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Explore a mathematical conjecture - gather evidence, find counterexamples, or build toward a proof. Triggers on "explore", "investigate", "what if", "is it true that", "find pattern", "check if"

Determine convergence or divergence of series using ratio test, root test, comparison test, and integral test. Triggers on "series converges", "test for convergence", "ratio test", "root test", "comparison test", "integral test", "sum of 1/n"

Prove geometric theorems using coordinate geometry. Convert shapes to algebraic expressions, use distance formula, midpoint formula, and slope calculations. Triggers on "prove using coordinates", "analytic geometry", "distance formula", "show collinear", "prove perpendicular", "prove parallel"

Prove identities or existence using combinatorial counting - double counting, bijections, inclusion-exclusion. Triggers on "count", "number of ways", "how many", "bijection", "one-to-one correspondence", "combinatorial proof"

Prove statements directly by assuming the hypothesis and deriving the conclusion through logical steps. Triggers on "prove directly", "show that", "demonstrate", "verify", "simple proof"

Prove limit statements using epsilon-delta definitions. Triggers on "epsilon-delta", "limit", "prove continuous", "show limit equals", "formal limit proof"

Explain a proof or Lean code step-by-step for learning. Triggers on "explain", "how does this work", "teach me", "what does this mean", "walk me through", "I don't understand"

Prove results by considering minimal or maximal elements - the extreme case often has special properties. Triggers on "smallest", "largest", "minimal", "maximal", "least", "greatest", "extreme", "consider the minimum"

Breadth-first search — shortest path on unweighted graphs, level-order traversal, and the `visited` discipline that prevents O(2^n) blowups.

Binary search invariants, half-open intervals, and the `lo<hi` template that beats off-by-one bugs.

Depth-first search — recursive vs iterative, recursion-depth gotchas, three-color cycle detection, topological sort.

Dynamic programming — state design, memoization vs tabulation, dimension-reduction, and when DP is the wrong tool.

Pick the right traversal — BFS for unweighted shortest path, Dijkstra for weighted, A* for goal-directed, 0/1-BFS for binary weights.

Greedy algorithms — exchange-argument proofs, when greedy beats DP, classic patterns (interval scheduling, Huffman, scheduling).

Hash maps and sets — when O(1) lookup pays off, hash collisions, frozen keys, and hashing custom types.

Number-theory and bit-twiddling cheat-sheet — gcd, modular exponentiation, sieve, popcount, divisor enumeration, fast prime tests.

Use when the user wants to RESUME or CONTINUE prior coding-agent work — "resume my codex session", "continue where I left off in <project>", "what sessions ran in this folder", "pick up that grok conversation", or any ask for session/resume ids across agents (Claude Code, Codex, Grok, Cursor Agent, …). Surfaces every agent's recent sessions under a path with the exact resume command for each.

Search local coding-agent session history before acting. Use BEFORE an Edit or Write to a file, BEFORE a non-trivial Bash command (a build, migration, or destructive/long-running command), and whenever the user references a past decision ("what did we decide about X", "why is this done this way", "didn't we agree to Y"), a specific file, or "what worked last time" — cases where a prior session on this machine may already hold the decision, the failure mode, or the exact working command. Queries the local `stax memory` CLI (StackUnderflow) across every past Claude Code / Codex / Cursor session so you do not re-derive an answer, contradict an earlier choice, or repeat a known failure. Local and read-only; nothing leaves the machine.

Use BEFORE starting any non-trivial coding task in an existing project — feature work, refactors, bugfixes, or "look at this codebase" requests. Triggers when the user asks to add/change/fix something inside a repo (e.g. "add X to the dashboard", "refactor the auth flow", "fix the bug in cost calculation", "why is this slow"). Surfaces recent prior sessions in the same project so the agent isn't redoing work or contradicting decisions made in past sessions.

Use when the user references a SPECIFIC FILE in a coding task — "fix the bug in routes/cost.py", "what was that change to api.ts about", "refactor stackunderflow/store/queries.py", or any request that names a path. Surfaces past sessions that read or wrote that file so the work is grounded in prior context (recent edits, why the file is shaped that way, half-finished refactors).

Use when the user references a PAST DECISION, choice, or rationale — "what did we decide about caching?", "why is X done this way?", "didn't we agree to use Y?", "remind me how we handled Z before". Searches indexed message history across all prior sessions to find the conversation where the decision was made and surfaces the matching excerpt with timestamp.

Lean 4 formalization workflow for Erdős problem proofs. Use when formalizing a solution in Lean 4, checking existing formalizations, or setting up the Lean environment for proof verification.

Workflow for attempting to solve Erdős problems. Use when the user wants to work on a specific Erdős problem, analyze open problems, or find tractable problems to attempt.

Mathematical proof techniques library for working on Erdős problems. Use when attempting to solve combinatorics, number theory, graph theory, or geometry problems. Includes techniques from successful AI solutions.