both_fibonacci_at_D3
plain-language theorem explainer
At spatial dimension three the fourth Fibonacci number equals the dimension while the sixth equals the ledger period of eight, confirming the eight-tick periodicity as a Fibonacci identity. Researchers working on the T7 step of the Recognition Science forcing chain cite this result. The proof is a term-mode conjunction that applies reflexivity to the constant definitions followed by a decision procedure.
Claim. $F_4 = 3$ and $F_6 = 8$ where $3$ is the spatial dimension $D$ and $8$ is the ledger period $2^D$ at $D=3$.
background
The module formalizes the eight-tick periodicity required by T7 of the forcing chain. spatialDim denotes the spatial dimension fixed at three; ledgerPeriod is defined as two raised to the power of spatialDim. F4 and F6 are the fourth and sixth Fibonacci numbers, preset to three and eight respectively. The upstream tick supplies the fundamental time quantum with one octave equal to eight ticks. Module documentation states: 'The ledger period is 2^D = 2^3 = 8 at D=3. This is called the 8-tick fundamental periodicity.'
proof idea
This is a one-line term proof that constructs the conjunction via reflexivity on the pre-defined constants F4, F6, spatialDim and ledgerPeriod, then applies the decide tactic to confirm the numerical identities.
why it matters
The theorem supplies the fibonacci_D component inside the eightTickCert definition. It realizes the module claim that D=3 and 2^D=8 are both Fibonacci numbers connected by the recurrence. In the Recognition Science framework it anchors the T7 eight-tick octave at D=3, with the associated five-rung depth giving period times depth equal to phi to the power 8.37.
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