IOUF Series: Paper XII, v1.1 (Emergence of Fields)

IOUF (Information–Observer Unified Framework) series, Paper XII, preprint v1.1. One question has remained open in the series: what is a field, and why must fields exist at all? Under Route A discipline: (1) a record-to-field map — under holographic saturation the boundary record space and the bulk state space are isomorphic, the map lossless and unique modulo the per-channel phase torus; (2) gauge symmetry — the group of record-invisible transformations is exactly that torus, whose continuum limit is the local U(1) gauge group; (3) connection existence — minimality over the record-invisible redundancy forces the compensating connection, upgrading minimal coupling from declared input to forced response; (4) dynamics — the image settled current is unique (minimal-current lemma) and the Madelung equivalence closes the system to the Schrödinger equation. With this paper every row of the standard-physics catalogue carries either a derived theorem or a labeled adoption.