Variant 11 as a Minimal Nontrivial Instance of the Common Support Interval.

This companion note clarifies the structural position of Variant 11 within the presentation-support framework established in Formal Frame, Syntactic Support, and Real Determination in Finite Boolean Functions and the subsequent Common Support Interval theorem. Variant 11 is the finite typed Boolean function f₁₁(p, q) = ¬q on the formal frame N = {p, q}, with determinational support R_{f₁₁} = {q}. The presentation-support theorem establishes that the exact syntactic supports of term presentations of a finite typed Boolean function form the interval between its determinational support and its formal frame. The Common Support Interval theorem further establishes that this family coincides with the corresponding factorization-support family. Applied to Variant 11, these results yield 𝔉_N(f₁₁) = 𝔖_N(f₁₁) = [{q}, {p, q}]_{⊆} = {{q}, {p, q}}. This equality concerns the families of admissible supports only. Coordinate factorization and term presentation remain structurally distinct constructions, even though their associated families of support sets coincide. The note also identifies the precise sense in which Variant 11 is minimal. Among nonconstant finite typed Boolean functions with proper determinational support, it attains the smallest possible ambient-frame size. Variant 11 is therefore a minimal nontrivial instance of the common support interval. No uniqueness or canonical-status claim is made.

Authors

Institutions

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-20
DOI
https://doi.org/10.5281/zenodo.23485162
Primary Topic
Advanced Algebra and Logic
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Variant 11 as a Minimal Nontrivial Instance of the Common Support Interval.

Piotr Dariusz Wójcik
Zenodo (CERN European Organization for Nuclear Research)
Advanced Algebra and Logic
preprint

Variant 11 as a Minimal Nontrivial Instance of the Common Support Interval.

Piotr Dariusz Wójcik
preprint en

Abstract

This companion note clarifies the structural position of Variant 11 within the presentation-support framework established in Formal Frame, Syntactic Support, and Real Determination in Finite Boolean Functions and the subsequent Common Support Interval theorem. Variant 11 is the finite typed Boolean function f₁₁(p, q) = ¬q on the formal frame N = {p, q}, with determinational support R_{f₁₁} = {q}. The presentation-support theorem establishes that the exact syntactic supports of term presentations of a finite typed Boolean function form the interval between its determinational support and its formal frame. The Common Support Interval theorem further establishes that this family coincides with the corresponding factorization-support family. Applied to Variant 11, these results yield 𝔉_N(f₁₁) = 𝔖_N(f₁₁) = [{q}, {p, q}]_{⊆} = {{q}, {p, q}}. This equality concerns the families of admissible supports only. Coordinate factorization and term presentation remain structurally distinct constructions, even though their associated families of support sets coincide. The note also identifies the precise sense in which Variant 11 is minimal. Among nonconstant finite typed Boolean functions with proper determinational support, it attains the smallest possible ambient-frame size. Variant 11 is therefore a minimal nontrivial instance of the common support interval. No uniqueness or canonical-status claim is made.

Zenodo (CERN European Organization for Nuclear Research)
Membrane Reactor Technologies (Canada) (CA)
Advanced Algebra and Logic
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.