Technique overview

Goal test

After reading only the abstract, introduction and overview, a reviewer can: (a) restate the main idea in two sentences, (b) write down the key formula, (c) say where each prior work sits relative to it, (d) believe the main theorem is plausibly true. Ask reviewer-sim (generalist persona) to perform exactly this test.

Procedure

1. List the prior routes from LITERATURE.md (usually 2, sometimes 3). For each paper in each route write: its key identity/formula, its cost, and the one factual thing it leaves open. Verify each against the original paper.
2. Find the common object. Phrase all routes as acting on the same mathematical object or optimising the same objective (Eq. (1) of the introduction). If no common object exists, the "unification" story is forced; tell the human author and consider a different framing (e.g. "two orthogonal improvements that compose", supported by a measured composition).
3. Reduce to questions. "Whether the routes compose reduces to two questions: (i) ... (ii) ...". Questions must be precise enough that a theorem answers them.
4. One Insight per question. Heading = declarative sentence stating the answer. Body: observation → reformulation → key formula (copied from the body theorem) → conclusion → why the boundary case is tight or where it fails.
5. Figure. A grid/axis diagram (prior works as corners/points, ours as the new region) or a data-flow diagram of the new algorithm. Ask figure-artist for it; caption = one sentence stating placement.
6. Composition paragraph with the combined identity and cost.
7. Optional scope extender. One paragraph showing the technique applies to a neighbouring scheme, quantified by formula only (cheap, raises significance). Mark it clearly as not implemented if so.
8. Consistency check: grep each displayed formula in the body; string-compare.

Style rules

• Describe prior work per paper and mathematically; do not write a tutorial with "Why X is needed / Where the cost goes" headings.
• Use "Suppose ..." to introduce hypotheses before derivations.
• For density/asymptotic results: "asymptotic density ..., certified per instance".
• No new claims that the body does not prove; no numbers that the experiments section does not contain.
• Keep limitations as short remarks at the end of the relevant insight, not in the contribution list.

Output

paper/sections/overview.tex (or inside intro.tex), figure request in paper/figs/REQUESTS.md.

Examples: skills/paper-playbook/sections/05_technique_overview.md, skills/paper-playbook/examples/toy_overview_and_related.md.