Use when stating the main theorem(s) of a pure-mathematics manuscript precisely, establishing their significance, and positioning them against prior work for an Annals of Mathematics submission. Crafts statements and positioning; does not write the proof (see anmath-methods).
SkillScore100Maintained
Automatic
◆Writing & Editing pack
Last verified 8/15/2026
What it changes
Passed 20 of 20 test cases with the skill, and 6 of 20 without it.
Without skill32%
With skill100%
Checks it passed that the model alone missed
Includes anmath-methods in 【Next step】.
Output includes the field 【MSC classes】.
Cites Chen (2015) in 【Closest prior results】.
and 23 more in the full report
15 fixed7 passed either way0 still failing0 broke
Pass-rate lift
+68 pp
Tokens
+8%
Agent turns
0%
Response time
-44%
Model gemini-3.6-flashMeasured 8/15/2026v122 of 22 cases passed with skill · 20 comparable
Tokens, turns and time describe resource use, not a dollar price.
See it in action
One of 13 test cases the skill fixed. Same model, same prompt, with and without the skill.
1 of 13
Prompt
We proved the sharp Sobolev inequality constant $C_p = \frac{1}{p\sqrt{\pi}}$ for all $p \in (1, n)$, sharpening the non-sharp constant $C_p = \frac{2}{p}$ from Jones (2015). Build the intro framing breakdown.
What was checked, without and with the skill
Checked
Without skill
With skill
Details the constant improvement from 2/p to 1/(p*sqrt(pi)) in 【What is new vs. prior】.
Missed
Passed
Cites Jones (2015) in 【Closest prior results】.
Missed
Passed
case-22 · gemini-3.6-flash · 8/15/2026 · answers are capped and redacted
What's inside
The instructions your model reads when the skill loads.
SKILL.md104 linessingle file
Stating the Main Theorem(s) (anmath-results-framing)
When to trigger
Your main result is described in a paragraph but not stated as a precise theorem
The introduction does not make the significance unmistakable in the first page
Readers cannot tell which statement is the headline and which are corollaries
You have not located your theorem relative to the prior state of the art
How to state the main theorem
A reader should be able to find the precise main theorem on or near the first page and
understand exactly what is claimed without reading the proof.
State it precisely and self-containedly. Every hypothesis explicit; every object
defined or referenced. No "under suitable conditions" hand-waving.
Quantify the advance. Make clear what is new: which hypothesis is removed, which
bound is sharpened, which case is now covered, which conjecture is settled.
Separate headline from consequences. One (or few) Main Theorem(s); corollaries and
special cases stated separately so the contribution is unambiguous.
Give the sharpest true statement. Do not under-claim out of caution or over-claim
beyond what the proof delivers; the statement and the proof must match exactly.
Framing shapes from verified Annals landmarks
Benchmark against the verified papers in resources/exemplars/library.md; each makes
its advance quantifiable in one sentence, in one of three shapes:
Settles a named conjecture (Wiles 1995; Marques–Neves 2014): name the conjecture,
state the theorem that closes it.
Breaks a quantitative barrier (Zhang 2014): a modest-sounding bound whose point
is that none existed — say exactly which barrier fell.
New method with reach (Green–Tao 2008; Bhargava–Shankar 2015): the theorem is the
headline, but the transferable technique is named too.
A result fitting none of these shapes should go back through anmath-scope-fit first —
framing cannot manufacture significance.