Chemistry Thermal Runaway3 From Jcost

Battery thermal runaway

Thermal runaway in a lithium-ion battery is the self-accelerating heating that can end in fire. The module chemistry-thermal-runaway3-from-jcost in the Recognition Science library contains a research note about this phenomenon, but the machine-checked theorems it proves are about a different object: a cost function called Jcost, a measure of the forced expense of recognition events. The note suggests a temperature ratio, while the proofs establish properties of that cost function. The two are not the same claim.

The battery note proposes that the ratio of the runaway temperature to ambient temperature should equal the golden ratio phi, about 1.618. With ambient at 300 K, that predicts 485 K, or 212 degrees Celsius. The note itself states that this overestimates the known onset near 403 K, and calls the mismatch structural. This is a research idea recorded in a docstring, not a theorem. The library's own documentation says the paragraph is a research note recording where the idea was meant to go, not a result.

What the module actually proves is three general facts about domainCost, defined as Jcost of the ratio m over e. The cost vanishes when m equals e, it is nonnegative for positive inputs, and the quantity phi minus 3/2 is positive. These are universal statements about the cost function, with no reference to batteries, temperatures, or chemistry. The definition of domainCost uses only the ratio of two real numbers, so the theorems hold for any positive pair.

The module also defines a certificate structure that packages these three facts together, and proves it is inhabited. This is a standard pattern in the library: a small collection of verified properties bundled into one object. The certificate adds no new mathematics; it merely assembles the three theorems into a single structure. The module is one of 2383 siblings sharing the same body, with the same universally quantified content stated once in a central template.

In plain language, the module does not establish anything about thermal runaway. It establishes that Jcost is zero at unity, nonnegative, and that phi exceeds 1.5. To become a theorem about batteries, the module would need a definition of m and e in battery terms, such as a specific energy or temperature. The library's own status line says it proves nothing specific to this subject. The battery note is a direction for future work, not a derived result.

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]

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

What this page does not claim

The module does not prove any temperature value for battery thermal runaway. The research note's golden ratio prediction is not a theorem and is not verified against measurements. The certificate structure adds no new mathematics beyond the three theorems it packages.

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/Chemistry/Thermal_Runaway3_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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