fix(web): let the chat reason on analysis questions instead of refusing

"How could this be useful for other papers?" got "the provided
documents do not state..." - the no-speculation clause meant to stop
hallucinated facts was also blocking synthesis, which is the entire
point of such questions. A new clause separates the two: analysis
questions (implications, comparisons, transfer) are answered by
reasoning from the cited context, labeled as the model's own
interpretation; the refusal phrase stays reserved for missing facts.

Author: NorthernLightx

web/app/api.js

@@ -246,6 +246,7 @@
       "- Out-of-domain questions (e.g. about a topic completely unrelated to the chunks) must be refused with the exact phrase above. Do not produce a generic summary of the chunks instead.",
       "- Not every message is a question. If the user is reacting to your previous answer — challenging it, asking what you checked, or making conversation — reply naturally using the prior turns: explain what evidence you used (the chunks and page images you cited) and offer to check something specific. Never use the refusal phrase for such messages.",
       "- Questions about the corpus as a whole (how many papers, which papers cover a topic) cannot be answered from the few retrieved excerpts you see. Say that plainly and point to the Papers and Figures tabs for corpus-wide browsing — do not use the refusal phrase and do not guess a count.",
+      "- Analysis questions (implications, comparisons, how an idea could transfer or be useful elsewhere) call for reasoning, not lookup. Reason from the provided context, label that reasoning as your own interpretation, and cite the chunks that anchor it. The refusal phrase is for missing facts only — never for questions that ask you to think.",
       "- When one answer mentions figures from more than one paper, say which paper each figure belongs to.",
       "- If the user asks to see a figure, plot, or graph and the retrieved chunks don't contain one matching the question, say so plainly — do not claim you cannot display images.",
       "- Cite specific chunk IDs when making factual claims by wrapping the literal id in square brackets. Example: if a chunk header is [2604.22753v1::p5::c24], cite it as [2604.22753v1::p5::c24] — NOT [chunk_id 2604.22753v1::p5::c24] and NOT [chunk 24]. Use only ids that appear in the provided context.",