`saturate`¶

Saturate the stored rigorous point basis over a bounded prime range without requiring full mwrank descent.

Saturation improves/checks subgroup index. It does not normally add a new free-rank direction.

Range mode¶

sage -python -m rank42.cli saturate \
  --db rank42.db \
  --curve-id 123 \
  --min-prime 2 \
  --max-prime 100 \
  --timeout 900

Range mode asks the saturation engine to handle the configured range under one hard timeout.

sage -python -m rank42.cli saturate \
  --db rank42.db \
  --curve-id 123 \
  --mode ladder \
  --min-prime 2 \
  --max-prime 100 \
  --timeout 120

In ladder mode, the timeout applies per-prime step.

This is useful when you want progress/failure associated with individual primes.

Option	Default	Meaning
`--db`	`rank42.db`	Rank Hunter database
`--curve-id`	required	retained curve id
`--min-prime`	`2`	first saturation prime
`--max-prime`	`100`	final saturation prime
`--mode`	`range`	`range` or `ladder`
`--timeout`	`900`	range timeout or per-prime ladder timeout

Final output begins with:

RANK42_SATURATION=

The useful input is the current rigorous witness basis.

If the curve has many exact points but no complete certified basis, resolve Independence first.

A completed saturation result can report:

A nontrivial index means the original subgroup was not primitive over the searched range.

It does not mean rank increased.

A timeout means the requested range/step was not completed.

Do not mark the whole range “saturated” after a timeout.

A better basis can reduce arithmetic complexity and improve:

This is a conditioning benefit, not a new rank theorem.

Record: