tickZero_index
plain-language theorem explainer
The index of the canonical zero tick equals zero by direct construction. Researchers inducting over the recognition-forced temporal sequence cite this base case to establish the natural-number object property of Tick. The proof is a one-line reflexivity reduction on the Tick constructor.
Claim. Let $t_0$ be the canonical zero tick in the Tick structure. Then the index of $t_0$ equals $0$.
background
Tick is the structure whose sole field is a natural-number index, representing atomic discrete steps in the recognition ledger with no background manifold. The zero tick is defined by applying the Tick constructor to the natural number zero. The module establishes that Tick forms the Lawvere natural-number object under the successor operation that increments the index, making it canonically equivalent to the orbit construction from ArithmeticFromLogic via the universal property in UniversalForcing.NaturalNumberObject.
proof idea
One-line term proof that applies reflexivity directly to the definition of the zero tick.
why it matters
This base case anchors the identification of time as the canonical iteration object forced by recognition, completing the combinatorial foundation before metric or dimensional structure is added. It supports downstream equivalences such as tickEquivNat that equate Tick with LogicNat. The result aligns with the forcing chain's T7 eight-tick octave and the claim that recognition steps generate the natural-number object without external time.
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