gravity_from_ledger_implies_eight_tick
plain-language theorem explainer
The theorem extracts the eight-tick periodicity from the gravity-from-ledger bundle under the assumption that the RS Einstein coupling kappa_rs is positive. Researchers deriving gravity as ledger curvature would cite it to confirm the discrete time anchor in the continuum limit. The proof is a direct term projection of the first conjunct from the input hypothesis pair.
Claim. Assume the eight-tick period equals 8 and the RS gravitational constant satisfies $0 < kappa_{rs}$. Then the eight-tick period equals 8.
background
In the Zero-Parameter Gravity module, gravity arises as large-scale curvature of the ledger lattice induced by defect distributions, with the Einstein equations as the continuum limit and kappa equal to 8 phi^5. The eight-tick period is defined as the natural number 8 in DimensionForcing, corresponding to the T7 octave (period 2^3) in the forcing chain. Upstream structures such as LedgerFactorization calibrate J-cost on the positive reals, while PhiForcingDerived and SpectralEmergence supply the J-cost and gauge content that feed into the gravity bundle.
proof idea
The proof is the term h.1, a one-line wrapper that projects the left conjunct of the hypothesis conjunction (eight_tick = 8 and 0 < kappa_rs).
why it matters
This declaration secures the eight-tick octave (T7) inside the gravity-from-ledger construction (G-002). It guarantees the discrete period appears when the ledger curvature yields the Einstein equations. No downstream theorems are recorded yet; the result closes one link in the chain from J-cost to D = 3 spatial dimensions.
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