arXiv:2610.29387v1 Announce Type: new Abstract: Public descriptions of the Starlink downlink specify synchronization sequences, edge pilots, and predictable symbol templates, but leave the coded control fields and explicit payload-code representations largely unresolved. We examine one continuous complex-baseband capture spanning approximately 24 ms and recover control and coding structure beyond those predictable elements. Reference-phase removal exposes terminated rate-1/3 convolutional control blocks with constraint length seven and a group-level cyclic redundancy check. A conditional descriptor layout predicts sequential allocations through per-codeword symbol rounding, agreeing exactly with independently estimated endpoints in 16 of 18 frame records and within two symbols in the remaining records. Quasi-cyclic closure, binary elimination, and sparse dual checks yield explicit systematic code representations at rates 1/2 and 5/8. Frozen encoders predict 78,848, 9,984, and 811,008 reserved parity bits for three formats without disagreement. A rank-deficient long-code fit is completed within a declared finite structural family, and shared encoders are tested across modulation formats. The recovered representations explain observed coded symbols; they do not authenticate transmitter-standard identities or plaintext semantics. Two high-order formats have only one target field each, while codes 28 and 37 admit verified shortened cores with unexplained extra bits and code 4 remains unresolved.