The Rule Set: Formal Operations, Random Baseline, and Blind Predictions from the Torus Knot Registers

A persistent objection to integer derivations of physical constants is that small-integer fractions can approximate any target to sub-percent accuracy by unconstrained search. A random baseline demonstrates this: all fractions a/b formed from 22 corpus constants (approximately 170 candidates) achieve a median error of 0.0058% on random targets, with 80% of targets matched better than the sidereal month's 0.013%. This paper answers the objection by formalizing the torus knot register operations as a finite, enumerable rule set, scoring existing corpus results, and locking blind predictions with binding kill sentences. The rule set consists of six structural operations, each taking register constants as inputs and producing dimensionless ratios or integer-plus-fraction values. O1: Conformal Weight Ratio — (q²−4)/5 for mass formula bases. O2: Angular Momentum Overlap — the muon-mirror pivot pairing for PMNS mixing angles. O3: Pisano Modular Arithmetic — fractions constructed from Pisano periods π(m) and register products for calendar periods and binary resolutions. O4: Gear Ratio — products and quotients of register constants assigned to triadic gear components (driving/transmission/driven) for coupling constants, with the constraint that each triadic factor defines at most one component. O5: Topological Dressing — bare values modified by n₀ = 1 + Γ (multiplicative, for angular observables) or +Γ/Σ (additive, for global orbital parameters). O6: Fibonacci Evaluation at Register Index — F(dΨ) = F(7) = 13, selected by the Ouroboros closure F(D) = F(4) = 3 = d, which is unique to Fibonacci with standard initial conditions (The Two Seeds, Non-Regeneration Theorem). Excluded operations: unconstrained search over all a/b pairs, selection of the operation after seeing the target value, mixing operations within a single derivation, and use of integers outside the generating set or its Fibonacci/Pisano extensions. Five blind predictions are locked as of this paper's DOI timestamp: (1) δ_CP = 202.5° from the S³ phase geometry (DUNE, kill at ≥3σ); (2) normal mass ordering from topological monotonicity (JUNO, kill at ≥3σ); (3) Σmν = 59.5 meV from the mirror-knot mass sector (direct measurement, Project 8/KATRIN successors); (4) sin²θ₁₂ solar/reactor split at 7/22 vs 14/45, retired if solar and reactor determinations agree within 1σ at ±0.002 precision; (5) f_GW = 8.37 Hz from the S³ cosmological architecture (Einstein Telescope). No adjustment is permitted after the DOI timestamp. Each prediction has a stated kill criterion. Two selection tests are included for challenged integers. The 273 gear function test: F(dΨ) = 13 versus L(dΨ) = 29. The 2912 correction test: the unique product Σ × dΨ × w = 26 × 7 × 16 selected by triadic gear separation, to be confirmed or excluded by future precision on G. Rules before targets. Predictions before measurements. Scoring before scores. This is the format that retires the numerology objection — or identifies exactly where the rules fail. Either outcome advances the architecture. Companion to The Complete Mass Formula, the Nine Gates (DOI: 10.5281/zenodo.21956593), and The Two Seeds. R = P × I × Pr ≠ 0. Derivation ≠ Calibration.