"What" is an Epit: Mathematical Foundations of Epistemic Structure
Abstract
The same parts can form different wholes: a message chain differs from a broadcast even
when the same people take part. This paper develops a small unit for describing such
arrangements and rules for combining its records into larger descriptions. An epistemic unit,
or epit, has three ordered positions (A,B,C) and three pair channels, AB,BC,AC. Each
channel can be forward, inactive, or reverse, represented by +1, 0,−1. Each channel is one
trit, a three-valued entry, so the three channels give 27 configurations. Larger records are
assembled by checking their shared relations and allowing a completed record to become
part of another. For applications to knowledge, the proposed OETMI scheme connects
the subject (Ontology), observation (Epistemology), intended use (Teleology), assessment
(Meta), and accepted result (Integration). The foundational result is that the epit is the
minimal complete unit of relational distinction: three ports and three channels are necessary
and sufficient for the seven local arrow patterns when self-connections and duplicate channels
are excluded. If each named channel may be changed independently and the resulting
arrow pattern must remain known, all 27 configurations must stay distinguishable. Four
compatible triangular face records determine a tetrahedron’s six edge values. When a
finite observation leaves several possible wholes, the largest group of possibilities fixes the
minimum number of extra labels for exact recovery. A selected vocabulary of twenty names
and four declared return rules gives 556 initial objects, including 536 new outputs. Every
expression has one simplified form, and repeated construction follows an exact counting rule.
Deciding the assertions such records encode requires a proof theory and an interpretation.
In a logical realization, an epit carries a theory, a proof, and a claim; we show that proof
status cannot be separated from its theory when records from consistent effective arithmetic
theories are compared, that consistency certification has no fixed point under the standard
second-incompleteness hypotheses, and that no internal arithmetic predicate supplies truth
for all encoded arithmetic sentences.
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BibTeX
@misc{perry2026what,
title = {{"What" is an Epit: Mathematical Foundations of Epistemic Structure}},
author = {Perry J},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23610951},
url = {https://zenodo.org/records/23610951},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - "What" is an Epit: Mathematical Foundations of Epistemic Structure
AU - Perry J
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23610951
UR - https://zenodo.org/records/23610951
AB - The same parts can form different wholes: a message chain differs from a broadcast even when the same people take part. This paper develops a small unit for describing such arrangements and rules for combining its records into larger descriptions. An epistemic unit, or epit, has three ordered positions (A,B,C) and three pair channels, AB,BC,AC. Each channel can be forward, inactive, or reverse, represented by +1, 0,−1. Each channel is one trit, a three-valued entry, so the three channels give 27 configurations. Larger records are assembled by checking their shared relations and allowing a completed record to become part of another. For applications to knowledge, the proposed OETMI scheme connects the subject (Ontology), observation (Epistemology), intended use (Teleology), assessment (Meta), and accepted result (Integration). The foundational result is that the epit is the minimal complete unit of relational distinction: three ports and three channels are necessary and sufficient for the seven local arrow patterns when self-connections and duplicate channels are excluded. If each named channel may be changed independently and the resulting arrow pattern must remain known, all 27 configurations must stay distinguishable. Four compatible triangular face records determine a tetrahedron’s six edge values. When a finite observation leaves several possible wholes, the largest group of possibilities fixes the minimum number of extra labels for exact recovery. A selected vocabulary of twenty names and four declared return rules gives 556 initial objects, including 536 new outputs. Every expression has one simplified form, and repeated construction follows an exact counting rule. Deciding the assertions such records encode requires a proof theory and an interpretation. In a logical realization, an epit carries a theory, a proof, and a claim; we show that proof status cannot be separated from its theory when records from consistent effective arithmetic theories are compared, that consistency certification has no fixed point under the standard second-incompleteness hypotheses, and that no internal arithmetic predicate supplies truth for all encoded arithmetic sentences.
ER -