HACI is the document; MACI is the structure. One is handed to the other and back — and if the conversion is faithful, nothing is lost in the crossing. Slide fidelity (or tap): a faithful hand-off round-trips exactly; a broken one drops structure on the way home.
The conversion invariant on a small canonical grammar — headings, bullet items, blank breaks, paragraphs — where each line maps to exactly one node and each node renders to exactly one line, so a faithful hand-off is lossless BY CONSTRUCTION. Fidelity below 1 stands in a broken renderer that drops list markers, so the round trip loses structure — visible as vanished nodes and a failed fixed-point parse(render(parse(x)))≠parse(x). At full fidelity it is lossless and the fixed point holds. A fail-loud self-check throws unless the faithful path round-trips exactly and a dropping renderer is caught as lossy.
A deliberately small grammar (not a full Markdown engine); 'fidelity' is a demonstration knob, not a probabilistic model of corruption. The parse/render, the loss count and the fixed-point check are computed exactly.