Track the whole increment history

Newer than the immediately previous value does not imply newer than every earlier value.

• Corollary 1: a defined increment produces a serial greater than or equal to its start, equal only for zero. Corollary 2: after a nonzero defined n and another defined m, no general older/newer conclusion follows relative to the original start, although the result is known not equal to it (§§4.1–4.2). This is a limit on a general inference, not a claim that every particular endpoint comparison is undefined.
• The published eight-bit chain 100→200→44 adds 100 twice. Each new serial is greater than its immediate predecessor, yet 44 is less than the original 100. In fact 100<200,200<44,44<100 forms a cycle under serial comparison. Sorting every possible serial as if this were an ordinary transitive comparator is unsound (§§3.2,4.2,5.2).
• Two defined increments of 64 from zero reach 128, an undefined comparison against zero. In contrast 0→60→120 has total increment 120 within the allowed 127 limit: Corollary 4 guarantees the final result is greater than the start. A small per-step increment alone is insufficient; the sum matters (§§4.2,4.4).
• Corollary 3 says a further increment leaves no generally known relationship to the original start. Chosen chain 0→100→200→0 uses increments 100,100,56, all individually defined; the last endpoint equals the original. These are offline arithmetic examples, not a prescribed DNS reset procedure (§4.3).