Global Exhaustive Proof Rewritten as an Independently Verifiable Sharded Architecture: A Reference Case Splits Into Three Shards and Re-Verifies Successfully, but the Real Global 0.8350 Run Remains Compute-Deferred

Round 11 (AMRAL-LUC-FC-R11, 2026-09-18) picks up where Round 10 left off: Round 10 first ran base leaf → B7 lift tree → certificate bytes → independent replay end to end, but a truly global computation of T=0.8350 cannot stay tied to a single process, a single machine, or a single AI conversation. This round first defines a prefix-free frontier (a set of seed paths, none of which is a prefix of another) and a complete frontier (recursing from the root, every infinite binary descent path first meets exactly one frontier prefix), then proves four results on top of them: the Complete-Frontier Coverage Theorem (Theorem 4.1: a complete frontier covers the whole root box), the Frontier Replacement Invariant (Theorem 5.1: any frontier seed p can legally be replaced by {p0,p1} without breaking the complete-prefix-free property, and this can be applied repeatedly to split a hard seed to arbitrary depth), the Shard Partition Theorem (Theorem 8.1: as long as the shards partition the frontier with no overlap and no gaps, and every seed inside every shard has been independently proved ∀q∈B(p), A(q)≥T, then the same holds over the whole root box — the core soundness theorem for the global merge), and the forest structural identity N=2L-S (exactly the 2L-n_seed=N global structural audit the Mishra verifier already uses). The round also establishes a content-addressed shard manifest (a SHA-256 hash of the canonical payload) and a sorted shard Merkle root for data-integrity binding, and compares two cross-machine deterministic-seed-identity modes — Mode A (implicit 0/1 bit paths: minimal metadata, but sensitive to cross-language/cross-floating-point implementation) and Mode B (explicit (axis,side) paths: a few more bits in exchange for portability) — recommending Mode B as the default for the production global certificate. The actual verification performed is a reference dry run: Round 10's 4-leaf local reference frontier {00,01,10,11} is deliberately split non-uniformly into 3 shards (Shard A = {00,11}, Shard B = {01}, Shard C = {10}), each bound to its own manifest and SHA-256 hash and combined into a shard Merkle root; a merge verifier then reconstructs the frontier, independently replays all 4 lift certificates, and checks the forest identity both per shard and globally: globally S=4, N=11372, L=5688, and 2L-S=2(5688)-4=11372=N checks out; Shard A (N_A=5686, L_A=2844), Shard B (N_B=2853, L_B=1427), and Shard C (N_C=2833, L_C=1417) each pass their own 2L-S audit too, with the result logged as REFERENCE-SHARDED-VERIFIED. The document states plainly that this verification is still scoped to Round 10's local base neighborhood and is not a_Leb≥0.835; this round never actually ran the complete Round 07 global base domain (D+B3+B5, |t3|≤0.194856180909, |t5|≤0.197820670401, φ5∈[0,2π/5)), so it is formally logged as SHARDED CERTIFICATE ARCHITECTURE: CLOSED while also formally logging GLOBAL 0.8350 HEAVY RUN: COMPUTE-DEFERRED, leaving five concrete compute work items — C11-1 global seed pilot through C11-5 global merge — as COMPUTE-DEFERRED for future rounds, and assigning Round 12 the topic Global Checkpoint Crystal and Multi-AI Shard Audit Protocol. Research direction and methodology are due to Neo.K; this round's AI collaborating researcher and primary executor was Aletheia / ChatGPT, GPT-5.6 Sol.