한국어: Observe the field
한국어: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
한국어: INPUT / Current workCOMPANY & ORIGIN
한국어: Turn mathematics into
한국어: software that works
한국어: in the field.
한국어: 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
- 한국어: January 6, 2022
- BASE
- 한국어: Usa City, Oita Prefecture
- FOCUS
- 한국어: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focus한국어: Mathematical systems development
Canonical page한국어: The new company profile is handled at /about/.
한국어: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
한국어: Before building, make the problem solvable.
한국어: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
한국어: Separate constraints and goals
한국어: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
한국어: MODEL / Constraints and evaluation한국어: Implement a usable system
한국어: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
한국어: OUTPUT / Operating system
OUR PURPOSE
한국어: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
한국어: Finite Field means a finite mathematical field.
한국어: 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
한국어: Limited elements. Consistent rules. Results that stay inside the set.
한국어: 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.
01한국어: Finite elements
한국어: The number of elements is a prime or a power of a prime.
02한국어: Closed under operations
한국어: Results return to elements in the same field.
03한국어: Inverses exist
한국어: Every nonzero element has a multiplicative inverse.
한국어: Important
한국어: 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
F5한국어: Try finite-field calculation
+
=
한국어: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
한국어: See limited resources
한국어: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
한국어: Make rules consistent
한국어: We organize business rules including exceptions so contradictions and priorities can be reviewed.
한국어: Make results reproducible
한국어: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
한국어: From mathematical models to business screens.
한국어: 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 / MODEL한국어: What must be kept and what should improve
한국어: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVE한국어: Search and compare candidates
한국어: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILD한국어: Enter, adjust, and share in the field
한국어: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
한국어: Be honest before being mathematical.
한국어: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
한국어: Start with field language
한국어: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
한국어: Field to conditions한국어: Results with reasons
한국어: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
한국어: Result to evidence한국어: Verify small before growing
한국어: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
한국어: Hypothesis to verification한국어: Implement usability too
한국어: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
한국어: Logic to adoptionWE SAY한국어: Organize conditions and create comparable plans
WE SHOW한국어: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIM한국어: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
한국어: Deepening from implementation strength into mathematics.
한국어: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
한국어: Finite Field, K.K. established
한국어: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
한국어: Toward automation of planning and assignment
한국어: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
FROM CODE TO FIELD
한국어: Show working assets, not only philosophy.
한국어: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
한국어: Mathematical demos
한국어: Change conditions and review results and unresolved points.
한국어: Try 02 / CASES한국어: Case studies
한국어: Implemented functions and confirmed changes are separated.
한국어: Read 03 / SECURITY한국어: Data handling
한국어: Receipt, retention, external AI, deletion, and responsibility are explained.
한국어: Check 04 / RESEARCHMath Lab
한국어: Research-stage technology is separated from completed products.
한국어: ViewCOMPANY PROFILE
Finite Field, K.K.
한국어: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPAN한국어: Usa City, Oita Prefecture
FINITE FIELD한국어: Usa City, Oita Prefecture
BASE / JAPAN
한국어: From a regional base, we use software to address complex operational problems.
- 한국어: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- 한국어: Japanese name
- 株式会社ファイナイトフィールド
- 한국어: Address
- 879-0151 Oita, Usa, Miyaguma 550, 일본
- 한국어: Established
- 한국어: January 6, 2022
- 한국어: Capital
- 한국어: JPY 3,000,000
- 한국어: Officers
- 대표이사 Toshiya Kazuyoshi 임원 Yoshie Kazuyoshi 임원 Hikaru Ono
- 한국어: Major client
- Matsuhisa Japan Co., Ltd.
- 한국어: Business domains
- 한국어: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
한국어: 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
한국어: About the company and the name
한국어: A short explanation of the relationship between a mathematical term and the actual service.
01한국어: What is a finite field?
한국어: 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.
02한국어: How does the name relate to business systems?
한국어: 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.
03한국어: Can we start with a mathematical consultation only?
한국어: 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.
04한국어: Can you develop the actual system too?
한국어: 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
한국어: What does your team think through every time?
한국어: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.