SCALE-1: The Volume Question — Can a Register Hold Trillions?

Institutional tokenization projects quote notional value: trillions in assets represented. None of them quote volume: how many transactions per second the operator's own hardware must process, hold and keep consistent. This note asks the second question and compares two architectures on it. THE COMPARISON: in the register model every ownership transfer is a stateful write on infrastructure the operator must size, staff, secure and reconcile, so per-transaction cost rises with volume. In the witness model a 32-byte digest of each ownership event is committed to public chains that act as permissionless replicated witnesses, so per-event cost is independent of notional value and falls with batch amortisation as volume rises. The load-bearing claim is narrow: what is anchored is a fingerprint, not the asset, so the trillions never enter the system and there is nothing for the operator to hold at scale. MEASURED RECEIPTS (all re-derived 2026-10-28): the FRACTAL-2 three-way 30/30/40 fractional ownership transfer across Bitcoin, Stellar and XRP costing $0.2509 total (DOI 10.5281/zenodo.23655614); 383 append-only ledger entries and 207 published Zenodo records produced by the same anchoring pipeline; and a containment record of 7,083 anomalies detected and 6,789 resolved across 60 recorded watch cycles with zero containment breaches (DOI 10.5281/zenodo.23703012). STATED LIMITS: the per-transaction cost arithmetic in section 2 is analytical reasoning about where state is written, not a hardware benchmark; no throughput benchmark of a competing register implementation was run. Chain-capacity statements rely on the public operational history of the anchor rails, not on independent testing by the author. Two-key curation: drafted and vetted by the operator's agent system (Gabriel); owner authorization Leon GO (chat authorization, 2026-10-28 09:54 CT) for documentation surfaces (Zenodo and GitHub). No social-media posting accompanies this record. Prototype disclaimer: this software and its measurements are prototypes provided for educational and research purposes only. They are not intended for production use, commercial deployment, or safety-critical environments. All systems are experimental and may contain defects.