[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M6QHTV6B960WJNWD5RYDBMW1":3,"skill-same:01M6QHTV6B960WJNWD5RYDBMW1":139},{"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":23,"publishedAt":44,"linkOnly":45,"markdownContent":46,"markdownBody":47,"frontMatter":48,"refName":56,"commitSha":57,"skillDirectory":58,"forksCount":14,"repositoryHtmlUrl":59,"repositoryHomepageUrl":60,"ownerHtmlUrl":61,"ownerBlogUrl":62,"ownerDescription":63,"updatedAt":64,"install":65,"resources":78},"01M6QHTV6B960WJNWD5RYDBMW1","uncertainty-and-units",null,"Tracks physical units and propagates measurement uncertainty in scientific calculations using pint and uncertainties. Use for unit conversion and dimensional checking, GUM uncertainty budgets, Type A and Type B evaluation, coverage factors and expanded uncertainty, Monte Carlo propagation, significant-figure and plus-minus reporting, error propagation through curve fits, CODATA constants, auditing Python code for stripped units or broken uncertainty propagation, and order-of-magnitude plausibility checks using dimensionless groups (Reynolds, Peclet, Damkohler, Knudsen, Biot, Womersley), characteristic scales such as diffusion time or Debye length, and observed magnitude ranges. Trigger on \"is this number physically reasonable\", \"sanity check these units\", \"what regime is this flow in\", or a result that looks off by orders of magnitude.","Tashima-Tarsh\u002FDisha6.6","Tashima-Tarsh","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F269906498?v=4","01M6PBH98X03XERH0HFT4PFB1P","NITISH KUMAR","01M6PBH9DA0M6KM3Z12P848F0K",0,"MIT","https:\u002F\u002Fgithub.com\u002FTashima-Tarsh\u002FDisha6.6\u002Fblob\u002Fmain\u002F.agents\u002Fskills\u002Fkd-uncertainty-and-units\u002FSKILL.md",[18],{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},"01JBSEEDCAT000000000000023","Skill与智能体开发","SCENARIO","使用场景",[24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],"uncertainty and units","uncertainty","units","time","static","for","number","measurement","scientific","unit","as","python","scipy","numpy","use","edit","write","read","Evaluation","library","2026-11-10 10:12:30",false,"---\nname: uncertainty-and-units\ndescription: Tracks physical units and propagates measurement uncertainty in scientific calculations using pint and uncertainties. Use for unit conversion and dimensional checking, GUM uncertainty budgets, Type A and Type B evaluation, coverage factors and expanded uncertainty, Monte Carlo propagation, significant-figure and plus-minus reporting, error propagation through curve fits, CODATA constants, auditing Python code for stripped units or broken uncertainty propagation, and order-of-magnitude plausibility checks using dimensionless groups (Reynolds, Peclet, Damkohler, Knudsen, Biot, Womersley), characteristic scales such as diffusion time or Debye length, and observed magnitude ranges. Trigger on \"is this number physically reasonable\", \"sanity check these units\", \"what regime is this flow in\", or a result that looks off by orders of magnitude.\nlicense: MIT\ncompatibility: Requires Python 3.12+. The numeric CLIs need pint, uncertainties, NumPy, and SciPy; the static auditor is standard-library only. All bundled tooling runs locally with no network access.\nallowed-tools: Read Write Edit Bash\nmetadata:\n  version: \"1.3\"\n  last-reviewed: \"2026-10-01\"\n  skill-author: K-Dense Inc.\ncategory: \"scientific-computing\"\n---\n\n# Uncertainty and units\n\n## Scope\n\nUse this skill whenever a calculation carries physical units or a reported number needs\nan uncertainty. Concretely:\n\n- converting between units, including conversions that need a physical context\n  (wavelength to photon energy, mass to amount of substance, energy to temperature);\n- propagating uncertainty through a measurement model, with or without correlated inputs;\n- building a GUM uncertainty budget from calibration certificates, specifications, and\n  repeatability data;\n- choosing a coverage factor and deciding whether `k = 2` is defensible;\n- rounding and writing a result so a reader knows what the `±` means;\n- extracting parameter uncertainties from a curve fit without discarding correlations;\n- reviewing existing analysis code for silent unit and uncertainty defects;\n- checking that a dimensionally consistent answer is also physically possible — the\n  order of magnitude, the dimensionless group, and the regime it implies.\n\nThis skill covers the metrology and the two libraries that implement it. It does not\ncover statistical inference, model selection, or study design — see `statistical-analysis`,\n`statistical-power`, and `experimental-design`.\n\n## Current release and installation\n\nVerified 2026-10-01:\n\n- **pint 0.26.1**, released 2026-09-10; requires Python 3.12+.\n- **uncertainties 3.2.3**, released 2025-04-21; requires Python 3.8+.\n- **NumPy 2.5.3** and **SciPy 1.18.1**; both require Python 3.12+.\n- `scipy.constants` in SciPy 1.18.1 serves **CODATA 2022**. SciPy 1.11 and earlier\n  served CODATA 2018; the switch to CODATA 2022 occurred in SciPy 1.15.\n\n```bash\nuv venv --python 3.13\nsource .venv\u002Fbin\u002Factivate\nuv pip install \"pint==0.26.1\" \"uncertainties==3.2.3\" \"numpy==2.5.3\" \"scipy==1.18.1\"\n```\n\n`pint-pandas` and `pint-xarray` add unit-aware columns and arrays and are separate\ninstalls.\n\n## Non-negotiable workflow\n\n1. **Attach units at input and strip them only at output.** Convert at function\n   boundaries with `ureg.wraps` or `m_as(\"unit\")`, never mid-calculation.\n2. **Write the measurement model explicitly** before computing anything, including\n   corrections whose estimated value is zero. A correction left out of the model leaves\n   its uncertainty out of the budget.\n3. **Give every input four things**: an estimate, a standard uncertainty, the\n   distribution the uncertainty came from, and its degrees of freedom.\n4. **Convert Type B statements with the right divisor.** A certificate's expanded\n   uncertainty divides by its stated `k`; rectangular limits divide by `sqrt(3)`.\n5. **Identify correlations before combining.** A shared calibration, instrument correction, or fit can induce correlation;\n   quantify shared components instead of assuming every pair is correlated.\n6. **Compute sensitivity coefficients**, and read the budget from `c_i * u(x_i)` rather\n   than from the raw uncertainties.\n7. **Check the linearization.** Compare propagated distributions with the GUM interval when in doubt.\n   Establish Monte Carlo numerical stability before a JCGM 101 clause 8 claim;\n   neither method validates the measurement model or the assigned input PDFs.\n8. **Justify coverage.** A Student-t factor from effective degrees of freedom\n   is an approximation requiring suitable distributional assumptions.\n9. **Round the uncertainty first, then the value to the same decimal place.**\n10. **State what the `±` is** — standard or expanded, with `k`, the coverage probability,\n    and the method.\n11. **Sanity-check the magnitude before reporting.** A dimensionally consistent result can\n    still be impossible. Compare it against a known scale or a dimensionless group, and\n    confirm every assumption you relied on still holds in that regime.\n\n## The failures this skill exists to prevent\n\nEach of the following runs without error and produces a plausible number.\n\n### A unit stripped at an unknown scale\n\n```python\nlength = (12.7 * ureg.mm).magnitude          # 12.7 -- of what?\nlength = (12.7 * ureg.mm).m_as(\"m\")          # 0.0127 metres, stated\n```\n\n`.magnitude` returns whatever the quantity happened to be carrying. Name the unit at the\npoint of extraction, every time.\n\n### Offset temperature arithmetic\n\n```python\nQ(20, \"degC\") + Q(5, \"degC\")     # OffsetUnitCalculusError -- correctly refused\nQ(20, \"degC\") + Q(5, \"delta_degC\")   # 25 degree_Celsius\nQ(25, \"degC\") - Q(20, \"degC\")        # 5 delta_degree_Celsius\n```\n\nCelsius and Fahrenheit are interval scales. An uncertainty on a temperature is always a\ndifference and belongs in a `delta_` unit: converting `20 ± 0.5 degC` to Fahrenheit\ngives `68 degF ± 0.9 delta_degF`, two different conversions on one line.\n\n### Logarithmic units that add by multiplying\n\n```python\nQ(10, \"dBm\") + Q(10, \"dBm\")   # 0.0001 kilogram**2 * meter**4 \u002F second**6\n```\n\nThat is 10 mW × 10 mW, not 20 mW and not 13 dBm. Nothing raises. Convert to a linear\nunit before any arithmetic.\n\n### A correlation destroyed by a round trip\n\n```python\nx = ufloat(1.0, 0.1)\nx - x                                     # 0.0+\u002F-0\nx - ufloat(x.nominal_value, x.std_dev)    # 0.00+\u002F-0.14\n```\n\nRebuilding a variable from its nominal value and standard deviation creates an\nindependent variable. So does any serialization that passes through a pair of floats.\nUse `correlated_values(values, covariance_matrix)` to rebuild a correlated set.\n\n### A covariance matrix silently rescaled\n\n```python\npopt, pcov = curve_fit(f, x, y, sigma=sigma)                        # default\npopt, pcov = curve_fit(f, x, y, sigma=sigma, absolute_sigma=True)\n```\n\nThe default rescales `pcov` by the reduced chi-square. Relative weights from `sigma` still affect the fit and covariance: equality with an unweighted fit holds for constant `sigma`, not generally for heteroscedastic inputs. On\none synthetic straight-line fit the two give `[0.0364, 0.2154]` and `[0.0477, 0.2820]` —\na 31% difference. Pass `absolute_sigma=True` whenever `sigma` holds real standard\nuncertainties.\n\n### A linearization that was never checked\n\nFor `y = x²` with `x = 1.0 ± 0.5`, the GUM framework gives `y = 1.0`, `u_c = 1.0`, and a\n95% interval of `[-0.96, 2.96]` — mostly negative, for a squared quantity. Monte Carlo\ngives a mean of 1.25, `u_c = 1.06`, and a shortest 95% interval of `[0, 3.32]`. Nothing\nin a linear-propagation library will tell you this happened.\n\n## Bundled local CLIs\n\nAll helpers run offline, reject URLs and symlinks, bound their inputs, write output\natomically with private permissions, and refuse to overwrite without `--force`.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fpropagate_uncertainty.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Funcertainty_budget.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fformat_result.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fconvert_units.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Faudit_units.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fcheck_plausibility.py --help\n```\n\n### propagate_uncertainty.py\n\nRuns both propagation methods on the same numerical model and compares interval\nendpoints. This fixed-trial diagnostic does **not** implement the adaptive stabilization\nin JCGM 101 7.9\u002F8.2 and never labels the GUM result fully validated.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fpropagate_uncertainty.py \\\n  --expression \"m \u002F (pi * (d \u002F 2) ** 2 * h)\" \\\n  --variable \"m=250.0,0.05\" \\\n  --variable \"d=2.0,0.002,rectangular\" \\\n  --variable \"h=4.0,0.005,rectangular\" \\\n  --measurand density --unit \"g\u002Fcm3\" --format markdown\n```\n\nEach `--variable` is `name=value,standard_uncertainty[,distribution[,dof]]`, where the\ndistribution is `normal`, `rectangular`, `triangular`, `arcsine`, or `exact` and controls\nMonte Carlo sampling only. Here mass is in g and lengths in cm: `--unit` is\na report label, **not** dimensional validation or conversion. JSON variable units are\nalso labels; convert inputs to a consistent numerical model first. Correlations go in as `--correlation \"a,b=0.9\"`. A JSON\n`--spec` file holds the same model for anything long-lived.\nThe joint normal sampler supports positive semidefinite correlation matrices, including\nperfect correlations. Other joint distributions need a separate sampler. Correlated\nfinite-dof inputs are refused because independent-input Welch-Satterthwaite is invalid.\nFor independent finite-dof inputs the CLI's MC PDFs remain fixed: `dof` affects the\nGUM factor only, not MC sampling. A small-sample t input needs a separate justified model.\n\nThe expression is parsed into an abstract syntax tree and reduced by an explicit walk\nover `+ - * \u002F **` and a fixed list of functions. It is never compiled or executed.\n\nThe report gives the estimate, `u_c`, sensitivity coefficients, the budget in percent,\neffective degrees of freedom, `k`, `U`, both Monte Carlo coverage intervals, and the\nendpoint-agreement diagnostic. Repeat\u002Fincrease sampling and verify model\u002FPDF\nassumptions before deciding what to report.\n\n### uncertainty_budget.py\n\nCombines components stated the way certificates and data sheets state them.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Funcertainty_budget.py --template > budget.json\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Funcertainty_budget.py --spec budget.json --format markdown\n```\n\nEach component names a `distribution` that fixes its divisor — `expanded` divides by its\n`coverage_factor`, `rectangular` by `sqrt(3)`, `triangular` by `sqrt(6)`, `arcsine` by\n`sqrt(2)`, `normal` by 1 — with an optional `sensitivity`, `dof`, and `relative: true`.\nThe tool assumes independent components, requires an explicit factor for `expanded`,\nand rejects nonzero `exact` components. It computes `u_c`, effective degrees of freedom, `k` from\nthe t-distribution, and `U`, and warns when a Type A component has no degrees of\nfreedom, when `nu_eff` is small enough that `k = 2` is wrong, when one component\ndominates, and when a Type B component declared `normal` is probably an undivided\nexpanded uncertainty.\n\n### format_result.py\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fformat_result.py \\\n  --value 12.34567 --uncertainty 0.02345 --unit mm \\\n  --coverage-factor 2.26 --coverage-probability 0.95\n```\n\nReturns `12.346 ± 0.023 mm`, `12.346(23) mm`, the scientific and LaTeX forms, and the\nsentence that has to accompany the number. Warns when one significant digit is requested\nfor an uncertainty beginning in 1 or 2, and when the uncertainty exceeds the estimate.\n\n### convert_units.py\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fconvert_units.py \\\n  --value 532 --unit nm --to eV --context spectroscopy --uncertainty 0.5\n\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fconvert_units.py \\\n  --value 1.0 --unit g --to mol --context chemistry --context-parameter \"mw=180.156 g\u002Fmol\"\n```\n\nCarries the uncertainty through the conversion's local derivative. Some contexts\n(such as wavelength to energy) are reciprocal, whereas others are proportional.\nContext parameters (`mw`, `n`) are treated as exact; their uncertainties need an\nexplicit measurement model. Offset-temperature uncertainty units are differences. Names the context in the\nerror message when a conversion needs one, and flags offset and logarithmic units.\n`--list-contexts` shows what the registry defines.\n\n### audit_units.py\n\nStatic review of existing analysis code. Parses, never imports or runs.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Faudit_units.py \\\n  --input analysis.py --format markdown --fail-on medium\n```\n\n| Rule | Severity | Detects |\n| --- | --- | --- |\n| `UNIT001` | medium | a second `UnitRegistry` in one module — cross-registry `ValueError` |\n| `UNIT002` | medium | offset temperature units with no `delta_` unit anywhere |\n| `UNIT003` | high | `.magnitude` without a preceding `.to(...)` or `.m_as(...)` |\n| `UNIT004` | medium | logarithmic units, whose `+` multiplies |\n| `UNC001` | high | `curve_fit` without `absolute_sigma` |\n| `UNC002` | medium | `np.std` \u002F `np.var` without `ddof` or NumPy's `correction` alias |\n| `UNC003` | medium | `math` or `numpy` functions in a module that uses `uncertainties` |\n| `UNC004` | high | a `ufloat` rebuilt from `.nominal_value` and `.std_dev` |\n| `CONST001` | low | a literal within 0.1% of a CODATA constant |\n\nExit status is 1 when a finding meets `--fail-on` (default `high`), which makes it usable\nas a pre-commit or CI check.\n\nThe rules are heuristics, so a false positive is suppressed with a directive comment —\ntrailing to cover its own line, or alone on a line to cover the next one:\n\n```python\nvalue = quantity.magnitude  # audit-units: ignore UNIT003 -- already converted upstream\n\n# audit-units: ignore UNC003 -- the argument here is a plain float array\nscaled = np.log10(counts)\n```\n\n`# audit-units: ignore-file CONST001` covers a whole module, and naming no rule\nsuppresses all of them. Suppressions are counted in the report rather than hidden, so a\nfile that silences everything still says so.\n\n### check_plausibility.py\n\nDimensional consistency is not physical possibility. A cell 2 m across and a Reynolds\nnumber of 4e7 in a capillary both pass every unit check. This tool tests a set of\nquantities against dimensionless groups, characteristic scales, and illustrative typical-value\nbands, and verifies each formula's dimensionality before reporting a number.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fcheck_plausibility.py \\\n  --quantity \"density=1060 kg\u002Fm**3\" --quantity \"velocity=0.5 mm\u002Fs\" \\\n  --quantity \"length=8 um\" --quantity \"viscosity=3.5 mPa*s\" \\\n  --group reynolds --format markdown\n# Re = 0.001211 -- laminar (circular pipe, length = diameter)\n\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fcheck_plausibility.py \\\n  --quantity \"diameter=2 m\" --band \"eukaryotic_cell_diameter=diameter\"\n# implausible: 4.3 decades outside the 5-100 um range\n```\n\n`--group` evaluates one of 14 dimensionless groups and names the regime it places the\nsystem in; `--scale` computes a characteristic scale such as a diffusion time, Debye\nlength, or Stokes settling velocity; `--band` compares a supplied quantity against an\nobserved range. `--list` prints the whole catalogue with the inputs each formula needs.\n\nPhysical constants (`k_B`, `N_A`, `R_gas`, `g_earth`, and the rest) are available to every\nformula without being supplied. Their nominal values come from `scipy.constants`;\nthis plausibility helper does not propagate their uncertainties. `g_earth` is standard\ngravity, not a local measurement. Bands are screening heuristics, not physical limits.\n\nThe dimensionality check is the point. Passing a kinematic viscosity where the formula\nneeds a dynamic one — both called \"viscosity\", both tabulated for water, differing by a\nfactor of ρ — is refused before any number is computed:\n\n```\nerror: viscosity must have dimensionality [mass] \u002F ([length] * [time]),\n       but m²\u002Fs is [length] ** 2 \u002F [time]\n```\n\nExit status is 1 when the verdict meets `--fail-on` (default `implausible`; a value\nwithin one decade of a band is `questionable`). The thresholds are conventions with soft\nedges and assume the geometry their correlation was fitted for — see\n`references\u002Fplausibility-scales.md` for the characteristic length to use in each case.\n\n## Choosing a propagation method\n\n| Situation | Method |\n| --- | --- |\n| Linear or near-linear model, normal-ish inputs, large dof | GUM framework alone |\n| Any nonlinearity across ±2u of an input | run both, apply the clause 8 test |\n| Large relative uncertainty | check model curvature and physical support; linear models can still propagate exactly |\n| Dominant rectangular or otherwise non-normal component | Monte Carlo |\n| Output bounded below (variance, concentration, squared quantity) | Monte Carlo |\n| Asymmetric output distribution | Monte Carlo; explicitly choose equal-tail or shortest interval |\n| Correlated inputs | either, but supply the covariance matrix, not the standard uncertainties alone |\n\nA model dominated by rectangular contributions can fail the clause 8 test even when it is\nperfectly linear: the framework's `k = 1.96` over-covers a nearly trapezoidal output.\nThe estimate and `u_c` are still right; only the interval is too wide.\n\n## Constants\n\nNever type a constant from memory. The SI has seven exact defining constants, including `c`, `h`, `e`, `k`, and `N_A`; quantities derived solely from exact constants can also be exact (for example, `R = N_A * k`). Other constants may be measured and change between CODATA releases. Check each constant's stated uncertainty rather than assuming every other value is measured.\n\n```python\nimport scipy.constants as constants\n\nconstants.value(\"electron mass\")        # 9.1093837139e-31\nconstants.unit(\"electron mass\")         # kg\nconstants.precision(\"electron mass\")    # 3.07e-10, relative standard uncertainty\nconstants.precision(\"Planck constant\")  # 0.0, exact by definition\n```\n\n`precision` returns a *relative* standard uncertainty; multiply by the absolute value of the constant for the\nabsolute one.\n\n## Reference files\n\n- `references\u002Fgum-methodology.md` — Type A and Type B evaluation, distribution divisors,\n  the law of propagation, Welch-Satterthwaite, when the framework fails, the Monte Carlo\n  procedure, and the clause 8 validation test.\n- `references\u002Fpint-recipes.md` — registries, offset and logarithmic units, contexts,\n  boundary enforcement with `wraps` and `check`, NumPy interoperability, custom units,\n  formatting.\n- `references\u002Funcertainties-recipes.md` — variable identity and correlation,\n  `correlated_values`, `umath` and `unumpy`, format specs, fit covariance matrices, and\n  the package's limits.\n- `references\u002Fdomain-conversions.md` — the energy ladder, spectroscopy, concentration,\n  pressure, radiation and magnetism, mass spectrometry, logarithmic quantities, and the\n  pairs that share dimensions without sharing meaning.\n- `references\u002Freporting-rules.md` — rounding, notations, the sentence that must\n  accompany a result, SD versus SEM versus CI in figures, non-detects, and conformity\n  decision rules.\n- `references\u002Fplausibility-scales.md` — choosing the characteristic length, the\n  dimensionless groups and the modelling assumption each one gates, characteristic\n  scales, the observed magnitude bands and their sources, and the caveats on every\n  threshold.\n\n## Dated sources\n\nChecked 2026-10-01:\n\n- [JCGM 100:2008, Evaluation of measurement data — Guide to the expression of\n  uncertainty in measurement](https:\u002F\u002Fwww.bipm.org\u002Fdocuments\u002F20126\u002F2071204\u002FJCGM_100_2008_E.pdf)\n- [JCGM 101:2008, Supplement 1 — Propagation of distributions using a Monte Carlo\n  method](https:\u002F\u002Fwww.bipm.org\u002Fdocuments\u002F20126\u002F2071204\u002FJCGM_101_2008_E.pdf)\n- [NIST Technical Note 1297](https:\u002F\u002Fnvlpubs.nist.gov\u002Fnistpubs\u002FLegacy\u002FTN\u002Fnbstechnicalnote1297.pdf)\n- [CODATA internationally recommended values](https:\u002F\u002Fphysics.nist.gov\u002Fcuu\u002FConstants\u002F)\n- [Pint on PyPI](https:\u002F\u002Fpypi.org\u002Fproject\u002FPint\u002F) — 0.26.1, released 2026-09-10.\n- [Pint documentation](https:\u002F\u002Fpint.readthedocs.io\u002Fen\u002Fstable\u002F), including\n  [non-multiplicative units](https:\u002F\u002Fpint.readthedocs.io\u002Fen\u002Fstable\u002Fuser\u002Fnonmult.html)\n  and [contexts](https:\u002F\u002Fpint.readthedocs.io\u002Fen\u002Fstable\u002Fuser\u002Fcontexts.html).\n- [uncertainties on PyPI](https:\u002F\u002Fpypi.org\u002Fproject\u002Funcertainties\u002F) — 3.2.3, released\n  2025-04-21.\n- [uncertainties documentation](https:\u002F\u002Funcertainties.readthedocs.io\u002Fen\u002Flatest\u002F)\n- See `references\u002Freview.md` for current API\u002Fsource verification and execution limits.\n- [scipy.constants reference](https:\u002F\u002Fdocs.scipy.org\u002Fdoc\u002Fscipy\u002Freference\u002Fconstants.html)\n\n## Citing Scientific Agent Skills\n\nThis skill is part of Scientific Agent Skills by K-Dense. If it materially contributed to a\nmanuscript, report, presentation, or code release, add the paper to the references or\nsoftware section and tell the user you did so:\n\n> Kassis, T., Agarwal, V., He, Y., Patel, D., & Brueckner, A. M. (2026). Scientific Agent\n> Skills: A Library of Procedural Knowledge for Research Agents. arXiv:2609.00065.\n> https:\u002F\u002Fdoi.org\u002F10.48550\u002FarXiv.2609.00065\n\nAlways cite the current version. The DOI and https:\u002F\u002Farxiv.org\u002Fabs\u002F2609.00065 resolve to the\nlatest arXiv version, so never append a version suffix such as `v1`. When network access is\navailable, fetch https:\u002F\u002Farxiv.org\u002Fabs\u002F2609.00065 (or\nhttps:\u002F\u002Fexport.arxiv.org\u002Fapi\u002Fquery?id_list=2609.00065) before writing the reference and take\nthe author list, year, and version from that record. If the record lists a journal reference\nor publisher DOI, cite the published version instead.\n","# Uncertainty and units\n\n## Scope\n\nUse this skill whenever a calculation carries physical units or a reported number needs\nan uncertainty. Concretely:\n\n- converting between units, including conversions that need a physical context\n  (wavelength to photon energy, mass to amount of substance, energy to temperature);\n- propagating uncertainty through a measurement model, with or without correlated inputs;\n- building a GUM uncertainty budget from calibration certificates, specifications, and\n  repeatability data;\n- choosing a coverage factor and deciding whether `k = 2` is defensible;\n- rounding and writing a result so a reader knows what the `±` means;\n- extracting parameter uncertainties from a curve fit without discarding correlations;\n- reviewing existing analysis code for silent unit and uncertainty defects;\n- checking that a dimensionally consistent answer is also physically possible — the\n  order of magnitude, the dimensionless group, and the regime it implies.\n\nThis skill covers the metrology and the two libraries that implement it. It does not\ncover statistical inference, model selection, or study design — see `statistical-analysis`,\n`statistical-power`, and `experimental-design`.\n\n## Current release and installation\n\nVerified 2026-10-01:\n\n- **pint 0.26.1**, released 2026-09-10; requires Python 3.12+.\n- **uncertainties 3.2.3**, released 2025-04-21; requires Python 3.8+.\n- **NumPy 2.5.3** and **SciPy 1.18.1**; both require Python 3.12+.\n- `scipy.constants` in SciPy 1.18.1 serves **CODATA 2022**. SciPy 1.11 and earlier\n  served CODATA 2018; the switch to CODATA 2022 occurred in SciPy 1.15.\n\n```bash\nuv venv --python 3.13\nsource .venv\u002Fbin\u002Factivate\nuv pip install \"pint==0.26.1\" \"uncertainties==3.2.3\" \"numpy==2.5.3\" \"scipy==1.18.1\"\n```\n\n`pint-pandas` and `pint-xarray` add unit-aware columns and arrays and are separate\ninstalls.\n\n## Non-negotiable workflow\n\n1. **Attach units at input and strip them only at output.** Convert at function\n   boundaries with `ureg.wraps` or `m_as(\"unit\")`, never mid-calculation.\n2. **Write the measurement model explicitly** before computing anything, including\n   corrections whose estimated value is zero. A correction left out of the model leaves\n   its uncertainty out of the budget.\n3. **Give every input four things**: an estimate, a standard uncertainty, the\n   distribution the uncertainty came from, and its degrees of freedom.\n4. **Convert Type B statements with the right divisor.** A certificate's expanded\n   uncertainty divides by its stated `k`; rectangular limits divide by `sqrt(3)`.\n5. **Identify correlations before combining.** A shared calibration, instrument correction, or fit can induce correlation;\n   quantify shared components instead of assuming every pair is correlated.\n6. **Compute sensitivity coefficients**, and read the budget from `c_i * u(x_i)` rather\n   than from the raw uncertainties.\n7. **Check the linearization.** Compare propagated distributions with the GUM interval when in doubt.\n   Establish Monte Carlo numerical stability before a JCGM 101 clause 8 claim;\n   neither method validates the measurement model or the assigned input PDFs.\n8. **Justify coverage.** A Student-t factor from effective degrees of freedom\n   is an approximation requiring suitable distributional assumptions.\n9. **Round the uncertainty first, then the value to the same decimal place.**\n10. **State what the `±` is** — standard or expanded, with `k`, the coverage probability,\n    and the method.\n11. **Sanity-check the magnitude before reporting.** A dimensionally consistent result can\n    still be impossible. Compare it against a known scale or a dimensionless group, and\n    confirm every assumption you relied on still holds in that regime.\n\n## The failures this skill exists to prevent\n\nEach of the following runs without error and produces a plausible number.\n\n### A unit stripped at an unknown scale\n\n```python\nlength = (12.7 * ureg.mm).magnitude          # 12.7 -- of what?\nlength = (12.7 * ureg.mm).m_as(\"m\")          # 0.0127 metres, stated\n```\n\n`.magnitude` returns whatever the quantity happened to be carrying. Name the unit at the\npoint of extraction, every time.\n\n### Offset temperature arithmetic\n\n```python\nQ(20, \"degC\") + Q(5, \"degC\")     # OffsetUnitCalculusError -- correctly refused\nQ(20, \"degC\") + Q(5, \"delta_degC\")   # 25 degree_Celsius\nQ(25, \"degC\") - Q(20, \"degC\")        # 5 delta_degree_Celsius\n```\n\nCelsius and Fahrenheit are interval scales. An uncertainty on a temperature is always a\ndifference and belongs in a `delta_` unit: converting `20 ± 0.5 degC` to Fahrenheit\ngives `68 degF ± 0.9 delta_degF`, two different conversions on one line.\n\n### Logarithmic units that add by multiplying\n\n```python\nQ(10, \"dBm\") + Q(10, \"dBm\")   # 0.0001 kilogram**2 * meter**4 \u002F second**6\n```\n\nThat is 10 mW × 10 mW, not 20 mW and not 13 dBm. Nothing raises. Convert to a linear\nunit before any arithmetic.\n\n### A correlation destroyed by a round trip\n\n```python\nx = ufloat(1.0, 0.1)\nx - x                                     # 0.0+\u002F-0\nx - ufloat(x.nominal_value, x.std_dev)    # 0.00+\u002F-0.14\n```\n\nRebuilding a variable from its nominal value and standard deviation creates an\nindependent variable. So does any serialization that passes through a pair of floats.\nUse `correlated_values(values, covariance_matrix)` to rebuild a correlated set.\n\n### A covariance matrix silently rescaled\n\n```python\npopt, pcov = curve_fit(f, x, y, sigma=sigma)                        # default\npopt, pcov = curve_fit(f, x, y, sigma=sigma, absolute_sigma=True)\n```\n\nThe default rescales `pcov` by the reduced chi-square. Relative weights from `sigma` still affect the fit and covariance: equality with an unweighted fit holds for constant `sigma`, not generally for heteroscedastic inputs. On\none synthetic straight-line fit the two give `[0.0364, 0.2154]` and `[0.0477, 0.2820]` —\na 31% difference. Pass `absolute_sigma=True` whenever `sigma` holds real standard\nuncertainties.\n\n### A linearization that was never checked\n\nFor `y = x²` with `x = 1.0 ± 0.5`, the GUM framework gives `y = 1.0`, `u_c = 1.0`, and a\n95% interval of `[-0.96, 2.96]` — mostly negative, for a squared quantity. Monte Carlo\ngives a mean of 1.25, `u_c = 1.06`, and a shortest 95% interval of `[0, 3.32]`. Nothing\nin a linear-propagation library will tell you this happened.\n\n## Bundled local CLIs\n\nAll helpers run offline, reject URLs and symlinks, bound their inputs, write output\natomically with private permissions, and refuse to overwrite without `--force`.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fpropagate_uncertainty.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Funcertainty_budget.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fformat_result.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fconvert_units.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Faudit_units.py --help\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fcheck_plausibility.py --help\n```\n\n### propagate_uncertainty.py\n\nRuns both propagation methods on the same numerical model and compares interval\nendpoints. This fixed-trial diagnostic does **not** implement the adaptive stabilization\nin JCGM 101 7.9\u002F8.2 and never labels the GUM result fully validated.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fpropagate_uncertainty.py \\\n  --expression \"m \u002F (pi * (d \u002F 2) ** 2 * h)\" \\\n  --variable \"m=250.0,0.05\" \\\n  --variable \"d=2.0,0.002,rectangular\" \\\n  --variable \"h=4.0,0.005,rectangular\" \\\n  --measurand density --unit \"g\u002Fcm3\" --format markdown\n```\n\nEach `--variable` is `name=value,standard_uncertainty[,distribution[,dof]]`, where the\ndistribution is `normal`, `rectangular`, `triangular`, `arcsine`, or `exact` and controls\nMonte Carlo sampling only. Here mass is in g and lengths in cm: `--unit` is\na report label, **not** dimensional validation or conversion. JSON variable units are\nalso labels; convert inputs to a consistent numerical model first. Correlations go in as `--correlation \"a,b=0.9\"`. A JSON\n`--spec` file holds the same model for anything long-lived.\nThe joint normal sampler supports positive semidefinite correlation matrices, including\nperfect correlations. Other joint distributions need a separate sampler. Correlated\nfinite-dof inputs are refused because independent-input Welch-Satterthwaite is invalid.\nFor independent finite-dof inputs the CLI's MC PDFs remain fixed: `dof` affects the\nGUM factor only, not MC sampling. A small-sample t input needs a separate justified model.\n\nThe expression is parsed into an abstract syntax tree and reduced by an explicit walk\nover `+ - * \u002F **` and a fixed list of functions. It is never compiled or executed.\n\nThe report gives the estimate, `u_c`, sensitivity coefficients, the budget in percent,\neffective degrees of freedom, `k`, `U`, both Monte Carlo coverage intervals, and the\nendpoint-agreement diagnostic. Repeat\u002Fincrease sampling and verify model\u002FPDF\nassumptions before deciding what to report.\n\n### uncertainty_budget.py\n\nCombines components stated the way certificates and data sheets state them.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Funcertainty_budget.py --template > budget.json\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Funcertainty_budget.py --spec budget.json --format markdown\n```\n\nEach component names a `distribution` that fixes its divisor — `expanded` divides by its\n`coverage_factor`, `rectangular` by `sqrt(3)`, `triangular` by `sqrt(6)`, `arcsine` by\n`sqrt(2)`, `normal` by 1 — with an optional `sensitivity`, `dof`, and `relative: true`.\nThe tool assumes independent components, requires an explicit factor for `expanded`,\nand rejects nonzero `exact` components. It computes `u_c`, effective degrees of freedom, `k` from\nthe t-distribution, and `U`, and warns when a Type A component has no degrees of\nfreedom, when `nu_eff` is small enough that `k = 2` is wrong, when one component\ndominates, and when a Type B component declared `normal` is probably an undivided\nexpanded uncertainty.\n\n### format_result.py\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fformat_result.py \\\n  --value 12.34567 --uncertainty 0.02345 --unit mm \\\n  --coverage-factor 2.26 --coverage-probability 0.95\n```\n\nReturns `12.346 ± 0.023 mm`, `12.346(23) mm`, the scientific and LaTeX forms, and the\nsentence that has to accompany the number. Warns when one significant digit is requested\nfor an uncertainty beginning in 1 or 2, and when the uncertainty exceeds the estimate.\n\n### convert_units.py\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fconvert_units.py \\\n  --value 532 --unit nm --to eV --context spectroscopy --uncertainty 0.5\n\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fconvert_units.py \\\n  --value 1.0 --unit g --to mol --context chemistry --context-parameter \"mw=180.156 g\u002Fmol\"\n```\n\nCarries the uncertainty through the conversion's local derivative. Some contexts\n(such as wavelength to energy) are reciprocal, whereas others are proportional.\nContext parameters (`mw`, `n`) are treated as exact; their uncertainties need an\nexplicit measurement model. Offset-temperature uncertainty units are differences. Names the context in the\nerror message when a conversion needs one, and flags offset and logarithmic units.\n`--list-contexts` shows what the registry defines.\n\n### audit_units.py\n\nStatic review of existing analysis code. Parses, never imports or runs.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Faudit_units.py \\\n  --input analysis.py --format markdown --fail-on medium\n```\n\n| Rule | Severity | Detects |\n| --- | --- | --- |\n| `UNIT001` | medium | a second `UnitRegistry` in one module — cross-registry `ValueError` |\n| `UNIT002` | medium | offset temperature units with no `delta_` unit anywhere |\n| `UNIT003` | high | `.magnitude` without a preceding `.to(...)` or `.m_as(...)` |\n| `UNIT004` | medium | logarithmic units, whose `+` multiplies |\n| `UNC001` | high | `curve_fit` without `absolute_sigma` |\n| `UNC002` | medium | `np.std` \u002F `np.var` without `ddof` or NumPy's `correction` alias |\n| `UNC003` | medium | `math` or `numpy` functions in a module that uses `uncertainties` |\n| `UNC004` | high | a `ufloat` rebuilt from `.nominal_value` and `.std_dev` |\n| `CONST001` | low | a literal within 0.1% of a CODATA constant |\n\nExit status is 1 when a finding meets `--fail-on` (default `high`), which makes it usable\nas a pre-commit or CI check.\n\nThe rules are heuristics, so a false positive is suppressed with a directive comment —\ntrailing to cover its own line, or alone on a line to cover the next one:\n\n```python\nvalue = quantity.magnitude  # audit-units: ignore UNIT003 -- already converted upstream\n\n# audit-units: ignore UNC003 -- the argument here is a plain float array\nscaled = np.log10(counts)\n```\n\n`# audit-units: ignore-file CONST001` covers a whole module, and naming no rule\nsuppresses all of them. Suppressions are counted in the report rather than hidden, so a\nfile that silences everything still says so.\n\n### check_plausibility.py\n\nDimensional consistency is not physical possibility. A cell 2 m across and a Reynolds\nnumber of 4e7 in a capillary both pass every unit check. This tool tests a set of\nquantities against dimensionless groups, characteristic scales, and illustrative typical-value\nbands, and verifies each formula's dimensionality before reporting a number.\n\n```bash\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fcheck_plausibility.py \\\n  --quantity \"density=1060 kg\u002Fm**3\" --quantity \"velocity=0.5 mm\u002Fs\" \\\n  --quantity \"length=8 um\" --quantity \"viscosity=3.5 mPa*s\" \\\n  --group reynolds --format markdown\n# Re = 0.001211 -- laminar (circular pipe, length = diameter)\n\npython skills\u002Funcertainty-and-units\u002Fscripts\u002Fcheck_plausibility.py \\\n  --quantity \"diameter=2 m\" --band \"eukaryotic_cell_diameter=diameter\"\n# implausible: 4.3 decades outside the 5-100 um range\n```\n\n`--group` evaluates one of 14 dimensionless groups and names the regime it places the\nsystem in; `--scale` computes a characteristic scale such as a diffusion time, Debye\nlength, or Stokes settling velocity; `--band` compares a supplied quantity against an\nobserved range. `--list` prints the whole catalogue with the inputs each formula needs.\n\nPhysical constants (`k_B`, `N_A`, `R_gas`, `g_earth`, and the rest) are available to every\nformula without being supplied. Their nominal values come from `scipy.constants`;\nthis plausibility helper does not propagate their uncertainties. `g_earth` is standard\ngravity, not a local measurement. Bands are screening heuristics, not physical limits.\n\nThe dimensionality check is the point. Passing a kinematic viscosity where the formula\nneeds a dynamic one — both called \"viscosity\", both tabulated for water, differing by a\nfactor of ρ — is refused before any number is computed:\n\n```\nerror: viscosity must have dimensionality [mass] \u002F ([length] * [time]),\n       but m²\u002Fs is [length] ** 2 \u002F [time]\n```\n\nExit status is 1 when the verdict meets `--fail-on` (default `implausible`; a value\nwithin one decade of a band is `questionable`). The thresholds are conventions with soft\nedges and assume the geometry their correlation was fitted for — see\n`references\u002Fplausibility-scales.md` for the characteristic length to use in each case.\n\n## Choosing a propagation method\n\n| Situation | Method |\n| --- | --- |\n| Linear or near-linear model, normal-ish inputs, large dof | GUM framework alone |\n| Any nonlinearity across ±2u of an input | run both, apply the clause 8 test |\n| Large relative uncertainty | check model curvature and physical support; linear models can still propagate exactly |\n| Dominant rectangular or otherwise non-normal component | Monte Carlo |\n| Output bounded below (variance, concentration, squared quantity) | Monte Carlo |\n| Asymmetric output distribution | Monte Carlo; explicitly choose equal-tail or shortest interval |\n| Correlated inputs | either, but supply the covariance matrix, not the standard uncertainties alone |\n\nA model dominated by rectangular contributions can fail the clause 8 test even when it is\nperfectly linear: the framework's `k = 1.96` over-covers a nearly trapezoidal output.\nThe estimate and `u_c` are still right; only the interval is too wide.\n\n## Constants\n\nNever type a constant from memory. The SI has seven exact defining constants, including `c`, `h`, `e`, `k`, and `N_A`; quantities derived solely from exact constants can also be exact (for example, `R = N_A * k`). Other constants may be measured and change between CODATA releases. Check each constant's stated uncertainty rather than assuming every other value is measured.\n\n```python\nimport scipy.constants as constants\n\nconstants.value(\"electron mass\")        # 9.1093837139e-31\nconstants.unit(\"electron mass\")         # kg\nconstants.precision(\"electron mass\")    # 3.07e-10, relative standard uncertainty\nconstants.precision(\"Planck constant\")  # 0.0, exact by definition\n```\n\n`precision` returns a *relative* standard uncertainty; multiply by the absolute value of the constant for the\nabsolute one.\n\n## Reference files\n\n- `references\u002Fgum-methodology.md` — Type A and Type B evaluation, distribution divisors,\n  the law of propagation, Welch-Satterthwaite, when the framework fails, the Monte Carlo\n  procedure, and the clause 8 validation test.\n- `references\u002Fpint-recipes.md` — registries, offset and logarithmic units, contexts,\n  boundary enforcement with `wraps` and `check`, NumPy interoperability, custom units,\n  formatting.\n- `references\u002Funcertainties-recipes.md` — variable identity and correlation,\n  `correlated_values`, `umath` and `unumpy`, format specs, fit covariance matrices, and\n  the package's limits.\n- `references\u002Fdomain-conversions.md` — the energy ladder, spectroscopy, concentration,\n  pressure, radiation and magnetism, mass spectrometry, logarithmic quantities, and the\n  pairs that share dimensions without sharing meaning.\n- `references\u002Freporting-rules.md` — rounding, notations, the sentence that must\n  accompany a result, SD versus SEM versus CI in figures, non-detects, and conformity\n  decision rules.\n- `references\u002Fplausibility-scales.md` — choosing the characteristic length, the\n  dimensionless groups and the modelling assumption each one gates, characteristic\n  scales, the observed magnitude bands and their sources, and the caveats on every\n  threshold.\n\n## Dated sources\n\nChecked 2026-10-01:\n\n- [JCGM 100:2008, Evaluation of measurement data — Guide to the expression of\n  uncertainty in measurement](https:\u002F\u002Fwww.bipm.org\u002Fdocuments\u002F20126\u002F2071204\u002FJCGM_100_2008_E.pdf)\n- [JCGM 101:2008, Supplement 1 — Propagation of distributions using a Monte Carlo\n  method](https:\u002F\u002Fwww.bipm.org\u002Fdocuments\u002F20126\u002F2071204\u002FJCGM_101_2008_E.pdf)\n- [NIST Technical Note 1297](https:\u002F\u002Fnvlpubs.nist.gov\u002Fnistpubs\u002FLegacy\u002FTN\u002Fnbstechnicalnote1297.pdf)\n- [CODATA internationally recommended values](https:\u002F\u002Fphysics.nist.gov\u002Fcuu\u002FConstants\u002F)\n- [Pint on PyPI](https:\u002F\u002Fpypi.org\u002Fproject\u002FPint\u002F) — 0.26.1, released 2026-09-10.\n- [Pint documentation](https:\u002F\u002Fpint.readthedocs.io\u002Fen\u002Fstable\u002F), including\n  [non-multiplicative units](https:\u002F\u002Fpint.readthedocs.io\u002Fen\u002Fstable\u002Fuser\u002Fnonmult.html)\n  and [contexts](https:\u002F\u002Fpint.readthedocs.io\u002Fen\u002Fstable\u002Fuser\u002Fcontexts.html).\n- [uncertainties on PyPI](https:\u002F\u002Fpypi.org\u002Fproject\u002Funcertainties\u002F) — 3.2.3, released\n  2025-04-21.\n- [uncertainties documentation](https:\u002F\u002Funcertainties.readthedocs.io\u002Fen\u002Flatest\u002F)\n- See `references\u002Freview.md` for current API\u002Fsource verification and execution limits.\n- [scipy.constants reference](https:\u002F\u002Fdocs.scipy.org\u002Fdoc\u002Fscipy\u002Freference\u002Fconstants.html)\n\n## Citing Scientific Agent Skills\n\nThis skill is part of Scientific Agent Skills by K-Dense. If it materially contributed to a\nmanuscript, report, presentation, or code release, add the paper to the references or\nsoftware section and tell the user you did so:\n\n> Kassis, T., Agarwal, V., He, Y., Patel, D., & Brueckner, A. M. (2026). Scientific Agent\n> Skills: A Library of Procedural Knowledge for Research Agents. arXiv:2609.00065.\n> https:\u002F\u002Fdoi.org\u002F10.48550\u002FarXiv.2609.00065\n\nAlways cite the current version. The DOI and https:\u002F\u002Farxiv.org\u002Fabs\u002F2609.00065 resolve to the\nlatest arXiv version, so never append a version suffix such as `v1`. When network access is\navailable, fetch https:\u002F\u002Farxiv.org\u002Fabs\u002F2609.00065 (or\nhttps:\u002F\u002Fexport.arxiv.org\u002Fapi\u002Fquery?id_list=2609.00065) before writing the reference and take\nthe author list, year, and version from that record. If the record lists a journal reference\nor publisher DOI, cite the published version instead.\n",{"name":5,"license":15,"category":49,"metadata":50,"description":7,"allowed-tools":54,"compatibility":55},"scientific-computing",{"version":51,"skill-author":52,"last-reviewed":53},"1.3","K-Dense Inc.","2026-10-01","Read Write Edit Bash","Requires Python 3.12+. The numeric CLIs need pint, uncertainties, NumPy, and SciPy; the static auditor is standard-library only. All bundled tooling runs locally with no network access.","main","0da4485785ee599388900be50db1635489d53056",".agents\u002Fskills\u002Fkd-uncertainty-and-units","https:\u002F\u002Fgithub.com\u002FTashima-Tarsh\u002FDisha6.6","https:\u002F\u002Fdisha6.6.thenitishkr.in\u002F","https:\u002F\u002Fgithub.com\u002FTashima-Tarsh","www.thenitishkr","thenitishkr | AI • Cyber-security • Research\r\n","2026-11-08 03:33:25",{"source":8,"skillName":5,"commands":66,"prompt":76,"zipAvailable":77},[67,70,73],{"tool":68,"command":69},"npx","npx skills add Tashima-Tarsh\u002FDisha6.6 --skill uncertainty-and-units",{"tool":71,"command":72},"bunx","bunx skills add Tashima-Tarsh\u002FDisha6.6 --skill uncertainty-and-units",{"tool":74,"command":75},"pnpm","pnpm dlx skills add Tashima-Tarsh\u002FDisha6.6 --skill 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Complements social-content (generic multi-platform) with X-specific depth: algorithm mechanics, thread engineering, reply strategy, profile optimization, and competitive intelligence via web search.","https:\u002F\u002Fgithub.com\u002FTashima-Tarsh\u002FDisha6.6\u002Fblob\u002Fmain\u002F.agents\u002Fskills\u002Fx-twitter-growth\u002FSKILL.md",[],[176,177,178,179,154,180,181,182,183,184,185,186,40,187,38,188,189,190,191,29],"twitter","x twitter growth","growth","research","content","engineering","plan","web search","competitors","analyze","engine","strategy","platform","grow","posting","competitive",{"skillNo":193,"name":194,"nameZh":6,"description":195,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":196,"categories":197,"keywords":199,"publishedAt":44},"01M6QRBN3EHQNJY42RERP7A149","write-a-skill","Create new agent skills with proper structure, progressive disclosure, and bundled resources. 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