What counts: predictions

Twelve stones meet matching blue tally marks, a long numeral and three keepers of a shared count.

What counts: predictions

Written before implementation and execution. These are predictions about a small designed apparatus, not measurements of people. Confidence is high for each finite claim. A failing comparison below counts against its corresponding claim.

ID	Prediction	Test and possible counterexample
P1	A correct sequence of twelve increments can accompany an incorrect one-to-one account of twelve objects.	Visit one object twice and omit another. The recitation reaches twelve; an independent incidence count finds one missing and one repeated unit.
P2	Persistent identity-linked marks preserve a completed correspondence through rearrangement. Splitting changes the answer only relative to a declared unit.	Shuffle twelve marked objects across many fixed seeds. Split one: twelve original lineages remain, thirteen present pieces exist, and the earlier piece record contains a retired identity. Rejoin restores the original piece identities.
P3	Producing a decimal successor does not require reading or rewriting the whole numeral.	Compare suffix-carry addition against native arbitrary-precision arithmetic over bounded inputs, including zero and all-nine boundaries. An unchanged prefix and a changed suffix give the same exact successor.
P4	Two unequal exact integers can have the same rounded display.	At 10^24 and its successor, six-significant-digit decimal rounding agrees while exact subtraction gives one. Test rounding independently at carry and tie boundaries.
P5	A cyclic symbol alone leaves multiple compatible totals; a retained quotient or a complete distributed receipt set restores the exact total.	The four-symbol cycle repeats after four additions. Each local keeper lacks the whole trace, but the union of stable event IDs matches independently counted distinct additions.
P6	Agreement of two totals does not itself verify the history. Duplicate delivery and omitted receipts expose what a verifier needs.	Duplicate a receipt: naive receipt count grows, unique-event count does not. Omit a keeper: the visible union undercounts additions; restoring that keeper repairs the account. Distinguish this from a failure of integer arithmetic.

The three encounters will permit custom notation, input or claims. No timer, forced forgetting, arbitrary human memory score or inference about consciousness is part of the apparatus. A large numeral is loaded as a test case, never described as reached by counting from one. The interface must permit support to succeed as well as to fail.

What counts: predictions?

What counts: predictions