Монгол: Observe the field
Монгол: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
Монгол: INPUT / Current workCOMPANY & ORIGIN
Монгол: Turn mathematics into
Монгол: software that works
Монгол: in the field.
Монгол: 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
- Монгол: January 6, 2022
- BASE
- Монгол: Usa City, Oita Prefecture
- FOCUS
- Монгол: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusМонгол: Mathematical systems development
Canonical pageМонгол: The new company profile is handled at /about/.
Монгол: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
Монгол: Before building, make the problem solvable.
Монгол: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
Монгол: Separate constraints and goals
Монгол: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
Монгол: MODEL / Constraints and evaluationМонгол: Implement a usable system
Монгол: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
Монгол: OUTPUT / Operating system
OUR PURPOSE
Монгол: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
Монгол: Finite Field means a finite mathematical field.
Монгол: 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
Монгол: Limited elements. Consistent rules. Results that stay inside the set.
Монгол: 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.
01Монгол: Finite elements
Монгол: The number of elements is a prime or a power of a prime.
02Монгол: Closed under operations
Монгол: Results return to elements in the same field.
03Монгол: Inverses exist
Монгол: Every nonzero element has a multiplicative inverse.
Монгол: Important
Монгол: 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
F5Монгол: Try finite-field calculation
+
=
Монгол: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
Монгол: See limited resources
Монгол: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
Монгол: Make rules consistent
Монгол: We organize business rules including exceptions so contradictions and priorities can be reviewed.
Монгол: Make results reproducible
Монгол: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
Монгол: From mathematical models to business screens.
Монгол: 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 / MODELМонгол: What must be kept and what should improve
Монгол: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVEМонгол: Search and compare candidates
Монгол: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDМонгол: Enter, adjust, and share in the field
Монгол: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
Монгол: Be honest before being mathematical.
Монгол: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
Монгол: Start with field language
Монгол: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
Монгол: Field to conditionsМонгол: Results with reasons
Монгол: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
Монгол: Result to evidenceМонгол: Verify small before growing
Монгол: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
Монгол: Hypothesis to verificationМонгол: Implement usability too
Монгол: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
Монгол: Logic to adoptionWE SAYМонгол: Organize conditions and create comparable plans
WE SHOWМонгол: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMМонгол: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
Монгол: Deepening from implementation strength into mathematics.
Монгол: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
Монгол: Finite Field, K.K. established
Монгол: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
IMPLEMENTATION
Монгол: Complex operations into usable screens
Монгол: We have built systems that connect data and operations, including ordering, visit availability, and unmanned sales workflows.
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
Монгол: Toward automation of planning and assignment
Монгол: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
VERIFY
Монгол: Researching ways to check correctness
Монгол: Theorem proving, formal verification, and inspectable calculation results are treated as research areas and clearly separated from production use.
FROM CODE TO FIELD
Монгол: Show working assets, not only philosophy.
Монгол: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
Монгол: Mathematical demos
Монгол: Change conditions and review results and unresolved points.
Монгол: Try 02 / CASESМонгол: Case studies
Монгол: Implemented functions and confirmed changes are separated.
Монгол: Read 03 / SECURITYМонгол: Data handling
Монгол: Receipt, retention, external AI, deletion, and responsibility are explained.
Монгол: Check 04 / RESEARCHMath Lab
Монгол: Research-stage technology is separated from completed products.
Монгол: ViewCOMPANY PROFILE
Finite Field, K.K.
Монгол: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANМонгол: Usa City, Oita Prefecture
FINITE FIELDМонгол: Usa City, Oita Prefecture
BASE / JAPAN
Монгол: From a regional base, we use software to address complex operational problems.
- Монгол: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- Монгол: Japanese name
- 株式会社ファイナイトフィールド
- Монгол: Address
- 879-0151 Oita, Usa, Miyaguma 550, Япон
- Монгол: Established
- Монгол: January 6, 2022
- Монгол: Capital
- Монгол: JPY 3,000,000
- Монгол: Officers
- Төлөөлөх захирал Toshiya Kazuyoshi Албан тушаалтан Yoshie Kazuyoshi Албан тушаалтан Hikaru Ono
- Монгол: Major client
- Matsuhisa Japan Co., Ltd.
- Монгол: Business domains
- Монгол: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
Монгол: 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
Монгол: About the company and the name
Монгол: A short explanation of the relationship between a mathematical term and the actual service.
01Монгол: What is a finite field?
Монгол: 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.
02Монгол: How does the name relate to business systems?
Монгол: 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.
03Монгол: Can we start with a mathematical consultation only?
Монгол: 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.
04Монгол: Can you develop the actual system too?
Монгол: 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
Монгол: What does your team think through every time?
Монгол: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.