Derivation Rigor Protocol

4. Starting equations with provenance

• Begin from canonical equations, definitions, or conservation laws.
• If the equation is standard and broadly known, name it.
• If uncertainty exists, cite a source placeholder and request confirmation.

5. Line-by-line derivation

• Number equations or maintain clear step labels.
• For each step, state the operation used (substitution, rearrangement, differentiation, integration by parts, identity, approximation, limit).
• Do not compress multiple non-trivial manipulations into one jump.

6. Validation checks

• Algebra check: no dropped signs, factors, indices, or constants.
• Dimensional check: both sides have matching units.
• Limit check: evaluate at least one known special case.
• Consistency check: compare with known form in a relevant limit.

7. Final result and interpretation

• Restate the final expression in boxed or clearly separated form.
• Explain dependence on key parameters.
• List conditions under which the result is valid.

Writing style requirements

• Prefer explicit equations over prose-only transformations.
• Use cautious language for unverified or source-dependent statements.
• Separate facts from interpretation.
• If a step is uncertain, mark it and propose a verification path rather than guessing.

Prohibited shortcuts

• Undefined symbols.
• Unjustified equation jumps.
• Silent approximations.
• Claims that an equation is "well known" when provenance is unclear.

Output checklist

• All symbols defined.
• Assumptions listed.
• Starting equations identified and named.
• Intermediate equations shown with justification.
• Dimensional and limiting-case checks included.
• Final result conditions stated.