channels
plain-language theorem explainer
On any ledger state the channel inventory is defined to be the empty list of naturals. Callers in multi-channel J-cost, multi-distinction geometry, and the alpha channel-budget bridge treat this as the passive-channel slot on the recognition operator state. The body is a pure definitional stub: constant empty list, no computation from the state.
Claim. For every ledger state $s$ (here an eight-tick signal), the associated channel list is $\mathrm{channels}(s)=[]\subseteq\mathbb{N}$.
background
In this module a ledger state is abbreviated to Signal8, the eight-component recognition signal that carries the discrete octave structure (T7). The LedgerState namespace exposes a small surface of accessors (time, Z-patterns, global phase, channels, active bonds, bond multipliers) that later layers read as if they were physical fields on the state.
Upstream, other modules define richer ledger states: variational dynamics uses $N$ positive real ratios indexed by tick; information-as-ledger uses a finite list of recognition events; thermodynamics uses a finset of active bonds with positive multipliers. The present accessor is the thin Foundation stand-in for the channel inventory those stories assume.
"Channels" in Recognition Science are the independent distinction directions that enter multi-channel cost $J_n$ and the passive dressing count in the alpha seed (solid angle times passive field edges).
proof idea
No proof. The declaration is a one-line definition: ignore the state argument and return the empty list [] : List ℕ. There are no lemmas, unfolds, or tactics.
why it matters
This slot is wired into the alpha pipeline and the multi-channel geometry. Downstream, geometric_seed_eq identifies the geometric seed with $4\pi\cdot 11$, and ChannelBudgetBridge states that the inverse EM coupling at leading order is the voxel solid angle spread over passive dressing channels (the same $11$ that appears in $\Omega_\Lambda=11/16$ and the lepton torsion ladder). Multi-channel J-cost uses the channel count for $J_n$ at the all-ones fixed point; multi-distinction geometry treats channels as independent binary coordinates whose mixed differences commute.
Until the body is replaced by a state-dependent inventory, those consumers see a vacuous channel list. The definition therefore marks the API boundary the channel-budget and multi-distinction developments hang on, without yet discharging the physical content of that list.
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