Though just six pages long, the paper, so dense with technical jargon, is basically incomprehensible to nonexperts.

But behind its complicated terminology is a simple question that affects every aspect of society and business: How much time do we have before the burning of fossil fuels pushes the climate system past tipping points?

It is prompting the financial world to re-evaluate the value of the world's fossil fuel reserves and bolstering environmentalists' assertions.

Worst-case scenario: We have about 11 years at current rates of fossil fuel use, according to the paper.

"Once you hear the numbers, at least for me, there is no more room for wishful thinking, for speculation or for doubt," said Bill McKibben, founder of the activist group 350.org. Last year, McKibben plucked the science from popular obscurity and used it in a Rolling Stone article and speaking tour to stoke the moral case for carbon controls.

The paper, "Greenhouse-Gas Emission Targets for Limiting Global Warming to 2C," was published in April 2009 in Nature, the prestigious science journal. It was the work of researchers from Germany, the U.K. and Switzerland, led by Malte Meinshausen, a climatologist at Germany's Potsdam Institute for Climate Impact.

The study filled a factual void in a simmering debate over climate change. By 2006, the year the scientists began their research, many world governments had endorsed the scientific consensus that global temperature rise should be kept below 2 degrees Celsius in this century. But governments didn't know how far down the path of global warming they had already gone - and how much further they could safely go.

Meinshausen and his team, which included his brother Nicolai, a statistician at the University of Oxford, took up the puzzle. "It seemed the obvious thing to do with so many governments asking the question," Meinshausen said.

The scientists created what is called a global "carbon budget," which details how much carbon countries have emitted in the atmosphere from burning coal, oil and natural gas - and how much more they can "spend" before crossing 2 degrees. They didn't invent the concept - many others had crunched carbon budgets. But none were as rigorous.

The paper's methodology was groundbreaking. It was the first to incorporate hundreds of uncertainties in the climate system into a single climate model - factors that had never been modeled together or that hadn't been given proper weight in previous studies, such as radiative forcing or unknowns in the carbon cycle like how much carbon is stored in the deep ocean. In total, 400 environmental parameters were run under 1,000 different emissions scenarios.

What they found was stark: To have a 50-50 chance of keeping temperature rise below 2 degrees, humans would have to stick to a carbon budget that allowed the release of no more than 1,437 gigatons of carbon dioxide from 2000 to 2050.

To have an 80 percent chance of avoiding that threshold, they would have to follow a stricter budget and emit just 886 gigatons.

The paper found that by 2006, nations had already spent a quarter of that amount, or 234 gigatons. Meaning, the planet's carbon budget would be exhausted by 2024 if emissions levels stayed the same, or even earlier if they continue their upward trend.

From a scientific point of view, burning all of the world's proven fossil fuel reserves is not an option, the paper suggested. The reserves "vastly exceed the allowable CO2 emission budget for staying below 2C" of warming, it said.

Less than four years later, the paper is one the most cited environmental science studies ever.

FROM SCIENCE TO FINANCE

For years, investors had been hearing of carbon budgets and the 2-degree threshold - and they were growing concerned. As much as 30 percent of the value of some of the world's stock exchanges is in proven coal, oil and gas reserves, which energy companies are banking on mining and selling one day.

But what if governments buckled to activist pressure and decided to require firms to keep some of those reserves in the ground? What would that do to the market values of powerful energy companies? What would that do to the world's financial systems?

A newly formed group, made up of green-minded investors in London and called the Carbon Tracker Initiative, sought to assess those risks in a scientific way. They used Meinshausen's paper as the basis of their own report, "Unburnable Carbon," published in 2011.

The report tackled a question that Meinshausen had answered, but not in any depth: How much CO2 is in the world's fossil fuel reserves?

Using official records from U.S. Securities and Exchange Commission filings, among other documents, Carbon Tracker discovered that the world's top 200 fossil fuel companies have 2,795 gigatons of CO2 trapped in their fossil fuel reserves. And that figure didn't include unconventional sources like tar sands, oil shale and methane hydrates.

They also found that in the first 10 years of this century, humans had burned through one-third of Meinhausen's 886-gigaton budget, leaving just 565 gigatons left to use over the next 40 years. In sum, 80 percent of all fossil fuel reserves would have to remain untouched to prevent uncontrollable warming, the report warned.

"Investors need to be wary that stocks may not hold the same value they once did - and companies need to stop putting more capital into finding more reserves," said James Leaton, research director for the Carbon Tracker Initiative. "The future won't resemble the past for these industries."

"Unburnable Carbon" was the first, but not the last, study to consider whether energy companies' values were based on assumptions that might never pan out. Last month, global banking giant HSBC released a similar report using Meinshausen's 50-50 carbon budget scenario. It found that the largest oil and gas companies, including BP, Shell and Statoil, could lose 60 percent of their market values if governments proceed with tough carbon reduction targets and force companies to leave reserves untapped.

InsideClimate News is a nonprofit, nonpartisan news organization that covers environmental science.