C.36.RP:5 - Archetypal Grounding

C.36.RP:5.1 - A replacement sensor and a changed interpretation

The following is a constructed laboratory case. A group infers position q from a sensor indication r under a linear working account. The earlier device has reference readings q=0, r=2 and q=1, r=5. They give r=3q+2, so indication 14 corresponds to position 4.

A replacement device has available reference readings q=0, r=4 and q=2, r=10. A saved notebook still returns 4 for indication 14. The group needs the method that relates a device’s indication to position.

The missing contribution is the replacement device’s relation. A technician supplies its reference readings and conditions. An AI obtains the slope (10-4)/(2-0)=3 and intercept 4. An engineer connects the resulting equation r=3q+4 to the device and infers q=(14-4)/3=10/3. The saved answer changes because the physical interpretation changed.

The group retains the two-point construction with its device and reference meanings and an obtainable way to perform each contribution. The technician need not derive every formula independently; the receiving engineer needs to recognize which device and account the formula concerns. The linear relation is a working assumption: two points determine its coefficients but leave empirical adequacy across a wider range open.

A later question about another range can use that retained construction to ask where the linear account is usable or what further account is needed. The current case finishes at the interpreted conditional position result; a new inquiry depends on the use that needs it.

C.36.RP:5.2 - Retain a rhythmic operation

In this constructed case, an ensemble uses an eight-pulse cycle with onsets at 0, 3 and 6. New participants can copy the recording. The next arrangement requires shifting each onset position by +2 modulo 8.

Adding two modulo eight gives 2, 5 and 0, or the ordered onset set 0, 2, 5. The operation depends on knowing the cycle, what an onset position means and how positions wrap at its end. Retaining those meanings lets a contributor produce the changed phrase.

One musician demonstrates the original and changed phrases while counting the cycle. Another participant may use written marks or a computational representation. The ensemble retains a way to obtain the rotation and perform it in the receiving arrangement. Its musical practice supplies the performance and judgement of fit.

The new phrase can become material for another variation. That continuation uses the operation and its means of performance. A claim about which phrase listeners find interesting adds the listener and musical-use question through E.10.INT.

C.36.RP:5.3 - Learn a strategy discovered by AI

Brinkmann and colleagues studied a machine-discovered strategy in a constrained reward-network task. Learners selected a demonstrator using available performance, watched and repeated its moves, attempted a solution, and then solved other networks. Nine of fifteen human-machine populations retained the strategy through the tested generations; six later lost it. This supports arranging receiving use while keeping later persistence open to observation. See Brinkmann et al., 2026.