Read the equation
Each next-state value is calculated from a previous-time neighbor: state one increments state seven, and state two decrements state one. Because updates are synchronous, a value must travel across ticks. This is a different system from both sequentially composing seven functions in one tick and averaging their outputs.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| s_1 | First stored state |
| s_2 | Second stored state |
| s_7 | Seventh stored state |
| t | Discrete time |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
6.4 A literal simultaneous ring does not equal the scalar average Consider seven independently stored scalar states updated synchronously: s1,t+1=s7,t+1, s2,t+1=s1,t−1. s3,t+1=s2,t, s4,t+1=s3,t. s5,t+1=1, s6,t+1=s5,t, s7,t+1=1/s6,t. At a valid equilibrium these equations give
Exact original notation
{s}_{1,t+1}={s}_{7,t}+1, {s}_{2,t+1}={s}_{1,t}-1.Sources & provenance
{s}_{1,t+1}={s}_{7,t}+1, {s}_{2,t+1}={s}_{1,t}-1.
{s}_{1,t+1}={s}_{7,t}+1, {s}_{2,t+1}={s}_{1,t}-1.