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Published

half-integer

vr.tr.half-integer · thing-q743139

Let an agent define half-integers precisely, distinguish them from integers and general fractions, relay their roles in physics and mathematics, and support calculation and notation.

Thing Registry Cross-cutting context XCT.QTY
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources

Bundle → Layer → Finding → Questions Filled

4 bundles · 8 layers · 8 findings · 16 questions

Define What a half-integer is.

Definition

Definition.

Definition

Definition.

  1. What is a half-integer, and how does it relate to integers and dyadic rationals? definition
  2. Is the number a half-integer or another fraction? boundary

Properties

Properties.

Properties

Properties.

  1. What arithmetic properties do half-integers have? definition
  2. Which entry fits rational numbers? action
Physics Spin and quantum numbers.

Spin

Fermion spin.

Spin

Spin.

  1. Why do fermions have half-integer spin, and what follows from it? provenance
  2. Which entry fits spin? action

Other

Other physical uses.

Other

Other.

  1. Where else do half-integers appear in physics, such as angular momentum coupling and lattices? provenance
  2. Which references are standard? provenance
Mathematics Mathematical roles.

Functions

Special functions.

Functions

Functions.

  1. What values do the gamma and Bessel functions take at half-integers? provenance
  2. Which entry fits the gamma function? action

Rounding

Rounding.

Rounding

Rounding.

  1. How do rounding conventions treat half-integers? action
  2. Which convention applies in the context? boundary
Learn Teaching.

Teach

Teaching.

Teach

Teaching.

  1. How are half-integers introduced in mathematics and physics teaching? action
  2. Which misconceptions arise? provenance

Notation

Notation.

Notation

Notation.

  1. How are half-integers written and typeset? provenance
  2. Which entry fits mathematical notation? action

Classifiers Filled

Family
Thing Registry
Category
Cross-cutting context
Entry kind
thing
Plane
XCT
Domain
XCT.QTY

What it is Filled

A number of the form n plus one half, where n is an integer, such as one half, three halves and minus five halves; half-integers arise as spins of fermions in quantum mechanics, in rounding conventions, in the arguments of certain special functions and in lattice geometry, and are the odd multiples of one half.

Why it exists Filled

Let an agent define half-integers precisely, distinguish them from integers and general fractions, relay their roles in physics and mathematics, and support calculation and notation.

Distinguishing features Filled

  • Form n plus one half
  • Closed under addition with integers
  • Fermion spins
  • Appear in Bessel functions and gamma function values

What robots and AI may and may not do Filled

Must not

  • Call any fraction a half-integer.
  • Round half-integers without stating the convention used.
  • Confuse half-integer spin with other quantum numbers.
  • Silently change totals through inconsistent rounding.

Only with a human decision

  • Choosing a rounding rule for financial or official figures.

May

  • Identify half-integers and explain where they arise.
  • State the rounding convention used when rounding half-integers.

Moral aspects Filled

  • Rounding rules at half values can shift money or votes in aggregate.

Who is affected

  • Readers of figures
  • Learners

Owners Filled

Steward

Nobody owns the concept; it belongs to the shared body of mathematics.

Links to other meta-models Filled

parent

  • Q2281400 - registry parent class

related

  • dyadic rational - a rational with denominator two
  • integer - the other residue class of halves
  • spin - fermion spin values
  • gamma function - values at half-integers

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.half-integer
  • Wikidata: Q743139 (https://www.wikidata.org/wiki/Q743139)

Direct properties not applicable Not applicable

Not applicable

Plane XCT: no invented physical properties.

Recognition optional Filled

  • Odd multiple of one half
  • Not an integer, but twice it is an odd integer
  • Integers and other dyadic rationals are neighbouring classes
  • Not visible; numbers written as odd numerators over two.

Capabilities and actions required Filled

  • define and recognise half-integers
  • explain their role in spin and other physics
  • explain their appearance in mathematics
  • support notation and calculation

Hazards and failure modes required Filled

  • Calling any fraction a half-integer
  • Rounding errors at half-integer boundaries
  • Confusing spin quantum numbers with measured values

Standards and interfaces required Filled

  • No regulation; notation follows standard mathematics

Context of use required Filled

  • Not for anything in itself; a class of numbers with recurring roles.
  • positive and negative half-integers
  • half-integer spins
  • half-integer arguments of special functions
  • half-integer coordinates in lattices
  • half-integer weights in modular forms

Sources Filled

  1. Wikidata item Q743139: half-integer - identity and sense of the item
  2. Wikipedia: Half-integer - general description of the item

Open questions

  • Should spin be the primary entry for the physics use?
  • How should special function references be linked?
  • How should rounding conventions be recorded?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q743139/spec.json