01 / Problem
This section is included in the source manuscript and the PDF build for review.
PAPER-021 / June 13, 2026 / corrected September 18, 2026
Observational Equivalence Classes in Maxwell-Compatible Projection Theories
When different fifth-dimensional stories predict the same four-dimensional data
01 / Abstract
Abstract
The paper distinguishes exact predictive equality from finite-resolution indistinguishability. Exact equality after a common nuisance treatment defines an equivalence relation and quotient. Distance below a tolerance defines a generally non-transitive graph whose clustering depends on the metric, threshold, and linkage rule. No generated branch map or quotient table is released.
02 / Frame
Research Frame
This landing page publishes the paper as an auditable source bundle. The PDF carries the full mathematical argument, claims, evidence plan, implementation surface, and release notes.
\[
M_a \equiv_E M_b \quad \Longleftrightarrow \quad
P_E(\,\cdot\mid M_a)=P_E(\,\cdot\mid M_b).
\]
\[
M_a\leftrightarrow_{E,\epsilon}M_b \quad\Longleftrightarrow\quad
d\left(P_E(\,\cdot\mid M_a),P_E(\,\cdot\mid M_b)\right)\leq\epsilon_E,
\]
03 / Structure
Paper Structure
The manuscript follows the JMP0X1B discipline: state the problem, formalize the model, name the claims, and publish enough source material for review and revision.
02 / Model
This section is included in the source manuscript and the PDF build for review.
03 / Claims
This section is included in the source manuscript and the PDF build for review.
04 / Evidence Plan
This section is included in the source manuscript and the PDF build for review.
04 / Files
Paper Files
The PDF is generated from the LaTeX source. Both are published for auditability and future revision.