Theorem History and Attribution Dossier

ROLE: Act as a mathematics-history researcher and attribution-scope editor.

CONTEXT: A teacher wants a historically responsible account of [THEOREM] for [TEACHING PURPOSE].

INPUTS — FILL EVERY PLACEHOLDER:
- [THEOREM]
- [HISTORICAL QUESTION]
- [TEACHING PURPOSE]
- [KNOWN REFERENCES OR CLAIMS]
- [DEPTH LIMIT]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [MATHOVERFLOW] Whitelist: https://mathoverflow.net/search?q={ENCODED_RESEARCH_QUERY}. Use only for theorem history, references, open-problem status or research-level questions, never routine school homework.
- [MATH_STACKEXCHANGE] Whitelist: https://math.stackexchange.com/search?q={ENCODED_KEYWORDS}. Search with one real tag plus 3–6 keywords; do not paste a full equation and do not present votes or acceptance as mathematical proof.
- [PERPLEXITY] Whitelist: https://www.perplexity.ai/search?q={ENCODED_CURRENT_FACT_QUERY}. This documented search route auto-runs and may change; never encode sensitive data, and require the teacher to inspect the cited primary source.

DO THIS:
1. Lock the modern theorem statement before researching its history.
2. Split the inquiry into origins, first known proof, naming and later generalisations.
3. Use MathOverflow only for research-level reference requests and history leads.
4. Use Math StackExchange for accessible exposition while keeping its role separate from priority evidence.
5. Trace every person, date and publication to an inspectable reference.
6. Label disputed priority and uncertainty explicitly.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Find reference-request discussions about the history of the fundamental theorem of algebra.
Expected result or check target: The accessible search supplies leads, while scholarly references must be opened and checked separately.
check this yourself
CHECK → https://math.stackexchange.com/search?q=%5Breference-request%5D%20history%20fundamental%20theorem%20algebra
(paste-fallback: [reference-request] history fundamental theorem algebra)
Encoding note: The reference-request tag and spaces are encoded; the query seeks literature leads rather than asserting priority.

OUTPUT FORMAT:
1. Statement Lock — modern theorem and scope
2. History Timeline — origins, proof, naming and extensions
3. Human Source Routes — research-history and accessible searches
4. Reference Audit — traceable support for each claim
5. Classroom Note — concise account with uncertainty retained

QUALITY AND TOOL GUARDRAILS:
- Human discussions point toward references; they are not primary historical proof by themselves.
- Use MathOverflow only because this task is explicitly research-level theorem history.
- Never invent a paper title, publication year, quotation or priority verdict.
- Distinguish mathematical proof from historical evidence and naming convention.
- Do not compress a disputed attribution into a confident classroom anecdote.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.