solving-model

name	solving-model
description	Systematically set up, solve, and verify an economic model with step-by-step derivations and cross-model mathematical checking. Use when user wants to formalize an economic idea into a model, solve a model, derive equilibrium conditions, check derivations, or verify mathematical results. Also use when user says "solve", "derive", "set up the model", "formalize", "verify the math", "check derivation", "model setup".
argument-hint	[model description or path] [--from=N] [--name=model-name] [--verify]

solving-model

Orchestrate economic model derivation and verification through five checkpointed phases, each dispatched to a dedicated sub-agent.

Architecture

SKILL.md (this file) — argument parsing, phase routing, checkpoint enforcement
  ├── references/phase-1-setup.md         — Model setup elicitation + Oracle review
  ├── references/phase-2-derivation.md    — Step-by-step derivation
  ├── references/phase-3-verification.md  — Local checks + Oracle re-derivation
  ├── references/phase-4-comp-statics.md  — Comparative statics + Oracle sign verification
  ├── references/phase-5-documentation.md — Assembly + compilation
  ├── references/oracle-prompts.md        — Oracle prompt templates
  └── references/example-walkthrough.md   — Concrete output pattern (collateral model)

Shared preferences (read by sub-agents as needed):
  ├── preferences/model-solving-conventions.md  — LaTeX templates
  ├── preferences/verification-protocol.md      — Check procedures + parameter tables
  └── preferences/latex-research.md             — General LaTeX conventions

Phase 0: Argument Parsing

Parse $ARGUMENTS for:

Argument	Effect
--from=N	Start at Phase N (1-5), reading prior phase outputs from disk
--verify	Alias for --from=3
--name=X	Set model name → working directory solving_models/X/
File path (.tex, .pdf)	Use as input; detect type by extension
Everything else	Treat as verbal model description

If --name not provided: Ask the user for a model name using AskUserQuestion.

Create working directory:

mkdir -p solving_models/[name]/

If --from=N with N > 1: Verify prior phase files exist:

Start phase	Required files
2	model_setup.tex
3	model_setup.tex, derivation.tex
4	model_setup.tex, derivation.tex, verification_log.tex
5	model_setup.tex, derivation.tex, verification_log.tex, comparative_statics.tex

If any required file is missing, explain what's needed and suggest the correct --from value.

Detect input type:

• .pdf extension → INPUT_TYPE=pdf
• .tex extension → INPUT_TYPE=latex
• Otherwise → INPUT_TYPE=verbal

---

Phase Dispatch

Execute phases sequentially. Each phase is dispatched as a sub-agent that reads its dedicated reference file for full instructions.

Dispatch pattern for each phase:

1. Read references/phase-N-*.md for the full phase instructions
2. Set context variables: $MODEL_NAME, $WORKING_DIR, $INPUT_TYPE, $INPUT_CONTENT
3. Execute the phase following its instructions exactly
4. At the phase CHECKPOINT: present results and wait for user approval via AskUserQuestion
5. Do NOT proceed to the next phase without explicit user approval
6. If the user requests changes, re-execute the relevant steps within the current phase

Phase 1: Model Setup

Read and follow references/phase-1-setup.md.

Summary: Elicit model primitives → write model_setup.tex → Oracle review → checkpoint.

Skip if: --from >= 2 (read existing model_setup.tex instead).

---

Phase 2: Derivation

Read and follow references/phase-2-derivation.md.

Summary: Identify targets → derive step-by-step → flag % VERIFY → weasel word scan → checkpoint.

Skip if: --from >= 3 (read existing derivation.tex instead).

Special: If derivation reveals model setup is incomplete, HALT and offer to return to Phase 1.

---

Phase 3: Verification

Read and follow references/phase-3-verification.md.

Summary: Collect flagged steps → user selects Oracle steps → run 3 local checks on all flagged → Oracle blind re-derivation on selected → HALT on any failure → checkpoint.

"Verify existing" entry: If --verify with an external file, or --from=3 when derivation.tex lacks \paragraph{Step labels, Phase 3 begins with step parsing (see the phase file for full parsing specification). Normal --from=3 resumes (where derivation.tex was produced by Phase 2) skip parsing and go straight to verification.

Critical rules:

• Oracle receives model_setup.tex only — NEVER derivation.tex
• Numerical checks execute via Python, not in-context arithmetic
• Any check failure triggers HALT with side-by-side presentation

---

Phase 4: Comparative Statics

Read and follow references/phase-4-comp-statics.md.

Summary: User selects parameters → derive and sign → Oracle batched verification → summary table → checkpoint.

Oracle budget: Max 5 sign claims per Oracle call. Split automatically if more.

---

Phase 5: Documentation & Compilation

Read and follow references/phase-5-documentation.md.

Summary: Assemble full_model.tex with \input{} → apply formatting → compile → present PDF.

Critical: Must cd to working directory before xelatex (relative \input paths). Only full_model.tex is compilable — phase files are fragments.

---

Error Handling

Error	Response
Oracle timeout/failure	Present error, offer retry or skip. Record "Oracle: SKIPPED (timeout)" in verification log. Show degraded-verification warning at checkpoint.
LaTeX compilation failure	Show error log. Try common fixes (missing packages, undefined refs). If stuck, present to user.
Missing prior phase files	Explain what's missing, suggest correct --from=N.
Phase 2 discovers setup gap	Re-execute Phase 1 to amend model_setup.tex (backup previous version), then restart Phase 2. Preserve partial derivation.tex as derivation.tex.partial.
Phase file overwrite	Always copy existing .tex to .bak before overwriting.

Oracle Budget

Budget 3-6 Oracle sessions total per model run:

1. Setup review (Phase 1) — 1 call
2. Blind re-derivation (Phase 3) — 1-2 calls (max 5 claims each)
3. Sign verification (Phase 4) — 1-3 calls (max 5 claims each)

First-Time Usage

On first invocation or when the user seems unfamiliar with the workflow, read references/example-walkthrough.md to show them the expected output format for each phase.