Gravity Coercive Projection Defect Bound Constant Value

The defect bound constant

The defect bound constant is the product of two quantities that appear in a formal theory of gravity as a projection. The first, K_net, is the squared ratio 81/49. The second, C_proj, is simply 2. Their product, 162/49, is what the declaration defect_bound_constant_value establishes by direct computation, a result checked in a machine-checked library of formal theorems.

To see why the product matters, consider the framework's starting picture. In Recognition Science, gravity is modeled not as a force pulling masses together but as a projection: a rule that takes a distribution of matter and returns the smoothest, lowest-energy configuration consistent with limited information. The framework proves that this projection has a unique energy minimizer, with a coercivity constant c_coercive = 49/162, a positive number that guarantees the energy cannot run away to negative infinity. The net constant K_net = (9/7)^2 arises from an eight-tick recognition cycle, a discrete counting step in the framework's ledger of events. The defect bound constant multiplies these two: 81/49 times 2 equals 162/49.

The declaration itself is a theorem in the machine-checked library: defect_bound_constant = 162/49, proved by unfolding definitions and normalizing numerals. It is a statement about the framework's internal arithmetic, not a measurement of any physical system. It establishes that the product of the two defined constants has this exact rational value, and that the value is greater than 1, since 162/49 is approximately 3.306. The theorem also carries a companion result, K_net_gt_one, which states that 81/49 exceeds 1, a property the framework uses to argue that the net constant is not a trivial identity.

What the declaration does not claim is equally important. It does not claim that 162/49 is a measured value of any gravitational quantity, nor that it predicts a specific experimental outcome. It does not assert that the projection model is the correct description of gravity; that is a modeling choice, not a theorem. The declaration establishes only an internal consistency: given the framework's definitions, the product of K_net and C_proj is exactly 162/49. The physical interpretation, that this constant bounds a defect in the projection, remains a paper-level claim, not a formal theorem in the library.

theorem defect_bound_constant_value :
    defect_bound_constant = 162 / 49 := by
  unfold defect_bound_constant K_net C_proj; norm_num

theorem K_net_value : K_net = 81 / 49 := by
  unfold K_net; norm_num

theorem c_coercive_pos : (0 : ℚ) < c_coercive := by
  unfold c_coercive; norm_num

What this page does not claim

The declaration does not claim 162/49 is a measured or predicted value of any physical constant. The declaration does not assert that the projection model is the correct theory of gravity. The declaration does not establish that the defect bound has a physical interpretation; that remains a paper-level claim.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/CoerciveProjection.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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