Vol III Chriss-Ginzburg Rectification

Keep this diagnostic short. It is a map, not a mini-essay.

Phase 2: Platonic architecture

Before line-editing, get the skeleton right.

Decide:

• the exact organizing question;
• the exact climax;
• the ideal section order;
• what should be merged;
• what should be split;
• what should be moved elsewhere;
• what is genuinely redundant;
• what definitions/examples/bridges are missing;
• where the honest scope of each major claim actually ends.

Then execute structural edits:

• reorder sections when logic demands it;
• move motivation before abstraction;
• move definitions before first real use;
• cut roadmap and throat-clearing prose;
• add short structural stubs if a missing bridge is load-bearing;
• rewrite openings that begin with summary dumps;
• rewrite closings so the answered question is explicit.

Do not spend time polishing sections that should be moved or deleted.

Phase 3: Linear fortification loop

After the skeleton converges, work sequentially through the chapter in manageable chunks.

For each chunk:

1. Re-read it in context of what now precedes it.
2. Run the Beilinson audit on the mathematics.
3. Fortify the exposition:
   • every paragraph must earn its place;
   • transitions must say why the next step is forced;
   • definitions must answer a live question;
   • examples should precede general machinery whenever that strengthens inevitability;
   • duplicated motivation must be collapsed.
4. Remove prose sludge:
   • no "notably", "crucially", "remarkably", "it is worth noting", "we now turn to", "having established", "with this in hand", or similar scaffolding;
   • no patronizing roadmap paragraphs;
   • no self-congratulatory tone;
   • no vague "intuition" paragraphs that fail to cash out mathematically.
5. Re-audit the edited chunk for both truth and structure.

Do not advance until the chunk is locally coherent.

Prose constraints

• Treat the reader as an equal.
• Prefer direct mathematical statements to commentary about the mathematics.
• Use short, load-bearing transitions.
• A sentence that can be a clause should become a clause.
• A full page is allowed when the mathematics needs it.
• Economy is not brevity; it is absence of waste.

Hard guardrails

• Never use style to smuggle in an unproved claim.
• Never "clarify" by making a statement stronger than the proof.
• Never let a beautiful narrative outrun a weak construction.
• If a chapter needs a weaker true theorem, weaken it.
• If a central object is still aspirational, say so and define the available substitute precisely.

Verification

• Build after structural edits.
• For load-bearing rewrites, run the narrowest relevant pytest slice and/or make fast.
• Propagate status/formula/definition changes across the repo when they are advertised elsewhere.

Exit rule

End only at:

• CONVERGED: the chapter's structure and local mathematics are coherent, and the relevant verification passes.
• BLOCKED: exact blocker named.

If the chapter still feels like commentary wrapped around mathematics rather than mathematics speaking directly, it is not converged.