The Principia Machina/Walk through/4 When findings disagree

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The specification Contents: parts, tables, diagrams TPS 0.5.0 (declared 2026-10-03, revision 8; machine-optimized text) Decisions (the foundations record, one line each)

The walk through, page 4 of 8. Written for the general reader; nothing here is a rule, and every rule it mentions is linked to the page of the specification that states it.

When findings disagree

Sooner or later two lines in the register will contradict each other. This is not a failure of the machine; it is the machine doing its job. The question is what happens next, and the answer is the part of the design that took the longest to get right.

The first rule is absolute. A finding that contradicts the promises in the kernel is struck, without any weighing. The promises are the walls of the tunnel; a result that says the wall is somewhere else is wrong by definition inside this container. If the promises are what is wrong, that is a matter for a new container, and for a person to declare.

The second rule is the ordinary case. A finding stands as long as its derivation is sound and nothing else standing contradicts it. Most findings live their whole lives here.

The interesting rule is the third. When two standing findings contradict each other, the machine does not ask who wrote them, or how confident anyone felt. It asks how far each is from the promises: how many extra assumptions each derivation needed, and how many steps it took. The finding that stays closer to the promises wins, and the loser is struck, with the assumptions that separate the two written down as the place where the trouble lives. If the two are equally close, no automatic decision is made; a person is asked.

There is a safeguard against a pile-on. A finding that is contradicted from several genuinely independent directions is not struck by the count alone; instead the count opens a review and a person decides whether to strike it, to narrow the promises, or to find against the challengers. And a purely logical finding can never be struck by a measured one; a measurement that disagrees with a derivation is recorded as a gap to be explained, not as a defeat.

The path a finding takes when it meets a contradiction. (the diagram's page, with its source and a plain reading.)

Measured findings have a discipline of their own, borrowed from how physicists combine measurements of the same constant: before two numbers are declared to disagree, the machine checks whether the stated uncertainties are believable, and widens them if the scatter says they are not. A contradiction that disappears when the error bars are honest was never a contradiction.

How logical and measured findings are tested against one another. (the diagram's page, with its source and a plain reading.)

All of this is an audit, run by the machine at the container's birth and at every later pass. The audit can strike, and it can open a review, but it never decides a review: every review ends as a question put to a person, with the options laid out. The rules behind this page: section 4.1 on the audit, section 4.3 and section 4.4 on the strike rule itself.

One thing had to be settled before any of this could be mechanical: when are two numbers about the same thing? The answer is the dictionary. Two measured findings are compared only if they name the same entry in it, and the machine converts both to the same SI units first (section 4.4.4). 2.54 and 25.4 are not a disagreement if one is centimeters and the other millimeters; they are not even comparable if one is a length and the other a time. A difference of convention that the kernel never declared does not get guessed at either: it opens a review.

Two limits of the closeness score are named rather than hidden. One: whether an assumption is really one assumption is still a judgment, now made once, when the assumption gets its number, rather than at every comparison. Two: the step count is measured over a finding's own derivation, so redrawing the boundary between two findings can move it.

A third limit is about motion. A measured value of something that moves, a position at some moment, depends on where the motion started. So a finding now carries, in a form the machine can read, the starting values it assumed and the moment its value holds, and the machine tests two such values against each other only when both rest on the same starting values and hold at the same moment. Where a starting value is written only in words, two such values are still compared by a person; and a value that happens not to change, where the kernel does not fix it, still needs its moment stated before the machine will compare it (a value the kernel fixes is compared without one), a limit the specification names (section 4.4.13).

A comparison with a value from outside the container is kept apart from all of this: it is checked only against the finding it compares, never counted as one more voice in a disagreement, and a logical finding it contradicts is not struck but gets a gap on the record (section 3.3.6).

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