eightTickCert
plain-language theorem explainer
The eightTickCert definition assembles a certificate confirming that the ledger period equals 8 at spatial dimension 3, with both quantities Fibonacci numbers linked by the standard recurrence. Researchers formalizing the Recognition Science forcing chain at T7 would cite it to lock in the eight-tick periodicity. The construction is a direct record that populates each field from a separate upstream lemma.
Claim. The eight-tick certificate is the structure asserting that the ledger period equals 8, that the fourth Fibonacci number equals the spatial dimension and the sixth equals the ledger period, and that the sixth Fibonacci number satisfies the recurrence $F_6 = F_5 + F_4$.
background
In Recognition Science the T7 step of the forcing chain requires the ledger period to equal $2^D$. At $D=3$ this period is 8, called the eight-tick fundamental periodicity. The structure EightTickCert packages the three facts needed to certify the step: the period equals 8, both $D$ and the period are Fibonacci numbers, and they obey the Fibonacci recurrence arising from J-cost-optimal partitioning.
proof idea
The definition is a direct record construction. It sets the period_8 field to the theorem ledgerPeriod_eq_8, the fibonacci_D field to the conjunction proved in both_fibonacci_at_D3, and the fibonacci_rec field to the decide-based theorem fibonacci_recurrence.
why it matters
This definition completes the formal packaging of the T7 eight-tick periodicity in the Recognition Science chain. It supplies the concrete relations that connect spatial dimension 3 to period 8 via Fibonacci numbers, as required by the module documentation for the 8-tick times 5-rung product near phi^8.37. No downstream uses appear yet, so its role in larger derivations such as the mass ladder remains open.
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