Հայերեն: Observe the field
Հայերեն: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
Հայերեն: INPUT / Current workCOMPANY & ORIGIN
Հայերեն: Turn mathematics into
Հայերեն: software that works
Հայերեն: in the field.
Հայերեն: Finite Field is named after the mathematical structure known as a finite field. We organize complex conditions into consistent models and implement them as web and app systems people can use every day.
- FOUNDED
- Հայերեն: January 6, 2022
- BASE
- Հայերեն: Usa City, Oita Prefecture
- FOCUS
- Հայերեն: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusՀայերեն: Mathematical systems development
Canonical pageՀայերեն: The new company profile is handled at /about/.
Հայերեն: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
Հայերեն: Before building, make the problem solvable.
Հայերեն: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
Հայերեն: Separate constraints and goals
Հայերեն: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
Հայերեն: MODEL / Constraints and evaluationՀայերեն: Implement a usable system
Հայերեն: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
Հայերեն: OUTPUT / Operating system
OUR PURPOSE
Հայերեն: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
Հայերեն: Finite Field means a finite mathematical field.
Հայերեն: A finite field is a mathematical structure with a finite number of elements where addition, subtraction, multiplication, and division except by zero are defined. It is important in cryptography, error-correcting codes, and computer science.
DEFINITION / PLAIN LANGUAGE
Հայերեն: Limited elements. Consistent rules. Results that stay inside the set.
Հայերեն: In F5, the elements are 0, 1, 2, 3, and 4. After ordinary calculation, the remainder modulo 5 is used. That is why 2 × 3 becomes 1 rather than 6.
01Հայերեն: Finite elements
Հայերեն: The number of elements is a prime or a power of a prime.
02Հայերեն: Closed under operations
Հայերեն: Results return to elements in the same field.
03Հայերեն: Inverses exist
Հայերեն: Every nonzero element has a multiplicative inverse.
Հայերեն: Important
Հայերեն: This does not mean that business operations are literally finite fields. The connection here is a company metaphor for how we work.
INTERACTIVE / PRIME FIELD
F5Հայերեն: Try finite-field calculation
+
=
Հայերեն: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
Հայերեն: See limited resources
Հայերեն: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
Հայերեն: Make rules consistent
Հայերեն: We organize business rules including exceptions so contradictions and priorities can be reviewed.
Հայերեն: Make results reproducible
Հայերեն: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
Հայերեն: From mathematical models to business screens.
Հայերեն: We are not only a mathematical consulting team, and not only a general contract developer. We design the decision logic and the software used every day as one system.
01 / MODEL
MATHEMATICAL MODEL
01 / MODELՀայերեն: What must be kept and what should improve
Հայերեն: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVEՀայերեն: Search and compare candidates
Հայերեն: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDՀայերեն: Enter, adjust, and share in the field
Հայերեն: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
Հայերեն: Be honest before being mathematical.
Հայերեն: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
Հայերեն: Start with field language
Հայերեն: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
Հայերեն: Field to conditionsՀայերեն: Results with reasons
Հայերեն: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
Հայերեն: Result to evidenceՀայերեն: Verify small before growing
Հայերեն: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
Հայերեն: Hypothesis to verificationՀայերեն: Implement usability too
Հայերեն: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
Հայերեն: Logic to adoptionWE SAYՀայերեն: Organize conditions and create comparable plans
WE SHOWՀայերեն: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMՀայերեն: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
Հայերեն: Deepening from implementation strength into mathematics.
Հայերեն: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
Հայերեն: Finite Field, K.K. established
Հայերեն: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
IMPLEMENTATION
Հայերեն: Complex operations into usable screens
Հայերեն: We have built systems that connect data and operations, including ordering, visit availability, and unmanned sales workflows.
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
Հայերեն: Toward automation of planning and assignment
Հայերեն: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
VERIFY
Հայերեն: Researching ways to check correctness
Հայերեն: Theorem proving, formal verification, and inspectable calculation results are treated as research areas and clearly separated from production use.
FROM CODE TO FIELD
Հայերեն: Show working assets, not only philosophy.
Հայերեն: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
Հայերեն: Mathematical demos
Հայերեն: Change conditions and review results and unresolved points.
Հայերեն: Try 02 / CASESՀայերեն: Case studies
Հայերեն: Implemented functions and confirmed changes are separated.
Հայերեն: Read 03 / SECURITYՀայերեն: Data handling
Հայերեն: Receipt, retention, external AI, deletion, and responsibility are explained.
Հայերեն: Check 04 / RESEARCHMath Lab
Հայերեն: Research-stage technology is separated from completed products.
Հայերեն: ViewCOMPANY PROFILE
Finite Field, K.K.
Հայերեն: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANՀայերեն: Usa City, Oita Prefecture
FINITE FIELDՀայերեն: Usa City, Oita Prefecture
BASE / JAPAN
Հայերեն: From a regional base, we use software to address complex operational problems.
- Հայերեն: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- Հայերեն: Japanese name
- 株式会社ファイナイトフィールド
- Հայերեն: Address
- 879-0151 Oita, Usa, Miyaguma 550, Ճապոնիա
- Հայերեն: Established
- Հայերեն: January 6, 2022
- Հայերեն: Capital
- Հայերեն: JPY 3,000,000
- Հայերեն: Officers
- Ներկայացուցիչ տնօրեն Toshiya Kazuyoshi Պաշտոնյա Yoshie Kazuyoshi Պաշտոնյա Hikaru Ono
- Հայերեն: Major client
- Matsuhisa Japan Co., Ltd.
- Հայերեն: Business domains
- Հայերեն: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
Հայերեն: Only information aligned with official company facts is shown. Unconfirmed employee count, sales, certification status, and similar claims are not listed.
PAGE DATA REVIEWED / 2026.06FAQ
Հայերեն: About the company and the name
Հայերեն: A short explanation of the relationship between a mathematical term and the actual service.
01Հայերեն: What is a finite field?
Հայերեն: A finite field is a mathematical structure with a finite number of elements. Addition, subtraction, multiplication, and division except by zero are defined, and the result stays inside the same set. This page visualizes prime fields Fp for prime p.
02Հայերեն: How does the name relate to business systems?
Հայերեն: It does not mean that business operations are literally finite fields. The name reflects how we work with limited resources, consistent rules, and reproducible results.
03Հայերեն: Can we start with a mathematical consultation only?
Հայերեն: Yes. We can begin by checking whether operational judgments, assignments, orders, and plans can be modeled. A small calculation prototype can verify the idea first.
04Հայերեն: Can you develop the actual system too?
Հայերեն: Yes. We design and build mathematical models, calculation logic, databases, web admin screens, and iOS and Android apps as one delivery path.
START WITH THE PROBLEM
Հայերեն: What does your team think through every time?
Հայերեն: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.