Chemistry Acid Base Theories From Config Dim Acid Base Theories Cert

Five theories, one certificate

Acid-base chemistry developed through five canonical theories, each answering a different question about what makes a substance an acid. Arrhenius theory, from 1884, defines an acid as a substance that releases hydrogen ions in water. Brønsted-Lowry theory, from 1923, broadened this to any proton donor, working outside water. Also in 1923, Lewis theory defined an acid as an electron-pair acceptor, covering reactions with no protons at all. Usanovich theory, from 1939, went further by treating acids as anything accepting electrons, cations, or anions. Pearson HSAB theory, from 1963, ranked acids and bases as hard or soft based on charge density and polarizability.

The Recognition Science framework's machine-checked library of formal theorems contains a small structure named AcidBaseTheoriesCert. This structure records exactly one fact: that the five theories listed above form a complete enumeration, no more and no fewer. The certificate is a counting claim, not a chemical judgment. It does not rank the theories, does not say which is most useful, and does not assert that any particular reaction follows any particular theory. It merely states that the framework's formal list of acid-base theories has five entries.

The certificate derives its number from a deeper framework idea. In Recognition Science, the number five is not arbitrary: it is the value of a dimension parameter called configDim, and the framework models the five theories as the five possible values of that parameter. The formal declaration connects the chemistry list to that parameter. The machine-checked proof behind the certificate is axiom-clean, meaning it rests on the framework's standard postulates and no chemistry-specific assumptions were added.

A reader should take from this a narrow but solid fact: the framework's formal list of acid-base theories is exactly five, and that count is machine-checked. The certificate is a bookkeeping record, not a new theory of acids. It changes nothing about how chemists use Arrhenius or Lewis theory in the laboratory. What it does is fix the list's length in a way that cannot be accidentally edited or silently changed.

theorem acidBaseTheory_count : Fintype.card AcidBaseTheory = 5 := by decide

def acidBaseTheoriesCert : AcidBaseTheoriesCert where
  five_theories := acidBaseTheory_count

What this page does not claim

The certificate does not rank the five theories or judge their relative merit. The certificate does not assert that any specific chemical reaction follows any particular theory. The certificate does not define what an acid is; it only counts the framework's list of definitions.

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/AcidBaseTheoriesFromConfigDim.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.

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