ქართული: Observe the field
ქართული: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
ქართული: INPUT / Current workCOMPANY & ORIGIN
ქართული: Turn mathematics into
ქართული: software that works
ქართული: in the field.
ქართული: 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
- ქართული: January 6, 2022
- BASE
- ქართული: Usa City, Oita Prefecture
- FOCUS
- ქართული: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusქართული: Mathematical systems development
Canonical pageქართული: The new company profile is handled at /about/.
ქართული: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
ქართული: Before building, make the problem solvable.
ქართული: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
ქართული: Separate constraints and goals
ქართული: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
ქართული: MODEL / Constraints and evaluationქართული: Implement a usable system
ქართული: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
ქართული: OUTPUT / Operating system
OUR PURPOSE
ქართული: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
ქართული: Finite Field means a finite mathematical field.
ქართული: 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
ქართული: Limited elements. Consistent rules. Results that stay inside the set.
ქართული: 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.
01ქართული: Finite elements
ქართული: The number of elements is a prime or a power of a prime.
02ქართული: Closed under operations
ქართული: Results return to elements in the same field.
03ქართული: Inverses exist
ქართული: Every nonzero element has a multiplicative inverse.
ქართული: Important
ქართული: 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
F5ქართული: Try finite-field calculation
+
=
ქართული: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
ქართული: See limited resources
ქართული: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
ქართული: Make rules consistent
ქართული: We organize business rules including exceptions so contradictions and priorities can be reviewed.
ქართული: Make results reproducible
ქართული: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
ქართული: From mathematical models to business screens.
ქართული: 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 / MODELქართული: What must be kept and what should improve
ქართული: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVEქართული: Search and compare candidates
ქართული: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDქართული: Enter, adjust, and share in the field
ქართული: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
ქართული: Be honest before being mathematical.
ქართული: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
ქართული: Start with field language
ქართული: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
ქართული: Field to conditionsქართული: Results with reasons
ქართული: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
ქართული: Result to evidenceქართული: Verify small before growing
ქართული: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
ქართული: Hypothesis to verificationქართული: Implement usability too
ქართული: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
ქართული: Logic to adoptionWE SAYქართული: Organize conditions and create comparable plans
WE SHOWქართული: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMქართული: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
ქართული: Deepening from implementation strength into mathematics.
ქართული: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
ქართული: Finite Field, K.K. established
ქართული: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
ქართული: Toward automation of planning and assignment
ქართული: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
VERIFY
ქართული: Researching ways to check correctness
ქართული: Theorem proving, formal verification, and inspectable calculation results are treated as research areas and clearly separated from production use.
FROM CODE TO FIELD
ქართული: Show working assets, not only philosophy.
ქართული: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
ქართული: Mathematical demos
ქართული: Change conditions and review results and unresolved points.
ქართული: Try 02 / CASESქართული: Case studies
ქართული: Implemented functions and confirmed changes are separated.
ქართული: Read 03 / SECURITYქართული: Data handling
ქართული: Receipt, retention, external AI, deletion, and responsibility are explained.
ქართული: Check 04 / RESEARCHMath Lab
ქართული: Research-stage technology is separated from completed products.
ქართული: ViewCOMPANY PROFILE
Finite Field, K.K.
ქართული: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANქართული: Usa City, Oita Prefecture
FINITE FIELDქართული: Usa City, Oita Prefecture
BASE / JAPAN
ქართული: From a regional base, we use software to address complex operational problems.
- ქართული: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- ქართული: Japanese name
- 株式会社ファイナイトフィールド
- ქართული: Address
- 879-0151 Oita, Usa, Miyaguma 550, იაპონია
- ქართული: Established
- ქართული: January 6, 2022
- ქართული: Capital
- ქართული: JPY 3,000,000
- ქართული: Officers
- წარმომადგენელი დირექტორი Toshiya Kazuyoshi ოფიცერი Yoshie Kazuyoshi ოფიცერი Hikaru Ono
- ქართული: Major client
- Matsuhisa Japan Co., Ltd.
- ქართული: Business domains
- ქართული: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
ქართული: 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
ქართული: About the company and the name
ქართული: A short explanation of the relationship between a mathematical term and the actual service.
01ქართული: What is a finite field?
ქართული: 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.
02ქართული: How does the name relate to business systems?
ქართული: 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.
03ქართული: Can we start with a mathematical consultation only?
ქართული: 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.
04ქართული: Can you develop the actual system too?
ქართული: 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
ქართული: What does your team think through every time?
ქართული: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.