Cosmology Inflaton Potential Structural Efold Count Eq

The e-fold count

In cosmology, an e-fold is a factor of e in the scale factor of the universe during inflation. A typical inflationary model produces 50 to 60 e-folds to solve the horizon and flatness problems. The Recognition Science library defines a constant efoldCount and proves, by definition, that it equals 44. That is the entire content of the declaration efoldCount_eq.

The number 44 comes from a structural ladder: the framework's gap-45 sequence, minus one tick for the reheating transit. The declaration itself is a definitional equality, not a derivation from first principles. It states that the chosen symbol for the e-fold count is 44, nothing more.

What the declaration does not claim: it does not prove that inflation actually happened, that 44 e-folds is the correct physical number, or that the framework derives this value from deeper axioms. The number is an input, a definitional choice, not an output of the forcing chain. The library also records five canonical regimes of the inflaton potential and slow-roll parameters, but those are separate definitions, not consequences of the e-fold count.

In plain terms: if you read the library, you will find a constant named efoldCount and a theorem that it equals 44. That is a bookkeeping statement, not a physical prediction.

theorem efoldCount_eq : efoldCount = 44 := rfl

What this page does not claim

The declaration does not prove that inflation occurred or that 44 e-folds is the physically correct value. The declaration does not derive 44 from deeper axioms; it is a definitional equality. The declaration does not imply the slow-roll parameters or spectral index are consequences of the e-fold count.

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/Cosmology/InflatonPotentialStructural.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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: