jet
Enable an agent to recognise a mathematical jet, record the local derivative information it retains, and determine which comparisons and operations are justified.
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 · 15 findings · 24 questions
Contact and identity Record what local information makes this jet the same as another.
Order and equivalence
Specify the derivative order retained and the agreement criterion.
Retained contact
Record the proposed order and how agreement through that order is established.
- What is k, and does the equality test include the map value and every partial derivative through order k? definition
- Which available expressions or derivative records establish the claimed agreement? provenance
Representative boundary
Separate retained local information from properties of a chosen representative.
Information not retained
Identify conclusions that depend on information beyond the recorded jet.
- Does the proposed conclusion depend only on derivatives through k, or also on higher derivatives or nearby values? boundary
- Is a property of the supplied representative being attributed to every representative of this jet? boundary
Geometric setting Locate the jet within the spaces and map category that give its data meaning.
Source and target
Identify where representatives start and where their values lie.
Anchored map data
Require explicit source and target anchors for the proposed jet.
- What are M, N, p, and q, and is q the common value of representatives at p? definition
- Are two jets being compared at the same source point and within the same target setting? boundary
Map category
Declare regularity and any section or geometric restrictions.
Allowed representatives
Record which kinds of local maps may represent this jet.
- Are representatives arbitrary maps or local sections of a specified bundle? definition
- What regularity assumptions support derivatives through the requested order? boundary
Derivative representation Make coordinate encodings interpretable and comparable.
Coefficient encoding
Specify derivative indexing, normalisation, and evidence quality.
Interpretable coefficients
Require enough annotation to reconstruct what each stored coefficient denotes.
- Which target component and derivative multi-index does each coefficient represent? measurement
- Are coefficients raw derivatives or factorial-normalised Taylor coefficients, and are their values exact or estimated? measurement
Chart comparison
Record the coordinate transformations needed to compare encodings.
Coordinate change evidence
Track the charts and transition data used to identify different representations.
- Which source and target charts produced these coefficients? provenance
- Are transition maps and their required derivatives available to transform both records into common coordinates? action
Operations and realisation Determine which manipulations and differential interpretations are supported.
Truncation and composition
Record compatibility and information requirements for jet operations.
Operation preconditions
Make the inputs, requested order, and compatibility checks explicit before an operation.
- For truncation, is the requested order no greater than the recorded order? action
- For composition, does the first jet's target value match the second jet's source point, and what order do both support? action
Differential constraints
Assess equation compatibility and the additional evidence needed for a jet field.
Local constraint test
Record a named differential constraint and the scope of the conclusion obtained from evaluating it.
- Which equation or differential relation is being tested, and does its order fit within k? measurement
- Does the result establish only admissibility at this point, or is there separate evidence for a solution on a neighbourhood? boundary
Jet field realisation
When individual jets are assembled over a region, record whether they come from one underlying map or section.
- Is this record an individual jet or a field of jets over a specified region? definition
- What compatibility conditions or supplied representative establish that the field is the jet prolongation of a map or section? provenance
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 jet 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 jet 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 jet this model covers, and on what evidence? provenance
Typical measurements
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these typical measurements hold for the sense of jet 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 jet 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 jet this model covers, and on what evidence? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Activities and processes
- Entry kind
- thing
- Plane
- ACT
- Domain
- ACT.ACT
What it is Filled
In differential geometry, an r-jet of a smooth map at a point is its equivalence class under agreement of its value and all derivatives through order r at that point, a condition independent of the chosen local coordinates.
In scope
- Order of contact and the equivalence relation defining an individual jet
- Source point, target value, and the spaces between which representatives map
- Derivative coordinates and their representation conventions
- Truncation, compatible composition, and comparison of jets
- Evidence for whether derivative data satisfy a specified local differential constraint
Out of scope
- Aircraft, propulsion jets, fluid streams, and jet gemstone
- Complete functions and their behaviour away from the source point
- Jet bundles as independently modelled geometric spaces
- General differential-equation solving and global existence theory
- Automatic differentiation software and numerical differentiation algorithms
- Algebraic jet schemes without an explicitly established connection to this entry
Why it exists Filled
Enable an agent to recognise a mathematical jet, record the local derivative information it retains, and determine which comparisons and operations are justified.
Distinguishing features Filled
- A proposed instance must specify an order and source point, rather than merely name a differentiable function.
- Representatives are compared through the retained derivative order; agreement of values alone does not establish equality of positive-order jets.
- A Taylor polynomial is a coordinate representation to interpret, rather than sufficient evidence of a coordinate-independent identity.
- An individual jet must be distinguished from a jet field assigning data across a region.
- A finite jet retains less information than a function germ; equality of finite jets does not establish equality on a neighbourhood.
What robots and AI may and may not do Filled
Must not
- Confuse the geometric jet with jet aircraft or fluid jets in answers.
- Present a computation in one chart as coordinate-independent without checking.
- Present an incomplete or incorrect proof as established.
- Claim results from the literature without citing them.
Only with a human decision
- Relying on jet computations in a published proof or engineering model.
May
- Define jets of smooth maps, compute them in local coordinates and state the order.
- Explain the coordinate independence of jets with sources.
Moral aspects Filled
- Mathematical errors in published work mislead others who build on it.
- Credit for results matters to mathematicians.
Who is affected
- Students
- Mathematicians
Owners Filled
Steward
Nobody owns the concept; it is shared mathematical knowledge.
Links to other meta-models Filled
parent
- Q3103996 - registry parent class
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.jet-q1324982
- Wikidata: Q1324982 (https://www.wikidata.org/wiki/Q1324982)
Direct properties not applicable Not applicable
- Retained order: Nonnegative integer k; infinite order requires an explicit extension
- Source and target: Source space M, source point p, target space N, target value q
- Representative category: Smooth maps, sufficiently differentiable maps, local sections, or explicitly declared alternative
- Derivative coordinates: Components indexed by target coordinate and derivative multi-index through order k; units inherited from coordinates
- Coefficient convention: Raw partial derivatives or Taylor coefficients divided by multi-index factorials
- Constraint assessment: Unchecked, satisfies specified constraint, violates specified constraint, or insufficient retained order
- Representation evidence: Symbolic exact data, certified bounds, numerical estimates, or unspecified
Plane ACT: no invented physical properties.
Recognition optional Filled
- Detector event displays may show a localized cluster of energy deposits in angular coordinates.
- Several reconstructed particle tracks may point in similar directions rather than forming one isolated track.
- A jet commonly contains multiple reconstructed constituents, although its appearance depends on detector coverage and display conventions.
Capabilities and actions required Filled
- Construct a jet from a representative map with sufficient derivative information.
- Compare two candidate jets after aligning their source, target, order, and coordinates.
- Discard higher-order information by truncating to a lower order.
- Compose compatible jets while recording the available resulting order.
- Translate derivative coordinates using a specified change of charts.
- Evaluate a local differential constraint whose required order is available.
Hazards and failure modes required Filled
- Background activity or overlapping collisions can be misidentified as a jet and bias results.
- Detector calibration errors can distort reconstructed jet energy and inferred collision properties.
- Comparing jets defined by incompatible reconstruction choices can produce misleading conclusions.
Standards and interfaces not applicable Not applicable
Not applicable
No single mandatory standard defines reconstructed particle jets across experiments and analysis methods.
Context of use required Filled
- In the supplied particle physics sense, jets are studied in collider and heavy ion experiments as collimated groups of particles associated with quarks or gluons.
- Reconstructed jets help researchers investigate strong interactions, collision dynamics and the properties of matter produced in collisions.
- Jet measurements depend on the reconstruction algorithm, detector response and treatment of background activity.
Sources Filled
- Wikidata item Q1324982: jet - identity and sense of the item
- Wikipedia: Jet (particle physics) - general description of the item
Open questions
- Does Q1324982 confirm the mathematical meaning of jet, and what explains the supplied ACT / ACT.ACT classification?
- Does an existing Vercy world model already own this concept, requiring a registry link instead of a separate publication?
- Should the entry cover only finite smooth jets, or also infinite, analytic, algebraic, and nonholonomic variants?
- Which reference conventions should govern derivative normalisation and the distinction between jets of maps and jets of sections?
- Which intended tasks require numerical comparison tolerances or explicit tests for realising a field of jets?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q1324982/spec.json