Measurement Rsnative Core Uncertainty

Uncertainty in measurement

Uncertainty, in the Recognition Science (RS) framework, is a formal structure attached to a measurement. It records either a standard deviation (a sigma value) or an interval with lower and upper bounds. This is the framework's way of saying how precise a result is, in a machine-readable form. The declaration itself is a definition, not a theorem: it defines the shape of uncertainty data, not a law about what uncertainty must be.

The framework's measurement scaffold is built around a few core ideas. A ledger, a discrete record of events, provides the base units: ticks (time steps), voxels (space cells), and quantities for action, coherence, and charge. Each measurement carries a value, an optional window of ticks, a protocol, an optional uncertainty, and notes. The protocol is the key part: it must name its assumptions and falsifiers when the status is hypothesis or scaffold. This makes arbitrary choices, like windowing or coarse-graining, explicit rather than hidden.

In plain terms, the Uncertainty declaration does not prove anything about the world. It is a container. It lets a researcher say "this value is 5, with a standard deviation of 0.1" or "this value lies between 4.8 and 5.2". The framework does not claim that these numbers are correct; it claims that they are recorded with a protocol that says how they were obtained. The honesty is in the structure, not in the numbers themselves.

The framework's library, a machine-checked collection of formal theorems, treats this as a scaffold for future work. Concrete observables, like specific physical quantities, live in separate catalog files. The core file is intentionally small and dependency-light. This means the Uncertainty declaration is a foundation for building measurements, not a result about measurement theory. It establishes a language, not a conclusion.

What the declaration does not claim is worth stating plainly. It does not claim that any particular measurement is accurate. It does not claim that the RS-native units (ticks, voxels) correspond to any SI unit. The connection to SI/CODATA is explicitly optional and lives outside the core. The framework's own constants, like hbar and G, are derived elsewhere, but this measurement scaffold does not depend on them. It is a tool for expressing uncertainty, not a theory of what uncertainty is.

@[simp] def sigmaVal : Uncertainty → Option ℝ
  | sigma σ _ => some σ
  | _ => none

@[simp] def intervalBounds : Uncertainty → Option (ℝ × ℝ)
  | interval lo hi _ => some (lo, hi)
  | _ => none

/-- A measurement value with protocol + (optional) time window + (optional) uncertainty. -/
structure Measurement (α : Type) where
  value : α
  window : Option Window := none
  protocol : Protocol
  uncertainty : Option Uncertainty := none
  notes : List String := []

/-- Protocol hygiene predicate (v1/v2).

Rules:
- `name` must be non-empty
- if `status` is `.hypothesis` or `.scaffold`, both `assumptions` and `falsifiers` must be non-empty -/
def hygienic (p : Protocol) : Prop :=
  p.name ≠ "" ∧
    match p.status with
    | .hypothesis | .scaffold => p.assumptions ≠ [] ∧ p.falsifiers ≠ []
    | _ => True

inductive CostUnit : Type

What this page does not claim

The Uncertainty declaration does not prove any theorem about measurement accuracy or error. It does not claim that RS-native units correspond to any SI unit. It does not establish a theory of what uncertainty is; it only defines a data structure for recording it.

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/Measurement/RSNative/Core.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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