"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 per fingerprint in the plausible number of fingers that can be the source of the latent fingerprint impression for the case at hand.

Example No. 1

Let the relevant population group for a case at hand be 300 million people (roughly the total United States population and equivalent to the population group used by the FBI to match routine DNA profiles).  

Let the T-Value for an arrangement of corresponding ridge features present in two impressions be equal to 100 billion, e.g., 11 excellent ending ridges in a funnel in excellent agreement.

Based on T-Model formula, the number of fingerprint "parts" (P) is defined as follows:

T^P=10^120

(100 billion)^P=10^120

P=10.9

As a result, the Relevant Population is defined as follows:

(300 million people) x (10 fingers) x (10.9 parts) = 32.7 billion

Based on the equation "If T>RP, then ID", the T-Value 100 billion is greater than the relevant population of 32.7 billion.  Therefore, the T-Model establishes inference for identification. 

The T-Model infers identification because less than 1 close match or look-alike is predicted to exist in the relevant population group, e.g., RP/T or 32.7 billion/100 billion is less than 1.  In other words, the T-Model predicts there is not a close match or look-alike present in the relevant population group.  As a result, there is valid basis to infer identification. 

Example No. 2

Let the relevant population group for a case at hand be 100 people (the total number of people who could have handled the bottom of a bank cash drawer since its manufacture, installation and use).  

Let the T-Value for an arrangement of corresponding ridge features present in two impressions be equal to 10,000, e.g., 4 excellent ending ridge in a funnel in excellent agreement.  Note:  Let the the ridge unit edge widths and contours in the arrangement, e.g., Level III detail, be blurred or indistinct and therefore contain no additional value.

Based on T-Model formula, the number of fingerprint "parts" (P) is defined as follows:

T^P=10^120

(10,000)^P=10^120

P=30

As a result, the Relevant Population is defined as follows:

(100 people) x (10 fingers) x (30 parts) = 30,000

Based on the equation "If T>RP, then ID", the T-Value 10,000 is less than the relevant population of 30,000.  Therefore, the T-Model does not establish inference for identification. 

The T-Model estimates there are 3 close matches or look-alikes present in the relevant population group, e.g., RP/T or 30,000/10,000 = 3.  As a result, the T-Model cannot infer identification to 1 and only 1 source absent additional weighted corresponding ridge features present in the two impressions.

Subjective Probability Statement

Absent a probability model or probabilistic numerics, the following verbal statement is based on "subjective probability", e.g., professional judgment based on training and experience, to elaborate on the demarcation for sufficiency to infer positive identification:

“There is sufficient quantity and quality of similar ridge features present in the two impressions to establish inference for positive identification, because based on my professional judgment, and taking under consideration the largest and best friction ridge look-alikes I have ever seen published, presented during examiner training and during the course of routine casework, I would not expect to find any look-alikes, e.g., amounts of similar corresponding ridge features from a different source, good enough to fool me, if I compared all the fingerprints in the relevant population group for the case at hand.”

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