Foundational Closure and Primitive Structural Input: A Four-Axis Taxonomy

Four logically independent axes of primitive structural input under closed-world scope
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First page of Foundational Closure and Primitive Structural Input
Research Paper

Chast K. Wolfe · v3 · June 13, 2026

Manuscript Record

Work code
CRI-FE
Work type
Research paper
Status
Public preprint; versioned research manuscript. Not peer reviewed unless otherwise stated.
Author identifier
Chast K. Wolfe, ORCID 0009-0008-8846-2539
Publisher
Closure Research Initiative
Version
v3, June 13, 2026
Citation target
Current version: closureresearchinitiative.org/fe/. DOI pending.
Canonical page
closureresearchinitiative.org/fe/
Files
PDF · LaTeX source
Rights
All rights reserved
Citation record
Use the canonical page and BibTeX block below for the current version.
A conditional taxonomy of primitive structural input in closed-world accounts. Externalization, artificial factorization, premature globalization, and reification of repair are formalized as independent predicates on framework data; the paper states the corresponding reconstruction burden for standard foundational settings.
Method
The paper defines closed-world admissibility and records four ways primitive structural input can enter a claimed closed-world account. Each axis is then compared with standard foundational situations in mechanics, quantum theory, field theory, relativity, and statistical mechanics.
Main result
Externalization, artificial factorization, premature globalization, and reification of repair are logically independent predicates on the stated class of framework data. No one axis is a Boolean consequence of the other three.
Scope
The taxonomy is diagnostic and conditional. It classifies where primitive input remains unreconstructed; it does not by itself establish the detailed recovery theorem for any one physical theory.

Scope: binding statements are the definitions, hypotheses, and independence results in the paper. Related internal sources: Structural Map for the page-level taxonomy, Logical Status for the closure criterion, and Reading Guide for linked background sources in mechanics, quantum theory, QFT, GR, and statistical mechanics.

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Version History

VersionDateStatusFileDetails
v3June 13, 2026Current versionPDF·Source
Theorem-status revision

The release clarifies the theorem status, operational terminology, and internal CRI citations. The four-axis independence result is explicitly scoped to the framework-data class. DOI pending for the current release.

v2June 10, 2026Superseded versionPDF·Source
CRI metadata release

Affiliation, correspondence, and manuscript format updated to the common Closure Research Initiative article style. Mathematical content unchanged from v1.

v1June 5, 2026Superseded versionPDF·Source
Initial preprint

Initial preprint; superseded archival release.

BibTeX Citation
@misc{wolfe2026foundational, author = {Chast K. Wolfe}, title = {Foundational Closure and Primitive Structural Input: A Four-Axis Taxonomy}, year = {2026}, version = {3}, howpublished = {Closure Research Initiative preprint}, note = {Version 3; DOI pending for the current release}, url = {https://closureresearchinitiative.org/fe/}, license = {All Rights Reserved. See https://closureresearchinitiative.org/license/} }