The framework's terms are exact and disciplined; these are their public readings.
- Readout / shadow
- An exact bounded presentation of a richer realization structure, such as a quotient, measurement, macrostate, or public summary. A shadow presents the source exactly as a quotient, can support valid internal laws, and remains distinct from the source-level structure.
- Reduced source
- The space of admissible realization states after all declared gauge and coordinate redundancy has been quotiented out. Every non-equivalence result concerns this reduced source, so a nontrivial readout fiber represents genuine physical multiplicity after gauge residue has been removed (Paper 1).
- Descent
- A physically invariant source relation descends through the readout, becoming a function of readout data alone, exactly when it is constant on every readout fiber. Descent is the criterion that makes a source relation an observable of the readout level (Paper 1).
- Target and correct-answer map
- A question posed of the source, formalized as a map assigning each source state its correct answer. Whether readout loss matters is a property of the target, not of the readout alone: loss obstructs a target exactly when the correct answer varies within some readout fiber (Paper 2).
- Canonical minimal completion
- For a nominated family of invariant source relations, the joint image of readout and relations is the coarsest extension on which every relation becomes well defined. It is terminal: every sufficient extension maps uniquely onto it. Minimality measures retained distinctions; reconstruction occurs exactly when the nominated family separates source points (Paper 3).
- Geometric realization / orbit space
- The physical geometric source is the orbit space of admissible field configurations under allowed bundle isomorphisms and diffeomorphisms. Invariant global relations such as holonomy, Wilson observables, characteristic numbers, and spectra descend to it. Descent and cocycle conditions characterize the exact domain on which the abstract completion has a geometric realization (Paper 4).
- Closure and memory
- Observable dynamics close autonomously exactly when the source evolution preserves the readout kernel. When closure fails, the exact projected law carries a deterministic unresolved-initial-state term and an exact memory kernel derived without stochastic or Markovian approximation. The minimal dynamical completion measures exactly what state must be restored (Paper 5).
- Non-source projection
- A readout tier exhibiting an essential non-gauge fiber distinction: two physically inequivalent source states with the same readout but different correct answers to a nominated target. For that model and target, the readout is provably a faithful quotient of a larger physical state space (Paper 6).
- Internal identifiability theorem
- When every admissible internal probe factors through the readout, all probe values, derived statistics, and deterministic selectors agree across a common readout fiber. Under the statistical counterpart, every test at every sample size has the same outcome law across the fiber. These are separate factorization theorems (Paper 6).
- Physical witness
- A concrete physical model that instantiates the abstract architecture. Paper 7 supplies one in Randall–Sundrum (RS2) gravity: gauge-inequivalent bulk states with identical instantaneous brane readout and different brane futures, an exact projected Einstein equation, and linked observable residues.
- Operational equivalence
- Every brane-only experiment, including adaptive protocols, is reproduced exactly by a four-dimensional pushforward theory of the brane record. The two source representations therefore generate the same complete brane-level outcome law (Paper 7).