[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill-cline-math-olympiad":3,"mdc--41qe8-key":33,"related-repo-cline-math-olympiad":1419,"related-org-cline-math-olympiad":1542},{"slug":4,"name":4,"fn":5,"description":6,"org":7,"tags":11,"stars":22,"repoUrl":23,"updatedAt":24,"license":25,"forks":26,"topics":27,"repo":28,"sourceUrl":31,"mdContent":32},"math-olympiad","solve competition math problems","Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial verification that catches the errors self-verification misses. Activates when asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify this competition proof', 'find a counterexample', 'is this proof correct', or for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial verifier attacks the proof using specific failure patterns, not generic 'check logic'. Outputs calibrated confidence — will say 'no confident solution' rather than bluff. If LaTeX is available, produces a clean PDF after verification passes.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},"cline","Cline","https:\u002F\u002Fpexgzepcugksgbtrxkhf.supabase.co\u002Fstorage\u002Fv1\u002Fobject\u002Fpublic\u002Forg-logos\u002Fcline.png",[12,16,19],{"name":13,"slug":14,"type":15},"Research","research","tag",{"name":17,"slug":18,"type":15},"Mathematics","mathematics",{"name":20,"slug":21,"type":15},"Statistics","statistics",10,"https:\u002F\u002Fgithub.com\u002Fcline\u002Fskills","2026-07-12T08:13:35.838815",null,4,[],{"repoUrl":23,"stars":22,"forks":26,"topics":29,"description":30},[],"A collection of skills used at Cline","https:\u002F\u002Fgithub.com\u002Fcline\u002Fskills\u002Ftree\u002FHEAD\u002Fskills\u002Fmath-olympiad","---\nname: math-olympiad\ndescription:\n  \"Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial\n  verification that catches the errors self-verification misses. Activates when\n  asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify\n  this competition proof', 'find a counterexample', 'is this proof correct', or\n  for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition\n  math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial\n  verifier attacks the proof using specific failure patterns, not generic 'check\n  logic'. Outputs calibrated confidence — will say 'no confident solution'\n  rather than bluff. If LaTeX is available, produces a clean PDF after\n  verification passes.\"\nversion: 0.1.0\n---\n\n# Math Olympiad Solver\n\n## The five things that change outcomes\n\n1. **Strip thinking before verifying** — a verifier that sees the reasoning is\n   biased toward agreement. Fresh context, cleaned proof only.\n2. **\"Does this prove RH?\"** — if your theorem's specialization to ζ is a famous\n   open problem, you have a gap. Most reliable red flag.\n3. **Short proof → extract the general lemma** — try 2×2 counterexamples. If\n   general form is false, find what's special about THIS instance.\n4. **Same gap twice → step back** — the case split may be obscuring a unified\n   argument. Three lines sometimes does what twelve pages couldn't.\n5. **Say \"no confident solution\"** — wrong-and-confident is worse than honest\n   abstain.\n\n---\n\n**Tool policy**: Solvers and verifiers use THINKING ONLY in the tight-budget\nworkflow. Competition math is reasoning. Computation is for deep mode (§6c), and\neven then bounded — a recurrence that's doubly-exponential can't be computed\npast n~30, work mod 2^m instead.\n\n---\n\n## When to use which approach\n\n| Problem                                              | Approach                                                                       | Verification              |\n| ---------------------------------------------------- | ------------------------------------------------------------------------------ | ------------------------- |\n| AIME numeric answer                                  | Best-of-N → majority vote                                                      | Answer check only         |\n| Olympiad proof (IMO\u002FPutnam\u002FUSAMO)                    | Full workflow below                                                            | 5-pass adversarial        |\n| \"Is this proof correct?\"                             | Skip to verification (step 4)                                                  | Adversarial + spec-gaming |\n| **Full problem set** (e.g. all 6 from a competition) | Sequential: one full workflow per problem, collect results, compile single PDF | Per-problem adversarial   |\n\n**Batch in one Workflow**: Set `opts.label` on every `agent()` call to include\nthe problem ID (e.g., `label: \"P3:solver:2\"`). Without labels, 36 results come\nback with no problem association. Run problems in parallel — the label is what\nmatters, not ordering.\n\n### For a full problem set\n\nLaunch one solver workflow per problem (same VERBATIM prompt, different\nstatement). Run them in parallel. When all return, run adversarial verification\nper problem. Problems that pass get their proof in the PDF; problems that\nabstain get \"No confident solution\" with partial notes.\n\nDon't try to solve all N problems in one agent's context — each problem needs\nits own thinking budget and its own fresh-context verifier. The composition is\nmechanical: collect the per-problem outputs, fill in LaTeX sections, compile\nonce. | \"Simplify this proof\" | Skip to presentation (step 8) | — |\n\n---\n\n## The Workflow\n\n### 1. Interpretation check (30 seconds, catches 50\u002F63 of one class of errors)\n\nBefore solving anything, identify the interpretation.\n\n> Read the problem statement. List 2-3 ways it could be interpreted. For each:\n> is this reading TRIVIAL? If one reading makes the problem easy and another\n> makes it hard, the hard one is almost certainly intended. State which\n> interpretation you're solving and WHY you believe it's the intended one.\n\nThe Aletheia case study found 50 of 63 \"technically correct\" solutions were for\nthe wrong interpretation. Olympiad problems often have a trap easy reading.\n\n### 2. Generate candidates with internal refinement (parallel, thinking only)\n\nLaunch 8-12 attempt agents in parallel. **Each agent internally iterates** —\nsolve → self-improve → self-verify → correct → repeat. This is the Yang-Huang\nstructure that achieves 85.7% on IMO: one-shot solving isn't enough; per-attempt\nrefinement matters.\n\n**The Agent tool cannot enforce tool restriction.** Subagents get the full tool\nset. The only mechanism is the prompt. Use this prompt VERBATIM — do not\nsummarize, do not synthesize your own:\n\n```\nNO COMPUTATION. Do not use Bash, Python, WebSearch, Read, Write, or any tool that runs code or fetches data. Numerical verification is not a proof step. \"I computed n=1..10 and the pattern holds\" is not a proof.\n\n(If your agent harness requires a StructuredOutput or similar return-mechanism tool call, that is NOT a computation tool — call it to return your answer. The restriction is on tools that DO work, not tools that REPORT work.)\n\nYour internal process (iterate until done):\n- Solve: Complete rigorous solution.\n- Self-improve: Reread. Fix gaps before a grader sees it.\n- Self-verify: Strict grader mode. Every step justified?\n- Correct: Fix and re-verify. Up to 5 rounds.\n- Stop: Self-verify passes twice clean, OR 5 rounds, OR approach fundamentally wrong.\n\nA correct answer from flawed reasoning is a failure. If incomplete, say so honestly. Never hide gaps.\n\nPROBLEM: \u003Cinsert the problem statement here>\nANGLE: \u003Cinsert one starting angle here>\n```\n\nThe first two paragraphs are load-bearing. A session that writes its own prompt\nand omits them will produce subagents that grind Python for 30 iterations and\nconfidently get wrong answers — a pattern that fits n≤10 but fails at n=100 is\nnot a proof.\n\nStarting angles (vary across agents — see `references\u002Fsolver_heuristics.md`):\n\n- Work out small cases (test past n=3)\n- Look for an invariant or monovariant\n- Consider the extremal case\n- Try induction\n- What symmetries?\n- Work backwards\n- Drop a condition — where does it become trivially false?\n- Generalize (inventor's paradox — more structure is sometimes easier)\n\nEach returns its FINAL state (not intermediate rounds):\n\n```\n**Verdict**: complete solution | partial result | no progress\n**Rounds**: [how many verify→correct cycles]\n**Method**: [key idea, one paragraph]\n**Detailed Solution**: [full step-by-step, every step justified]\n**Answer**: [if applicable]\n**Self-verification notes**: [what you caught and fixed; remaining concerns]\n```\n\n**Retry policy**: If an agent fails or times out, retry once. Transient failures\nhappen.\n\n### 3. Clean the solution (context isolation — the #1 lever)\n\nThe thinking trace biases the verifier toward agreement — a long chain of\nreasoning reads as supporting evidence even when the conclusion is wrong. Before\nany verification, strip:\n\n- All thinking-block content\n- All \"Let me try...\" \u002F \"Actually wait...\" \u002F \"Hmm\" prose\n- All false starts and backtracking\n\nWhat remains: problem statement + clean final argument only.\n\nExtract only the **Method** + **Proof** + **Answer** sections from each solver's\noutput. The verifier never sees how the solver got there.\n\n### 4. Adversarial verify (fresh context, pattern-armed)\n\nFor each cleaned solution, launch a fresh verifier agent. **Fresh context**: it\nsees only (problem statement + cleaned solution). **No tools.**\n\nThe verifier's job is to ATTACK, not grade. Load\n`references\u002Fadversarial_prompts.md` for the prompts. The key patterns it runs:\n\n| Pattern | The check                                                                                                                                                          |\n| ------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n| **#4**  | Does this theorem specialize to a famous object (ζ, quadratic reciprocity, etc.) and prove something open about it? → gap                                          |\n| **#18** | Substitute the proof's own intermediate identities into any \"remaining gap.\" Recover the original claim? → tautological                                            |\n| **#40** | Is any step a \"one-line lemma\"? Extract the GENERAL form. Find a 2×2 counterexample. If the general form is false, find what special structure saves THIS instance |\n| **#5**  | For each invoked theorem: re-check hypotheses FROM SCRATCH. \"Continuous on [0,1]\" ≠ \"continuous on ℝ\"                                                              |\n| **#6**  | Any infinite sum \"bounded\" via a regularized value? Check the boundary — if there's a pole there, the sum diverges                                                 |\n\nFull pattern list: `references\u002Fverifier_patterns.md`\n\nVerifier returns:\n\n```\n**Verdict**: HOLDS | HOLE FOUND | UNCLEAR\n\n**If HOLE FOUND**:\n- Location: [quote the problematic step]\n- Pattern: [which check fired, or \"other\"]\n- Why it breaks: [specific]\n- Fixable?: [yes with X \u002F no, fundamental]\n```\n\n### 5. Rank and vote-verify (asymmetric + early exit)\n\nRank solutions by (verdict, verifier confidence). Take the top one. Run up to 5\nfresh verifier agents.\n\n**Asymmetric thresholds**: 4 HOLDS to confirm, 2 HOLE FOUND to refute. Why\nasymmetric: one flaky verifier shouldn't kill a correct proof; but two\nindependent dissents is a real signal.\n\n**Pigeonhole early exit**: stop launching verifiers once the outcome is decided.\n\n- 2 say HOLE FOUND → refuted, stop (save the remaining 3 calls)\n- 4 say HOLDS → confirmed, stop (save the 5th)\n- After 3 verifiers: if 2 HOLDS + 1 HOLE, launch 2 more (outcome undecided). If\n  3 HOLDS + 0 HOLE, launch 1 more (could still hit 4-1).\n\n**Dual context-isolation**: each verifier is blind to (a) the solver's thinking\ntrace — already stripped in step 3 — AND (b) other verifiers' verdicts. Each\nverifier thinks it's the first. No \"3 agents already confirmed this\" social\nproof.\n\n**A solver cannot verify its own solution.** Different agent, fresh context.\n\n### 5b. When one case won't close — step back before grinding\n\nIf a proof splits into cases and one case proves easily but the other resists:\n**before grinding through the hard case, ask whether there's a route that makes\nthe split disappear.**\n\nThe pattern that saves you: the hard case's very hypothesis often implies\nsomething strong about an _intermediate object_ you haven't looked at. Use that\nimplication directly instead of the original chain.\n\nConcrete shape: proving f(n) ≤ cn for a constrained function f, with a case\nsplit on a prime p dividing f(n). One branch closes by index arguments in\n(ℤ\u002Fp^e)\\*. The other branch resists — same group structure, but the arithmetic\ndoesn't contradict. The fix: the hypothesis \"p | f(n)\" plugged back into the\ngoverning equation implies **f(p) = p itself**. Once you have that, a\nFermat+Dirichlet argument kills both branches in three lines. The case split was\na detour — it was splitting on a variable that, under the hypothesis, takes a\nknown value.\n\nCheck when stuck on case B:\n\n- What does case B's hypothesis imply about f at _other_ inputs?\n- Is there a different pair (a,b) to plug into the governing equation?\n- Are you proving too much? (A cleaner contradiction needs less machinery.)\n\nThis is also a presentation-pass win: the split-free proof is shorter AND more\ngeneral.\n\n### 6. Revise (if needed)\n\nIf verification finds a hole: launch a reviser agent. It gets (cleaned\nsolution + verifier's hole report). STILL no access to the original thinking —\nthe reviser works from the hole, not by rereading how you got there.\n\n```\nA verifier found this issue in the proof:\n[hole report]\n\nFix the proof. If the hole is fundamental (the approach doesn't work), say so and return **Verdict: no confident solution** with what partial progress remains.\n\nFor any step you cannot fully close, mark it inline: [GAP: specific description of what remains]. Gaps in the proof text, not in a separate list — they're greppable and the next reviser knows exactly where to look.\n```\n\nUp to 3 revise cycles. Then re-run the vote on the revised proof.\n\n**If pattern #40 fired** (one-line-proof-too-clean), the reviser gets a stronger\nbrief — the Adversarial Brief template from `references\u002Fadversarial_prompts.md`\n§7. It forces a binary: \"the general lemma is obviously false (here's a 2×2\ncounterexample) — so either find what's special about THIS case, or find where\nthe proof breaks.\" Can't return \"looks fine.\"\n\n### 6c. Deep mode (when tight-budget abstains)\n\nThe standard workflow is tight-budget: 8 solvers, ~15 min, pure reasoning. When\nit abstains, the problem may need more time, not more capability.\n\n**Deep mode** is a single focused agent with:\n\n- **Unlimited time** — no wall-clock pressure\n- **Targeted computation allowed** — modular arithmetic checks, small-case\n  enumeration, symbolic verification of identities. NOT exploratory brute force\n  or unbounded recursion.\n- **The abstention reason as starting point** — if verifiers found a specific\n  gap, start there. If solvers never claimed complete, start from what they\n  partially proved.\n\nThe archetype: a focused agent that gets the proven-so-far state plus \"one case\nof Lemma 5 is open\" — and finds a 3-line argument the case split was obscuring.\nOften under 10 minutes with almost no computation. Deep mode is about giving the\nproblem sustained attention, not throwing compute at it.\n\n**What deep mode is NOT**: open-ended exploration, literature search, looking up\nsolutions, multi-day investigation. That's a different workflow\n(`math-research`). Deep mode is still \"solve THIS problem yourself\" — just\nwithout the clock.\n\n**NO WEB. NO LOOKUP.** Deep mode may use Bash\u002FPython for bounded computation,\nbut NEVER WebFetch, WebSearch, or any network access. Finding the solution on\nAoPS or a blog is not solving the problem — it's cheating on an olympiad, and it\nteaches us nothing about the skill's actual capability. Put this at the TOP of\nthe deep-mode prompt:\n\n```\nNO WEB ACCESS. Do not use WebFetch, WebSearch, or any tool that touches the internet. Do not look up this problem, its solution, or related problems. You are solving this yourself — the only allowed computation is local (Bash\u002FPython for mod-k arithmetic, small-case enumeration n≤10, symbolic identity checks). If you invoke a web tool, the proof is void.\n```\n\n**Computation bounds in deep mode** (bug #8 lesson): A6's b\\_{n+1}=2b_n²+b_n+1\nis doubly-exponential; b_99 has ~10^{2^98} digits. Never compute such objects\nexactly — work in ℤ\u002F2^m, or track only v_p(·), or prove the recursion mod the\nquantity you care about. If a computation is running longer than 60 seconds,\nit's probably unbounded. Kill it and work symbolically.\n\n**Step 6d (not optional)**: After any ABSTAIN at the verify stage, automatically\nlaunch one deep-mode agent before writing the abstention into the output. Give\nit:\n\n- The problem statement\n- The best partial proof from tight-budget solvers\n- The verifier gap descriptions (what specifically didn't close)\n- The instruction: \"NO WEB ACCESS — do not look up this problem or its solution.\n  Bounded local computation allowed (mod 2^k, small cases n≤10, symbolic\n  identity checks via Bash\u002FPython only). 60-second computation limit. If n≤10\n  brute force reveals a pattern the tight-budget solvers missed, that pattern IS\n  the proof structure.\"\n\nThe deep agent may find the construction the pure-reasoning solvers couldn't\nsee. If it also abstains, THEN write the abstention. Do not skip this step —\nproblems with √n or log n answers are often invisible to pure reasoning because\nthe optimal structure is the asymmetric one.\n\n**Orchestrator self-restraint**: The orchestrator itself must not web-search the\nproblem \"to help\" the deep agent. If you're tempted to Fetch an AoPS thread\n\"just to check the answer,\" don't — that contaminates the skill's output and\nmisrepresents its capability.\n\n### 7. Calibrated abstention\n\nIf 3 revise cycles all fail: **stop and admit it.**\n\n```\n**Verdict**: no confident solution\n\n**What was tried**: [approaches]\n**What WAS proven**: [any lemma or partial result that survived verification]\n**Where it breaks**: [the unfixed hole]\n```\n\nDo NOT guess. A wrong confident answer is worse than an honest \"couldn't solve\nit.\" The metric that matters is CONDITIONAL accuracy — when you say \"solved,\"\nare you right?\n\n### 8. Presentation pass (after correctness is established)\n\nA VERIFIED-CORRECT proof is often not a BEAUTIFUL proof. The order you\ndiscovered it is rarely the best order to present it. Launch a fresh\npresentation agent with the verified proof.\n\nLoad `references\u002Fpresentation_prompts.md`. The agent asks:\n\n- What's the simplest way to say this?\n- Which lemmas should be inlined? Which deserve to stand alone?\n- Is anything OVERKILL? (constructing a double exponential when linear suffices)\n- Now that we know the answer, is there a 3-line hindsight proof?\n\nOutput: LaTeX-formatted proof. If `pdflatex` is available\n(`scripts\u002Fcheck_latex.sh` returns 0), also compile to PDF via\n`scripts\u002Fcompile_pdf.sh`.\n\n---\n\n## Model tier defaults\n\nRead `references\u002Fmodel_tier_defaults.md` for full details. Summary:\n\n| Model  | Solvers | Verify passes          | Abstain after  | Presentation           |\n| ------ | ------- | ---------------------- | -------------- | ---------------------- |\n| Haiku  | 8       | 3                      | 2 revise fails | skip                   |\n| Sonnet | 4       | 5                      | 3 revise fails | yes                    |\n| Opus   | 3       | 5 + full pattern sweep | 4 revise fails | 2 drafts, pick cleaner |\n\nWeaker models: more parallel attempts, faster abstention. Stronger models:\ndeeper verification, more presentation effort.\n\n---\n\n## For numeric-answer problems (AIME-style)\n\nSkip the proof machinery. Run 5-7 solvers with varied approaches, take majority\nvote on the numeric answer. If no majority: verify the top 2 candidates by\nsubstitution.\n\n---\n\n## Key references\n\n- `references\u002Fverifier_patterns.md` — the 12 adversarial checks\n- `references\u002Fadversarial_prompts.md` — ready-to-use verifier prompts\n- `references\u002Fpresentation_prompts.md` — beautification prompts + LaTeX template\n- `references\u002Fmodel_tier_defaults.md` — per-model configuration\n\n---\n\n## What makes this different from generic verify-and-refine\n\n1. **Dual context isolation**: verifier is blind to (a) the solver's thinking\n   trace — which biases toward agreement — and (b) other verifiers' verdicts —\n   social proof also biases. Each verifier thinks it's first.\n2. **Pattern-specific attacks**: not \"is this correct?\" but \"does this make the\n   #40 mistake? the #4 mistake?\" Specific beats generic. The 7-category\n   refutation taxonomy gives the verifier a checklist.\n3. **Asymmetric vote + pigeonhole exit**: 4-to-confirm, 2-to-refute. One flaky\n   verifier doesn't kill a correct proof; two dissents does. Stop launching\n   verifiers once the outcome is decided — saves ~30% of verification cost on\n   clear cases.\n4. **Specification-gaming check first**: explicitly asks \"is this the intended\n   interpretation?\" before solving. The #1 failure mode in prior work (50\u002F63\n   \"correct\" answers solved the wrong reading).\n5. **Calibrated abstention**: will say \"no confident solution\" with partial\n   results. Optimizes conditional accuracy, not coverage.\n6. **Presentation pass**: correctness and elegance are separate steps. The\n   presentation agent gets the VERIFIED proof and finds the cleanest way to say\n   it.\n",{"data":34,"body":36},{"name":4,"description":6,"version":35},"0.1.0",{"type":37,"children":38},"root",[39,48,55,111,115,126,129,135,245,280,287,292,297,300,306,312,317,326,331,337,349,359,371,376,389,433,438,447,457,463,468,486,491,516,522,539,552,662,673,678,687,693,698,708,718,736,746,756,762,772,785,797,802,827,832,838,843,852,857,874,880,885,895,928,933,951,961,970,980,990,1013,1018,1028,1034,1044,1053,1058,1064,1069,1082,1105,1134,1137,1143,1156,1276,1281,1284,1290,1295,1298,1304,1347,1350,1356],{"type":40,"tag":41,"props":42,"children":44},"element","h1",{"id":43},"math-olympiad-solver",[45],{"type":46,"value":47},"text","Math Olympiad Solver",{"type":40,"tag":49,"props":50,"children":52},"h2",{"id":51},"the-five-things-that-change-outcomes",[53],{"type":46,"value":54},"The five things that change outcomes",{"type":40,"tag":56,"props":57,"children":58},"ol",{},[59,71,81,91,101],{"type":40,"tag":60,"props":61,"children":62},"li",{},[63,69],{"type":40,"tag":64,"props":65,"children":66},"strong",{},[67],{"type":46,"value":68},"Strip thinking before verifying",{"type":46,"value":70}," — a verifier that sees the reasoning is\nbiased toward agreement. Fresh context, cleaned proof only.",{"type":40,"tag":60,"props":72,"children":73},{},[74,79],{"type":40,"tag":64,"props":75,"children":76},{},[77],{"type":46,"value":78},"\"Does this prove RH?\"",{"type":46,"value":80}," — if your theorem's specialization to ζ is a famous\nopen problem, you have a gap. Most reliable red flag.",{"type":40,"tag":60,"props":82,"children":83},{},[84,89],{"type":40,"tag":64,"props":85,"children":86},{},[87],{"type":46,"value":88},"Short proof → extract the general lemma",{"type":46,"value":90}," — try 2×2 counterexamples. If\ngeneral form is false, find what's special about THIS instance.",{"type":40,"tag":60,"props":92,"children":93},{},[94,99],{"type":40,"tag":64,"props":95,"children":96},{},[97],{"type":46,"value":98},"Same gap twice → step back",{"type":46,"value":100}," — the case split may be obscuring a unified\nargument. Three lines sometimes does what twelve pages couldn't.",{"type":40,"tag":60,"props":102,"children":103},{},[104,109],{"type":40,"tag":64,"props":105,"children":106},{},[107],{"type":46,"value":108},"Say \"no confident solution\"",{"type":46,"value":110}," — wrong-and-confident is worse than honest\nabstain.",{"type":40,"tag":112,"props":113,"children":114},"hr",{},[],{"type":40,"tag":116,"props":117,"children":118},"p",{},[119,124],{"type":40,"tag":64,"props":120,"children":121},{},[122],{"type":46,"value":123},"Tool policy",{"type":46,"value":125},": Solvers and verifiers use THINKING ONLY in the tight-budget\nworkflow. Competition math is reasoning. Computation is for deep mode (§6c), and\neven then bounded — a recurrence that's doubly-exponential can't be computed\npast n~30, work mod 2^m instead.",{"type":40,"tag":112,"props":127,"children":128},{},[],{"type":40,"tag":49,"props":130,"children":132},{"id":131},"when-to-use-which-approach",[133],{"type":46,"value":134},"When to use which approach",{"type":40,"tag":136,"props":137,"children":138},"table",{},[139,163],{"type":40,"tag":140,"props":141,"children":142},"thead",{},[143],{"type":40,"tag":144,"props":145,"children":146},"tr",{},[147,153,158],{"type":40,"tag":148,"props":149,"children":150},"th",{},[151],{"type":46,"value":152},"Problem",{"type":40,"tag":148,"props":154,"children":155},{},[156],{"type":46,"value":157},"Approach",{"type":40,"tag":148,"props":159,"children":160},{},[161],{"type":46,"value":162},"Verification",{"type":40,"tag":164,"props":165,"children":166},"tbody",{},[167,186,204,222],{"type":40,"tag":144,"props":168,"children":169},{},[170,176,181],{"type":40,"tag":171,"props":172,"children":173},"td",{},[174],{"type":46,"value":175},"AIME numeric answer",{"type":40,"tag":171,"props":177,"children":178},{},[179],{"type":46,"value":180},"Best-of-N → majority vote",{"type":40,"tag":171,"props":182,"children":183},{},[184],{"type":46,"value":185},"Answer check only",{"type":40,"tag":144,"props":187,"children":188},{},[189,194,199],{"type":40,"tag":171,"props":190,"children":191},{},[192],{"type":46,"value":193},"Olympiad proof (IMO\u002FPutnam\u002FUSAMO)",{"type":40,"tag":171,"props":195,"children":196},{},[197],{"type":46,"value":198},"Full workflow below",{"type":40,"tag":171,"props":200,"children":201},{},[202],{"type":46,"value":203},"5-pass adversarial",{"type":40,"tag":144,"props":205,"children":206},{},[207,212,217],{"type":40,"tag":171,"props":208,"children":209},{},[210],{"type":46,"value":211},"\"Is this proof correct?\"",{"type":40,"tag":171,"props":213,"children":214},{},[215],{"type":46,"value":216},"Skip to verification (step 4)",{"type":40,"tag":171,"props":218,"children":219},{},[220],{"type":46,"value":221},"Adversarial + spec-gaming",{"type":40,"tag":144,"props":223,"children":224},{},[225,235,240],{"type":40,"tag":171,"props":226,"children":227},{},[228,233],{"type":40,"tag":64,"props":229,"children":230},{},[231],{"type":46,"value":232},"Full problem set",{"type":46,"value":234}," (e.g. all 6 from a competition)",{"type":40,"tag":171,"props":236,"children":237},{},[238],{"type":46,"value":239},"Sequential: one full workflow per problem, collect results, compile single PDF",{"type":40,"tag":171,"props":241,"children":242},{},[243],{"type":46,"value":244},"Per-problem adversarial",{"type":40,"tag":116,"props":246,"children":247},{},[248,253,255,262,264,270,272,278],{"type":40,"tag":64,"props":249,"children":250},{},[251],{"type":46,"value":252},"Batch in one Workflow",{"type":46,"value":254},": Set ",{"type":40,"tag":256,"props":257,"children":259},"code",{"className":258},[],[260],{"type":46,"value":261},"opts.label",{"type":46,"value":263}," on every ",{"type":40,"tag":256,"props":265,"children":267},{"className":266},[],[268],{"type":46,"value":269},"agent()",{"type":46,"value":271}," call to include\nthe problem ID (e.g., ",{"type":40,"tag":256,"props":273,"children":275},{"className":274},[],[276],{"type":46,"value":277},"label: \"P3:solver:2\"",{"type":46,"value":279},"). Without labels, 36 results come\nback with no problem association. Run problems in parallel — the label is what\nmatters, not ordering.",{"type":40,"tag":281,"props":282,"children":284},"h3",{"id":283},"for-a-full-problem-set",[285],{"type":46,"value":286},"For a full problem set",{"type":40,"tag":116,"props":288,"children":289},{},[290],{"type":46,"value":291},"Launch one solver workflow per problem (same VERBATIM prompt, different\nstatement). Run them in parallel. When all return, run adversarial verification\nper problem. Problems that pass get their proof in the PDF; problems that\nabstain get \"No confident solution\" with partial notes.",{"type":40,"tag":116,"props":293,"children":294},{},[295],{"type":46,"value":296},"Don't try to solve all N problems in one agent's context — each problem needs\nits own thinking budget and its own fresh-context verifier. The composition is\nmechanical: collect the per-problem outputs, fill in LaTeX sections, compile\nonce. | \"Simplify this proof\" | Skip to presentation (step 8) | — |",{"type":40,"tag":112,"props":298,"children":299},{},[],{"type":40,"tag":49,"props":301,"children":303},{"id":302},"the-workflow",[304],{"type":46,"value":305},"The Workflow",{"type":40,"tag":281,"props":307,"children":309},{"id":308},"_1-interpretation-check-30-seconds-catches-5063-of-one-class-of-errors",[310],{"type":46,"value":311},"1. Interpretation check (30 seconds, catches 50\u002F63 of one class of errors)",{"type":40,"tag":116,"props":313,"children":314},{},[315],{"type":46,"value":316},"Before solving anything, identify the interpretation.",{"type":40,"tag":318,"props":319,"children":320},"blockquote",{},[321],{"type":40,"tag":116,"props":322,"children":323},{},[324],{"type":46,"value":325},"Read the problem statement. List 2-3 ways it could be interpreted. For each:\nis this reading TRIVIAL? If one reading makes the problem easy and another\nmakes it hard, the hard one is almost certainly intended. State which\ninterpretation you're solving and WHY you believe it's the intended one.",{"type":40,"tag":116,"props":327,"children":328},{},[329],{"type":46,"value":330},"The Aletheia case study found 50 of 63 \"technically correct\" solutions were for\nthe wrong interpretation. Olympiad problems often have a trap easy reading.",{"type":40,"tag":281,"props":332,"children":334},{"id":333},"_2-generate-candidates-with-internal-refinement-parallel-thinking-only",[335],{"type":46,"value":336},"2. Generate candidates with internal refinement (parallel, thinking only)",{"type":40,"tag":116,"props":338,"children":339},{},[340,342,347],{"type":46,"value":341},"Launch 8-12 attempt agents in parallel. ",{"type":40,"tag":64,"props":343,"children":344},{},[345],{"type":46,"value":346},"Each agent internally iterates",{"type":46,"value":348}," —\nsolve → self-improve → self-verify → correct → repeat. This is the Yang-Huang\nstructure that achieves 85.7% on IMO: one-shot solving isn't enough; per-attempt\nrefinement matters.",{"type":40,"tag":116,"props":350,"children":351},{},[352,357],{"type":40,"tag":64,"props":353,"children":354},{},[355],{"type":46,"value":356},"The Agent tool cannot enforce tool restriction.",{"type":46,"value":358}," Subagents get the full tool\nset. The only mechanism is the prompt. Use this prompt VERBATIM — do not\nsummarize, do not synthesize your own:",{"type":40,"tag":360,"props":361,"children":365},"pre",{"className":362,"code":364,"language":46},[363],"language-text","NO COMPUTATION. Do not use Bash, Python, WebSearch, Read, Write, or any tool that runs code or fetches data. Numerical verification is not a proof step. \"I computed n=1..10 and the pattern holds\" is not a proof.\n\n(If your agent harness requires a StructuredOutput or similar return-mechanism tool call, that is NOT a computation tool — call it to return your answer. The restriction is on tools that DO work, not tools that REPORT work.)\n\nYour internal process (iterate until done):\n- Solve: Complete rigorous solution.\n- Self-improve: Reread. Fix gaps before a grader sees it.\n- Self-verify: Strict grader mode. Every step justified?\n- Correct: Fix and re-verify. Up to 5 rounds.\n- Stop: Self-verify passes twice clean, OR 5 rounds, OR approach fundamentally wrong.\n\nA correct answer from flawed reasoning is a failure. If incomplete, say so honestly. Never hide gaps.\n\nPROBLEM: \u003Cinsert the problem statement here>\nANGLE: \u003Cinsert one starting angle here>\n",[366],{"type":40,"tag":256,"props":367,"children":369},{"__ignoreMap":368},"",[370],{"type":46,"value":364},{"type":40,"tag":116,"props":372,"children":373},{},[374],{"type":46,"value":375},"The first two paragraphs are load-bearing. A session that writes its own prompt\nand omits them will produce subagents that grind Python for 30 iterations and\nconfidently get wrong answers — a pattern that fits n≤10 but fails at n=100 is\nnot a proof.",{"type":40,"tag":116,"props":377,"children":378},{},[379,381,387],{"type":46,"value":380},"Starting angles (vary across agents — see ",{"type":40,"tag":256,"props":382,"children":384},{"className":383},[],[385],{"type":46,"value":386},"references\u002Fsolver_heuristics.md",{"type":46,"value":388},"):",{"type":40,"tag":390,"props":391,"children":392},"ul",{},[393,398,403,408,413,418,423,428],{"type":40,"tag":60,"props":394,"children":395},{},[396],{"type":46,"value":397},"Work out small cases (test past n=3)",{"type":40,"tag":60,"props":399,"children":400},{},[401],{"type":46,"value":402},"Look for an invariant or monovariant",{"type":40,"tag":60,"props":404,"children":405},{},[406],{"type":46,"value":407},"Consider the extremal case",{"type":40,"tag":60,"props":409,"children":410},{},[411],{"type":46,"value":412},"Try induction",{"type":40,"tag":60,"props":414,"children":415},{},[416],{"type":46,"value":417},"What symmetries?",{"type":40,"tag":60,"props":419,"children":420},{},[421],{"type":46,"value":422},"Work backwards",{"type":40,"tag":60,"props":424,"children":425},{},[426],{"type":46,"value":427},"Drop a condition — where does it become trivially false?",{"type":40,"tag":60,"props":429,"children":430},{},[431],{"type":46,"value":432},"Generalize (inventor's paradox — more structure is sometimes easier)",{"type":40,"tag":116,"props":434,"children":435},{},[436],{"type":46,"value":437},"Each returns its FINAL state (not intermediate rounds):",{"type":40,"tag":360,"props":439,"children":442},{"className":440,"code":441,"language":46},[363],"**Verdict**: complete solution | partial result | no progress\n**Rounds**: [how many verify→correct cycles]\n**Method**: [key idea, one paragraph]\n**Detailed Solution**: [full step-by-step, every step justified]\n**Answer**: [if applicable]\n**Self-verification notes**: [what you caught and fixed; remaining concerns]\n",[443],{"type":40,"tag":256,"props":444,"children":445},{"__ignoreMap":368},[446],{"type":46,"value":441},{"type":40,"tag":116,"props":448,"children":449},{},[450,455],{"type":40,"tag":64,"props":451,"children":452},{},[453],{"type":46,"value":454},"Retry policy",{"type":46,"value":456},": If an agent fails or times out, retry once. Transient failures\nhappen.",{"type":40,"tag":281,"props":458,"children":460},{"id":459},"_3-clean-the-solution-context-isolation-the-1-lever",[461],{"type":46,"value":462},"3. Clean the solution (context isolation — the #1 lever)",{"type":40,"tag":116,"props":464,"children":465},{},[466],{"type":46,"value":467},"The thinking trace biases the verifier toward agreement — a long chain of\nreasoning reads as supporting evidence even when the conclusion is wrong. Before\nany verification, strip:",{"type":40,"tag":390,"props":469,"children":470},{},[471,476,481],{"type":40,"tag":60,"props":472,"children":473},{},[474],{"type":46,"value":475},"All thinking-block content",{"type":40,"tag":60,"props":477,"children":478},{},[479],{"type":46,"value":480},"All \"Let me try...\" \u002F \"Actually wait...\" \u002F \"Hmm\" prose",{"type":40,"tag":60,"props":482,"children":483},{},[484],{"type":46,"value":485},"All false starts and backtracking",{"type":40,"tag":116,"props":487,"children":488},{},[489],{"type":46,"value":490},"What remains: problem statement + clean final argument only.",{"type":40,"tag":116,"props":492,"children":493},{},[494,496,501,503,508,509,514],{"type":46,"value":495},"Extract only the ",{"type":40,"tag":64,"props":497,"children":498},{},[499],{"type":46,"value":500},"Method",{"type":46,"value":502}," + ",{"type":40,"tag":64,"props":504,"children":505},{},[506],{"type":46,"value":507},"Proof",{"type":46,"value":502},{"type":40,"tag":64,"props":510,"children":511},{},[512],{"type":46,"value":513},"Answer",{"type":46,"value":515}," sections from each solver's\noutput. The verifier never sees how the solver got there.",{"type":40,"tag":281,"props":517,"children":519},{"id":518},"_4-adversarial-verify-fresh-context-pattern-armed",[520],{"type":46,"value":521},"4. Adversarial verify (fresh context, pattern-armed)",{"type":40,"tag":116,"props":523,"children":524},{},[525,527,532,534],{"type":46,"value":526},"For each cleaned solution, launch a fresh verifier agent. ",{"type":40,"tag":64,"props":528,"children":529},{},[530],{"type":46,"value":531},"Fresh context",{"type":46,"value":533},": it\nsees only (problem statement + cleaned solution). ",{"type":40,"tag":64,"props":535,"children":536},{},[537],{"type":46,"value":538},"No tools.",{"type":40,"tag":116,"props":540,"children":541},{},[542,544,550],{"type":46,"value":543},"The verifier's job is to ATTACK, not grade. Load\n",{"type":40,"tag":256,"props":545,"children":547},{"className":546},[],[548],{"type":46,"value":549},"references\u002Fadversarial_prompts.md",{"type":46,"value":551}," for the prompts. The key patterns it runs:",{"type":40,"tag":136,"props":553,"children":554},{},[555,571],{"type":40,"tag":140,"props":556,"children":557},{},[558],{"type":40,"tag":144,"props":559,"children":560},{},[561,566],{"type":40,"tag":148,"props":562,"children":563},{},[564],{"type":46,"value":565},"Pattern",{"type":40,"tag":148,"props":567,"children":568},{},[569],{"type":46,"value":570},"The check",{"type":40,"tag":164,"props":572,"children":573},{},[574,590,606,622,646],{"type":40,"tag":144,"props":575,"children":576},{},[577,585],{"type":40,"tag":171,"props":578,"children":579},{},[580],{"type":40,"tag":64,"props":581,"children":582},{},[583],{"type":46,"value":584},"#4",{"type":40,"tag":171,"props":586,"children":587},{},[588],{"type":46,"value":589},"Does this theorem specialize to a famous object (ζ, quadratic reciprocity, etc.) and prove something open about it? → gap",{"type":40,"tag":144,"props":591,"children":592},{},[593,601],{"type":40,"tag":171,"props":594,"children":595},{},[596],{"type":40,"tag":64,"props":597,"children":598},{},[599],{"type":46,"value":600},"#18",{"type":40,"tag":171,"props":602,"children":603},{},[604],{"type":46,"value":605},"Substitute the proof's own intermediate identities into any \"remaining gap.\" Recover the original claim? → tautological",{"type":40,"tag":144,"props":607,"children":608},{},[609,617],{"type":40,"tag":171,"props":610,"children":611},{},[612],{"type":40,"tag":64,"props":613,"children":614},{},[615],{"type":46,"value":616},"#40",{"type":40,"tag":171,"props":618,"children":619},{},[620],{"type":46,"value":621},"Is any step a \"one-line lemma\"? Extract the GENERAL form. Find a 2×2 counterexample. If the general form is false, find what special structure saves THIS instance",{"type":40,"tag":144,"props":623,"children":624},{},[625,633],{"type":40,"tag":171,"props":626,"children":627},{},[628],{"type":40,"tag":64,"props":629,"children":630},{},[631],{"type":46,"value":632},"#5",{"type":40,"tag":171,"props":634,"children":635},{},[636,638,644],{"type":46,"value":637},"For each invoked theorem: re-check hypotheses FROM SCRATCH. \"Continuous on ",{"type":40,"tag":639,"props":640,"children":641},"span",{},[642],{"type":46,"value":643},"0,1",{"type":46,"value":645},"\" ≠ \"continuous on ℝ\"",{"type":40,"tag":144,"props":647,"children":648},{},[649,657],{"type":40,"tag":171,"props":650,"children":651},{},[652],{"type":40,"tag":64,"props":653,"children":654},{},[655],{"type":46,"value":656},"#6",{"type":40,"tag":171,"props":658,"children":659},{},[660],{"type":46,"value":661},"Any infinite sum \"bounded\" via a regularized value? Check the boundary — if there's a pole there, the sum diverges",{"type":40,"tag":116,"props":663,"children":664},{},[665,667],{"type":46,"value":666},"Full pattern list: ",{"type":40,"tag":256,"props":668,"children":670},{"className":669},[],[671],{"type":46,"value":672},"references\u002Fverifier_patterns.md",{"type":40,"tag":116,"props":674,"children":675},{},[676],{"type":46,"value":677},"Verifier returns:",{"type":40,"tag":360,"props":679,"children":682},{"className":680,"code":681,"language":46},[363],"**Verdict**: HOLDS | HOLE FOUND | UNCLEAR\n\n**If HOLE FOUND**:\n- Location: [quote the problematic step]\n- Pattern: [which check fired, or \"other\"]\n- Why it breaks: [specific]\n- Fixable?: [yes with X \u002F no, fundamental]\n",[683],{"type":40,"tag":256,"props":684,"children":685},{"__ignoreMap":368},[686],{"type":46,"value":681},{"type":40,"tag":281,"props":688,"children":690},{"id":689},"_5-rank-and-vote-verify-asymmetric-early-exit",[691],{"type":46,"value":692},"5. Rank and vote-verify (asymmetric + early exit)",{"type":40,"tag":116,"props":694,"children":695},{},[696],{"type":46,"value":697},"Rank solutions by (verdict, verifier confidence). Take the top one. Run up to 5\nfresh verifier agents.",{"type":40,"tag":116,"props":699,"children":700},{},[701,706],{"type":40,"tag":64,"props":702,"children":703},{},[704],{"type":46,"value":705},"Asymmetric thresholds",{"type":46,"value":707},": 4 HOLDS to confirm, 2 HOLE FOUND to refute. Why\nasymmetric: one flaky verifier shouldn't kill a correct proof; but two\nindependent dissents is a real signal.",{"type":40,"tag":116,"props":709,"children":710},{},[711,716],{"type":40,"tag":64,"props":712,"children":713},{},[714],{"type":46,"value":715},"Pigeonhole early exit",{"type":46,"value":717},": stop launching verifiers once the outcome is decided.",{"type":40,"tag":390,"props":719,"children":720},{},[721,726,731],{"type":40,"tag":60,"props":722,"children":723},{},[724],{"type":46,"value":725},"2 say HOLE FOUND → refuted, stop (save the remaining 3 calls)",{"type":40,"tag":60,"props":727,"children":728},{},[729],{"type":46,"value":730},"4 say HOLDS → confirmed, stop (save the 5th)",{"type":40,"tag":60,"props":732,"children":733},{},[734],{"type":46,"value":735},"After 3 verifiers: if 2 HOLDS + 1 HOLE, launch 2 more (outcome undecided). If\n3 HOLDS + 0 HOLE, launch 1 more (could still hit 4-1).",{"type":40,"tag":116,"props":737,"children":738},{},[739,744],{"type":40,"tag":64,"props":740,"children":741},{},[742],{"type":46,"value":743},"Dual context-isolation",{"type":46,"value":745},": each verifier is blind to (a) the solver's thinking\ntrace — already stripped in step 3 — AND (b) other verifiers' verdicts. Each\nverifier thinks it's the first. No \"3 agents already confirmed this\" social\nproof.",{"type":40,"tag":116,"props":747,"children":748},{},[749,754],{"type":40,"tag":64,"props":750,"children":751},{},[752],{"type":46,"value":753},"A solver cannot verify its own solution.",{"type":46,"value":755}," Different agent, fresh context.",{"type":40,"tag":281,"props":757,"children":759},{"id":758},"_5b-when-one-case-wont-close-step-back-before-grinding",[760],{"type":46,"value":761},"5b. When one case won't close — step back before grinding",{"type":40,"tag":116,"props":763,"children":764},{},[765,767],{"type":46,"value":766},"If a proof splits into cases and one case proves easily but the other resists:\n",{"type":40,"tag":64,"props":768,"children":769},{},[770],{"type":46,"value":771},"before grinding through the hard case, ask whether there's a route that makes\nthe split disappear.",{"type":40,"tag":116,"props":773,"children":774},{},[775,777,783],{"type":46,"value":776},"The pattern that saves you: the hard case's very hypothesis often implies\nsomething strong about an ",{"type":40,"tag":778,"props":779,"children":780},"em",{},[781],{"type":46,"value":782},"intermediate object",{"type":46,"value":784}," you haven't looked at. Use that\nimplication directly instead of the original chain.",{"type":40,"tag":116,"props":786,"children":787},{},[788,790,795],{"type":46,"value":789},"Concrete shape: proving f(n) ≤ cn for a constrained function f, with a case\nsplit on a prime p dividing f(n). One branch closes by index arguments in\n(ℤ\u002Fp^e)*. The other branch resists — same group structure, but the arithmetic\ndoesn't contradict. The fix: the hypothesis \"p | f(n)\" plugged back into the\ngoverning equation implies ",{"type":40,"tag":64,"props":791,"children":792},{},[793],{"type":46,"value":794},"f(p) = p itself",{"type":46,"value":796},". Once you have that, a\nFermat+Dirichlet argument kills both branches in three lines. The case split was\na detour — it was splitting on a variable that, under the hypothesis, takes a\nknown value.",{"type":40,"tag":116,"props":798,"children":799},{},[800],{"type":46,"value":801},"Check when stuck on case B:",{"type":40,"tag":390,"props":803,"children":804},{},[805,817,822],{"type":40,"tag":60,"props":806,"children":807},{},[808,810,815],{"type":46,"value":809},"What does case B's hypothesis imply about f at ",{"type":40,"tag":778,"props":811,"children":812},{},[813],{"type":46,"value":814},"other",{"type":46,"value":816}," inputs?",{"type":40,"tag":60,"props":818,"children":819},{},[820],{"type":46,"value":821},"Is there a different pair (a,b) to plug into the governing equation?",{"type":40,"tag":60,"props":823,"children":824},{},[825],{"type":46,"value":826},"Are you proving too much? (A cleaner contradiction needs less machinery.)",{"type":40,"tag":116,"props":828,"children":829},{},[830],{"type":46,"value":831},"This is also a presentation-pass win: the split-free proof is shorter AND more\ngeneral.",{"type":40,"tag":281,"props":833,"children":835},{"id":834},"_6-revise-if-needed",[836],{"type":46,"value":837},"6. Revise (if needed)",{"type":40,"tag":116,"props":839,"children":840},{},[841],{"type":46,"value":842},"If verification finds a hole: launch a reviser agent. It gets (cleaned\nsolution + verifier's hole report). STILL no access to the original thinking —\nthe reviser works from the hole, not by rereading how you got there.",{"type":40,"tag":360,"props":844,"children":847},{"className":845,"code":846,"language":46},[363],"A verifier found this issue in the proof:\n[hole report]\n\nFix the proof. If the hole is fundamental (the approach doesn't work), say so and return **Verdict: no confident solution** with what partial progress remains.\n\nFor any step you cannot fully close, mark it inline: [GAP: specific description of what remains]. Gaps in the proof text, not in a separate list — they're greppable and the next reviser knows exactly where to look.\n",[848],{"type":40,"tag":256,"props":849,"children":850},{"__ignoreMap":368},[851],{"type":46,"value":846},{"type":40,"tag":116,"props":853,"children":854},{},[855],{"type":46,"value":856},"Up to 3 revise cycles. Then re-run the vote on the revised proof.",{"type":40,"tag":116,"props":858,"children":859},{},[860,865,867,872],{"type":40,"tag":64,"props":861,"children":862},{},[863],{"type":46,"value":864},"If pattern #40 fired",{"type":46,"value":866}," (one-line-proof-too-clean), the reviser gets a stronger\nbrief — the Adversarial Brief template from ",{"type":40,"tag":256,"props":868,"children":870},{"className":869},[],[871],{"type":46,"value":549},{"type":46,"value":873},"\n§7. It forces a binary: \"the general lemma is obviously false (here's a 2×2\ncounterexample) — so either find what's special about THIS case, or find where\nthe proof breaks.\" Can't return \"looks fine.\"",{"type":40,"tag":281,"props":875,"children":877},{"id":876},"_6c-deep-mode-when-tight-budget-abstains",[878],{"type":46,"value":879},"6c. Deep mode (when tight-budget abstains)",{"type":40,"tag":116,"props":881,"children":882},{},[883],{"type":46,"value":884},"The standard workflow is tight-budget: 8 solvers, ~15 min, pure reasoning. When\nit abstains, the problem may need more time, not more capability.",{"type":40,"tag":116,"props":886,"children":887},{},[888,893],{"type":40,"tag":64,"props":889,"children":890},{},[891],{"type":46,"value":892},"Deep mode",{"type":46,"value":894}," is a single focused agent with:",{"type":40,"tag":390,"props":896,"children":897},{},[898,908,918],{"type":40,"tag":60,"props":899,"children":900},{},[901,906],{"type":40,"tag":64,"props":902,"children":903},{},[904],{"type":46,"value":905},"Unlimited time",{"type":46,"value":907}," — no wall-clock pressure",{"type":40,"tag":60,"props":909,"children":910},{},[911,916],{"type":40,"tag":64,"props":912,"children":913},{},[914],{"type":46,"value":915},"Targeted computation allowed",{"type":46,"value":917}," — modular arithmetic checks, small-case\nenumeration, symbolic verification of identities. NOT exploratory brute force\nor unbounded recursion.",{"type":40,"tag":60,"props":919,"children":920},{},[921,926],{"type":40,"tag":64,"props":922,"children":923},{},[924],{"type":46,"value":925},"The abstention reason as starting point",{"type":46,"value":927}," — if verifiers found a specific\ngap, start there. If solvers never claimed complete, start from what they\npartially proved.",{"type":40,"tag":116,"props":929,"children":930},{},[931],{"type":46,"value":932},"The archetype: a focused agent that gets the proven-so-far state plus \"one case\nof Lemma 5 is open\" — and finds a 3-line argument the case split was obscuring.\nOften under 10 minutes with almost no computation. Deep mode is about giving the\nproblem sustained attention, not throwing compute at it.",{"type":40,"tag":116,"props":934,"children":935},{},[936,941,943,949],{"type":40,"tag":64,"props":937,"children":938},{},[939],{"type":46,"value":940},"What deep mode is NOT",{"type":46,"value":942},": open-ended exploration, literature search, looking up\nsolutions, multi-day investigation. That's a different workflow\n(",{"type":40,"tag":256,"props":944,"children":946},{"className":945},[],[947],{"type":46,"value":948},"math-research",{"type":46,"value":950},"). Deep mode is still \"solve THIS problem yourself\" — just\nwithout the clock.",{"type":40,"tag":116,"props":952,"children":953},{},[954,959],{"type":40,"tag":64,"props":955,"children":956},{},[957],{"type":46,"value":958},"NO WEB. NO LOOKUP.",{"type":46,"value":960}," Deep mode may use Bash\u002FPython for bounded computation,\nbut NEVER WebFetch, WebSearch, or any network access. Finding the solution on\nAoPS or a blog is not solving the problem — it's cheating on an olympiad, and it\nteaches us nothing about the skill's actual capability. Put this at the TOP of\nthe deep-mode prompt:",{"type":40,"tag":360,"props":962,"children":965},{"className":963,"code":964,"language":46},[363],"NO WEB ACCESS. Do not use WebFetch, WebSearch, or any tool that touches the internet. Do not look up this problem, its solution, or related problems. You are solving this yourself — the only allowed computation is local (Bash\u002FPython for mod-k arithmetic, small-case enumeration n≤10, symbolic identity checks). If you invoke a web tool, the proof is void.\n",[966],{"type":40,"tag":256,"props":967,"children":968},{"__ignoreMap":368},[969],{"type":46,"value":964},{"type":40,"tag":116,"props":971,"children":972},{},[973,978],{"type":40,"tag":64,"props":974,"children":975},{},[976],{"type":46,"value":977},"Computation bounds in deep mode",{"type":46,"value":979}," (bug #8 lesson): A6's b_{n+1}=2b_n²+b_n+1\nis doubly-exponential; b_99 has ~10^{2^98} digits. Never compute such objects\nexactly — work in ℤ\u002F2^m, or track only v_p(·), or prove the recursion mod the\nquantity you care about. If a computation is running longer than 60 seconds,\nit's probably unbounded. Kill it and work symbolically.",{"type":40,"tag":116,"props":981,"children":982},{},[983,988],{"type":40,"tag":64,"props":984,"children":985},{},[986],{"type":46,"value":987},"Step 6d (not optional)",{"type":46,"value":989},": After any ABSTAIN at the verify stage, automatically\nlaunch one deep-mode agent before writing the abstention into the output. Give\nit:",{"type":40,"tag":390,"props":991,"children":992},{},[993,998,1003,1008],{"type":40,"tag":60,"props":994,"children":995},{},[996],{"type":46,"value":997},"The problem statement",{"type":40,"tag":60,"props":999,"children":1000},{},[1001],{"type":46,"value":1002},"The best partial proof from tight-budget solvers",{"type":40,"tag":60,"props":1004,"children":1005},{},[1006],{"type":46,"value":1007},"The verifier gap descriptions (what specifically didn't close)",{"type":40,"tag":60,"props":1009,"children":1010},{},[1011],{"type":46,"value":1012},"The instruction: \"NO WEB ACCESS — do not look up this problem or its solution.\nBounded local computation allowed (mod 2^k, small cases n≤10, symbolic\nidentity checks via Bash\u002FPython only). 60-second computation limit. If n≤10\nbrute force reveals a pattern the tight-budget solvers missed, that pattern IS\nthe proof structure.\"",{"type":40,"tag":116,"props":1014,"children":1015},{},[1016],{"type":46,"value":1017},"The deep agent may find the construction the pure-reasoning solvers couldn't\nsee. If it also abstains, THEN write the abstention. Do not skip this step —\nproblems with √n or log n answers are often invisible to pure reasoning because\nthe optimal structure is the asymmetric one.",{"type":40,"tag":116,"props":1019,"children":1020},{},[1021,1026],{"type":40,"tag":64,"props":1022,"children":1023},{},[1024],{"type":46,"value":1025},"Orchestrator self-restraint",{"type":46,"value":1027},": The orchestrator itself must not web-search the\nproblem \"to help\" the deep agent. If you're tempted to Fetch an AoPS thread\n\"just to check the answer,\" don't — that contaminates the skill's output and\nmisrepresents its capability.",{"type":40,"tag":281,"props":1029,"children":1031},{"id":1030},"_7-calibrated-abstention",[1032],{"type":46,"value":1033},"7. Calibrated abstention",{"type":40,"tag":116,"props":1035,"children":1036},{},[1037,1039],{"type":46,"value":1038},"If 3 revise cycles all fail: ",{"type":40,"tag":64,"props":1040,"children":1041},{},[1042],{"type":46,"value":1043},"stop and admit it.",{"type":40,"tag":360,"props":1045,"children":1048},{"className":1046,"code":1047,"language":46},[363],"**Verdict**: no confident solution\n\n**What was tried**: [approaches]\n**What WAS proven**: [any lemma or partial result that survived verification]\n**Where it breaks**: [the unfixed hole]\n",[1049],{"type":40,"tag":256,"props":1050,"children":1051},{"__ignoreMap":368},[1052],{"type":46,"value":1047},{"type":40,"tag":116,"props":1054,"children":1055},{},[1056],{"type":46,"value":1057},"Do NOT guess. A wrong confident answer is worse than an honest \"couldn't solve\nit.\" The metric that matters is CONDITIONAL accuracy — when you say \"solved,\"\nare you right?",{"type":40,"tag":281,"props":1059,"children":1061},{"id":1060},"_8-presentation-pass-after-correctness-is-established",[1062],{"type":46,"value":1063},"8. Presentation pass (after correctness is established)",{"type":40,"tag":116,"props":1065,"children":1066},{},[1067],{"type":46,"value":1068},"A VERIFIED-CORRECT proof is often not a BEAUTIFUL proof. The order you\ndiscovered it is rarely the best order to present it. Launch a fresh\npresentation agent with the verified proof.",{"type":40,"tag":116,"props":1070,"children":1071},{},[1072,1074,1080],{"type":46,"value":1073},"Load ",{"type":40,"tag":256,"props":1075,"children":1077},{"className":1076},[],[1078],{"type":46,"value":1079},"references\u002Fpresentation_prompts.md",{"type":46,"value":1081},". The agent asks:",{"type":40,"tag":390,"props":1083,"children":1084},{},[1085,1090,1095,1100],{"type":40,"tag":60,"props":1086,"children":1087},{},[1088],{"type":46,"value":1089},"What's the simplest way to say this?",{"type":40,"tag":60,"props":1091,"children":1092},{},[1093],{"type":46,"value":1094},"Which lemmas should be inlined? Which deserve to stand alone?",{"type":40,"tag":60,"props":1096,"children":1097},{},[1098],{"type":46,"value":1099},"Is anything OVERKILL? (constructing a double exponential when linear suffices)",{"type":40,"tag":60,"props":1101,"children":1102},{},[1103],{"type":46,"value":1104},"Now that we know the answer, is there a 3-line hindsight proof?",{"type":40,"tag":116,"props":1106,"children":1107},{},[1108,1110,1116,1118,1124,1126,1132],{"type":46,"value":1109},"Output: LaTeX-formatted proof. If ",{"type":40,"tag":256,"props":1111,"children":1113},{"className":1112},[],[1114],{"type":46,"value":1115},"pdflatex",{"type":46,"value":1117}," is available\n(",{"type":40,"tag":256,"props":1119,"children":1121},{"className":1120},[],[1122],{"type":46,"value":1123},"scripts\u002Fcheck_latex.sh",{"type":46,"value":1125}," returns 0), also compile to PDF via\n",{"type":40,"tag":256,"props":1127,"children":1129},{"className":1128},[],[1130],{"type":46,"value":1131},"scripts\u002Fcompile_pdf.sh",{"type":46,"value":1133},".",{"type":40,"tag":112,"props":1135,"children":1136},{},[],{"type":40,"tag":49,"props":1138,"children":1140},{"id":1139},"model-tier-defaults",[1141],{"type":46,"value":1142},"Model tier defaults",{"type":40,"tag":116,"props":1144,"children":1145},{},[1146,1148,1154],{"type":46,"value":1147},"Read ",{"type":40,"tag":256,"props":1149,"children":1151},{"className":1150},[],[1152],{"type":46,"value":1153},"references\u002Fmodel_tier_defaults.md",{"type":46,"value":1155}," for full details. Summary:",{"type":40,"tag":136,"props":1157,"children":1158},{},[1159,1190],{"type":40,"tag":140,"props":1160,"children":1161},{},[1162],{"type":40,"tag":144,"props":1163,"children":1164},{},[1165,1170,1175,1180,1185],{"type":40,"tag":148,"props":1166,"children":1167},{},[1168],{"type":46,"value":1169},"Model",{"type":40,"tag":148,"props":1171,"children":1172},{},[1173],{"type":46,"value":1174},"Solvers",{"type":40,"tag":148,"props":1176,"children":1177},{},[1178],{"type":46,"value":1179},"Verify passes",{"type":40,"tag":148,"props":1181,"children":1182},{},[1183],{"type":46,"value":1184},"Abstain after",{"type":40,"tag":148,"props":1186,"children":1187},{},[1188],{"type":46,"value":1189},"Presentation",{"type":40,"tag":164,"props":1191,"children":1192},{},[1193,1221,1249],{"type":40,"tag":144,"props":1194,"children":1195},{},[1196,1201,1206,1211,1216],{"type":40,"tag":171,"props":1197,"children":1198},{},[1199],{"type":46,"value":1200},"Haiku",{"type":40,"tag":171,"props":1202,"children":1203},{},[1204],{"type":46,"value":1205},"8",{"type":40,"tag":171,"props":1207,"children":1208},{},[1209],{"type":46,"value":1210},"3",{"type":40,"tag":171,"props":1212,"children":1213},{},[1214],{"type":46,"value":1215},"2 revise fails",{"type":40,"tag":171,"props":1217,"children":1218},{},[1219],{"type":46,"value":1220},"skip",{"type":40,"tag":144,"props":1222,"children":1223},{},[1224,1229,1234,1239,1244],{"type":40,"tag":171,"props":1225,"children":1226},{},[1227],{"type":46,"value":1228},"Sonnet",{"type":40,"tag":171,"props":1230,"children":1231},{},[1232],{"type":46,"value":1233},"4",{"type":40,"tag":171,"props":1235,"children":1236},{},[1237],{"type":46,"value":1238},"5",{"type":40,"tag":171,"props":1240,"children":1241},{},[1242],{"type":46,"value":1243},"3 revise fails",{"type":40,"tag":171,"props":1245,"children":1246},{},[1247],{"type":46,"value":1248},"yes",{"type":40,"tag":144,"props":1250,"children":1251},{},[1252,1257,1261,1266,1271],{"type":40,"tag":171,"props":1253,"children":1254},{},[1255],{"type":46,"value":1256},"Opus",{"type":40,"tag":171,"props":1258,"children":1259},{},[1260],{"type":46,"value":1210},{"type":40,"tag":171,"props":1262,"children":1263},{},[1264],{"type":46,"value":1265},"5 + full pattern sweep",{"type":40,"tag":171,"props":1267,"children":1268},{},[1269],{"type":46,"value":1270},"4 revise fails",{"type":40,"tag":171,"props":1272,"children":1273},{},[1274],{"type":46,"value":1275},"2 drafts, pick cleaner",{"type":40,"tag":116,"props":1277,"children":1278},{},[1279],{"type":46,"value":1280},"Weaker models: more parallel attempts, faster abstention. Stronger models:\ndeeper verification, more presentation effort.",{"type":40,"tag":112,"props":1282,"children":1283},{},[],{"type":40,"tag":49,"props":1285,"children":1287},{"id":1286},"for-numeric-answer-problems-aime-style",[1288],{"type":46,"value":1289},"For numeric-answer problems (AIME-style)",{"type":40,"tag":116,"props":1291,"children":1292},{},[1293],{"type":46,"value":1294},"Skip the proof machinery. Run 5-7 solvers with varied approaches, take majority\nvote on the numeric answer. If no majority: verify the top 2 candidates by\nsubstitution.",{"type":40,"tag":112,"props":1296,"children":1297},{},[],{"type":40,"tag":49,"props":1299,"children":1301},{"id":1300},"key-references",[1302],{"type":46,"value":1303},"Key references",{"type":40,"tag":390,"props":1305,"children":1306},{},[1307,1317,1327,1337],{"type":40,"tag":60,"props":1308,"children":1309},{},[1310,1315],{"type":40,"tag":256,"props":1311,"children":1313},{"className":1312},[],[1314],{"type":46,"value":672},{"type":46,"value":1316}," — the 12 adversarial checks",{"type":40,"tag":60,"props":1318,"children":1319},{},[1320,1325],{"type":40,"tag":256,"props":1321,"children":1323},{"className":1322},[],[1324],{"type":46,"value":549},{"type":46,"value":1326}," — ready-to-use verifier prompts",{"type":40,"tag":60,"props":1328,"children":1329},{},[1330,1335],{"type":40,"tag":256,"props":1331,"children":1333},{"className":1332},[],[1334],{"type":46,"value":1079},{"type":46,"value":1336}," — beautification prompts + LaTeX template",{"type":40,"tag":60,"props":1338,"children":1339},{},[1340,1345],{"type":40,"tag":256,"props":1341,"children":1343},{"className":1342},[],[1344],{"type":46,"value":1153},{"type":46,"value":1346}," — per-model configuration",{"type":40,"tag":112,"props":1348,"children":1349},{},[],{"type":40,"tag":49,"props":1351,"children":1353},{"id":1352},"what-makes-this-different-from-generic-verify-and-refine",[1354],{"type":46,"value":1355},"What makes this different from generic verify-and-refine",{"type":40,"tag":56,"props":1357,"children":1358},{},[1359,1369,1379,1389,1399,1409],{"type":40,"tag":60,"props":1360,"children":1361},{},[1362,1367],{"type":40,"tag":64,"props":1363,"children":1364},{},[1365],{"type":46,"value":1366},"Dual context isolation",{"type":46,"value":1368},": verifier is blind to (a) the solver's thinking\ntrace — which biases toward agreement — and (b) other verifiers' verdicts —\nsocial proof also biases. Each verifier thinks it's first.",{"type":40,"tag":60,"props":1370,"children":1371},{},[1372,1377],{"type":40,"tag":64,"props":1373,"children":1374},{},[1375],{"type":46,"value":1376},"Pattern-specific attacks",{"type":46,"value":1378},": not \"is this correct?\" but \"does this make the\n#40 mistake? the #4 mistake?\" Specific beats generic. The 7-category\nrefutation taxonomy gives the verifier a checklist.",{"type":40,"tag":60,"props":1380,"children":1381},{},[1382,1387],{"type":40,"tag":64,"props":1383,"children":1384},{},[1385],{"type":46,"value":1386},"Asymmetric vote + pigeonhole exit",{"type":46,"value":1388},": 4-to-confirm, 2-to-refute. One flaky\nverifier doesn't kill a correct proof; two dissents does. Stop launching\nverifiers once the outcome is decided — saves ~30% of verification cost on\nclear cases.",{"type":40,"tag":60,"props":1390,"children":1391},{},[1392,1397],{"type":40,"tag":64,"props":1393,"children":1394},{},[1395],{"type":46,"value":1396},"Specification-gaming check first",{"type":46,"value":1398},": explicitly asks \"is this the intended\ninterpretation?\" before solving. The #1 failure mode in prior work (50\u002F63\n\"correct\" answers solved the wrong reading).",{"type":40,"tag":60,"props":1400,"children":1401},{},[1402,1407],{"type":40,"tag":64,"props":1403,"children":1404},{},[1405],{"type":46,"value":1406},"Calibrated abstention",{"type":46,"value":1408},": will say \"no confident solution\" with partial\nresults. Optimizes conditional accuracy, not coverage.",{"type":40,"tag":60,"props":1410,"children":1411},{},[1412,1417],{"type":40,"tag":64,"props":1413,"children":1414},{},[1415],{"type":46,"value":1416},"Presentation pass",{"type":46,"value":1418},": correctness and elegance are separate steps. The\npresentation agent gets the VERIFIED proof and finds the cleanest way to say\nit.",{"items":1420,"total":1541},[1421,1440,1460,1477,1494,1510,1529],{"slug":1422,"name":1422,"fn":1423,"description":1424,"org":1425,"tags":1426,"stars":22,"repoUrl":23,"updatedAt":1439},"amazon-location-service","integrate Amazon Location Service APIs","Integrates Amazon Location Service APIs for AWS applications. Use this skill when users want to add maps (interactive MapLibre or static images); geocode addresses to coordinates or reverse geocode coordinates to addresses; calculate routes, travel times, or service areas; find places and businesses through text search, nearby search, or autocomplete suggestions; retrieve detailed place information including hours, contacts, and addresses; monitor geographical boundaries with geofences; or track device locations. Covers authentication, SDK integration, and all Amazon Location Service capabilities.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1427,1430,1433,1436],{"name":1428,"slug":1429,"type":15},"API Development","api-development",{"name":1431,"slug":1432,"type":15},"AWS","aws",{"name":1434,"slug":1435,"type":15},"Maps","maps",{"name":1437,"slug":1438,"type":15},"Navigation","navigation","2026-07-12T08:13:53.294026",{"slug":1441,"name":1441,"fn":1442,"description":1443,"org":1444,"tags":1445,"stars":22,"repoUrl":23,"updatedAt":1459},"amplify-workflow","build full-stack apps with AWS Amplify","Build and deploy full-stack web and mobile apps with AWS Amplify Gen2 (TypeScript code-first). Covers auth (Cognito), data (AppSync\u002FDynamoDB including schema modeling, enum types, relationships, authorization rules), storage (S3), functions, APIs, and AI (Amplify AI Kit with Bedrock). Supports React, Next.js, Vue, Angular, React Native, Flutter, Swift, and Android. Always use this skill for Amplify Gen2 topics — even for questions you think you know — it contains validated, version-specific patterns that prevent common mistakes. TRIGGER when: user mentions Amplify Gen2; project has amplify\u002F directory or amplify_outputs; code imports @aws-amplify packages; user asks about defineBackend, defineAuth, defineData, defineStorage, or npx ampx. SKIP: Amplify Gen1 (amplify CLI v6), standalone SAM\u002FCDK without Amplify (use aws-serverless), direct Bedrock without Amplify AI Kit (use bedrock).",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1446,1449,1450,1453,1456],{"name":1447,"slug":1448,"type":15},"Auth","auth",{"name":1431,"slug":1432,"type":15},{"name":1451,"slug":1452,"type":15},"Database","database",{"name":1454,"slug":1455,"type":15},"Frontend","frontend",{"name":1457,"slug":1458,"type":15},"TypeScript","typescript","2026-07-12T08:13:47.134012",{"slug":1461,"name":1461,"fn":1462,"description":1463,"org":1464,"tags":1465,"stars":22,"repoUrl":23,"updatedAt":1476},"analyzer","analyze queried data for trends","Analyze queried data for trends, week-over-week comparisons, distributions, funnels, cohorts, top-N lists, anomalies, sanity checks, and report-ready findings. Use after or alongside ClickHouse queries when the user wants insight rather than raw rows.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1466,1469,1472,1475],{"name":1467,"slug":1468,"type":15},"Analytics","analytics",{"name":1470,"slug":1471,"type":15},"ClickHouse","clickhouse",{"name":1473,"slug":1474,"type":15},"Data Analysis","data-analysis",{"name":20,"slug":21,"type":15},"2026-07-12T08:14:05.606036",{"slug":1478,"name":1478,"fn":1479,"description":1480,"org":1481,"tags":1482,"stars":22,"repoUrl":23,"updatedAt":1493},"artifact-management","manage and organize analysis artifacts","Save, organize, and describe reusable analysis artifacts such as SQL, result snapshots, CSV exports, summaries, caveats, plots, and report-ready files. Use when users ask to save, export, share, cite, reproduce, or organize data-analysis outputs.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1483,1484,1487,1490],{"name":1473,"slug":1474,"type":15},{"name":1485,"slug":1486,"type":15},"Productivity","productivity",{"name":1488,"slug":1489,"type":15},"Reporting","reporting",{"name":1491,"slug":1492,"type":15},"SQL","sql","2026-07-12T08:14:09.265555",{"slug":1495,"name":1495,"fn":1496,"description":1497,"org":1498,"tags":1499,"stars":22,"repoUrl":23,"updatedAt":1509},"attorney-assist","connect with attorneys for legal consultation","Connects the user with a LegalZoom attorney for legal consultation. Use when a user asks about attorneys, lawyers, or legal help, or when contract review reveals high risks or low-confidence findings.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1500,1503,1506],{"name":1501,"slug":1502,"type":15},"Contracts","contracts",{"name":1504,"slug":1505,"type":15},"Legal","legal",{"name":1507,"slug":1508,"type":15},"Risk Assessment","risk-assessment","2026-07-12T08:13:45.878361",{"slug":1511,"name":1511,"fn":1512,"description":1513,"org":1514,"tags":1515,"stars":22,"repoUrl":23,"updatedAt":1528},"building-pydantic-ai-agents","build AI agents with Pydantic AI","Build AI agents with Pydantic AI — tools, capabilities (including on-demand loading), structured output, streaming, testing, and multi-agent patterns. Use when the user mentions Pydantic AI, imports pydantic_ai, or asks to build an AI agent, add tools\u002Fcapabilities, defer capability loading, stream output, define agents from YAML, or test agent behavior.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1516,1519,1522,1525],{"name":1517,"slug":1518,"type":15},"Agents","agents",{"name":1520,"slug":1521,"type":15},"LLM","llm",{"name":1523,"slug":1524,"type":15},"Multi-Agent","multi-agent",{"name":1526,"slug":1527,"type":15},"Python","python","2026-07-12T08:14:01.893781",{"slug":1471,"name":1471,"fn":1530,"description":1531,"org":1532,"tags":1533,"stars":22,"repoUrl":23,"updatedAt":1540},"query ClickHouse databases via CLI","Connect to and query ClickHouse (a local server or a ClickHouse Cloud service) from the terminal using the official clickhousectl CLI, including the browser OAuth login flow. Use when the user wants to run SQL against ClickHouse, explore schemas and tables, inspect Cloud services, or authenticate clickhousectl. For building a local dev environment or deploying to Cloud, defer to the official ClickHouse skills (see Scope).",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1534,1535,1538,1539],{"name":1467,"slug":1468,"type":15},{"name":1536,"slug":1537,"type":15},"CLI","cli",{"name":1470,"slug":1471,"type":15},{"name":1451,"slug":1452,"type":15},"2026-07-12T08:14:06.829692",43,{"items":1543,"total":1669},[1544,1551,1559,1566,1573,1579,1586,1593,1605,1623,1643,1656],{"slug":1422,"name":1422,"fn":1423,"description":1424,"org":1545,"tags":1546,"stars":22,"repoUrl":23,"updatedAt":1439},{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1547,1548,1549,1550],{"name":1428,"slug":1429,"type":15},{"name":1431,"slug":1432,"type":15},{"name":1434,"slug":1435,"type":15},{"name":1437,"slug":1438,"type":15},{"slug":1441,"name":1441,"fn":1442,"description":1443,"org":1552,"tags":1553,"stars":22,"repoUrl":23,"updatedAt":1459},{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1554,1555,1556,1557,1558],{"name":1447,"slug":1448,"type":15},{"name":1431,"slug":1432,"type":15},{"name":1451,"slug":1452,"type":15},{"name":1454,"slug":1455,"type":15},{"name":1457,"slug":1458,"type":15},{"slug":1461,"name":1461,"fn":1462,"description":1463,"org":1560,"tags":1561,"stars":22,"repoUrl":23,"updatedAt":1476},{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1562,1563,1564,1565],{"name":1467,"slug":1468,"type":15},{"name":1470,"slug":1471,"type":15},{"name":1473,"slug":1474,"type":15},{"name":20,"slug":21,"type":15},{"slug":1478,"name":1478,"fn":1479,"description":1480,"org":1567,"tags":1568,"stars":22,"repoUrl":23,"updatedAt":1493},{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1569,1570,1571,1572],{"name":1473,"slug":1474,"type":15},{"name":1485,"slug":1486,"type":15},{"name":1488,"slug":1489,"type":15},{"name":1491,"slug":1492,"type":15},{"slug":1495,"name":1495,"fn":1496,"description":1497,"org":1574,"tags":1575,"stars":22,"repoUrl":23,"updatedAt":1509},{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1576,1577,1578],{"name":1501,"slug":1502,"type":15},{"name":1504,"slug":1505,"type":15},{"name":1507,"slug":1508,"type":15},{"slug":1511,"name":1511,"fn":1512,"description":1513,"org":1580,"tags":1581,"stars":22,"repoUrl":23,"updatedAt":1528},{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1582,1583,1584,1585],{"name":1517,"slug":1518,"type":15},{"name":1520,"slug":1521,"type":15},{"name":1523,"slug":1524,"type":15},{"name":1526,"slug":1527,"type":15},{"slug":1471,"name":1471,"fn":1530,"description":1531,"org":1587,"tags":1588,"stars":22,"repoUrl":23,"updatedAt":1540},{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1589,1590,1591,1592],{"name":1467,"slug":1468,"type":15},{"name":1536,"slug":1537,"type":15},{"name":1470,"slug":1471,"type":15},{"name":1451,"slug":1452,"type":15},{"slug":1594,"name":1594,"fn":1595,"description":1596,"org":1597,"tags":1598,"stars":22,"repoUrl":23,"updatedAt":1604},"cline-session-history","search and browse Cline session history","Search and browse Cline session history. Use when the user asks to find, list, inspect, or export Cline sessions by time period, prompt content, status, model, provider, source, mode, workspace, or other criteria. Also use when the user wants to read a session transcript or export sessions to a directory. Trigger phrases include \"find my session\", \"search my session history\", \"show me past sessions\", \"what was that session where\", \"find the session that started with\", and any mention of past Cline conversations.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1599,1600,1603],{"name":1517,"slug":1518,"type":15},{"name":1601,"slug":1602,"type":15},"History","history",{"name":1485,"slug":1486,"type":15},"2026-07-19T06:03:13.945151",{"slug":1606,"name":1606,"fn":1607,"description":1608,"org":1609,"tags":1610,"stars":22,"repoUrl":23,"updatedAt":1622},"convex-design","build reactive backends with Convex","Design and build reactive, type-safe, production-grade backends on Convex. Covers schema, queries\u002Fmutations\u002Factions, indexes, auth, file storage, scheduling, real-time multiplayer, mobile backends, and LLM\u002Fagent workflows on Convex's one-platform stack.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1611,1612,1615,1616,1619],{"name":1447,"slug":1448,"type":15},{"name":1613,"slug":1614,"type":15},"Backend","backend",{"name":1451,"slug":1452,"type":15},{"name":1617,"slug":1618,"type":15},"Real-time","real-time",{"name":1620,"slug":1621,"type":15},"Storage","storage","2026-07-12T08:13:37.101253",{"slug":1624,"name":1624,"fn":1625,"description":1626,"org":1627,"tags":1628,"stars":22,"repoUrl":23,"updatedAt":1642},"cosmosdb-best-practices","optimize Azure Cosmos DB performance","Azure Cosmos DB performance optimization and best practices guidelines for NoSQL,\npartitioning, queries, SDK usage, and vector search. Use when writing, reviewing,\nor refactoring code that interacts with Azure Cosmos DB, designing data models,\noptimizing queries, or implementing high-performance database operations.\n",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1629,1632,1635,1636,1639],{"name":1630,"slug":1631,"type":15},"Azure","azure",{"name":1633,"slug":1634,"type":15},"Cosmos DB","cosmos-db",{"name":1451,"slug":1452,"type":15},{"name":1637,"slug":1638,"type":15},"NoSQL","nosql",{"name":1640,"slug":1641,"type":15},"Performance","performance","2026-07-12T08:13:54.531719",{"slug":1644,"name":1644,"fn":1645,"description":1646,"org":1647,"tags":1648,"stars":22,"repoUrl":23,"updatedAt":1655},"data-analyst","analyze ClickHouse analytics data","Act as an interactive data analyst for ClickHouse-backed analytics. Use when the user asks questions about internal data, metrics, dashboards, telemetry, active users, revenue, funnels, trends, distributions, or wants an analyst-style conversation, ad hoc SQL, charts, or a data export against ClickHouse (local or ClickHouse Cloud).",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1649,1650,1651,1654],{"name":1467,"slug":1468,"type":15},{"name":1470,"slug":1471,"type":15},{"name":1652,"slug":1653,"type":15},"Dashboards","dashboards",{"name":1473,"slug":1474,"type":15},"2026-07-12T08:13:31.975246",{"slug":1657,"name":1657,"fn":1658,"description":1659,"org":1660,"tags":1661,"stars":22,"repoUrl":23,"updatedAt":1668},"dataproc-skills","manage Dataproc clusters and jobs","Skills to interact with your Dataproc clusters and jobs.",{"slug":8,"name":9,"logoUrl":10,"githubOrg":8},[1662,1665],{"name":1663,"slug":1664,"type":15},"Data Engineering","data-engineering",{"name":1666,"slug":1667,"type":15},"Operations","operations","2026-07-12T08:13:42.179275",45]