TL;DR
One sentence. Observation is a resource: different budgets draw different boundaries between what is and is not distinguishable — and in at least one physical case (attention-mediated interactions), resource-bounded distinction-making moves the system.
The thesis. Seven established theories — Turing machines, quantum measurement, persistent homology, the renormalization group, constructive type theory, measure theory, and non-reciprocal active matter — instantiate a single shared structure: the Resource-Bounded Distinction System (RBDS, §1.5) and its generalization, the Resource-Indexed Theory of Experiments (RITE, §1.9), built from a state space, a budgeted distinction operator, an operational monoid, and a resource bound.
The candidate structural contribution. Generic resource-aware attention, state-dependent neighbor selection, and perception-induced non-reciprocity are established neighboring ideas. The sharper claim developed here is quotient-compatible Resource-Indexed Attention: attention at budget $B$ must factor through the operational quotient $q_B : X \to Q_B$, with the resulting column-imbalance functional providing one drift calculus for mechanics and representation updates (§1.10). A second structural construction is the resource-bounded / graded Karoubi envelope: idempotent splitting under a cost budget with resource-non-increasing morphisms (§1.5–1.6).
What is not new. The mechanical theorems in §7 (the Antisymmetric Momentum Principle and the complete energy ledger) are clean derivations or unifications of established results (Ivlev et al. 2015; odd elasticity; ratchet / information-engine physics). The remainder is synthesis, with attribution.