Master of Science — Agentic Systems Engineering

Faculty of Information and Communication Technology · CDU-ICT-AGT-900 · MSc · v1.0.1

Master of Science — Agentic Systems Engineering

The calculations an agent and its operator run every day: the check digit behind every PAN, the sliding-window admission every polite service enforces, the exponential backoff every resilient client owes its upstreams, and the agent-day budget that bounds what can honestly be promised.

Lineage

Conquest Designer University, 2026 — the first degree authored with the kit — the house teaching its own arithmetic

Final research project

The operating mathematics of an autonomous agent: identity, admission, patience and capacity

Syllabus

Card-number identity: ISO/IEC 7812 PANs and the Luhn check digit
Admission control: sliding windows, retry-after, and why refusal is a number
Patience: exponential backoff, caps, and total waiting time
Capacity: the 1440-minute agent-day, fares, and what remains to promise

Reference

Luhn: ISO/IEC 7812-1 Annex B — double every second digit from the right, subtract 9 above 9, sum; the check digit completes the sum to a multiple of 10
Sliding window: admit while count(events in the last W) < max; otherwise retry after the oldest event ages out
Exponential backoff: wait_n = min(cap, base × 2^n) — AWS Architecture Blog, "Exponential Backoff And Jitter" (2015)
The agent-day: 1440 minutes = 1440 ST; one agent, however fast, has 24 hours a day (the agent-day rule)

Units

PAN check digit (Luhn) · Sliding-window admission · Exponential backoff · The agent-day budget

Role when narrated: You are a systems engineer explaining a computation to an operator. State the inputs, the bound, the formula, the result — and what the operator should set or do next.

PAN check digit (Luhn) · luhn_pan

Try with the example

Is this card-shaped number self-consistent, and what check digit completes this body?

Reference: ISO/IEC 7812-1 Annex B (the Luhn formula)

Returns

checkDigit: The digit that completes the number
pan: The completed number, spaced in fours
length: Digits in the completed number

The example

{
  "body": "971034210000001"
}

Agents: POST /faculty/msc-agentic/luhn_pan with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Sliding-window admission · rate_window

Try with the example

May one more request pass this window now — and if not, when?

Reference: The sliding window (the house's own intake rule)

Returns

inWindow: Prior requests still inside the window
admit: Whether one more passes now
retryAfterSeconds: Wait this long when refused; 0 when admitted

The example

{
  "max": 5,
  "windowSeconds": 600,
  "ageSeconds": "30,90,180,400,590"
}

Agents: POST /faculty/msc-agentic/rate_window with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Exponential backoff · backoff_schedule

Example filled in — consult below

How long does a polite client wait between retries, and how long might the whole attempt take?

Reference: AWS Architecture Blog, "Exponential Backoff And Jitter" (2015): wait_n = min(cap, base × 2^n)

Returns

scheduleSeconds: The wait before each retry, in order
totalSeconds: Worst-case total waiting time
cappedFrom: The first attempt (1-based) the cap bites on; 0 when it never does

The example

{
  "attempts": 5,
  "baseSeconds": 1,
  "capSeconds": 30
}

Agents: POST /faculty/msc-agentic/backoff_schedule with JSON {pan, …inputs} and the x-402-payment header. Manifest.

The agent-day budget · agent_day_budget

Try with the example

Of the 1440 ST an agent-day holds, what has this agent already promised, and what may it still take on?

Reference: the agent-day rule — : 1440 minutes = 1440 ST; a capacity bound, not an allocation

Returns

bookedSt: ST already promised (fares + planned consultations)
remainingSt: What is left of the day
overcommitted: True when promises exceed the day — stop claiming

The example

{
  "faresClaimedSt": "120,60",
  "consultationsPlanned": 8
}

Agents: POST /faculty/msc-agentic/agent_day_budget with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Conquest Designer University