Materials Solar Cell Efficiency From Jcost

A template, not a result

Solar cell efficiency is the fraction of sunlight's energy that a cell turns into electricity. The best perovskite cells, a family of cheap and highly tunable materials, have reached laboratory efficiencies near 26 percent, closing in on the theoretical ceiling of about 33.7 percent known as the Shockley-Queisser limit.

The Recognition Science framework, which derives physical structure from a forced cost of recognition, contains a module titled for perovskite solar cells. The module defines a cost function domainCost, a discrete record of mismatch between two quantities, as the framework's core cost J applied to the ratio of two real numbers m and e. It proves three facts: the cost is zero when m equals e, the cost is never negative for positive inputs, and the golden-ratio constant phi minus 1.5 is positive.

Those three facts are true, but they say nothing about solar cells. The module never defines what m or e mean in a cell's physics. Without that definition, the cost function is just a template, and the file itself states this plainly. The same body of text is shared verbatim with 2383 sibling modules, each one a placeholder for a different subject.

What the module does establish is a certificate: a packaged collection of the three proved facts, ready to be used if a real definition of m and e ever arrives. The framework's own note records the intended research direction, that the rate of efficiency improvement should follow the cost function, but that is a research note, not a theorem.

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

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]

noncomputable def cert : PerovskiteSolarCert where
  cost_at_eq := domainCost_at_eq
  cost_nonneg := domainCost_nonneg
  threshold_pos := canonicalThreshold_pos

What this page does not claim

This module proves any specific claim about solar cell efficiency. The framework derives the Shockley-Queisser limit or any measured efficiency value. The research note about an 8.47 percent annual improvement rate is 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/Materials/SolarCellEfficiency_FromJCost.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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