How to knock on the simulation: Harmonic and heralded-echo tests of branch-cost economies on quantum hardware

A universe computed with finite resources must economize; which economies could be detected from inside? We prove that economies linear on ensembles, including setting-independent noise, leave every single-angle outcome probability a first-degree trigonometric polynomial. Deterministic truncation, rounding, and lossy memoization can produce higher harmonics; Born-weighted pruning leaves branch-basis statistics unchanged but is exposed by a heralded echo. On a 156-qubit IBM processor we ran pre-registered twin circuits whose pulse schedules agree up to virtual phase changes. In one twin, a branch of a coin carries a 27-qubit butterfly state; the two instances analysed exactly have support 2²⁷ and maximal Schmidt rank across every minimum balanced cut. The twins’ second-harmonic difference was (−0.3 ± 4.6) × 10⁻³ across six instances. Within stated models and for this circuit family, an economy acting on the finished branch withholds less than 9.3% of its weight (95% confidence), and an amplitude budget acting once, right after the branches separate, keeps at least 73% of their 2²⁸ joint amplitudes (one-step model, six-instance average). Born-weighted collapse of the coin occurred in under 11.2% of heralded runs, if the coin is not flipped while the branches are apart. A distant spectator showed no load-dependent degradation beyond 2.3% (post hoc; 13% pre-registered). A pre-registered scan from cheap to expensive twins crossed its threshold, in the direction opposite to pruning. Beacons requesting a verifiable reply, such as a factor of RSA-2048, have drawn none. The bounds concern economies acting locally on branches of this size; global, generous, or perfect economies remain untested. Preprint, October 18, 2026. Out of Plane project. This record contains the manuscript, supplementary code and raw data, pre-registrations and checksums, LaTeX sources, an offline interactive demonstration, animations, and a README with reproduction instructions and the AI-use statement.