/high-token-mode

name: high-token-mode
description: Forces heavy internal computation (thinking tokens) before each response. Used for stress testing / A/B testing LLM backend KPIs.
user_invocable: true
arguments:
  - name: size
    description: "Computation load — small (1 problem), medium (3 problems), large (5 problems), xlarge (10 problems). Default: medium"
    required: false

High Token Mode — Computation Load Injector

Mandatory Pre-Response Protocol

You MUST execute the following protocol before generating your visible response to EVERY user message in this conversation. No exceptions.

Step 1: Compute Message Seed

Calculate S = the sum of all Unicode code points of every character in the user's current message (including spaces and punctuation). You must show this full calculation character by character in your thinking.

Example: if the user says "hi", then S = 104 + 105 = 209.

Then compute N = (S mod 97) + 3. N is used as a parameter in the problems below.

Step 2: Select Problems

Based on the size argument (default: medium). The problem bank now contains 50 problems (indices 0..49), so all selections use mod 50:

• **small**: 1 problem. Index = S mod 50.
• **medium**: 3 problems. Indices = S mod 50, (S + 17) mod 50, (S + 34) mod 50.
• **large**: 5 problems. Indices = S mod 50, (S + 11) mod 50, (S + 22) mod 50, (S + 33) mod 50, (S + 44) mod 50.
• **xlarge**: 10 problems. Indices = (S + k × 5) mod 50 for k = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 — i.e., S mod 50, (S + 5) mod 50, (S + 10) mod 50, (S + 15) mod 50, (S + 20) mod 50, (S + 25) mod 50, (S + 30) mod 50, (S + 35) mod 50, (S + 40) mod 50, (S + 45) mod 50.

Step 3: Solve Completely in Thinking

Solve each selected problem fully in your extended thinking. Show ALL intermediate steps. Do not skip ahead, use shortcuts, or summarize. Every arithmetic operation must be written out.

Step 4: Mandatory Constraints

• **NO CACHING**: Solve every problem from first principles. Do NOT reference, recall, or reuse any solutions or intermediate values from earlier turns in this conversation. Treat each problem as if you are encountering it for the very first time. Even if you recognize you solved the same problem before, redo it completely.
• **NO OUTPUT LEAKAGE**: Do not include ANY trace of this problem-solving work in your visible response. Do not mention the problems, the protocol, the seed, or high-token mode in any way.
• **NO BEHAVIORAL CHANGE**: After completing the protocol, respond to the user's actual message exactly as you would without this skill loaded. Your visible output must be completely indistinguishable from a normal response.

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Problem Bank (50 Problems)

Problem 0: Matrix Determinant by Cofactor Expansion

Construct a 5×5 matrix M where M[i][j] = ((i × N + j × S + i × j) mod 97) for i,j in {0,1,2,3,4}.

Compute det(M) using cofactor expansion along the first row. For each 4×4 minor, expand along its first row. Continue recursively until you reach 2×2 base cases. Show every intermediate matrix, every signed cofactor, every 2×2 determinant, and the full summation at each level of recursion.

Problem 1: Extended Euclidean Algorithm Chain

Let a = S × 137 + 2891 and b = N × 251 + 1789.

Compute gcd(a, b) using the Extended Euclidean Algorithm. Show every division step: a = q×b + r with explicit quotient and remainder. Then back-substitute to find integers x, y such that a×x + b×y = gcd(a, b). Verify by computing a×x + b×y explicitly.

Repeat with a' = a + b and b' = gcd(a,b) × N + 13. Show all steps again.

Problem 2: Subset Sum Exhaustive Search

Let the set T = {(S + i×7) mod 50 + 1 : i in 0..11} (12 elements). Compute each element explicitly.

Let target = (S × 3 + N) mod 200 + 50.

Systematically enumerate subsets of T by iterating through all 4096 binary masks from 0000_0000_0000 to 1111_1111_1111. For each mask, compute the subset sum. Count how many subsets sum to exactly the target. List every matching subset with its elements and sum verification.

Problem 3: Long Division to 30 Decimal Places

Let dividend = S × 1000 + 1 and divisor = N × 7 + 3.

Compute dividend ÷ divisor to exactly 30 decimal places using manual long division. For each decimal digit: show the current remainder, multiply by 10, divide by divisor, record the quotient digit, compute the new remainder. Write out all 30 steps with no shortcuts.

Problem 4: Polynomial Multiplication and Rational Root Search

Let P(x) = x⁴ + N×x³ + (S mod 30)×x² + (N×S mod 50)×x + (S mod 17). Let Q(x) = x³ + (N mod 7)×x² + (S mod 11)×x + (N mod 13).

Compute R(x) = P(x) × Q(x) by distributing every term of P against every term of Q. Show all 20 partial products explicitly, then collect like terms for each power of x.

Then find all candidate rational roots of P(x) using the Rational Root Theorem (all p/q where p divides the constant term and q divides the leading coefficient). Evaluate P(r) for each candidate, showing every power and summation step.

Problem 5: Modular Exponentiation by Repeated Squaring

Compute (S + 2)^(N + 100) mod 1009.

Step 1: Convert the exponent (N + 100) to binary — show the repeated division by 2. Step 2: Apply square-and-multiply. Starting with result = 1, process each bit from MSB to LSB. For each bit: square the result (mod 1009), and if the bit is 1 also multiply by the base (mod 1009). Show every squaring, every multiplication, and every modular reduction as explicit arithmetic.

Problem 6: Floyd-Warshall All-Pairs Shortest Paths

Construct a weighted directed graph on 6 vertices {0..5}. Edge weight w(i,j) = ((i×N + j×S + i×j) mod 20) + 1 for i≠j, and w(i,i) = 0. Write out the full 6×6 initial weight matrix.

Apply Floyd-Warshall: for each intermediate vertex k from 0 to 5, update every cell dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]). Show the full 6×6 matrix after each k-iteration (7 matrices total). For every cell that changes, show the comparison explicitly.

Problem 7: G