derivationSummary
plain-language theorem explainer
Gauge symmetry emerges in Recognition Science from ledger redundancy rather than being postulated as a symmetry principle. A researcher tracing the origin of U(1) and SU(N) groups in QFT would cite this summary when connecting discrete ledger structure to continuum gauge fields. The definition simply enumerates the four emergence steps without invoking lemmas or reductions.
Claim. The derivation summary is the list of four statements: ledger redundancy implies gauge freedom; local gauge freedom requires compensating gauge fields; eight-tick discreteness yields a discrete $Z_8$ phase that becomes $U(1)$ in the continuum; and multiple ledger colors generate $SU(N)$ gauge groups.
background
The QFT-008 module derives gauge invariance from the Recognition Science ledger rather than assuming it. Gauge symmetry is the freedom to choose among equivalent ledger representations of the same physical state, with local phase freedom compensated by gauge fields whose dynamics follow from information cost. The fundamental time quantum is the tick, defined as the RS-native unit with value 1, and the RSUnits structure U normalizes $c=1$, voxel length, and tick time to unity.
proof idea
This is a direct definition that constructs the List String by enumerating the four emergence statements. No upstream lemmas are applied; the content is supplied verbatim to record the chain from redundancy through eight-tick periodicity to the standard gauge groups.
why it matters
The definition records the central claim of the module that gauge symmetry is not fundamental but follows from ledger redundancy, supporting the proposed Nature Physics paper on gauge symmetry from information redundancy. It links directly to the eight-tick octave in the foundation, where the period-8 structure forces the discrete $Z_8$ to continuum $U(1)$. The summary positions the result as input to later QFT constructions that derive Yang-Mills dynamics from the same information cost.
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