This is classical Piezas input supply and a scoped fibre-identity test,
not a septuple or a new 20-root point. Read697_native_input_family.md and
711_general_piezas_result.md. All arithmetic is exact.

Run with Sage:
  sage -python 697_native_input_family.py
  sage -python 706_general_piezas_calibration.py
  sage -python 708_general_character_admission.py
  sage -python 709_correlated_extra_characters.py
  sage -python 710_product_one_linear_return.py
Run with ordinary Python:
  python 677_piezas_three_input.py
  python 707_general_piezas_fraction_replay.py

No network or external corpus is needed. Existing694/704 JSON values
are used to compare the independently simplified formulas.
