Theory of Mathematical Integrity

Years ago I posed a hypothesis that financial statement had, or should have, mathematical integrity.  After significant testing, between 2015 and about 2018, I have reached the conclusion that my hypothesis was correct and now I have my theory of mathematical integrity.

Here are many of the best details related to my testing, poking, and prodding and prototypes that I constructed to test my hypothesis:

Fundamentally, much of a financial statement (but not all) comes from information that flows through a general ledger which follows the double entry bookkeeping mathematical model. That double entry bookkeeping model is based on well-known mathematics construction from undergraduate algebra.  One would expect that financial reports, as an accountant would say, "foots", "crosscasts", "ticks", and "ties".  No accountant would, or could really, dispute this notion.

The mathematics of a financial statement describe the financial statement relations and, if those mathematical rules are represented in a machine readable form, can be used to verify that in fact the mathematical relations are intact, and prove to anyone making use of that financial statement information that the financial statement mathematics is provably sound.

But if those machine readable mathematical rules are not provided with the financial statement, the mathematics of the financial statement are still expected to foot, crosscast, tick, and tie.  That is the natural state of a financial statement.  That is what is expected.

The mathematics of every important/significant computation should be tested and proven including roll ups, roll forwards, prior period adjustments, and any other such mathematical computation.


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