future
plain-language theorem explainer
The future declaration defines the set of ledger snapshots whose tick indices exceed the current now. Researchers on time emergence and the arrow of time cite it to isolate uncommitted entries from the fixed past. It is realized as a direct set comprehension over the indexed state sequence.
Claim. Let $(s_k)_{k∈ℕ}$ be a sequence of ledger snapshots. For current index $n_0$, the future is the set $ { s | ∃ n > n_0 such that s_n = s } $.
background
The module formalizes time as the ledger tick counter with no background continuum. LedgerSnapshot is the structure carrying a tick index and a nonnegative defect value. The companion past definition extracts states with indices strictly below now. Upstream, defect is the J-functional from LawOfExistence, and the 8-tick cycle supplies the minimal update period.
proof idea
This is a definition realized by a one-line set comprehension that collects every snapshot s for which there exists a tick index n strictly larger than now with states n equal to s.
why it matters
The definition supplies the uncommitted side of the present/past/future partition required by F-006. It is invoked by arrow_of_time, recognition_irreversible, and downstream results including dark_energy_w and vs_multiverse. It anchors the claim that recognition steps are irreversible because only later ticks remain open.
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