IndisputableMonolith.Chemistry.BufferCapacityFromJCost
Defines chemical buffer capacity from the RS J-cost: a domain cost functional, its nonnegativity, a positive canonical threshold, and an inhabited BufferCapacityCert. RS chemists bridging cost geometry to acid-base capacity would cite it. Mostly definitional scaffolding with elementary positivity and equality lemmas over Constants and Cost.
claimFrom the J-cost one obtains a domain cost $C$, with $C\ge 0$ and an evaluation identity at equality cases; a canonical threshold $T>0$; and a certificate type $\mathrm{BufferCapacityCert}$ that is inhabited, packaging buffer-capacity bounds in these RS-native units.
background
Recognition Science measures mismatch by the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the T5 step of the unified forcing chain and obeying the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS time quantum $\tau_0=1$ tick and related native units.
This chemistry module treats buffer capacity as a capacity-to-absorb deviation measured in that same cost geometry, rather than as a purely empirical titration slope. Sibling definitions introduce a domain-restricted cost, record that it is nonnegative, fix a canonical positive threshold, and wrap the resulting bound in a certificate structure.
The local setting is therefore a thin bridge: import J and constants, specialize cost to a chemical domain, and expose a cert type that downstream chemistry developments can inhabit or discharge.
proof idea
Definition-first module, not a deep proof development. domainCost is built from the imported J-cost; domainCost_at_eq and domainCost_nonneg are short algebraic or order lemmas. canonicalThreshold and canonicalThreshold_pos fix a positive cutoff. BufferCapacityCert, cert, and cert_inhabited package and witness the certificate. No multi-step tactic argument; structure is defs plus elementary positivity/equality facts.
why it matters in Recognition Science
Places buffer capacity on the same J-cost footing as the rest of RS quantitative chemistry, so acid-base capacity is not an external empirical input. Feeds the Chemistry domain layer; the page records no downstream used_by edges yet, so this is currently a leaf certificate surface rather than a link in a longer proved chain.
In the broader framework it sits downstream of T5 J-uniqueness and the Cost module, and upstream of any later claim that a concrete buffer (pH window, concentration scale) meets an RS-native capacity bound. It does not itself invoke the mass ladder, eight-tick octave, or alpha band; those enter only if a parent chemistry theorem specializes the cert further.
scope and limits
- Does not derive empirical pKa tables or species-specific titration curves from first principles.
- Does not prove a numerical match to laboratory buffer-capacity units without further calibration.
- Does not connect buffer capacity to the phi-ladder mass formula or T7 eight-tick structure.
- Does not supply downstream theorems; used_by is currently empty.
- Does not claim uniqueness of the canonical threshold beyond the positivity lemma.