Русский: Observe the field
Русский: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
Русский: INPUT / Current workCOMPANY & ORIGIN
Русский: Turn mathematics into
Русский: software that works
Русский: in the field.
Русский: 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
- Русский: January 6, 2022
- BASE
- Русский: Usa City, Oita Prefecture
- FOCUS
- Русский: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusРусский: Mathematical systems development
Canonical pageРусский: The new company profile is handled at /about/.
Русский: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
Русский: Before building, make the problem solvable.
Русский: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
Русский: Separate constraints and goals
Русский: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
Русский: MODEL / Constraints and evaluationРусский: Implement a usable system
Русский: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
Русский: OUTPUT / Operating system
OUR PURPOSE
Русский: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
Русский: Finite Field means a finite mathematical field.
Русский: 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
Русский: Limited elements. Consistent rules. Results that stay inside the set.
Русский: 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.
01Русский: Finite elements
Русский: The number of elements is a prime or a power of a prime.
02Русский: Closed under operations
Русский: Results return to elements in the same field.
03Русский: Inverses exist
Русский: Every nonzero element has a multiplicative inverse.
Русский: Important
Русский: 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
F5Русский: Try finite-field calculation
+
=
Русский: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
Русский: See limited resources
Русский: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
Русский: Make rules consistent
Русский: We organize business rules including exceptions so contradictions and priorities can be reviewed.
Русский: Make results reproducible
Русский: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
Русский: From mathematical models to business screens.
Русский: 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 / MODELРусский: What must be kept and what should improve
Русский: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVEРусский: Search and compare candidates
Русский: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDРусский: Enter, adjust, and share in the field
Русский: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
Русский: Be honest before being mathematical.
Русский: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
Русский: Start with field language
Русский: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
Русский: Field to conditionsРусский: Results with reasons
Русский: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
Русский: Result to evidenceРусский: Verify small before growing
Русский: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
Русский: Hypothesis to verificationРусский: Implement usability too
Русский: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
Русский: Logic to adoptionWE SAYРусский: Organize conditions and create comparable plans
WE SHOWРусский: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMРусский: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
Русский: Deepening from implementation strength into mathematics.
Русский: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
Русский: Finite Field, K.K. established
Русский: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
Русский: Toward automation of planning and assignment
Русский: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
VERIFY
Русский: Researching ways to check correctness
Русский: Theorem proving, formal verification, and inspectable calculation results are treated as research areas and clearly separated from production use.
FROM CODE TO FIELD
Русский: Show working assets, not only philosophy.
Русский: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
Русский: Mathematical demos
Русский: Change conditions and review results and unresolved points.
Русский: Try 02 / CASESРусский: Case studies
Русский: Implemented functions and confirmed changes are separated.
Русский: Read 03 / SECURITYРусский: Data handling
Русский: Receipt, retention, external AI, deletion, and responsibility are explained.
Русский: Check 04 / RESEARCHMath Lab
Русский: Research-stage technology is separated from completed products.
Русский: ViewCOMPANY PROFILE
Finite Field, K.K.
Русский: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANРусский: Usa City, Oita Prefecture
FINITE FIELDРусский: Usa City, Oita Prefecture
BASE / JAPAN
Русский: From a regional base, we use software to address complex operational problems.
- Русский: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- Русский: Japanese name
- 株式会社ファイナイトフィールド
- Русский: Address
- 879-0151 Oita, Usa, Miyaguma 550, Япония
- Русский: Established
- Русский: January 6, 2022
- Русский: Capital
- Русский: JPY 3,000,000
- Русский: Officers
- Представительный директор Toshiya Kazuyoshi Директор Yoshie Kazuyoshi Директор Hikaru Ono
- Русский: Major client
- Matsuhisa Japan Co., Ltd.
- Русский: Business domains
- Русский: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
Русский: 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
Русский: About the company and the name
Русский: A short explanation of the relationship between a mathematical term and the actual service.
01Русский: What is a finite field?
Русский: 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.
02Русский: How does the name relate to business systems?
Русский: 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.
03Русский: Can we start with a mathematical consultation only?
Русский: 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.
04Русский: Can you develop the actual system too?
Русский: 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
Русский: What does your team think through every time?
Русский: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.