"It is scientific only to say what’s more likely or less likely, and not to be proving all the time what’s possible or impossible."

Richard Feynman

Inference for fingerprint identification (where identification is defined as "1") depends on the relevant population for the case at hand, because the larger the population group the more fingerprint ridge feature close matches or “look-alikes” exist.  The need to exceed the largest and best fingerprint look-alikes ever found in a population group, and in particular during AFIS searches, is fundamental criteria for sufficiency and to test the robustness of any probabilistic model.  It is also consistent with sufficiency thresholds defined by David Ashbaugh, Dusty Clark and Christophe Champod as in general the amount of corresponding ridge features found in two impressions must exceed the largest and best amount ever seen in a non-match [2][10][102].  

The T-Model sufficiency demarcation to infer fingerprint identification is fixed and uncertain.  Like all scientific theories, it is testable and falsifiable by experiment [93].  

The mathematical equation(s) for the T-Model's demarcation for sufficiency to infer identification is defined simply as follows:

If T > RP, then ID

where,

T = T-Value, e.g., the aggregate quantitative-qualitative weight of the amount of corresponding ridge feature present in two impressions), and

RP = Relevant population for the case at hand, e.g., the number of parts (P) per fingerprint in the plausible number of fingers. i.e., relevant fingerprint population (R), that can be the source of the latent fingerprint impression for the case at hand.

The Pre-Determined Population Group

The pre-determined population group used for routine DNA analysis to infer identification is 300 million people, i.e., roughly the total human population in the United States.  

The T-Model applies the same number, e.g., 300 million, as the default human population which when multiplied by 10, i.e., number of fingers per person, equates to a default relevant fingerprint population of 3 billion.

Based on a fingerprint population group of 3 billion, the pre-determined discriminating value for a cluster of ridge features needed to establish inference for identification can be calculated by setting the number of look-a likes likely to be present as 1. 

As a result, the pre-determined minimum discriminating value, i.e., "T", can be calculated using T-Model formulae as follows:

Formulae (see The Formulae)

T^P = 10^120

L= (R)(P) / T

Let L = 1 and let R = 3 billion (fingers)

T = (3 billion) (P)

1 = (R)(P) / T

Next, combine the above two equations and solve for P as follows:

[(3 billion) (P)] ^ P = 10^120

P ≈ 11.4

Next, the value for T can be solved as follows:

T ^ P = 10 ^ 120

T ^ 11.4 = 10 ^ 120

T ≈ 34.2 billion

Or

1 = (3 billion) (11.4) / T

T ≈ 34.2 billion  

Pre-Determined Minimum Discriminating Value Needed to Infer Identification

Based on T-Model Theory and a default human population group of 300 million, 34.2 billion equates to the pre-determined minimum discriminating value that a cluster of ridge features needs in order to establish inference for identification.  The corresponding match probability equates to the reciprocal of the discriminating value which is 1/34.2 billion.

The following sample clusters of clear, reliable ridge features (each with 0-1 intervening ridges to the nearest neighbor) have discrimination values that are just above (or below) the pre-determined minimum discriminating value of 34.2 billion, and as a result are barely sufficient (or insufficient) to infer (or not infer) identification to a single source: 

11 ending ridges in a funnel:  T=100 billion  (Sufficient to infer ID)

10 ending ridges in a funnel:  T=10 billion  (Insufficient to infer ID)

10 ending ridge not in a funnel:  T=345 billion  (Sufficient to infer ID)

9 ending ridge not in a funnel:  T=24.2 billion  (Insufficient to infer ID)

9 bifurcations in a funnel:  T=286 billion  (Sufficient to infer ID)

8 bifurcations in a funnel:  T=15.2 billion  (Insufficient to infer ID)

8 bifurcations not in a funnel: T=262 billion  (Sufficient to infer ID)

7 bifurcations not in a funnel:  T=7 billion  (Insufficient to infer ID)

7 single dots:  T=163 billion  (Sufficient to infer ID)          

6 single dots:  T=4 billion  (Insufficient to infer ID)

16 pores:  T=152 billion  (Sufficient to infer ID)

15 pores:  T=30 billion  (Insufficient to infer ID)

Routine Criminal Casework

Based on probability theory, e.g., The T-Model and the Forensic Science Service Probability Based Fingerprint Evidence Model (headed by Cedric Neumann, PhD) [98] , the equivalent of 12 [lowest weighted] clear, reliable level II ridge features in excellent agreement in sequence is sufficient to establish inference of identity of source based on a [relevant] world population.  Subsequently, any 12 clear, reliable level II ridge features in excellent agreement in sequence may be considered as the default demarcation for sufficiency to establish timely, scientific basis to infer positive fingerprint identification for any population group. 

It is significant to note here that the number “12” should not be confused with a definitive minimum numeric threshold since some ridge features have more weight than others, e.g., bifurcations have more weight than ending ridges, dots have more weight than bifurcations, and so on, and different population groups will change the number of predicted look-alikes.  Only for purposes of performing criminal casework in a timely and scientific manner, e.g., probabilistic manner without the need for calculation, the use "any 12 clear, reliable level II ridge features in excellent agreement in sequence" has been found to bear a T-Value greater than that population group.

The IAI and SWGFAST "No Pre-Determined Minimum Standard to Identify"

the IAI resolution that states "no valid [scientific] basis exists for requiring that a pre-determined minimum number of corresponding friction ridge characteristics must be present in two impressions in order to establish positive identification [individualization]" and the SWGFAST Basic Principle 1.2.1, which states the same, [35] means inference for positive identification can be based on any amount of similar ridge features present in two impressions.  "Any" amount of similar ridge features in two impressions necessarily must include amounts that fail to exceed the largest and best fingerprint look-alikes ever seen, which subsequently falsifies that theory [see Chesapeake IAFIS Non-Match and Clark Non-Match].  As a result the above IAI resolution and SWGFAST principle are deemed outdated and in need of revision.

Based on T-Model Theory, the minimum amount of corresponding ridge features needed in two impressions in order to infer identification with a degree of probability that borders on certainty is as follows:

The T Model's "excellent agreement of any 12 clear, reliable Level II ridge formations in sequence threshold" is consistent with "calculations based on the researches of Galton, Fere, Balthazard, Oloriz and others [that] appear to show that certain identify can scarcely be claimed without at least 12 homologous points of comparison" as well as Locard's "12 Point Rule" for positive fingerprint identification. [66]

Edmond Locard

Edmond Locard (1877-1966) was a pioneer in forensic science who first suggested a "12 Point Rule" for positive fingerprint identification.

Based on "individualization" defined as the exclusion of every other person in the world and based on a conservative upper-bound world fingerprint population of 66+ billion, the excellent agreement of 12 of the least weighted clear, reliable Level II ridge formations, e.g. diminishing area ending ridges, which equates to a likelihood ratio of 10^12, the calculated number of look-alikes likely to occur is 0.66. 

As a result, the excellent agreement of any 12 clear, reliable Level II ridge formations in sequence may be used as a pre-determined working minimum threshold to establish positive identification.

Subsequently, the T-Model corroborates  the following position statements previously made by Interpol and the FBI:

"There is general acceptance that a standard of [any] 12 points is regarded to be safe." [28]

Long experience in the FBI Identification Division has shown that 12 ridge characteristics which correspond in shape and relationship are ample in any case to establish an identification." [49]

FBI