Cyclic-chain length is computable for bounded finite examples
Family 314; scoped reading addendum, 9 October 2026 Australia/Brisbane. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
Source finding
The introduction defines cyclic length as the shortest subnormal subgroup chain with cyclic successive quotients and claims equality with chromatic fixed-point loss for every finite p-group, embedded subgroup and nonnegative height. A cyclic quotient of order p squared counts once. The source gives two differently embedded subgroups in C_(p squared) times C_p with losses two and one.
Applicability boundary
Abstract subgroup isomorphism type is insufficient. Exhaustive subgroup enumeration is a finite reference method, not a polynomial algorithm. The spectrum hypotheses and proof remain outside a subgroup calculator. No family formal-scope document is available.
Business decision
A small exact subgroup-chain utility is a viable research/teaching component; no lucrative standalone market has been established.
Exact sections read
These readings establish recorded source scope, not proof correctness. No independent Lean verification was run. Companion manuscripts and construction effectiveness remain separately tracked. See source metadata.