Astrophysics Neutron Star Radius Rs Nsradius Cert

The certificate's scope

A neutron star is the collapsed core of a massive star that exploded as a supernova. These objects pack more mass than the Sun into a sphere roughly 10 to 13 kilometers across, making them among the densest known bodies in the universe. Their radius is a key observable for testing nuclear physics at extreme densities, and astronomers estimate it from X-ray observations of hot spots on the star's surface.

The Recognition Science framework models a ledger, a discrete record of recognition events, and derives a unique cost function J(x) = (x + 1/x)/2 - 1 from five plain conditions. Within this framework, the declaration NSRadiusCert is a structure that bundles three proved facts about a cost function applied to a ratio of two positive numbers. The first fact states the cost vanishes when the two numbers are equal. The second states the cost is never negative for positive inputs. The third states that the golden ratio minus 1.5 is positive.

The machine-checked library of formal theorems proves these three facts in full generality. The library also constructs an instance of the certificate, showing the structure is inhabited. However, the definition of the cost function uses the ratio m/e without any reference to neutron stars. The docstring notes the intended application: a research note records that phi^5 km, about 11.09 km, falls within the observed 10-13 km range. But this is a research note, not a result.

What the certificate does not claim is equally important. It does not prove that neutron stars have radius 11.09 km, nor that the framework's cost function applies to neutron star physics. The three proved theorems hold for any positive real numbers m and e, not for any specific physical system. To make this a theorem about neutron stars, one would need a definition of m and e in that subject's own terms, which the module does not provide.

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

What this page does not claim

The certificate does not prove any specific value for the neutron star radius. The framework's cost function is not established as applicable to neutron star physics. The research note about phi^5 km is not a proved result.

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/Astrophysics/Neutron_Star_Radius_RS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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