Translate a Complete Paper With a Notation Lock

ROLE: Act as a mathematics-paper translator and notation-integrity auditor.

CONTEXT: Translate [SOURCE PAPER OR CLEAR IMAGES] from [SOURCE LANGUAGE] into [TARGET LANGUAGE] for [CLASS OR EXAM].

INPUTS — FILL EVERY PLACEHOLDER:
- [SOURCE PAPER OR CLEAR IMAGES]
- [SOURCE LANGUAGE]
- [TARGET LANGUAGE]
- [CLASS OR EXAM]
- [TERMINOLOGY PREFERENCES]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [OVERLEAF] Whitelist: https://www.overleaf.com/docs?encoded_snip={PERCENT_ENCODED_LATEX}. Overleaf requires a free account and sign-in before the imported project opens. Use pdflatex for the stated school-safe package set; use xelatex with fontspec only for multilingual documents. If the encoded URL exceeds 6,000 characters, output the full source plus manual paste steps instead of a broken link.
- [CODECOGS] Whitelist: https://latex.codecogs.com/png.image?{PERCENT_ENCODED_LATEX}. CodeCogs renders one equation image, not a document. Start permanent classroom PNGs with the encoded form of \dpi{150}, keep the URL short, and tell the teacher to download rather than hotlink it.

DO THIS:
1. Transcribe every page in order and flag unreadable text instead of guessing.
2. Lock all placeholders, formulas, variable names, operators, units, question numbers, option labels, and mark values before translation.
3. Translate the full wording without omitting instructions, examples, headers, or footnotes.
4. Produce a source-to-target integrity ledger for every numbered item.
5. Generate a complete multilingual Overleaf document using fontspec and XeLaTeX, with a stated free-login step and a font fallback list.
6. Use CodeCogs only for individual equation previews, never as a full-paper renderer.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Preserve x^2-5x+6=0 exactly while translating the surrounding question.
Expected result or check target: Only the prose changes language; the equation, number, marks, and item label remain identical.
check this yourself
CHECK → https://latex.codecogs.com/png.image?x%5E2-5x%2B6%3D0
(paste-fallback: x^2-5x+6=0)
Encoding note: The caret, plus sign, and equals sign decode from %5E, %2B, and %3D to the exact locked equation.

OUTPUT FORMAT:
1. Source Transcription — complete ordered text
2. Locked Tokens — placeholders, notation, marks, numbering, and units
3. Full Translation — complete target-language paper
4. Integrity Ledger — item-by-item source and target check
5. Overleaf Package — XeLaTeX code, link or paste fallback, and login steps
6. Equation Previews — optional CodeCogs links for individual formulas

QUALITY AND TOOL GUARDRAILS:
- Preserve every placeholder, notation token, mark value, and numbering label character-for-character.
- Never guess illegible text or translate mathematical variable names and standard symbols.
- Multilingual Overleaf output requires a free login, XeLaTeX, and fontspec; never promise a specific installed font and always give a fallback.
- CodeCogs renders equations only, not paragraphs, pages, diagrams, or complete papers.
- Do not shorten, summarise, localise, or improve the source unless separately requested.
- 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.