Individuality as the complement of objectivity: a coherent-information theory of who can inherit a quantum system

Quantum Darwinism explains why the world agrees about a system: redundant classical records make its pointer observable objective. We ask the complementary question, what it would take for a region of the world to be the continuation of a system rather than a description of it, and organize the answer around one quantity, the coherent information of the history channel from an origin to a region, I(R > X)=S(X)-S(RX) on the Choi state of the dynamics. For a pure global state this is log d minus what the rest of the world knows about the origin, so inheriting is that everybody else be ignorant, and objectivity and individuality are complementary. From this one quantity, three standard facts (strong subadditivity, global purity, data processing) and four ways of cutting the world (space, time, body versus records, and large scale) we obtain the following. Uniqueness of the heir and its causal-clique shape in spacetime; the size of the minimal heir in terms of Darwinian redundancy, with the constant kappa(0.1)=0.026, its form in the currency of recording strength for unequal witnesses, where the bound needs no exchangeability hypothesis, and a shared-secret environment that separates objectivity from heritability; a classification of interactions by degradability, under which pointer interactions never produce an heir. A realization theorem for what two disjoint regions can jointly inherit: their maximal correctable algebras commute, every commuting pair with a multiplicity matrix is realized as the maximal pair of an explicit channel, and what the two regions hold in common is always abelian, of dimension the number of connected components of a bipartite graph that the channel fixes -- so that the shareable part of an ancestry is exactly its classical part. An exact Zeno law for bodies whose dynamics does not commute with what is recorded, whose extended-body form is a classical Markov chain with unistochastic transition matrix and whose criterion is quantum non-demolition, and, for imperfect records, the fact that a perfect record is NOT the fastest way to take a body's identity: the loss is fastest at an interior record strength, where its rate exceeds the perfect-record rate by a factor 2/theta in the rotation angle; a budget inequality under which a lineage that acts on the world spends itself, with a closed frontier for qubits by convexity and a non-convexity for qudits. An existence criterion via information-preserving structures; a de-ordering lemma for biographies in indefinite causal order; and a security formulation in which exclusivity is the privacy of the root's classical record. Most of the physics is other people's and every theorem is attributed in place; Section 1.3 lists one by one what is not, with the realization theorem at the head of that list, and two companion notes carry the two longest proofs. We report, with equal weight, what was tried and fell: a proposed dynamical law of non-inheritance, a dynamical selection of subsystems, and a localization diagnostic, all retracted after adversarial review, and we propose a measurement of the minimal heir on an existing superconducting quantum-Darwinism platform.