center
Enable an agent to identify, determine and use a center relative to a specified object, space and centering rule while preserving ambiguity and uncertainty.
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.
Researched by: Codex
Bundle → Layer → Finding → Questions Filled
5 bundles · 9 layers · 14 findings · 22 questions
Center meaning Establishes what is being centered and what center means in this instance.
Centered referent
Identifies the object and extent to which the centering relation applies.
Referent extent
A center must be tied to a specified whole, subset or distribution.
- What exact object, subset or distribution is being centered? definition
- Does the referent include its interior, only its boundary or only selected observations? boundary
Centering definition
Distinguishes the selected center concept from neighboring concepts.
Defining rule
The result is governed by an explicit construction, symmetry condition or optimization criterion.
- Which mathematical rule defines this center? definition
- What source or task requirement establishes that this is the intended rule? provenance
Geometry and contributions Records the space, distances and contributions that determine the center.
Space and metric
Establishes the setting in which location, distance and admissible constructions are interpreted.
Geometric assumptions
The centering rule must be meaningful in the declared ambient space.
- In what space and dimension is the referent represented, and what distance rule applies? definition
- Would curvature, periodic coordinates or a change of metric alter this center? boundary
Weights and measure
Identifies how parts of the referent contribute to the result.
Contribution basis
Boundary, area, volume, mass and sample weighting must not be treated as equivalent without justification.
- Which measure or weights govern the center, or does the rule require none? measurement
- Are those contributions observed, specified or assumed, and where is that basis documented? provenance
Existence and determination Determines whether the rule yields a center and how the result is established.
Existence and uniqueness
Checks the prerequisites and possible multiplicity of the selected center.
Admissible center set
The outcome may be one center, multiple centers or no center under the chosen definition.
- Does the referent satisfy the selected rule's existence conditions? boundary
- Is the center unique, and if not, what identifies the full candidate set? definition
Calculation and error
Connects the reported center to a construction or calculation and its limitations.
Determination evidence
A reported location needs a reproducible basis and a distinction between input uncertainty and approximation error.
- Which construction, algorithm or observation produced the center from the stated inputs? provenance
- What uncertainty or numerical error applies to the result, and how was it assessed? measurement
Representation and use Makes a determined center usable for a particular operation.
Location and membership
Expresses the center and checks its relationship to the referent's extent.
Usable location
The result must carry sufficient positional context and must not imply membership merely by being called a center.
- How is the center represented, including coordinate frame and units where applicable? measurement
- Does the center lie inside, on or outside the referent, and does the intended operation permit that relationship? action
Change and substitution
Controls reuse after changes and replacement by a differently defined center.
Reuse conditions
Reusing a center requires checking whether its defining inputs and task requirements still hold.
- After a change to shape, membership, weights or frame, can this center be transformed directly or must it be recomputed? action
- What evidence and tolerance justify substituting another type of center for this task? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Check these first
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these check these first hold for the sense of center this model covers, and on what evidence? provenance
Kinds and varieties
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these kinds and varieties hold for the sense of center this model covers, and on what evidence? provenance
Real-world use
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these real-world use hold for the sense of center this model covers, and on what evidence? provenance
Failure modes and hazards
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these failure modes and hazards hold for the sense of center this model covers, and on what evidence? provenance
Regional variation
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these regional variation hold for the sense of center this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of center this model covers, and on what evidence? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QTY
What it is Filled
In geometry and quantitative modelling, a center is a point designated as central to an object or distribution by a specified criterion, such as symmetry, balance, or distance, and need not exist or be unique.
In scope
- The object, region, distribution or structure whose center is sought
- The definition of centrality and conditions under which it applies
- A center expressed as a point, element, set or explicitly unresolved result
- Dependence on geometry, distance, weighting and reference frame
- Existence, uniqueness, uncertainty and permitted uses of the result
Out of scope
- Institutions, facilities or settlements named a center, including immigration detention centers
- Units of measurement and the quantities they measure
- Complete models of the objects or distributions being centered
- General ranking or network centrality scores without a specified center-selection rule
- Specialized algebraic centers pending confirmation of the registry sense
Why it exists Filled
Enable an agent to identify, determine and use a center relative to a specified object, space and centering rule while preserving ambiguity and uncertainty.
Distinguishing features Filled
- A center must be attributable to a specified referent and centering rule; a position alone is insufficient.
- A center is not a measurement unit: coordinates may use units, but center itself supplies no unit definition.
- Midpoint, centroid, center of mass and circumcenter are interchangeable only when their defining conditions make them coincide.
- A center need not belong to the object being centered; membership must be checked separately.
- The word center in a facility name does not establish the abstract centering relation modeled here.
What robots and AI may and may not do Filled
Must not
- Report a center without saying which definition of center was used.
- Treat the center of a distribution as typical of every member, such as each person in a population.
- Confuse a geometric center with an institution or facility named a center.
Only with a human decision
- Choosing which center to use when the result drives a decision about people, such as siting a service.
May
- Compute a center by a stated criterion, such as centroid, circumcenter or median.
- State which criterion was used and whether the center lies inside the object.
Moral aspects Filled
- Choice of center, mean or median, can make a group look better or worse off than it is.
Who is affected
- People described by statistics
- Users of analyses
Owners Filled
Steward
Nobody owns the concept; the analyst answers for the criterion chosen.
Links to other meta-models Filled
parent
- Q110699729 - registry parent class
- Q13196193 - registry parent class
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.center
- Wikidata: Q191169 (https://www.wikidata.org/wiki/Q191169)
Direct properties not applicable Not applicable
- Centered referent: Identified segment, figure, region, distribution, point set or other explicitly supported structure
- Centering rule: Midpoint, centroid, center of mass, circumcenter, incenter, symmetry center, optimization-defined center or another explicit definition
- Ambient space and distance: Specified space, dimensionality and metric where applicable
- Weighting basis: Unweighted elements, length, area, volume, mass, probability or explicitly defined weights
- Center representation: Coordinates with frame and axis units where applicable; otherwise an identified element or set
- Existence and multiplicity: Not assessed, nonexistent under the rule, unique, multiple or unresolved
- Membership in referent: Interior, boundary, exterior, member, nonmember, not applicable or unknown
- Result uncertainty: Error bound or uncertainty region in declared units, with method; exact or unassessed where appropriate
Plane XCT: no invented physical properties.
Recognition optional Filled
- Usually marked as a labelled point, often O or C, at a symmetry or balance position.
- Different centers of the same triangle appear as distinct points, which coincide only in special cases.
Capabilities and actions required Filled
- Select a centering rule appropriate to a stated task and referent.
- Compute or identify candidate centers when the rule's prerequisites are satisfied.
- Compare centers produced by different definitions without silently substituting one for another.
- Transform a center's representation between compatible reference frames.
- Check uniqueness, membership and uncertainty before using a center for alignment, placement or distance measurement.
- Reassess a center when the referent, weights or geometry change.
Hazards and failure modes required Filled
- A centroid can lie outside a non-convex shape, misleading placement decisions.
- Means pulled by outliers misrepresent the center of skewed data.
Standards and interfaces required Filled
- The Laws of Chess, issued by the International Chess Federation, define the board and algebraic square notation used to identify d4, d5, e4 and e5.
Context of use required Filled
- In chess, the center comprises the four squares d4, d5, e4 and e5.
- Players and analytical systems use this region to discuss piece activity, pawn structure and control of central routes.
Sources Filled
- Wikidata item Q191169: center - identity and sense of the item
- Wikipedia (de): Zentrum (Schach) - general description of the item
Open questions
- Does vr.tr.center denote a geometric center, a broader mathematical concept or another sense, given the missing registry definition?
- Which center definitions are intended to be covered by this entry, and which already have authoritative neighboring models?
- Should graph centers and specialized algebraic centers be included, linked as related concepts or excluded?
- Does XCT.QTY indicate a deliberate quantitative classification, or does the registry classification require review?
- Which authoritative references should establish the supported definitions and their existence, uniqueness and transformation conditions?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q191169/spec.json