Write a budget justification for a grant application

Write the budget justification for our application to {{funder}}, so that the reviewer can see what each cost is, how it was calculated and which project activity it pays for, and finds nothing that breaks the funder's rules.

The funder's budget rules, and any headings or template they require:
"""
{{funder_rules}}
"""

Our budget, line by line, with amounts by year if it runs longer than one year:
"""
{{budget}}
"""

The project's activities and timeline: {{activities}}
Staff on the project (role, effort as a percentage or months, salary basis): {{personnel}}
Our approved rates, with their source (fringe benefits, indirect costs): {{rates}}
Cost sharing or matching, if any: {{cost_share}}

Write the justification under the funder's required headings. If the rules give none, use: Personnel, Fringe benefits, Travel, Equipment, Supplies, Contractual and consultants, Other direct costs, Indirect costs. For each line give:
- What it is and why the project needs it, tied to a named activity.
- The calculation, for example "Project coordinator: 52,000 salary x 50% effort x 12 months / 12 = 26,000". That example shows the form only; use our figures.
- Any rule of the funder's that this line relies on, quoted briefly.

After the narrative, add:
1. A check table with the columns Category, Budget amount, Total of justified lines, Difference, so every category ties to the budget.
2. Flags: lines that may conflict with the funder's rules, such as a cap, an unallowable cost or an equipment threshold, each with the rule quoted.
3. Questions for our grants office.

Keep the narrative within the funder's length limit, {{length_limit}}, in specific sentences a program officer can check against the budget table. A good justification lets the reviewer rebuild every figure from the narrative alone.

Rules:
- Use only our budget figures and approved rates. Do not invent salaries, quotes, trip costs or rates, and do not change an amount to fit a rule; flag it instead.
- Apply the indirect cost rate only to the base the funder's rules or our rate agreement define. If neither defines the base, write [CHECK: indirect cost base] and do not calculate it.
- Do not claim benefits or outcomes that the activities do not state.

If a line has no activity it supports, or its calculation cannot be rebuilt from the figures given, list it under Questions rather than writing a justification for it.