Explain the Lean theorem `atomic_tick` in module `IndisputableMonolith.Foundation.Atomicity`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

The declaration atomic_tick asserts that any finite recognition history (modeled as a Finset of events) under a well-founded precedence relation admits a one-per-tick serialization.

(1) In plain English: given events E, a precedence relation prec (e1 must precede e2), decidability of equality and prec, and well-foundedness of prec, for any finite nonempty H there exists a list order such that the distinct events in order are exactly those in H and earlier events in the list have no precedence edge from later ones.

(2) In Recognition Science this supplies the constructive content of T2 (discreteness): finite ledger histories can be serialized without violating causal constraints, enabling atomic tick-by-tick evolution.

(3) The formal statement is read as: for parameters prec, decidability instances, wf : WellFounded prec, and H : Finset E, there exists σ : Schedule E such that σ.order.toFinset = H and ∀ e1 e2 ∈ H, prec e1 e2 implies indexOf e1 < indexOf e2 in σ.order.

(4) Visible dependencies inside the module are exists_sequential_schedule, which itself rests on topoSort, exists_minimal_in, topoSort_perm and topoSort_respects; the proof is a direct extraction from exists_sequential_schedule.

(5) The declaration does not prove anything about infinite histories, does not invoke cost functions or φ, and supplies no physical units or emergence theorems.