parity
Let an agent handle parity by domain, definition and use, from arithmetic to permutations, and route physics and computing senses.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent handle parity by domain, definition and use, from arithmetic to permutations, and route physics and computing senses.
The property of an integer of being even or odd; more generally, whether a quantity is divisible by two, with extensions such as permutation parity, and related uses in physics (spatial parity) and computing (parity bits).
What it is for: Arithmetic reasoning, combinatorics, error detection and physics.
It can be determine whether a number is even or odd; compute permutation parity; use parity in proofs; link to parity bits and physical parity.
Distinguishing features
Divisibility by two
Simple but powerful in proofs
Extends to permutations
Several technical senses
What it looks like
Labels even or odd; signs +1 or -1 for permutations.
How it is recognised
Even or odd
Sign of a permutation
Parity in physics and computing are related senses
Related models
is a kind of - category
is used in - computing
is related to - field
is confused with - another sense
In practice
Families and kinds
parity of integers
parity of permutations
parity of functions (even and odd functions)
parity bits
spatial parity in physics
Failure modes and hazards
Confusing senses
Off-by-one in parity checks
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.parity
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Integers Even or odd.
The basic sense.
Check
Even or odd.
Check
Parity check.
- Is the number even or odd? measurement
- How is that determined for large numbers? action
Rules
Arithmetic.
Rules
Parity rules.
- What is the parity of a sum or product? definition
- How can it simplify a proof? action
Permutations Sign.
Permutations have parity.
Sign
Even or odd permutation.
Sign
Permutation sign.
- Is this permutation even or odd? measurement
- How many transpositions does it need? measurement
Applications
Determinants and puzzles.
Applications
Applications.
- How is permutation parity used, for example in determinants or puzzle solvability? definition
- Which examples help? action
Computing Parity bits.
Parity detects errors.
Parity bits
Error detection.
Bits
Parity bits.
- Is even or odd parity used? definition
- What errors can it detect? boundary
Implementation
Code.
Implementation
Implementation.
- How is parity computed efficiently? action
- Is it tested? provenance
Senses Physics and economics.
Parity has other senses.
Physics
Spatial parity.
Physics
Physics sense.
- Is spatial parity in physics meant? boundary
- Which entry fits? action
Economics
Equality of value.
Economics
Economic sense.
- Is parity in the sense of equality, such as purchasing power parity, meant? boundary
- Which entry fits? action
What the second pass must settle
- Should parity senses be separate entries?
- How should physics parity be linked?
- How should the economic sense be split off?