quantitative-research

name	quantitative-research
description	Execute auditable quantitative research across preregistered study design, statistical inference, numerical verification, dimensional analysis, uncertainty propagation, counterexample search, and formal proof. Use when a scientific or mathematical question needs actual computation and machine-readable evidence rather than only explanation.
license	MIT

Quantitative Research

Turn a mathematical or scientific question into evidence lanes whose conclusions cannot silently exceed their checks.

Decision contract

Before computation, record:

• the exact question and stable claim IDs;
• population or mathematical domain, experimental unit, observational unit, variables, units, assumptions, and quantifiers;
• whether the intended result is descriptive, statistical, causal, numerical, finite exhaustive, deductive, or kernel-checked;
• primary estimand or theorem statement, decision threshold, stopping rule, and falsifier;
• which result would remain only tested, which may become proved-finite, and which requires a deductive or formal proof receipt.

Do not select a test, solver tolerance, search domain, or proof statement after seeing the desired conclusion without recording the change as exploratory.

Reference usage

Inspect references/index.json and load only the entries required for the selected lanes.

• Read research design and statistics before research-design-audit or statistical-analysis.
• For a finite action choice, information-value calculation, or prior decision threshold, invoke $cx-statistical-decision-analysis and read its indexed finite runtime before creating a decision-analysis receipt.
• Read mathematical claims and proof levels before counterexample-search, proof-obligation-authoring, or any proved-* status.
• Read numerical, dimensional, and uncertainty verification before numerical-verification, dimension-check, or uncertainty-propagation.
• Read formal proof execution before executing Lean or accepting a kernel-check receipt.
• Read artifact and review handoff before packaging a claim-bearing quantitative run.

For a material computation or claim, record the loaded reference hashes with "<plugin-root>/scripts/python_runtime.sh" "<plugin-root>/scripts/reference_lookup.py". Do not infer CLI arguments, result schemas, evidence levels, or proof semantics from command names.

Workflow

1. Specify. Normalize assumptions, quantifiers, variables, units, experimental units, outcomes, estimands, and claim status. Give each material claim an ID.
2. Preregister. For empirical work, author a research-design input and run "<plugin-root>/scripts/python_runtime.sh" "<plugin-root>/scripts/validate_research_design.py" --require-clean before outcome-driven analysis.
3. Route evidence lanes. Use $cx-statistical-inference-experimental-design, $cx-statistical-decision-analysis, $cx-proof-and-counterexample, $cx-formal-theorem-proving, $cx-numerical-analysis-error-control, $cx-dimensional-analysis-units, and $cx-experimental-uncertainty-propagation as applicable.
4. Execute. Use only the bounded CLIs described in the selected references. Write results to files; never paste a large result stream into the conversation.
5. Cross-check. Require independent checks appropriate to the lane: exact randomization, sensitivity analysis, refinement order, residual, invariant, unit balance, covariance-aware propagation, counterexample verification, proof obligations, or kernel execution.
6. Package. Save quantitative sidecars under one hash-validated manifest with $science-provenance.
7. Review. Run $science-review. A statistical computation, numerical convergence trace, symbolic simplification, or bounded search cannot by itself justify a general proof or empirical causal claim.

Outputs

A complete run uses the applicable machine-readable artifacts:

• research-design
• statistical-analysis
• decision-analysis
• mathematical-claim
• counterexample-search
• proof-obligation-graph
• proof-receipt
• formal-proof-check
• numerical-verification
• dimension-check
• uncertainty-propagation
• report, manifest, environment, execution record, and independent review receipt

Every receipt records hashes, explicit limitations, and a status whose meaning is narrower than the scientific conclusion.

Boundaries

• A p-value is not effect size, practical importance, replication, or causality.
• Technical observations do not increase independent sample size.
• Failure to find a counterexample is not proof unless the declared finite exact domain was exhausted.
• Finite exhaustive proof does not automatically generalize beyond that finite domain.
• Computer algebra, random testing, numerical agreement, and convergence plots are not deductive proofs.
• Dimensional consistency is necessary but not sufficient for a correct physical equation.
• Monte Carlo uncertainty is conditional on the declared distributions and covariance model.
• A formal proof receipt covers the exact hashed theorem statement and trusted kernel environment, not an informal claim that merely resembles it.
• Stop rather than weaken assumptions, bounds, review, or evidence semantics to obtain a desired answer.