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All Journal International Journal of Evaluation and Research in Education (IJERE) JMPM: Jurnal Matematika dan Pendidikan Matematika M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Madaniya LOSARI: Jurnal Pengabdian Kepada Masyarakat Kognitif: Jurnal Riset HOTS Pendidikan Matematika D'computare: Jurnal Ilmiah Teknologi Informasi dan Ilmu Komputer Edumatika Pedagogy : Jurnal Pendidikan Matematika Journal of Advanced Sciences and Mathematics Education Venn: Journal of Sustainable Innovation on Education, Mathematics and Natural Sciences Jurnal Pengabdian Masyarakat Bangsa Jurnal Ilmu Pengetahuan dan Teknologi Bagi Masyarakat Journal of Mathematics, Computation and Statistics (JMATHCOS)
Wahidin Ashari, Nur
Universitas Cokroaminoto Palopo
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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

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The Coefficient Parallelisator Matrix: A Diagonal Similarity Operator for Symmetry Preservation in Knot Semantic Logic Ja'faruddin, Ja'faruddin; Ashari, Nur Wahidin; Baharuddin, Baharuddin; Asyari, Syahrullah; Fadiyah, Wulan Nur; Farhan, Muhammad
Journal of Mathematics, Computations and Statistics Vol. 8 No. 2 (2025): Volume 08 Nomor 02 (Oktober 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i2.10762

Abstract

This study introduces the Coefficient Parallelisator Matrix (CPM) as a novel diagonal similarity operator designed to preserve structural and semantic symmetry within the framework of Knot Semantic Logic (KSL). The CPM formalizes the process of parallelization in linguistic and conceptual structures by transforming semantic matrices through similarity operations that maintain eigenvalues, determinants, and symmetry invariants. Each element of the CPM acts as a scaling coefficient, re- balancing semantic weights while conserving the overall interpretive equilibrium of the text. Mathematically, the transformation A′ = MAM−1 establishes a spectral equivalence between the original and parallelized structures, ensuring that both share identical eigen-spectra, determinant, and Hermitian invariants. This invariance reflects a form of semantic gauge symmetry, wherein the un- derlying topology of meaning remains stable despite local transformations in semantic intensity. Conceptually, the operator bridges linguistic theory, topology, and algebraic representation, providing a formal mechanism for analyzing reflective relations such as parallelism, chiasmus, and concentric composition. The findings extend the mathematical foundation of KSL by establishing the Coefficient Parallelisator as an analytical framework for quantifying semantic symmetry—enabling deeper integration between mathematical logic, structural linguistics, and computational semantics.
Co-Authors Ahmad, Asdar Alimuddin, Herman Amin, Arfianty Baharuddin Baharuddin Djam’an, Nurwati Fadiyah, Wulan Nur Fahrul Basir Fauziah Fauziah Fauziyyah Alimuddin Fitrah Eka Susilawati Fitriani A. Hajrah Hajrah, Hajrah Hassan, Muhammad Nasiru Hisyam Ihsan I Luh Sumber Dani Ilyas, Muhammad Irawan, Agustina Ja'faruddin, Ja'faruddin Jusriati Jusriati Kadek Widiani Kriswinarso, Tri Bondan La Eru Ugi Lestari, Wiwit Damayanti Ma'rufi, Ma'rufi Mar Athul Wazithah T. Marufi, Marufi Merry Sul Muhammad Ammar Naufal Muhammad Farhan Muhammad Ikram Muhammad Ilyas Nirsal Nurazizah, Andi Nurfitrah NURWAHIDAH NURWAHIDAH Pakan, Astri Yunianti Rachmat Fajar Halim Rahmat Hidayat Ramadhany , Nuramaliyah Ririt Marsuki Sabri Sabri Salwah Samsuddin, Auliaul Fitrah Sukarna Sunardin, Sunardin Suradi Suradi Syahrullah Asyari, Syahrullah Syam, Nur Anisa Syamsuddin Mas'ud Tahir, Nasliya Tampa, Alimuddin Vianingrum Wisnu Kurniadi Zainal, Zaid