Card authentication layer

Figure 01 / 12

The evaluated population

The cohort contains 24,000 card attempts, of which 360 have the defined synthetic outcome: Synthetic confirmed card fraud. The outcome is known by construction here. In production, label uncertainty and selection must be recorded separately.

Figure data and text version

Outcome	Count
Synthetic confirmed card fraud	360
Other labeled outcomes	23,640

The checkout has an authentication result, transaction evidence, and a later outcome label. A successful authentication is useful evidence but does not settle every loss path.

The reference case starts with the stated population and a functioning evidence path. The owner is risk operations.

All amounts, rates, capacity limits, and outcomes in this case are synthetic. The three conditions are separate assumptions for comparison. A better result in the response condition is not measured proof that the proposed control causes that improvement. The figures expose the calculation and its limits; a real deployment needs its own evidence.

Read the result

The rule flags 643 of 24,000 card attempts. Of those flags, 288 meet the synthetic target, giving 44.79% precision. It misses 72 target events. Under the stated cost assumptions, residual loss and operating friction total $20,984. The important result is the connection between the population, action, capacity, and outcome—not one isolated score.

Figure 02 / 12

Four outcomes of the rule

The rule flags 288 synthetic positives and 355 negatives. It misses 72 positives. A flagged item is a decision to intervene; it is not proof of fraud, a legal prohibition, or any other real-world conclusion.

Figure data and text version

Known outcome	Flagged	Not flagged
Synthetic confirmed card fraud	288	72
Other outcome	355	23,285

Figure 03 / 12

Three rates with different denominators

Precision is 44.79%, recall is 80%, and the false-positive rate is 1.5%. Changing the denominator changes the meaning. This record keeps each numerator attached to the population from which it came.

Figure data and text version

Metric	Numerator	Denominator	Result
Precision	288	643	44.79%
Recall	288	360	80%
False-positive rate	355	23,640	1.5%

Figure 04 / 12

Precision changes with prevalence

This sensitivity plot holds recall at 80% and false-positive rate at 1.5%, then changes prevalence. It is an algebraic comparison, not a forecast. Even unchanged detection quality can produce a very different review queue when the base rate changes. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Assumed prevalence	Precision %
0.1%	5.07
0.5%	21.14
1%	35.01
2%	52.12
5%	73.73
10%	85.56

Figure 05 / 12

The threshold trade-off

Six illustrative score bands use a stated pair of detection rates. Lower sensitivity can reduce false alarms but miss more target events. These points do not come from a trained model and do not establish the best operating threshold. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Score band	True positives	False positives
Band 1	353	3,546
Band 2	338	1,891
Band 3	310	827
Band 4	259	284
Band 5	180	95
Band 6	90	24

Figure 06 / 12

A transparent loss-and-friction calculation

At $240 severity per missed synthetic positive, residual loss is $17,280. Review costs $1,929; lost contribution on false alarms is $1,775. The calculation assumes intervention prevents all flagged-positive loss and each false alarm loses the stated contribution. Relax those assumptions before applying it to a real policy.

Figure data and text version

Cost component	USD
Missed-positive loss	17,280
Review cost	1,929
False-alarm contribution	1,775

Figure 07 / 12

Observed outcomes mature over time

The final synthetic positive count is 360. Earlier observations reveal only a stated fraction. Comparing a day-1 cohort with a day-30 cohort would confuse label age with control quality. This curve models observation delay only; it does not change the final outcome. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Days after event	Observed positives
1	65
3	126
7	216
14	295
30	360

Figure 08 / 12

Review demand and available capacity

The flag count is 643. The comparison capacity is an illustrative 960 reviews per cohort window. A mathematical rule can be coherent while its resulting workload exceeds the operating team’s capacity. Capacity is not permission to ignore an applicable mandatory control.

Figure data and text version

Queue measure	Items
Flagged for review	643
Available capacity	960
Excess demand	0

Figure 09 / 12

A feature is an observation with provenance

This evidence contract supports authentication is one layer. A value needs its event time, arrival time, scope, and source. Keeping unavailable evidence distinct from a measured zero prevents an outage from becoming a falsely reassuring feature.

Figure data and text version

Field	Example	Meaning
entity_ref	Card authentication layer	Subject of this case
event_time	2026-09-18T09:00:00Z	When the event occurred
received_time	2026-09-18T09:00:02Z	When the system learned it
signal_status	available	Evidence quality, not an outcome
label_definition	Synthetic confirmed card fraud	The target used in these calculations

Figure 10 / 12

Missing evidence changes the observed population

The cells show an explicitly constructed completeness profile for three signal groups. The stress condition removes more history and device evidence. Missingness does not prove the target outcome; it changes what the decision process knows.

Figure data and text version

Signal group	Available	Missing
Identity evidence	23,760	240
Activity history	23,520	480
Context signal	22,800	1,200

Figure 11 / 12

Evidence, score, and action remain separate

The policy can use authentication is one layer only within its approved scope. The action record must retain which evidence was available, which model or rule ran, and which action was actually applied. The final action can differ from the score recommendation when a separate constraint applies.

Figure data and text version

Stage	Record
Observe	Card authentication layer: evidence as of the decision time
Evaluate	Rule flags 643 of 24,000 card attempts
Apply	Record action, reason, owner, and expiry
Reconcile	Join the action to later outcomes without overwriting history

Figure 12 / 12

What the result cannot establish

Observed classifications do not reveal every counterfactual. The synthetic labels make arithmetic possible, but production decline data is selected by prior policy. Keep measured outcomes, assumed prevention, and unknown alternatives separate when reporting impact.

Figure data and text version

Claim	Evidence in this case	Limit
Detected target	288 known synthetic positives flagged	Production labels may be delayed or wrong
Prevented loss	Assumed 69,120 USD	Requires an intervention-effect assumption
Customer impact	355 synthetic negatives flagged	Not every flag causes abandonment
Unobserved alternative	Outcome without the action	Needs a valid evaluation design

Connect the result to the system

Evaluate the action policy with mature labels and preserve authentication scope.

Check the population, evidence, permitted action, and actual effect together. A balanced calculation can still use the wrong population; a successful response can still leave an unknown financial outcome. The case’s numerical result applies only to its stated assumptions.