[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M79H6D12G795CTTNJDP693PR":3,"skill-same:01M79H6D12G795CTTNJDP693PR":95},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":16,"categories":17,"keywords":18,"publishedAt":19,"linkOnly":20,"markdownContent":21,"markdownBody":22,"frontMatter":23,"refName":24,"commitSha":25,"skillDirectory":26,"forksCount":27,"repositoryHtmlUrl":28,"repositoryHomepageUrl":29,"ownerHtmlUrl":30,"ownerBlogUrl":6,"ownerDescription":31,"updatedAt":32,"install":33,"resources":46},"01M79H6D12G795CTTNJDP693PR","math-manifold",null,"Use when verifying novel or uncertain differential-geometry claims about a concrete structure — a given metric, connection, chart, Lie group, or local bundle presentation — including Christoffel\u002FRiemann\u002FRicci identities, metric compatibility and torsion, geodesic and exp\u002Flog map checks, parallel transport and holonomy, Euler-Lagrange and action-stationarity residuals, gauge equivariance, curvature of a connection, and symplectic closedness, via symbolic tensor computation in low dimension plus seeded numeric probes with PASS\u002FFAIL exit codes. Not for restating established textbook or literature geometry (cite them), abstract existence\u002Funiqueness\u002Fclassification theorems, flat Euclidean checks without geometric structure (math-numeric), or non-geometric symbolic identities (symbolic-math).","yibocat\u002Fprismnext","yibocat","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F98038316?v=4","01M79H3HDXFS2RDP1ED51TDF87","yibo","01M79H3HEG17B8ZH9AD0A06RBK",4,"MIT","https:\u002F\u002Fgithub.com\u002Fyibocat\u002Fprismnext\u002Fblob\u002Fmaster\u002Fresources\u002Fteams\u002Fprismnext.core\u002Fskills\u002Fmath-manifold\u002FSKILL.md",[],[],"2026-11-15 14:19:17",false,"---\nname: math-manifold\ndescription: Use when verifying novel or uncertain differential-geometry claims about a concrete structure — a given metric, connection, chart, Lie group, or local bundle presentation — including Christoffel\u002FRiemann\u002FRicci identities, metric compatibility and torsion, geodesic and exp\u002Flog map checks, parallel transport and holonomy, Euler-Lagrange and action-stationarity residuals, gauge equivariance, curvature of a connection, and symplectic closedness, via symbolic tensor computation in low dimension plus seeded numeric probes with PASS\u002FFAIL exit codes. Not for restating established textbook or literature geometry (cite them), abstract existence\u002Funiqueness\u002Fclassification theorems, flat Euclidean checks without geometric structure (math-numeric), or non-geometric symbolic identities (symbolic-math).\nlicense: MIT\n---\n\n# Math Manifold\n\nDifferential geometry derivations fail quietly: a dropped index, a wrong\nsign in a Christoffel symbol, a connection that is not quite\nmetric-compatible. This skill covers the **verification family of\ndifferential geometry** — Riemannian and pseudo-Riemannian geometry,\nconnections and curvature, geodesics, parallel transport and holonomy,\nfiber bundles and gauge fields, variational principles, symplectic\nstructure — with one discipline: **the claim must be about a concrete\nstructure and must reduce to tensor components or ODEs**. Then the same\nloop as every math skill applies: claim → script → PASS\u002FFAIL exit code →\nmanuscript note.\n\nTwo layers, one skill:\n\n- **Symbolic layer (SymPy)** — tensor components in closed form for\n  manifolds of dimension ≤ 3–4: Christoffel from metric, Riemann\u002FRicci,\n  metric compatibility, torsion, curvature 2-forms of matrix-group\n  connections, dω for a symplectic form.\n- **Numeric layer (numpy)** — anything that integrates or samples:\n  geodesic ODE residuals, conservation of g(ẋ, ẋ), parallel transport,\n  holonomy vs enclosed curvature, action stationarity, gauge equivariance.\n\n## When to use\n\nReach for this skill when the geometric claim is **new or uncertain** in this\nproject — proposed in discussion, not yet established, or tied to **your**\nmetric\u002Fconnection\u002Fimplementation — and it is about a **concrete** structure\n(chart + components) that reduces to tensors or ODEs:\n\n- **Your** metric or connection in coordinates: verify claimed Christoffel \u002F\n  Riemann \u002F Ricci \u002F scalar curvature, or that a **proposed** metric solves\n  an equation (e.g. your ansatz for constant curvature)\n- Verify **your** connection is metric-compatible (∇g = 0) and torsion-free\n  when the components were derived or coded, not quoted from a textbook\n- Check a **claimed** geodesic, exp\u002Flog map, or implementation against the\n  geodesic equation; conservation of the norm along geodesics\n- Parallel transport or holonomy for **your** connection around a specified\n  loop (local computational content, not the global theorem statement)\n- Variational claims: a **proposed** solution satisfies Euler–Lagrange\n  (residual ≈ 0); action stationarity at **your** extremum\n- Gauge \u002F bundle claims on a concrete group: **your** layer's equivariance\n  f(g·x) = g·f(x); **your** A and claimed F = dA + A∧A; Bianchi for **your**\n  components\n- Symplectic claims for **your** 2-form or map: dω = 0, ω preservation\n- ML on manifolds: **your** Riemannian gradients, retractions vs exponential\n  maps, geodesic losses on sphere \u002F hyperbolic \u002F SO(3) \u002F SPD implementations\n\nStandard formulas for a well-known manifold (unit sphere Christoffels, flat\nMinkowski, hyperbolic metric in standard coordinates) are **citations** —\nverify only the **novel coupling** (new loss, new connection, new chart glue,\nimplementation) unless the human explicitly asks to re-derive the standard\npiece.\n\n## When NOT to use\n\n- **Established results** — textbook Christoffel\u002FRiemann tables, named\n  metrics, standard gauge identities, and literature formulas with known\n  derivations. Cite the source; do not re-run scripts on what is already\n  settled.\n- **Human override only** — re-derive or re-probe a standard geometric\n  formula when the human explicitly asks.\n- **Abstract theorems** — existence\u002Funiqueness of Levi-Civita connections,\n  bundle classification, characteristic classes as theorems, \"this structure\n  satisfies the axioms\". Cite the literature; formal proof is `math-formal`\n  (deferred).\n- **Flat Euclidean numeric checks without geometric structure** — matrix\n  identities, ordinary gradient-vs-autodiff → `math-numeric`. Rule of thumb:\n  if the claim never mentions a metric, connection, or chart, it is not this\n  skill.\n- **Non-geometric symbolic identities** (calculus, algebra, ODEs without\n  geometric structure) → `symbolic-math`.\n- **Statistical claims** → `statistical-rigor`.\n\n## Runtime profile\n\n- **Tier:** fast-verify — scripts finish in seconds on CPU. Symbolic layer\n  limited to dimension ≤ 3–4 (Christoffel counts grow like n³; beyond\n  that, go numeric). Numeric layer: thousands of integration steps,\n  hundreds of probes.\n- **Dependencies:** numpy + SymPy. One-time per project:\n  `uv pip install -r requirements-verify.txt` into `.prismnext\u002F.venv` —\n  never the system Python.\n- **Why only these two:** both install as plain wheels into the project\n  venv, matching the family's dependency discipline. Beyond that, keeping\n  the check on bare numpy\u002FSymPy is a *verification-strength* choice: the\n  scripts recompute everything from the metric\u002Fcomponents, so the check\n  stays independent of whatever library (geomstats, geoopt, …) the claim's\n  implementation itself uses — verifying a geomstats-based claim *with*\n  geomstats would be circular. If the user's code already uses such a\n  library, import it in the check only as the object under test, never as\n  the reference. xAct \u002F Cadabra stay documentation pointers. SageMath is\n  the one optional step up: never installed into the venv, but when the\n  user's machine already has it, SageManifolds extends the symbolic layer\n  past dimension 3–4 via the dual-lane pattern in\n  `references\u002Fsage-backend.md` (`experiment-run interpreter=\"external\"\n  pythonPath=\"sage\"`; provenance grade R1) — the independence rule still\n  applies (never verify a SageManifolds implementation with SageManifolds).\n- **Device:** CPU. For ML-manifold checks against a CUDA implementation,\n  verify on CPU first and report `device=` in stdout for both.\n\n## Boundaries\n\nmath-manifold is the differential-geometry member of the math skill family\n(`math-*`), covering both the symbolic-tensor and numeric-geometric layers\n(the former `math-diffgeo` plan is merged here):\n\n| Claim type | Skill | Status |\n| --- | --- | --- |\n| Symbolic identities, calculus, small linear algebra, ODEs | `symbolic-math` | bundled |\n| Purely numerical checks without geometric structure | `math-numeric` | bundled |\n| Differential geometry of concrete structures — tensors, geodesics, transport\u002Fholonomy, variational, gauge | **math-manifold** (this skill) | bundled |\n| Rings, ideals, lattices, polynomial quotients, LLL | `math-lattice` | bundled |\n| Structure theorems (existence, uniqueness, classification) | `math-formal` (proof assistant), or cite the literature | deferred |\n| Commutative diagrams, bundle schematics | `figure-tikz` — draws, does not verify | bundled |\n\nA claim can chain skills: derive the closed form with `symbolic-math`,\nverify its geometric content here, and check its flat-space numerics with\n`math-numeric`. Say in the manuscript block which layer verified what.\n\n## Files in this skill\n\nRead on demand:\n\n- `references\u002Fconnections-curvature.md` — Christoffel from metric, metric\n  compatibility and torsion, Riemann\u002FRicci formulas and index conventions,\n  curvature 2-forms, symplectic closedness; symbolic scale limits.\n- `references\u002Fmaps-transport.md` — geodesic ODE and its residuals,\n  conservation laws as checks, parallel-transport ODE, holonomy vs\n  enclosed curvature, probe design near chart boundaries and poles.\n- `references\u002Fvariational-gauge.md` — Euler–Lagrange residuals, action\n  stationarity by perturbation, gauge equivariance checks, F = dA + A∧A\n  for matrix groups, Bianchi identity.\n- `references\u002Fsage-backend.md` — optional SageMath heavy lane: dual-lane\n  wrapper pattern, external-interpreter invocation, independence and\n  provenance rules.\n- `scripts\u002Fverify_tensor.py` — symbolic: Christoffel\u002FRicci\u002Fscalar from a\n  given metric + metric compatibility (unit-sphere example).\n- `scripts\u002Fverify_geodesic.py` — numeric: claimed geodesic satisfies the\n  geodesic equation; integrated geodesics conserve g(ẋ, ẋ).\n- `scripts\u002Fverify_holonomy.py` — numeric: parallel transport around a loop;\n  defect angle ≡ enclosed curvature (mod 2π).\n- `scripts\u002Fverify_variational.py` — numeric: Euler–Lagrange residual and\n  quadratic action-stationarity of a claimed extremum.\n- `scripts\u002Fverify_gauge.py` — numeric: group equivariance\n  f(g·x) = g·f(x) with sampled group elements.\n- `templates\u002Fgeometry-claim-block.md` — manuscript block: structure,\n  chart, layer (symbolic\u002Fnumeric), probes, worst error, script path.\n\n## Workflow\n\n1. **Fix the concrete structure** — manifold and chart, metric or\n   connection components, group action. A claim about \"some connection\" is\n   not verifiable; a claim about *these* components is.\n2. **Choose the layer** — closed-form tensor claim in low dimension →\n   symbolic (`verify_tensor.py` pattern); anything integrated, sampled, or\n   implemented in code → numeric. Read the matching reference file first.\n3. **Copy the script into the experiment island**, fill in the CLAIM\n   section, run via `experiment-run`. Exit 0\u002F1 gates the manuscript step.\n   If imports fail: `uv pip install -r requirements-verify.txt`.\n4. **Mind the chart** — probes must respect chart boundaries, poles, and\n   coordinate singularities; a check that wanders off the chart verifies\n   nothing. See `references\u002Fmaps-transport.md`.\n5. **Report per layer** — symbolic results may be stated as verified\n   (given the components); numeric results follow the honesty contract:\n   \"numerically verified\" with domain, probes, seed, worst error. Present\n   via `templates\u002Fgeometry-claim-block.md`.\n\n## Done when\n\n- Script exits 0 via `experiment-run`, seed recorded for numeric layers.\n- Symbolic checks include a numeric probe at interior chart points (a\n  sign-convention error can survive pure algebra).\n- Numeric checks respect the chart: no probe crosses a pole, cut locus, or\n  coordinate singularity unless the claim is about exactly that.\n- The manuscript block names the concrete structure, the layer(s), and\n  worst-case error with tolerance.\n- The verification script stays next to the experiment island.\n\n## Rules\n\n- Concrete structures only. \"The Levi-Civita connection exists\" is a\n  citation; \"Γᵏᵢⱼ for this metric equals this formula\" is a script.\n- Index conventions are claims too — record the Riemann sign convention\n  next to the result; conventions differ by sign across the literature.\n- Symbolic layer caps at dimension 3–4; beyond it, verify numerically at\n  random points rather than letting SymPy explode.\n- A numeric pass on one chart is evidence on that chart — say which chart.\n- Conservation laws (g(ẋ,ẋ) along geodesics, energy along EL solutions)\n  are the cheapest strong check: always include one when available.\n- Established theorems and standard coordinate formulas are cited, not\n  re-verified; scripts exist for novel or implementation-level claims\n  unless the human explicitly asks otherwise.\n","# Math Manifold\n\nDifferential geometry derivations fail quietly: a dropped index, a wrong\nsign in a Christoffel symbol, a connection that is not quite\nmetric-compatible. This skill covers the **verification family of\ndifferential geometry** — Riemannian and pseudo-Riemannian geometry,\nconnections and curvature, geodesics, parallel transport and holonomy,\nfiber bundles and gauge fields, variational principles, symplectic\nstructure — with one discipline: **the claim must be about a concrete\nstructure and must reduce to tensor components or ODEs**. Then the same\nloop as every math skill applies: claim → script → PASS\u002FFAIL exit code →\nmanuscript note.\n\nTwo layers, one skill:\n\n- **Symbolic layer (SymPy)** — tensor components in closed form for\n  manifolds of dimension ≤ 3–4: Christoffel from metric, Riemann\u002FRicci,\n  metric compatibility, torsion, curvature 2-forms of matrix-group\n  connections, dω for a symplectic form.\n- **Numeric layer (numpy)** — anything that integrates or samples:\n  geodesic ODE residuals, conservation of g(ẋ, ẋ), parallel transport,\n  holonomy vs enclosed curvature, action stationarity, gauge equivariance.\n\n## When to use\n\nReach for this skill when the geometric claim is **new or uncertain** in this\nproject — proposed in discussion, not yet established, or tied to **your**\nmetric\u002Fconnection\u002Fimplementation — and it is about a **concrete** structure\n(chart + components) that reduces to tensors or ODEs:\n\n- **Your** metric or connection in coordinates: verify claimed Christoffel \u002F\n  Riemann \u002F Ricci \u002F scalar curvature, or that a **proposed** metric solves\n  an equation (e.g. your ansatz for constant curvature)\n- Verify **your** connection is metric-compatible (∇g = 0) and torsion-free\n  when the components were derived or coded, not quoted from a textbook\n- Check a **claimed** geodesic, exp\u002Flog map, or implementation against the\n  geodesic equation; conservation of the norm along geodesics\n- Parallel transport or holonomy for **your** connection around a specified\n  loop (local computational content, not the global theorem statement)\n- Variational claims: a **proposed** solution satisfies Euler–Lagrange\n  (residual ≈ 0); action stationarity at **your** extremum\n- Gauge \u002F bundle claims on a concrete group: **your** layer's equivariance\n  f(g·x) = g·f(x); **your** A and claimed F = dA + A∧A; Bianchi for **your**\n  components\n- Symplectic claims for **your** 2-form or map: dω = 0, ω preservation\n- ML on manifolds: **your** Riemannian gradients, retractions vs exponential\n  maps, geodesic losses on sphere \u002F hyperbolic \u002F SO(3) \u002F SPD implementations\n\nStandard formulas for a well-known manifold (unit sphere Christoffels, flat\nMinkowski, hyperbolic metric in standard coordinates) are **citations** —\nverify only the **novel coupling** (new loss, new connection, new chart glue,\nimplementation) unless the human explicitly asks to re-derive the standard\npiece.\n\n## When NOT to use\n\n- **Established results** — textbook Christoffel\u002FRiemann tables, named\n  metrics, standard gauge identities, and literature formulas with known\n  derivations. Cite the source; do not re-run scripts on what is already\n  settled.\n- **Human override only** — re-derive or re-probe a standard geometric\n  formula when the human explicitly asks.\n- **Abstract theorems** — existence\u002Funiqueness of Levi-Civita connections,\n  bundle classification, characteristic classes as theorems, \"this structure\n  satisfies the axioms\". Cite the literature; formal proof is `math-formal`\n  (deferred).\n- **Flat Euclidean numeric checks without geometric structure** — matrix\n  identities, ordinary gradient-vs-autodiff → `math-numeric`. Rule of thumb:\n  if the claim never mentions a metric, connection, or chart, it is not this\n  skill.\n- **Non-geometric symbolic identities** (calculus, algebra, ODEs without\n  geometric structure) → `symbolic-math`.\n- **Statistical claims** → `statistical-rigor`.\n\n## Runtime profile\n\n- **Tier:** fast-verify — scripts finish in seconds on CPU. Symbolic layer\n  limited to dimension ≤ 3–4 (Christoffel counts grow like n³; beyond\n  that, go numeric). Numeric layer: thousands of integration steps,\n  hundreds of probes.\n- **Dependencies:** numpy + SymPy. One-time per project:\n  `uv pip install -r requirements-verify.txt` into `.prismnext\u002F.venv` —\n  never the system Python.\n- **Why only these two:** both install as plain wheels into the project\n  venv, matching the family's dependency discipline. Beyond that, keeping\n  the check on bare numpy\u002FSymPy is a *verification-strength* choice: the\n  scripts recompute everything from the metric\u002Fcomponents, so the check\n  stays independent of whatever library (geomstats, geoopt, …) the claim's\n  implementation itself uses — verifying a geomstats-based claim *with*\n  geomstats would be circular. If the user's code already uses such a\n  library, import it in the check only as the object under test, never as\n  the reference. xAct \u002F Cadabra stay documentation pointers. SageMath is\n  the one optional step up: never installed into the venv, but when the\n  user's machine already has it, SageManifolds extends the symbolic layer\n  past dimension 3–4 via the dual-lane pattern in\n  `references\u002Fsage-backend.md` (`experiment-run interpreter=\"external\"\n  pythonPath=\"sage\"`; provenance grade R1) — the independence rule still\n  applies (never verify a SageManifolds implementation with SageManifolds).\n- **Device:** CPU. For ML-manifold checks against a CUDA implementation,\n  verify on CPU first and report `device=` in stdout for both.\n\n## Boundaries\n\nmath-manifold is the differential-geometry member of the math skill family\n(`math-*`), covering both the symbolic-tensor and numeric-geometric layers\n(the former `math-diffgeo` plan is merged here):\n\n| Claim type | Skill | Status |\n| --- | --- | --- |\n| Symbolic identities, calculus, small linear algebra, ODEs | `symbolic-math` | bundled |\n| Purely numerical checks without geometric structure | `math-numeric` | bundled |\n| Differential geometry of concrete structures — tensors, geodesics, transport\u002Fholonomy, variational, gauge | **math-manifold** (this skill) | bundled |\n| Rings, ideals, lattices, polynomial quotients, LLL | `math-lattice` | bundled |\n| Structure theorems (existence, uniqueness, classification) | `math-formal` (proof assistant), or cite the literature | deferred |\n| Commutative diagrams, bundle schematics | `figure-tikz` — draws, does not verify | bundled |\n\nA claim can chain skills: derive the closed form with `symbolic-math`,\nverify its geometric content here, and check its flat-space numerics with\n`math-numeric`. Say in the manuscript block which layer verified what.\n\n## Files in this skill\n\nRead on demand:\n\n- `references\u002Fconnections-curvature.md` — Christoffel from metric, metric\n  compatibility and torsion, Riemann\u002FRicci formulas and index conventions,\n  curvature 2-forms, symplectic closedness; symbolic scale limits.\n- `references\u002Fmaps-transport.md` — geodesic ODE and its residuals,\n  conservation laws as checks, parallel-transport ODE, holonomy vs\n  enclosed curvature, probe design near chart boundaries and poles.\n- `references\u002Fvariational-gauge.md` — Euler–Lagrange residuals, action\n  stationarity by perturbation, gauge equivariance checks, F = dA + A∧A\n  for matrix groups, Bianchi identity.\n- `references\u002Fsage-backend.md` — optional SageMath heavy lane: dual-lane\n  wrapper pattern, external-interpreter invocation, independence and\n  provenance rules.\n- `scripts\u002Fverify_tensor.py` — symbolic: Christoffel\u002FRicci\u002Fscalar from a\n  given metric + metric compatibility (unit-sphere example).\n- `scripts\u002Fverify_geodesic.py` — numeric: claimed geodesic satisfies the\n  geodesic equation; integrated geodesics conserve g(ẋ, ẋ).\n- `scripts\u002Fverify_holonomy.py` — numeric: parallel transport around a loop;\n  defect angle ≡ enclosed curvature (mod 2π).\n- `scripts\u002Fverify_variational.py` — numeric: Euler–Lagrange residual and\n  quadratic action-stationarity of a claimed extremum.\n- `scripts\u002Fverify_gauge.py` — numeric: group equivariance\n  f(g·x) = g·f(x) with sampled group elements.\n- `templates\u002Fgeometry-claim-block.md` — manuscript block: structure,\n  chart, layer (symbolic\u002Fnumeric), probes, worst error, script path.\n\n## Workflow\n\n1. **Fix the concrete structure** — manifold and chart, metric or\n   connection components, group action. A claim about \"some connection\" is\n   not verifiable; a claim about *these* components is.\n2. **Choose the layer** — closed-form tensor claim in low dimension →\n   symbolic (`verify_tensor.py` pattern); anything integrated, sampled, or\n   implemented in code → numeric. Read the matching reference file first.\n3. **Copy the script into the experiment island**, fill in the CLAIM\n   section, run via `experiment-run`. Exit 0\u002F1 gates the manuscript step.\n   If imports fail: `uv pip install -r requirements-verify.txt`.\n4. **Mind the chart** — probes must respect chart boundaries, poles, and\n   coordinate singularities; a check that wanders off the chart verifies\n   nothing. See `references\u002Fmaps-transport.md`.\n5. **Report per layer** — symbolic results may be stated as verified\n   (given the components); numeric results follow the honesty contract:\n   \"numerically verified\" with domain, probes, seed, worst error. Present\n   via `templates\u002Fgeometry-claim-block.md`.\n\n## Done when\n\n- Script exits 0 via `experiment-run`, seed recorded for numeric layers.\n- Symbolic checks include a numeric probe at interior chart points (a\n  sign-convention error can survive pure algebra).\n- Numeric checks respect the chart: no probe crosses a pole, cut locus, or\n  coordinate singularity unless the claim is about exactly that.\n- The manuscript block names the concrete structure, the layer(s), and\n  worst-case error with tolerance.\n- The verification script stays next to the experiment island.\n\n## Rules\n\n- Concrete structures only. \"The Levi-Civita connection exists\" is a\n  citation; \"Γᵏᵢⱼ for this metric equals this formula\" is a script.\n- Index conventions are claims too — record the Riemann sign convention\n  next to the result; conventions differ by sign across the literature.\n- Symbolic layer caps at dimension 3–4; beyond it, verify numerically at\n  random points rather than letting SymPy explode.\n- A numeric pass on one chart is evidence on that chart — say which chart.\n- Conservation laws (g(ẋ,ẋ) along geodesics, energy along EL solutions)\n  are the cheapest strong check: always include one when available.\n- Established theorems and standard coordinate formulas are cited, not\n  re-verified; scripts exist for novel or implementation-level claims\n  unless the human explicitly asks otherwise.\n",{"name":5,"license":15,"description":7},"master","bea8e76eec5d154324b095a78e731876fc136f75","resources\u002Fteams\u002Fprismnext.core\u002Fskills\u002Fmath-manifold",0,"https:\u002F\u002Fgithub.com\u002Fyibocat\u002Fprismnext","https:\u002F\u002Fprismnext.pages.dev\u002F","https:\u002F\u002Fgithub.com\u002Fyibocat","Data Science and Artificial Intelligence","2026-09-05 14:31:57",{"source":8,"skillName":5,"commands":34,"prompt":44,"zipAvailable":45},[35,38,41],{"tool":36,"command":37},"npx","npx skills add yibocat\u002Fprismnext --skill 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Never cites from memory.","https:\u002F\u002Fgithub.com\u002Fyibocat\u002Fprismnext\u002Fblob\u002Fmaster\u002Fresources\u002Fteams\u002Fprismnext.core\u002Fskills\u002Fwriting-related-work\u002FSKILL.md",[],[],{"skillNo":119,"name":120,"nameZh":6,"description":121,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":122,"categories":123,"keywords":124,"publishedAt":19},"01M79H7WTP45W9KJQKQHX22PBR","writing-preliminaries","Use when drafting a Preliminaries \u002F Background \u002F Notation section — definitions, problem setup, and formal statements the rest of the paper builds on, with notation consistency and machine-checked formal claims. Reference patterns, not molds; include only what later sections actually use.","https:\u002F\u002Fgithub.com\u002Fyibocat\u002Fprismnext\u002Fblob\u002Fmaster\u002Fresources\u002Fteams\u002Fprismnext.core\u002Fskills\u002Fwriting-preliminaries\u002FSKILL.md",[],[],{"skillNo":126,"name":127,"nameZh":6,"description":128,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":129,"categories":130,"keywords":131,"publishedAt":19},"01M79H7RYRFZ3J74Z15JNG6FD6","writing-methods","Use when drafting a Methods \u002F Methodology \u002F Approach \u002F Model section — expounding the ideas and the reasoning behind the method, grounded in the project's brief, notes, and prior discussions, with empirical details from run receipts. Structure follows the idea's shape; reference angles, not fixed templates.","https:\u002F\u002Fgithub.com\u002Fyibocat\u002Fprismnext\u002Fblob\u002Fmaster\u002Fresources\u002Fteams\u002Fprismnext.core\u002Fskills\u002Fwriting-methods\u002FSKILL.md",[],[],{"skillNo":133,"name":134,"nameZh":6,"description":135,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":136,"categories":137,"keywords":138,"publishedAt":19},"01M79H7MPZB0KTWZBDFVN9NKP2","writing-introduction","Use when drafting or rewriting a paper's Introduction — framing the problem, positioning against prior work, and stating contributions as checkable claims, grounded in the brief, notes, and the library. 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