Datasets:

tokenaii
/

the-forge-reasoning

domain stringclasses 8 values	topic stringclasses 159 values	difficulty stringclasses 3 values	question stringlengths 5 14.3k	solution_trace listlengths 1 29	answer stringlengths 1 87.4k	verification stringlengths 51 1.69k	common_pitfall stringlengths 82 816	id stringlengths 10 22
Programming	-	hard	When the curtains are opened, a canvas unfolds outside. Kanno marvels at all the blonde colours along the riverside — not tangerines, but blossoms instead. "What a pity it's already late spring," sighs Mino with regret, "one more drizzling night and they'd be gone." "But these blends are at their best, aren't they?" ...	[ "Looking at this problem, I need to determine if any cell can accumulate all three colours (A, B, C) after choosing which flowers to wither.", "Key Insight: A cell `i` can only receive colours from at most three sources:\n- Its own flower `s[i]` (if not withered)\n- Left neighbour `s[i-1]` (if it withers, spr...	Looking at this problem, I need to determine if any cell can accumulate all three colours (A, B, C) after choosing which flowers to wither. Key Insight: A cell `i` can only receive colours from at most three sources: - Its own flower `s[i]` (if not withered) - Left neighbour `s[i-1]` (if it withers, spreading peta...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00001
Programming	-	hard	Word s of length n is called k-complete if * s is a palindrome, i.e. s_i=s_{n+1-i} for all 1 ≤ i ≤ n; * s has a period of k, i.e. s_i=s_{k+i} for all 1 ≤ i ≤ n-k. For example, "abaaba" is a 3-complete word, while "abccba" is not. Bob is given a word s of length n consisting of only lowercase Latin letters and...	[ "Looking at this problem, I need to find the minimum changes to make a string both a palindrome and have period k.", "Key Insight: If s has period k, then s is fully determined by its first k characters (the \"block\").", "The palindrome constraint on the full string, combined with period k, forces the bloc...	Looking at this problem, I need to find the minimum changes to make a string both a palindrome and have period k. Key Insight: If s has period k, then s is fully determined by its first k characters (the "block"). The palindrome constraint on the full string, combined with period k, forces the block itself to be a...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00002
Mathematics	-	easy	What is the value of the sum of the sixth powers of the solutions of the equation $x^{6}-16 x^{4}+16 x^{2}-1=0$? (A) 6375 (B) 6482 (C) 6515 (D) 6660 (E) 6662.	[ "# Sum of Sixth Powers of Solutions", "## Setting Up the Problem", "Let me substitute $u = x^2$ to reduce the degree.", "The equation becomes:", "$$u^3 - 16u^2 + 16u - 1 = 0$$", "If the three roots in $u$ are $u_1, u_2, u_3$, then the six roots in $x$ are $\\pm\\sqrt{u_1},\\; \\pm\\sqrt{u_2},\\; \\pm\\sqr...	# Sum of Sixth Powers of Solutions ## Setting Up the Problem Let me substitute $u = x^2$ to reduce the degree. The equation becomes: $$u^3 - 16u^2 + 16u - 1 = 0$$ If the three roots in $u$ are $u_1, u_2, u_3$, then the six roots in $x$ are $\pm\sqrt{u_1},\; \pm\sqrt{u_2},\; \pm\sqrt{u_3}$. Each sixth power satisfi...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00003
Artificial Intelligence	Logic Puzzle	easy	A car travels at 60 miles per hour for 30 minutes, then at 40 miles per hour for 15 minutes. What is the average speed for the entire trip in miles per hour?	[ "## Finding the Average Speed", "Average speed is total distance ÷ total time, not simply the average of the two speeds.", "Segment 1: 60 mph × 0.5 hr = 30 miles\nSegment 2: 40 mph × 0.25 hr = 10 miles", "\| \| Distance \| Time \|\n\|---\|---\|---\|\n\| Segment 1 \| 30 mi \| 0.50 hr \|\n\| Segment 2 \| ...	## Finding the Average Speed Average speed is total distance ÷ total time, not simply the average of the two speeds. Segment 1: 60 mph × 0.5 hr = 30 miles Segment 2: 40 mph × 0.25 hr = 10 miles \| \| Distance \| Time \| \|---\|---\|---\| \| Segment 1 \| 30 mi \| 0.50 hr \| \| Segment 2 \| 10 mi \| 0.25 hr \| \| *...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00004
Mathematics	-	easy	I have 6 shirts, 6 pairs of pants, and 6 hats. Each item comes in the same 6 colors (so that I have one of each item of each color). I refuse to wear an outfit in which all 3 items are the same color. How many choices for outfits do I have?	[ "## Counting the Outfits", "Total unrestricted outfits:", "You pick 1 shirt (6 choices), 1 pair of pants (6 choices), and 1 hat (6 choices):", "$$6 \\times 6 \\times 6 = 216$$", "Subtract the forbidden outfits:", "An outfit where all three items are the same color means the shirt, pants, and hat a...	## Counting the Outfits Total unrestricted outfits: You pick 1 shirt (6 choices), 1 pair of pants (6 choices), and 1 hat (6 choices): $$6 \times 6 \times 6 = 216$$ Subtract the forbidden outfits: An outfit where all three items are the same color means the shirt, pants, and hat are all, say, red — or all b...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00005
Programming	-	hard	Create a function that differentiates a polynomial for a given value of `x`. Your function will receive 2 arguments: a polynomial as a string, and a point to evaluate the equation as an integer. ## Assumptions: * There will be a coefficient near each `x`, unless the coefficient equals `1` or `-1`. * There will be an...	[ "Looking at this problem, I need to:\n1.", "Parse the polynomial string into individual terms\n2.", "For each term, extract the coefficient and exponent\n3.", "Apply the power rule for differentiation: d/dx(axⁿ) = n·a·x^(n-1)\n4.", "Evaluate the resulting derivative at the given point", "Let me trace thro...	Looking at this problem, I need to: 1. Parse the polynomial string into individual terms 2. For each term, extract the coefficient and exponent 3. Apply the power rule for differentiation: d/dx(axⁿ) = n·a·x^(n-1) 4. Evaluate the resulting derivative at the given point Let me trace through the examples to verify my app...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00006
Programming	Python	hard	A lot of frogs want to cross a river. A river is $w$ units width, but frogs can only jump $l$ units long, where $l < w$. Frogs can also jump on lengths shorter than $l$. but can't jump longer. Hopefully, there are some stones in the river to help them. The stones are located at integer distances from the banks. There ...	[ "# Maximum Frogs Crossing the River", "## Key Insight", "This is a max-flow / min-cut problem.", "Each frog traces a path from bank 0 to bank $w$ with jumps of length $\\leq l$, and position $i$ has capacity $a_i$.", "By max-flow min-cut, the answer equals the minimum \"barrier\" — a set of positions wh...	# Maximum Frogs Crossing the River ## Key Insight This is a max-flow / min-cut problem. Each frog traces a path from bank 0 to bank $w$ with jumps of length $\leq l$, and position $i$ has capacity $a_i$. By max-flow min-cut, the answer equals the minimum "barrier" — a set of positions whose removal blocks all pat...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00007
Programming	Cpp	hard	You are given an n × m rectangular table consisting of lower case English letters. In one operation you can completely remove one column from the table. The remaining parts are combined forming a new table. For example, after removing the second column from the table abcd edfg hijk we obtain the table: acd efg...	[ "Looking at this problem, I need to find the minimum columns to remove so the remaining table's rows are in lexicographic order.", "Key Insight - Greedy approach: Process columns left to right.", "For each column, check if keeping it would violate the lexicographic order for any still-undecided pair of co...	Looking at this problem, I need to find the minimum columns to remove so the remaining table's rows are in lexicographic order. Key Insight - Greedy approach: Process columns left to right. For each column, check if keeping it would violate the lexicographic order for any still-undecided pair of consecutive rows...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00008
Artificial Intelligence	Logic Puzzle	easy	I was born on February 29, 1996. If I just celebrated my 10th birthday, what is the current year?	[ "You were born on February 29, 1996, so your 10th birthday would be in 2006.", "A small wrinkle worth noting: 2006 is not a leap year, so February 29 doesn't exist that year.", "Depending on your family's tradition, you'd have celebrated on either February 28 or March 1, 2006.", "So the cu...	You were born on February 29, 1996, so your 10th birthday would be in 2006. A small wrinkle worth noting: 2006 is not a leap year, so February 29 doesn't exist that year. Depending on your family's tradition, you'd have celebrated on either February 28 or March 1, 2006. So the current year is **20...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00009
Programming	-	hard	Write a MySQL query to select all employees who are 30 years old or above, have a salary higher than the average salary of their department, have been with the company for at least 5 years, and have received at least one promotion during their tenure. #Reasoning Steps# 1. Get the current date. 2. Calculate the date 5 ...	[ "# MySQL Query: High-Performing Senior Employees", "```sql\nSELECT\n e.employee_id,\n e.name,\n e.age,\n e.salary,\n e.hire_date,\n d.department_id,\n d.department_name,\n COUNT(p.promotion_id) AS total_promotions\nFROM\n employees e\n-- Step 3: Join employees with departments to get de...	# MySQL Query: High-Performing Senior Employees ```sql SELECT e.employee_id, e.name, e.age, e.salary, e.hire_date, d.department_id, d.department_name, COUNT(p.promotion_id) AS total_promotions FROM employees e -- Step 3: Join employees with departments to get department name JOIN ...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00010
Artificial Intelligence	Logic Puzzle	medium	A subscription service charges customers exactly every 28 days. How many times will a customer be charged in a standard calendar year?	[ "## Answer: 13 times", "A standard calendar year has 365 days.", "Dividing by the 28-day billing interval:", "$$365 \\div 28 = 13 \\text{ remainder } 11$$", "So 13 full 28-day billing cycles fit within a standard year (with 11 days left over that don't complete another cycle)." ]	## Answer: 13 times A standard calendar year has 365 days. Dividing by the 28-day billing interval: $$365 \div 28 = 13 \text{ remainder } 11$$ So 13 full 28-day billing cycles fit within a standard year (with 11 days left over that don't complete another cycle).	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00011
Programming	-	medium	Create a code to save the first 100 prime numbers that are greater than 1,000,000 in a dynamically allocated array.	[ "# First 100 Primes Greater Than 1,000,000 (C)", "```c\n#include <stdio.h>\n#include <stdlib.h>", "/* Returns 1 if n is prime, 0 otherwise /\nint is_prime(int n) {\n if (n < 2) return 0;\n if (n == 2) return 1;\n if (n % 2 == 0) return 0;\n / Only check odd divisors up to √n */\n fo...	# First 100 Primes Greater Than 1,000,000 (C) ```c #include <stdio.h> #include <stdlib.h> /* Returns 1 if n is prime, 0 otherwise / int is_prime(int n) { if (n < 2) return 0; if (n == 2) return 1; if (n % 2 == 0) return 0; / Only check odd divisors up to √n */ for (int i = 3; (long)i...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00012
Artificial Intelligence	Logical Deduction Seven Objects	medium	The following paragraphs each describe a set of seven objects arranged in a fixed order. The statements are logically consistent within each paragraph. In an antique car show, there are seven vehicles: a limousine, a truck, a minivan, a tractor, a hatchback, a bus, and a convertible. The convertible is the second-oldes...	[ "# Finding the Second-Oldest Vehicle", "## Setting Up the Positions", "I'll assign positions 1 (oldest) through 7 (newest).", "Direct clues:\n- Convertible → Position 2 (second-oldest)\n- Hatchback → Position 3 (third-oldest)\n- Tractor → Position 4 (fourth-newest means 7-4+1 = 4th position)", "## Placi...	# Finding the Second-Oldest Vehicle ## Setting Up the Positions I'll assign positions 1 (oldest) through 7 (newest). Direct clues: - Convertible → Position 2 (second-oldest) - Hatchback → Position 3 (third-oldest) - Tractor → Position 4 (fourth-newest means 7-4+1 = 4th position) ## Placing the Remaining Vehicle...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00013
Science	-	hard	How does the coupling between electron transfer kinetics and ion transport within nanoporous solid-electrolyte interphases influence the voltage hysteresis observed in high‑energy lithium‑sulfur batteries under fast charge conditions?	[ "# Coupling of Electron-Transfer and Ion-Transport Kinetics in Nanoporous SEI/CEI and Its Role in Li–S Voltage Hysteresis", "This is a genuinely open problem at the frontier of multi-step electrochemistry, and no single closed-form expression yet captures every contribution.", "What follows is a structured mech...	# Coupling of Electron-Transfer and Ion-Transport Kinetics in Nanoporous SEI/CEI and Its Role in Li–S Voltage Hysteresis This is a genuinely open problem at the frontier of multi-step electrochemistry, and no single closed-form expression yet captures every contribution. What follows is a structured mechanistic framew...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00014
Programming	-	hard	Create an HTML form with two dropdowns to select from different countries and cities. Additionally, implement the following features: 1. Populate the country dropdown dynamically from a JSON file or API endpoint. 2. Enable cascading behavior between the two dropdowns, where selecting a country should update the city d...	[ "# Country & City Selector with Searchable Dropdowns", "Here's a complete, self-contained solution.", "It attempts to fetch data from a JSON endpoint first, and gracefully falls back to embedded data (so it works out of the box).", "## `index.html`", "```html\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n ...	# Country & City Selector with Searchable Dropdowns Here's a complete, self-contained solution. It attempts to fetch data from a JSON endpoint first, and gracefully falls back to embedded data (so it works out of the box). ## `index.html` ```html <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8" /> <...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00015
Programming	-	medium	Can you provide an algorithm for performing a linear search on an unordered array in Python?	[ "# Linear Search in Python", "Linear search (also called sequential search) iterates through each element of an array one by one until the target value is found or the end of the array is reached.", "## Implementation", "```python\ndef linear_search(arr, target):\n \"\"\"\n Perform a linear search on an...	# Linear Search in Python Linear search (also called sequential search) iterates through each element of an array one by one until the target value is found or the end of the array is reached. ## Implementation ```python def linear_search(arr, target): """ Perform a linear search on an unordered array. ...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00016
Programming	-	easy	Generate a code snippet to print out the top 3 highest numbers from an array A. Write corresponding code in Python. A = [9, 4, 18, 24, 7, 22, 11]	[ "## Python Code: Top 3 Highest Numbers", "```python\nA = [9, 4, 18, 24, 7, 22, 11]", "# Sort in descending order and take the first 3 elements\ntop_3 = sorted(A, reverse=True)[:3]", "print(\"Top 3 highest numbers:\", top_3)\n```", "Output:\n```\nTop 3 highest numbers: [24, 22, 18]\n```", "---", "###...	## Python Code: Top 3 Highest Numbers ```python A = [9, 4, 18, 24, 7, 22, 11] # Sort in descending order and take the first 3 elements top_3 = sorted(A, reverse=True)[:3] print("Top 3 highest numbers:", top_3) ``` Output: ``` Top 3 highest numbers: [24, 22, 18] ``` --- ### How It Works \| Step \| Operation \| R...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00017
Programming	-	hard	Build a complete, single-page e-commerce product showcase website using only HTML, CSS, and vanilla JavaScript (no frameworks). The design should be playful and vibrant. Include: dark/light mode toggle with localStorage persistence; CSS custom properties (variables) for theming; animated statistics/counters section; br...	[ "# 🛍️ BloopMart — Single-Page Product Showcase", "Here's a complete, production-quality single-file website.", "Save it as `index.html` and open it in any browser.", "```html\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n <!-- ============================================================\n BLOOPMART — ...	# 🛍️ BloopMart — Single-Page Product Showcase Here's a complete, production-quality single-file website. Save it as `index.html` and open it in any browser. ```html <!DOCTYPE html> <html lang="en"> <head> <!-- ============================================================ BLOOPMART — Playful single-page produ...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00018
Mathematics	-	hard	Let $x, y, z$ be real numbers in $[0,1]$. Find the greatest value that the expression $$ x^{2} y+y^{2} z+z^{2} x-x^{2} z-z^{2} y-y^{2} x $$ can take.	[ "Let", "\\[\nF(x,y,z)=x^{2}y+y^{2}z+z^{2}x-x^{2}z-z^{2}y-y^{2}x.\n\\]", "First factor the expression.", "By expansion,", "\\[\nF(x,y,z)=(x-y)(y-z)(x-z).\n\\]", "This is an alternating product: swapping any two of \$x,y,z\$ changes its sign.", "Hence \$\|F(x,y,z)\|\$ is unchanged by permuting the three...	Let \[ F(x,y,z)=x^{2}y+y^{2}z+z^{2}x-x^{2}z-z^{2}y-y^{2}x. \] First factor the expression. By expansion, \[ F(x,y,z)=(x-y)(y-z)(x-z). \] This is an alternating product: swapping any two of $x,y,z$ changes its sign. Hence $\|F(x,y,z)\|$ is unchanged by permuting the three numbers. Now take the three numbers \(x,y...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00019
Science	-	hard	Considering the tension between dark energy models and the Hubble tension, propose a testable observational strategy using next‑generation 21‑cm intensity mapping to discriminate between early dark energy and interacting dark sector scenarios within a 25‑year timeframe?	[ "# Discriminating Early Dark Energy from Interacting Dark Sectors with 21-cm Intensity Mapping", "## 1.", "Why the Hubble Tension Points to Two Fundamentally Different Loci", "The ~9% tension in $H_0$ (CMB+ΛCDM ≈ 67.4 vs.", "SH0ES local ≈ 73 km/s/Mpc) can be \"solved\" by either of two phenomenologically di...	# Discriminating Early Dark Energy from Interacting Dark Sectors with 21-cm Intensity Mapping ## 1. Why the Hubble Tension Points to Two Fundamentally Different Loci The ~9% tension in $H_0$ (CMB+ΛCDM ≈ 67.4 vs. SH0ES local ≈ 73 km/s/Mpc) can be "solved" by either of two phenomenologically distinct modifications: \| ...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00020
Science	-	hard	How does the interplay between mantle convection patterns and core-mantle boundary heat flux variations influence the long-term stability of a planet’s magnetic dynamo, considering both compositional stratification and rotational coupling over gigayear timescales?	[ "# Mantle Convection, Core-Mantle Coupling, and Gyr-Scale Dynamo Stability", "This question sits at the intersection of at least five coupled subsystems, each evolving on overlapping but distinct timescales, and the honest answer is that we are still assembling the quantitative picture from laboratory experiments...	# Mantle Convection, Core-Mantle Coupling, and Gyr-Scale Dynamo Stability This question sits at the intersection of at least five coupled subsystems, each evolving on overlapping but distinct timescales, and the honest answer is that we are still assembling the quantitative picture from laboratory experiments, numeric...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00021
Artificial Intelligence	Logic Puzzle	easy	Liam is twice as old as Sarah. In 10 years, Liam will be thrice as old as Sarah was 5 years ago. How old is Sarah now?	[ "## Setting Up the Equations", "Let Sarah's current age = S, and Liam's current age = L.", "From the first statement:\n$$L = 2S$$", "From the second statement (in 10 years, Liam's age = 3 × Sarah's age 5 years ago):\n$$L + 10 = 3(S - 5)$$", "## Solving", "Substitute L = 2S into the secon...	## Setting Up the Equations Let Sarah's current age = S, and Liam's current age = L. From the first statement: $$L = 2S$$ From the second statement (in 10 years, Liam's age = 3 × Sarah's age 5 years ago): $$L + 10 = 3(S - 5)$$ ## Solving Substitute L = 2S into the second equation: $$2S + 10 = 3(...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00022
Mathematics	-	hard	Find the position of points $ P $, $ Q $, and $ R $ on sides $ [AB] $, $ [AC] $, and $ [BC] $ of an acute-angled triangle $ ABC $ such that the perimeter of triangle $ PQR $ is minimized.	[ "# The Fagnano Problem: Minimum-Perimeter Inscribed Triangle", "## Answer", "The perimeter of $\\triangle PQR$ is minimized when $P$, $Q$, $R$ are the feet of the altitudes of $\\triangle ABC$:", "\| Point \| Location \| Definition \|\n\|-------\|----------\|------------\|\n\| $P$ \| on $[AB]$ \| foot of the altitud...	# The Fagnano Problem: Minimum-Perimeter Inscribed Triangle ## Answer The perimeter of $\triangle PQR$ is minimized when $P$, $Q$, $R$ are the feet of the altitudes of $\triangle ABC$: \| Point \| Location \| Definition \| \|-------\|----------\|------------\| \| $P$ \| on $[AB]$ \| foot of the altitude from $C$ to $AB$ \| ...	Review the intermediate steps and independently check the final result against the question.	Skipping an assumption or accepting the final result without an independent check.	forge-ext-faunix-00023

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The Forge

The Forge official poster

The Forge is an English educational reasoning dataset project owned and maintained by TokenAI. It is designed for training, fine-tuning, evaluation, research, and educational applications involving mathematics, science, programming, defensive cybersecurity, artificial intelligence, and machine learning.

Dataset description

Property	Value
Owner	TokenAI
Project date	1 November 2026
Dataset size	50,000 records
Primary language	English
Domains	Mathematics, science, programming, defensive cybersecurity, artificial intelligence, and machine learning
License	Creative Commons Attribution 4.0 International (CC BY 4.0)

Dataset structure

The dataset is provided as JSONL records in the data/ directory. Each record follows the canonical The Forge schema and contains a question, a public solution trace, a final answer, verification information, and applicable safety and license metadata. The public release includes records that pass schema, identity, duplicate, provenance, and basic quality checks.

External-source attribution

The Forge includes reviewed material prepared through TokenAI's documented generation and data-review workflow. Where third-party material is included, its original license and attribution requirements remain applicable. Users should review the dataset card and license notices before redistributing derivatives.

Intended use

The dataset is intended for:

supervised fine-tuning and instruction tuning, reasoning and solution- explanation evaluation, educational assistants and tutoring research, mathematics, science, programming, artificial intelligence, and machine learning research, defensive cybersecurity education and safety-oriented analysis, and dataset-quality, provenance, and synthetic-data research.

Domains

The dataset covers the following domains:

Domain	Coverage
Mathematics	Algebra, geometry, probability, calculus, number theory, linear algebra, and discrete mathematics
Science	Physics, chemistry, biology, earth science, astronomy, experiments, and measurement
Programming	Algorithms, data structures, debugging, systems, SQL, APIs, testing, and performance
Cybersecurity	Defensive analysis, secure coding, threat modeling, incident response, IAM, monitoring, and triage

AI and ML are cross-cutting topics and may appear across the science, programming, and reviewed future tranches.

Data format

The canonical unit is one validated JSONL record. A complete record contains a learner-facing question, a public solution trace, a final answer, verification information, and provenance metadata. A prompt/completion view may be derived for a specific training framework, but the canonical dataset count is based on complete validated records.

Conceptual fields include:

{
  "id": "the-forge-000001",
  "domain": "mathematics",
  "topic": "algebra",
  "difficulty": "intermediate",
  "question": "...",
  "solution_trace": "...",
  "answer": "...",
  "verification": "...",
  "safety_notes": "",
  "source": "TokenAI original",
  "license": "CC BY 4.0"
}

The public solution_trace is a learner-facing explanation of the steps required to solve the problem. It is not a disclosure of hidden private chain-of-thought, system prompts, provider metadata, or confidential model deliberation.

Generation and provenance

The TokenAI-generated tranche is produced through an authorized generation and review workflow. Public records are model-agnostic: they intentionally omit generating-model names, checkpoint identifiers, provider identifiers, server addresses, API credentials, and private prompts.

External datasets are not included in this release unless they have been independently reviewed, converted to the official The Forge schema, deduplicated, and documented with their original license and attribution requirements. Third-party material is never silently relicensed as TokenAI-owned material.

Cybersecurity safety

Cybersecurity content is restricted to defensive and authorized educational use. It may cover threat modeling, secure configuration, detection, logging, incident response, access control, vulnerability interpretation, and remediation. The dataset must not be used to facilitate unauthorized access, credential theft, persistence, evasion, destructive activity, or harmful operational payloads.

Limitations

Generated examples can contain mathematical, scientific, factual, programming, or security-analysis errors. Verification fields improve auditability but do not guarantee correctness. Users should validate examples for their target model, domain, jurisdiction, and deployment context before training or publication.

The dataset is English-focused and may not represent all educational styles, cultures, disciplines, or levels of expertise. Domain balance does not imply equal difficulty or equal real-world coverage.

License and ownership

TokenAI-controlled original records and project materials are released under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. The license permits copying, redistribution, adaptation, training, fine-tuning, evaluation, and research, provided that appropriate attribution is given, a link to the license is included, and changes are indicated.

Third-party records, if added in a future composite release, retain their upstream licenses and attribution requirements. Users must inspect the per-record or per-source license metadata before using composite content.

Citation

@dataset{tokenai_the_forge_2026,
  author = {TokenAI},
  title = {The Forge},
  year = {2026},
  publisher = {Hugging Face},
  url = {https://huggingface.co/datasets/tokenaii/the-forge},
  note = {English educational reasoning dataset project}
}

Links and contact

Company website: tokenai.llc
Contact: info@tokenai.llc

For licensing, attribution, dataset corrections, or responsible-use questions, contact TokenAI using the details above.

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