|
|
|
class DAGNode:
|
|
def __init__(self, node_id, node_type, state, sidon_result, moduli, depth):
|
|
self.node_id = node_id
|
|
self.node_type = node_type
|
|
self.state = state
|
|
self.sidon_result = sidon_result
|
|
self.moduli = moduli
|
|
self.depth = depth
|
|
self.children = []
|
|
self.max_modulus = max(moduli) if moduli else 0
|
|
M = math.prod(moduli) if moduli else 1
|
|
self.capacity = math.log2(max(M, 1)) - math.log2(max(self.max_modulus, 1))
|
|
|
|
def is_sidon(self):
|
|
return self.sidon_result["collisions"] == 0
|
|
|
|
# ── DAG traversal ───────────────────────────────────────────────────────────
|
|
|
|
def explore_component(label_set, S, n_strands, max_depth, start_moduli=None):
|
|
if start_moduli is None:
|
|
start_moduli = pick_stride_moduli(n_strands, identity_base=3, first_reflection=101, min_gap=10)
|
|
|
|
embedded, M = embed(label_set, S, start_moduli)
|
|
sidon = sidon_check(embedded, start_moduli)
|
|
|
|
root = DAGNode("root", "initial", embedded, sidon, start_moduli, 0)
|
|
|
|
frontier = [root]
|
|
visited_signatures = set()
|
|
sidon_nodes = 0
|
|
sidon_paths = 0
|
|
max_modulus_seen = max(start_moduli)
|
|
|
|
sig = tuple(sorted(start_moduli))
|
|
visited_signatures.add(sig)
|
|
if root.is_sidon():
|
|
sidon_nodes += 1
|
|
sidon_paths += 1
|
|
|
|
depth = 0
|
|
while frontier and depth < max_depth:
|
|
new_frontier = []
|
|
depth += 1
|
|
for parent in frontier:
|
|
n = len(parent.moduli)
|
|
for i in range(1, n):
|
|
for j in range(i + 1, n):
|
|
new_moduli = list(parent.moduli)
|
|
new_moduli[i], new_moduli[j] = new_moduli[j], new_moduli[i]
|
|
|
|
for delta in [2, -2]:
|
|
adj_moduli = list(new_moduli)
|
|
adj_moduli[0] += delta
|
|
if adj_moduli[0] <= 0:
|
|
continue
|
|
if not pairwise_coprime(adj_moduli):
|
|
continue
|
|
|
|
sig = tuple(sorted(adj_moduli))
|
|
if sig in visited_signatures:
|
|
continue
|
|
visited_signatures.add(sig)
|
|
|
|
embedded_n, M_n = embed(label_set, S, adj_moduli)
|
|
sidon_n = sidon_check(embedded_n, adj_moduli)
|
|
|
|
node = DAGNode(f"d{depth}_{i}_{j}_{delta}",
|
|
"swap", embedded_n, sidon_n,
|
|
adj_moduli, depth)
|
|
parent.children.append(node)
|
|
new_frontier.append(node)
|
|
|
|
max_modulus_seen = max(max_modulus_seen, max(adj_moduli))
|
|
|
|
if node.is_sidon():
|
|
sidon_nodes += 1
|
|
sidon_paths += 1
|
|
|
|
frontier = new_frontier
|
|
if not frontier:
|
|
break
|
|
|
|
return {
|
|
"label_set": label_set,
|
|
"S": S,
|
|
"n_strands": n_strands,
|
|
"max_depth": max_depth,
|
|
"total_states": len(visited_signatures),
|
|
"sidon_states": sidon_nodes,
|
|
"sidon_paths": sidon_paths,
|
|
"max_modulus": max_modulus_seen,
|
|
"M": M,
|
|
"capacity_headroom_bits": round(math.log2(M) - math.log2(max_modulus_seen), 2) if max_modulus_seen > 0 else 0,
|
|
}
|
|
|
|
# ── Main ─────────────────────────────────────────────────────────────────────
|
|
|
|
def main():
|
|
max_depth = 50
|
|
if len(sys.argv) > 1:
|
|
max_depth = int(sys.argv[1])
|
|
|
|
print("=" * 60)
|
|
print(f" CRT Torus Braid DAG — Capacity Envelope (max_depth={max_depth})")
|
|
print(" Integer-only. No float. No eigenvalue products.")
|
|
print("=" * 60)
|
|
|
|
label_sets = [
|
|
("sidon_pow2", [1, 2, 4, 8, 16], 32),
|
|
("sidon_singer5", [0, 1, 4, 14, 16], 30),
|
|
("sidon_pow6", [1, 2, 4, 8, 16, 32], 64),
|
|
("nonsidon_seq5", [0, 1, 2, 3, 4], 5),
|
|
("nonsidon_seq6", [0, 1, 2, 3, 4, 5], 5),
|
|
]
|
|
|
|
strand_counts = [8, 12, 16]
|
|
results = []
|
|
|
|
for desc, labels, S in label_sets:
|
|
print(f"\n{'='*60}")
|
|
print(f" Label set: {desc} (n={len(labels)}, S={S})")
|
|
print(f"{'='*60}")
|
|
|
|
for n_strands in strand_counts:
|
|
print(f"\n --- {n_strands} strands ---")
|
|
t0 = time.time()
|
|
|
|
result = explore_component(labels, S, n_strands, max_depth)
|
|
elapsed = time.time() - t0
|
|
|
|
result["desc"] = desc
|
|
result["elapsed_s"] = round(elapsed, 2)
|
|
is_sidon_label = "sidon" in desc
|
|
result["collapsed"] = result["total_states"] <= n_strands * 2
|
|
result["stays_sidon"] = is_sidon_label and result["sidon_states"] == result["total_states"]
|
|
|
|
results.append(result)
|
|
|
|
sys_s = "✓" if result["stays_sidon"] else ("✗" if is_sidon_label else "n/a")
|
|
print(f" Total states: {result['total_states']}")
|
|
print(f" Sidon states: {result['sidon_states']}")
|
|
print(f" Sidon paths: {result['sidon_paths']}")
|
|
print(f" Stays Sidon: {sys_s}")
|
|
print(f" Max modulus: {result['max_modulus']}")
|
|
print(f" Capacity: {result['capacity_headroom_bits']} bits")
|
|
print(f" Collapsed: {result['collapsed']}")
|
|
print(f" Elapsed: {result['elapsed_s']}s")
|
|
|
|
# Summary table
|
|
print(f"\n{'='*60}")
|
|
print(f" Summary — Capacity Envelope (max_depth={max_depth})")
|
|
print(f"{'='*60}")
|
|
print(f" {'Label set':20s} {'Strands':8s} {'States':8s} {'Sidon':8s} {'Stays?':6s} {'Max mod':8s} {'Capacity':10s}")
|
|
print(f" {'-'*20} {'-'*8} {'-'*8} {'-'*8} {'-'*6} {'-'*8} {'-'*10}")
|
|
for r in results:
|
|
cap = f"{r['capacity_headroom_bits']} bits" if not r['collapsed'] else "COLLAPSED"
|
|
stays = "✓" if r.get("stays_sidon") else ("✗" if "sidon" in r["desc"] else "-")
|
|
print(f" {r['desc']:20s} {r['n_strands']:8d} {r['total_states']:8d} "
|
|
f"{r['sidon_states']:8d} {stays:6s} {r['max_modulus']:8d} {cap:10s}")
|
|
|
|
# Summary text
|
|
print(f"\n{'='*60}")
|
|
print(f" KEY METRICS (max_depth={max_depth})")
|
|
print(f"{'='*60}")
|
|
print(f" {'Label set':20s} {'Strnd':5s} {'States':7s} {'Sidon':7s} {'Stay?':6s} {'Headroom':10s} {'Time':7s}")
|
|
print(f" {'-'*20} {'-'*5} {'-'*7} {'-'*7} {'-'*6} {'-'*10} {'-'*7}")
|
|
for r in results:
|
|
cap = f"{r['capacity_headroom_bits']} bits" if not r['collapsed'] else "COLLAPSED"
|
|
stays = "✓" if r.get("stays_sidon") else ("✗" if "sidon" in r["desc"] else "-")
|
|
print(f" {r['desc']:20s} {r['n_strands']:5d} {r['total_states']:7d} {r['sidon_states']:7d} {stays:6s} {cap:10s} {r['elapsed_s']:>5.1f}s")
|
|
|
|
if __name__ == "__main__":
|
|
main()
|