pith. sign in
theorem

K_net_value

proved
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module
IndisputableMonolith.Gravity.CoerciveProjection
domain
Gravity
line
50 · github
papers citing
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plain-language theorem explainer

The theorem asserts that the net constant K_net from the eight-tick structure equals 81/49. Gravity modelers using the coercive projection law would reference this exact rational value when substituting into energy minimizers or pressure equivalence relations. The proof is a one-line wrapper that unfolds the definition of K_net and evaluates the rational arithmetic directly.

Claim. The net constant satisfies $K_{net} = 81/49$.

background

In the Coercive Projection Law of Gravity the net constant K_net encodes the factor arising from the eight-tick structure with epsilon = 1/8. The sibling definition sets K_net : ℚ := (9/7)^2, where the numerator 9 incorporates the full cycle including the return tick. The module formalizes the unique energy minimizer of the ILG functional together with pressure equivalence to the standard Poisson equation under an effective source p = w rho_b.

proof idea

The proof is a one-line wrapper that unfolds the definition of K_net and applies norm_num to confirm the rational equality.

why it matters

This pins the numerical value of K_net used when computing the coercivity constant c = 49/162 for the ILG energy functional. It connects to the eight-tick octave in the forcing chain, where the period 2^3 produces epsilon = 1/8 and the resulting (9/7)^2 factor. The equality supports the pressure-equivalence and unique-minimizer claims stated in the module documentation.

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