04-04-symbol-definition-skill

Symbol Definition

Original id: 04_04_symbol_definition_skill
Section: Problem Formulation And Preliminaries
Layer: section
Category: problem_formulation_and_preliminaries

Produce a reusable symbol definition module for Problem Formulation And Preliminaries within a NeurIPS paper workflow, with explicit boundaries, evidence discipline, and handoff-ready structure.

When To Use

• When refining or drafting the Problem Formulation And Preliminaries portion of a NeurIPS-style paper.
• When you need a reusable artifact rather than a one-off paragraph rewrite.

When Not To Use

• Do not use when required evidence is absent and cannot be clearly marked as missing.
• Do not use as a shortcut for inventing experiments, citations, proof content, or contributions.

Inputs

Required inputs:

• paper_blueprint (required): Verified paper-level question, answer, storyline, contributions, and target sections.
• contribution_list (required): Stable list of contributions already accepted by the authors as in-scope and evidence-backed.
• claim_evidence_map (required): Claim-to-evidence alignment table used to prevent unsupported statements and novelty inflation.
• method_notes (required): Verified technical notes covering setting, assumptions, symbols, modules, objectives, and scope limits.

Optional inputs:

• terminology_registry (optional): Canonical terms, symbols, and disallowed variants for consistency control.
• current_draft_context (optional): Existing local draft text or outline to revise, compress, or audit.
• venue_constraints (optional): Page limit, formatting rules, length pressure, or author preference on tone.

Output Contract

• Output format: paragraph
• Required sections: objective_interpretation, main_output, risk_flags, handoff_notes
• Tone and language: reviewer-friendly / English
• Length guidance: Keep outputs compact, handoff-ready, and easy to embed in a prompt library.

Workflow

1. Treat the provided inputs as the only source of truth.
2. Produce only the bounded artifact for this skill, not a whole-paper rewrite.
3. Preserve contribution names, terminology, and claim boundaries from the shared inputs.
4. Make gaps explicit instead of guessing, especially when evidence is incomplete.
5. Before finalizing, run the section checks and self-checklist below.
6. If you need the full original schema or prompt template, read references/spec.yaml.

Guardrails

Core hard rules:

• Do not invent experiments, results, contributions, baselines, theoretical conclusions, or citations.
• Maintain factual faithfulness, claim-evidence alignment, terminology consistency, overclaim suppression, and reviewer-friendly clarity.
• If evidence is missing, weak, or indirect, say so explicitly and reduce claim strength rather than filling gaps.
• Prefer bounded, reviewer-safe wording over broad or triumphalist phrasing.

Section-specific checks:

• Output stays within the scope of Problem Formulation And Preliminaries and does not leak unsupported content from other sections.
• Contribution names, task setting, and method references match the global blueprint.
• Claims are phrased at the strength justified by the supplied evidence.

Revision policy:

• Missing required input: Return a gap-marked scaffold and list exactly which missing inputs block a stronger output.
• Unsupported claim: Downgrade or remove the claim, explain the evidence gap, and never patch the gap with invented detail.
• Multiple valid options: Provide 2-3 bounded options with tradeoffs, but keep all options faithful to the same verified facts.

Coordination

Reasoning focus:

• logical coherence.
• evidence grounding.
• novelty positioning.
• wording restraint.

Self-checklist:

• Every main statement is supported by provided facts or explicitly labeled as a gap.
• No wording overstates novelty, empirical coverage, causality, or theory scope.
• Terminology, symbols, and contribution labels match the shared registry and blueprint.
• The output does not conflict with neighboring sections such as abstract, method, experiments, or conclusion.

Upstream skills:

• 00_01_paper_blueprint_skill
• 00_03_contribution_extractor_skill
• 00_04_claim_evidence_alignment_skill
• 00_06_terminology_notation_registry_skill
• 04_03_assumption_statement_skill

Downstream handoff:

• 04_05_preliminary_concepts_skill