---
slug: "ParetoFront"
name: "ParetoFront"
type: "Primitives"
layer: "Infrastructure"
ref: "ParetoFront#e6f5"
sema_id: "sema:ParetoFront#mh:SHA-256:e6f5d6269118c342b52699a99154c79dc1e7b39e04c12bafc2f605805c0dfd02"
tags: ["Infrastructure","Primitives"]
updated: 2026-11-11
mindscape: "bootstrap"
index_url: https://mindscape.world/scapes/bootstrap.json
url: https://mindscape.world/bootstrap/ParetoFront/
related: ["Compare","PUREOptimization","sema:OpportunityCost#mh:SHA-256:f0a3f074464fb30b60adac59167d2d34aeadf8fdd47de6c433f278c0036223fb","sema:Satisfice#mh:SHA-256:fa75c44d4d400749a16f521c8c2793207877c783154cc00a93390beae85d2e0d"]
---

# ParetoFront

Nondominated candidates across declared axes

Layer: Infrastructure · Category: Primitives

## Mechanism

Given an input candidate set and declared axes, use [Compare](https://mindscape.world/scapes/bootstrap/Compare.md) under each axis's no-worse relation. Candidate X dominates Y when X is no worse than Y on every axis and, on at least one axis, Y is not no worse than X. Return every input candidate not dominated by another input candidate. Ordering or selecting among returned candidates is caller policy.

## Invariants

- Dominance: X dominates Y iff X is no worse than Y on every declared axis and there is at least one axis on which Y is not no worse than X.
- Frontier Completeness: Every undominated input candidate is returned, and no dominated input candidate is returned.

## Preconditions

- At least two axes are declared.
- Each axis supplies a reflexive, transitive no-worse relation applicable to every candidate pair.

## Failure modes

—

## Builds on

- [Compare](https://mindscape.world/scapes/bootstrap/Compare.md) (Infrastructure; Composes with)

## Used by

- [PUREOptimization](https://mindscape.world/scapes/bootstrap/PUREOptimization.md) (Mind; Composes with)

## Identity

- Sema ID: `sema:ParetoFront#mh:SHA-256:e6f5d6269118c342b52699a99154c79dc1e7b39e04c12bafc2f605805c0dfd02`
- Ref: `ParetoFront#e6f5`
- Supersedes:
  - `sema:ParetoFront#mh:SHA-256:9091ffbe5c96a8da82e0aba315ad4bc9191b92a69656df4ffe18706a954bf822`
  - `sema:ParetoFront#mh:SHA-256:c1fb20ece1fc1f524f90d03106f76a4fcbb7107640a6258153bb273177d654be`
  - `sema:ParetoFront#mh:SHA-256:10a7d315172e2163bed132c3943b3008d5a566e5b4b4941af614838dcbecffe0`

## Links

- [Pattern page](https://mindscape.world/bootstrap/ParetoFront/)
- [View in the interactive graph](https://mindscape.world/bootstrap/#ParetoFront)
- [JSON](https://mindscape.world/scapes/bootstrap/ParetoFront.json)
- [Index of all patterns](https://mindscape.world/scapes/bootstrap.json)