`rank-bounds`¶

Run Rank Hunter's bounded rigorous rank-bounds pipeline on one retained curve.

This command is for upper-bound / exact-rank work, not rational-point discovery.

Basic use¶

sage -python -m rank42.cli rank-bounds \
  --db rank42.db \
  --curve-id 123 \
  --engine auto \
  --timeout 300

The command prints human progress plus a final machine-readable marker:

RANK42_RANK_RESULT=...

Parse the JSON after that marker in automation.

Preconditions¶

The curve id must refer to a retained curve with a valid stored five-term Weierstrass model.

Before spending significant time, inspect the current curve state:

rigorous lower bound;
existing upper-bound evidence;
exact rank if already closed;
prior engine failures/timeouts.

Options¶

Option	Default	Meaning
`--db`	`rank42.db`	Rank Hunter database
`--curve-id`	required	retained curve id
`--engine`	`auto`	`auto`, `pari`, or `mwrank`
`--timeout`	`300`	hard timeout for PARI/selected engine
`--mwrank-timeout`	`300`	hard timeout for mwrank
`--pari-stack-max-gib`	`4`	maximum PARI stack after overflow retry
`--escalate`	off	request deeper fallback chain
`--force`	off	ignore compatible cached evidence

Use the installed release's --help as parser authority.

Automatic mode¶

--engine auto is PARI-first.

The runner reduces the live rank state after each accepted evidence record.

If PARI closes the rank interval, no deeper engine is needed.

If PARI fails/times out, available fallbacks may run according to the release logic. Explicit --escalate requests deeper fallback work.

Cache behavior¶

Compatible prior evidence may prevent unnecessary recomputation.

Use --force only when you intentionally want another engine attempt on the same exact model/configuration class.

Do not use --force merely because you dislike the previous mathematical answer.

PARI stack limit¶

PARI can fail through stack exhaustion on large curves.

--pari-stack-max-gib places an upper bound on controlled stack escalation after an overflow.

This is a memory-safety budget, not a mathematical parameter.

Outcomes¶

Exact rank¶

If accepted rigorous lower and upper bounds meet, the curve state can close to exact rank.

Rigorous upper only¶

The result may improve the upper bound without closing the gap.

Timeout¶

Inconclusive. The existing lower/upper evidence remains.

Engine error¶

Operational failure. Do not reinterpret it as “rank = lower bound.”

Evidence conflict¶

If a new rigorous upper is below the existing rigorous lower, Rank Hunter flags the state as inconsistent for investigation.

Example: explicit PARI run¶

sage -python -m rank42.cli rank-bounds \
  --db "$PWD/rank42.db" \
  --curve-id 417 \
  --engine pari \
  --timeout 900 \
  --pari-stack-max-gib 6

Example: deliberate deeper escalation¶

sage -python -m rank42.cli rank-bounds \
  --db "$PWD/rank42.db" \
  --curve-id 417 \
  --engine auto \
  --timeout 300 \
  --mwrank-timeout 900 \
  --escalate

Scientific interpretation¶

This command can support statements such as:

PARI produced a rigorous rank upper bound 12; together with the certified lower bound 12, Rank Hunter records rank = 12.

It cannot support:

PARI timed out, so the rank must equal the lower bound.

See Descent & Rank Bounds.

rank-bounds¶