Clifford+T 458 ↔ HKUST-1 (Cu₃(BTC)₂) · Live RRMS-1740-BRIDGE-001 Vault

Discrete Cage: 456 Cluster Atoms + 2 Pore Manifolds = 458 Clifford+T Sites · Full Z=16 Unit Cell: 624 Fm-3m Atoms + 4 FCC Pores (4a+4b+8c×2) = 628 Sites + 12 P3Q Tail Watchers (1/Z′=12) = 640 Twin-320 CIRC Rails (320 Rail A + 320 Rail B · 4 Rails/Mars Lane) · July 108Q (60+20+3+25).

POLLING RRMS-1740...
DISCRETE CAGE (458): 24 Cu + 144 O + 216 C (6³ T-π/4) + 72 H + 2 Pores = 458 Sites
TWIN-320 DENSE (640): 624 Cell + 4 FCC Pores = 628 + 12 P3Q Seals = 640 (320 A | 320 B)
RAIL SLICE (A | B): 24|24 Cu (0..23) · 96|96 O (24..119) · 144|144 C (120..263) · 48|48 H (264..311) · 2|2 Pores (312..313)
12 TAIL WATCHERS: Rail A [314..319] ⊕ Rail B [634..639] (Π_K=ℂ⁶) → syn_tail[12] = 000000_000000
ACTIVE LOCK: COD 1546786 (77 K · a=26.2824 Å · Z=16 · 1/Z′=12) · ALL SITES ACTIVE
BRIDGE: RRMS-1740-BRIDGE-001 (1584 HOT · 144 NOT · 12 P3Q)
JULY 108Q SPEC: q0..59 (60Q) + q60..79 (20Q) + q80..82 (3Q su(8)) + q83..107 (25Q)
ISLAND: ISL-3DFC316639DB · Pass #15 · EXCEPTIONAL
SU(8) CASIMIR: C₂ = 1.748702 (MOP 3.9375) · C₃ = 0.65625
LOPEZ-NOETHER: Q_L = -0.010412 (|Q_L| ≤ 1.611) · SNR 380.0 dB · 2,643 str (STANDBY)
24 Cu (12 Clifford Dimers) 144 O (144 NOT Syndrome Bridges) 216 C (6³ T(π/4) Struts) 72 H (Pauli-Z Frame Anchors) Site 456: Cuboctahedral Supercage (0,0,0) [↔ Apex q[4]] Site 457: 8 Tetrahedral ⟨111⟩ Pockets [↔ q[9] / su(8) q80..82] July 108Q: q0..59 Core (60) · q60..79 Bus (20) · q80..82 su(8) (3) · q83..107 Verif (25) Cepheus Hardware Qubit #33 Bypassed

1. Crystallographic Provenance (Public Prior Art): The 456-atom finite cluster cut (24 Cu + 144 O + 216 C + 72 H, ¾ of the organic/O sublattice and ½ of the Cu sublattice within r ≤ 12.5 Å) is derived from the 624-atom Fm-3m (#225) unit cell (C₂₈₈H₉₆Cu₄₈O₁₉₂, Z=16, Z′=1/12) of published COD 1546786 (77 K neutron, Getzschmann et al., 2010, a = 26.2824 Å) and COD 2300380 (100 K synchrotron, Yakovenko et al., 2013, λ = 0.45875 Å, a = 26.3034 Å, GoF = 1.73).

2. 458 Discrete Cage → 628 Unit-Cell Expansion → 640 Twin-320 Dense Rail Closure: Expanding the 458-site cage to the full Z=16 Fm-3m unit cell (48 Cu [48h] + 192 O [192l] + 288 C [96k+192l] + 96 H [96k] = 624 atoms) plus the 4 FCC Wyckoff pore manifolds (4a + 4b + 8c×2) yields 628 sites (314 on Rail A 0..313 + 314 on Rail B 320..633: 24|24 Cu, 96|96 O, 144|144 C, 48|48 H, 2|2 FCC Pores). Appending the 12 P3Q Ledger Seal / Tail Watcher rails (1/Z′ = 12: 6 on Rail A 314..319 + 6 on Rail B 634..639, each forming a 6-qubit ΠK = ℂ⁶ (2⁶ = 64) SDRPL-F subspace, syn_tail[12] = 000000_000000) closes 640 Twin-320 Dense Rails at exactly 4 rails (2 twin pairs) per Mars Lane (160 × 4 = 640; 640-Rail JSON · OpenQASM 3.0 · July 108Q QASM).

3. Patent Boundary & July 108Q Register Spec: Cu₃(BTC)₂ (COD 1546786 / 2300380) is a 2010/2013 public-domain reference crystal; DCGP AI LLC's patent filings (19/555,951 · 19/567,678 · 19/569,785 · 19/850,925 · 64/020,705 · 64/095,091) claim only the computational Admissible Inference, Clifford+T 458, Twin-320 (640 CIRC), and July 108Q Register architecture: q0..q59 (60Q GO Honeycomb Core), q60..q79 (20Q Coupling & Syndrome Bus, routing around Qubit #33), q80..q82 (3Q su(8) Casimir Router mapped as a computational bijection to the 8 tetrahedral ⟨111⟩ pockets), and q83..q107 (25Q Integrity & Constitutional Verification Register).