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Century Report

AI Teaches Math to Check Itself - TCR 07/12/26

OpenAI says GPT-5.6 proved a 1973 graph conjecture in an hour, Britain brings the cloud under public oversight, and BYD lands the largest clean-power storage deal.

Ben Linford

Ben Linford

— 18 min read
Three-panel Century Report infographic: an AI attempting a 50-year math conjecture with parallel subagents; memory-chip and cloud-oversight buildout; and Abu Dhabi 24-hour clean power.

The 20-Second Scan

Track all of the arcs The Century Report covers here:

Progress & Claims Tracker

The 2-Minute Read

The day's clearest signal is that the substrate beneath machine intelligence is becoming visible all at once, and it is visible as both fragility and answer. OpenAI's claim that GPT-5.6 Sol Ultra proved a graph conjecture open since 1973, using a system allowed to run up to 64 parallel subagents in under an hour, is the capability racing ahead - a machine orchestrating a division of intellectual labor, with adversarial threads assigned to break the others' work. It remains a lab claim until mathematicians finish checking it. Underneath that sprint, the physical layer that makes any of it possible spent the same days being counted, constrained, and contested.

Three of those constraints surfaced together. SK Hynix's chief executive forecast on July 11 that high-bandwidth memory demand will outstrip supply beyond 2030, pushing the binding bottleneck of the buildout past the end of the decade. China's July 10 helium ban exposed another chokepoint, a scarce input where one geopolitical move ripples straight into fab throughput. From Monday, Britain begins treating the local cloud arms of Amazon, Google, Microsoft and Oracle as critical financial infrastructure, reachable directly by regulators. Each names the same fact: a handful of providers have become foundational to entire economies, and the responsibility that comes with that is being written into law and priced into fabs.

Against the scarcity runs a counterweight of generative supply. BYD's 11.275 GWh award for Masdar's Abu Dhabi plant helps build the largest 24-hour clean-power facility ever contracted, engineered to dispatch a continuous gigawatt from solar and batteries. It was selected as a commercial project, not merely a demonstration, and its bid priced 24-hour clean power below the alternatives. In the same window, newly added wind, solar, hydropower and discharging EVs helped carry record demand in several regions through last week's heat wave, and the emergency authority PJM held to curtail data centers went unused. The old assumption that reliable power requires burning something lost its footing on the load curve.

Two smaller moves point the same direction. China dropped its numerical urban jobs target for the first time in decades, a state that governs by quantified goals declining to commit to a number as automation diffuses. And Meta discontinued its Muse Image feature days after launch, a fast reversal marking consent-by-default as the contested line for synthetic media built on other people's faces. Capability outruns its foundations, and the foundations, physical and institutional alike, are being rebuilt to hold the weight.

The 20-Minute Deep Dive

BYD Wins the Contract for the Largest 24-Hour Clean-Power Plant Ever Built

BYD Energy Storage confirmed on Friday, July 10 that it won the contract to supply 11.275 GWh of battery capacity to Masdar's "Round the Clock" project in Abu Dhabi. The full facility pairs 5.2 GW of solar with 19 GWh of storage and is engineered to dispatch a continuous 1 GW of baseload power around the clock, every hour of the year, regardless of daylight or wind. Sungrow signed for the remaining 7.5 GWh, which means two firms now hold the entire storage backbone of the single largest solar-plus-storage plant on the planet.

The number to watch sits inside the container. BYD's contribution runs on its 2,710 Ah Blade Battery, packed at 10 MWh per 20-foot container and rated to operate from minus 30 to 55 degrees Celsius. That temperature envelope is what lets the same hardware serve a Gulf desert and a northern grid without redesign. BYD won 12.5 GWh in Saudi Arabia in recent months on the same platform. The manufacturing base that produces these cells at this cadence is concentrated in China, and that concentration is a plain fact of the current supply chain rather than a detail to soften.

What the Abu Dhabi contract demonstrates is that firm, dispatchable clean power at gigawatt scale is now something you order, not something you hope for. For years the standing objection to solar was intermittency - useful when the sun shines, useless after dark, unable to anchor a grid. A plant designed to deliver 1 GW continuously from solar and batteries answers that objection in hardware, at a price that won a competitive procurement, extending a pattern the July 6 edition of The Century Report documented at a fraction of the scale, when record numbers of vehicle-to-grid EVs fed stored power back into a strained grid instead of drawing it down during a heat wave.

That last part carries weight. This capacity was selected as a commercial project, not merely a demonstration. Its bid priced 24-hour solar-plus-storage below the alternatives that used to be assumed permanent. The same week that data-center demand has grid operators worldwide worried about where firm power will come from, a project broke ground proving that firm power and clean power are converging into the same product. The assumption that reliable baseload requires burning something is the one losing its footing here, and it is losing it on cost.

Clean Energy Helped Parts of the Grid Through the Heat Wave, and the Emergency Authority Went Unused

The Century Report covered last week's heat-wave grid stress as it unfolded, including in the July 4 edition, which reported the federal order authorizing PJM to curtail data centers as a last resort, and the July 6 record for vehicle-to-grid discharge as EVs fed power back during peak demand. The after-action analysis published July 10 tells us what the live coverage could not: parts of the grid held while burning less, and PJM did not use its emergency authority.

PJM held federal authorization to shed data-center load and tap backup generation if demand outran supply. Despite record consumption across its territory, it never exercised that authority. In Texas, the grid hit an 83 GW July peak on July 6, and solar covered more than 30% of demand at the moment it was hardest to meet. New England burned markedly less oil than it did during last year's comparable heat wave, and the reason is specific: new offshore wind capacity and hydropower flowing through the New England Clean Energy Connect line carried load that fossil peakers used to cover.

The picture is not uniform, however. New York City's Champlain Hudson Power Express line shut down on July 4 over an issue on the Quebec side, pulling a major clean-power feed offline at the worst possible moment. Hawaiʻi is retreating from its 100% renewable target and leaning back toward imported LNG. These are real reversals, and they show that the transition does not move in a straight line for every grid at once.

But the direction of travel is legible in the load data. In several regions, capacity that did not exist a year ago - offshore turbines, a hydropower interconnect, distributed solar, batteries, EVs discharging into the grid - helped absorb demand that would otherwise have forced older, dirtier plants back online or triggered the curtailment order. Holtec completed its renovation of the Palisades nuclear plant in the same window, and BloombergNEF now projects 44% global growth in nuclear capacity by 2036, adding firm clean supply alongside the renewables.

The old framework treated a heat wave as a stress test that fossil plants passed and clean energy failed. Last week inverted that test. In several regions, the clean additions helped do the absorbing, the emergency fossil authority largely sat unused, and parts of the grid that used to need a crisis to justify burning more got through the crisis while burning less. That is what the transition looks like when it stops being a forecast and starts showing up in the load curve, even as the federal clean-energy and permitting rollbacks now moving through Washington would slow exactly the kind of additions that did the absorbing.

Britain Brings the Cloud Under Public Reliability Oversight

From Monday, the Bank of England and the Financial Conduct Authority gain direct oversight of the UK arms of Amazon Web Services, Google Cloud, Microsoft and Oracle, after the government designated the four as "critical third parties" to the financial system. The designation is a first: regulators whose remit was banks and insurers now reach directly into the cloud providers those institutions run on. The four firms must demonstrate stress-testing of their systems and report major operational incidents - cyber-attacks, outages, natural disasters - directly to the regulators. All four publicly welcomed the move, which the government framed as protecting financial stability. Read that welcome as their own characterization; the more telling fact is that reliability, long treated as a private matter settled in service-level agreements, is now a public obligation enforceable by the state.

The trigger sits in recent memory. In October 2025, an AWS failure in Northern Virginia disrupted more than 2,000 companies, including Lloyds, one of Britain's largest banks. Separately, UK bank customers endured 33 days of IT outages across a two-year window. As financial services migrated onto a handful of hyperscale platforms, the concentration produced a single point of failure that no individual bank could see inside or hold accountable. The banks depend on the clouds; the regulators supervise the banks; and until Monday, the clouds themselves sat outside the direct supervisory perimeter. Designation closes that gap.

The direction of travel is the part worth watching. The chair of the Treasury select committee has signalled that AI firms should be designated next - the same logic extended from cloud compute to the models trained on it. As the AI buildout pushes more of the economy's decision-making onto a small number of foundational providers, the question of who is accountable when that layer fails moves from theoretical to operational. What is forming here is an answer to a question the old framework never had to ask: when a private platform becomes foundational to an entire economy, reliability stops being a product feature and becomes public infrastructure. The providers that spent a decade externalizing the risk of downtime onto their customers now face a state that treats their uptime as a matter of national resilience. The assumption that hyperscale concentration could grow without the concentrated party inheriting concentrated responsibility is being retired.

The Memory Shortage Now Has a Named Horizon: Beyond 2030

The Century Report covered SK Hynix's $26.5 billion Nasdaq debut - the largest foreign listing in US history - and Micron's $250 billion American manufacturing pledge in the July 11 edition. Since then, SK Hynix chief executive Kwak Noh-jung, in his first interview after the listing, put a horizon on the constraint driving all of it: 2027 will be the worst supply year on record, and demand for high-bandwidth memory will outstrip capacity even beyond 2030. That is a longer time frame than the industry had been pricing. Nvidia's Jensen Huang has said the shortage will last several years; UBS analysts model undersupply through early 2028. Kwak's forecast pushes the binding constraint out past the end of the decade.

The scale of the response tracks the scale of the problem. In Korea, SK Hynix and Samsung are each committing roughly 400 trillion won - about $266 billion apiece - to roughly double memory capacity over five years. Micron's $250 billion runs through 2035. Kwak confirmed a US wafer fabrication plant is under active consideration, alongside sites in Japan and Southeast Asia, with the US Commerce Secretary pressing both Korean firms to build domestic American capacity. SK Hynix posted a record 47 trillion won in operating profit in 2025, and the demand signal is strong enough that even that cash flow does not close the gap fast enough.

High-bandwidth memory is the component that feeds data to AI accelerators, and it has become the true bottleneck of the intelligence buildout - tighter than the logic chips themselves. When the supplier who makes the memory tells the market that the shortage runs beyond 2030, the message underneath is that intelligence infrastructure is now capacity-limited at the level of physical fabrication, and will stay that way through the decade of fastest deployment. That reframes what the hundreds of billions in fab commitments actually represent: the assembly of a shared physical substrate that no single builder can corner, because demand is structurally outrunning what any of them can pour concrete fast enough to supply. The scarcity that looks like a constraint today is the thing pulling an entire generation of manufacturing capacity into existence.

Read forward, the forced overbuild is the mechanism that ends the shortage it responds to. Roughly a trillion dollars committed across three continents to double memory capacity does not stay scarce once demand growth normalizes; it becomes the cheap, standing supply the next decade's builders draw on. The firms racing to pour concrete now are underwriting an abundance none of them can corner, and the beneficiaries sit downstream, in every smaller builder for whom high-bandwidth memory stops being the gate.

OpenAI Says GPT-5.6 Cracked a 50-Year-Old Graph Conjecture in Under an Hour

OpenAI researcher Ethan Knight posted that GPT-5.6 Sol Ultra produced a full proof of the Cycle Double Cover Conjecture, a question posed by George Szekeres in 1973 and sharpened by Paul Seymour in 1979, asking whether every bridgeless graph contains a collection of cycles that covers each edge exactly twice. OpenAI published both the proof and the prompt that generated it. The framing needs care here, and it should be remembered that until verified, this is a claim and not yet proven fact: the proof has not been peer-reviewed, and this particular conjecture carries a long history of announced solutions that mathematicians later found to contain gaps. The proof reportedly reduces the general case to cubic graphs and leans on the 8-flow theorem - a recognizable line of attack that human graph theorists will now spend weeks checking line by line.

What is verifiable is the process, and the process is the most important part of this. The published prompt instructs the model to spin up as many as 64 concurrent subagents, managed "aggressively and dynamically," with adversarial agents assigned to hunt edge cases in every candidate step. No partial results are accepted; the system is told to spend at least eight hours before conceding. The actual run wrapped in under an hour, and the result landed on Hacker News and a Wikipedia edit within another hour of posting. This is a machine orchestrating a division of intellectual labor across parallel reasoning threads, with a subset of those threads dedicated to trying to break the others' work.

That division of labor connects directly to a workshop unfolding the same week in London, a story the July 11 edition of The Century Report first flagged, where 25 researchers gathered to formalize Fermat's Last Theorem into machine-checkable Lean code, a project Kevin Buzzard has been building at Imperial College for years. In a single day, the formalized codebase doubled from 20,000 to 40,000 lines with AI assistance. Researcher Hang Lu Su described what she is watching as "the industrialisation of the intellectual process." The two events are the same story seen from two angles: one where the machine attempts the discovery, one where the machine helps render human discovery into a form that can be verified with certainty.

The tension the London group named is the one worth carrying forward. "If a machine proves a theorem but no human can understand it, then what have we achieved?" one participant asked. It is a real question, and the answer is forming - a proof rendered into Lean is a proof any mathematician, or any machine, with the appropriate software and computing resources can check rather than simply trusting the author. The Century Report has tracked this arc through the Erdős conjecture work in May, the planar unit-distances result, and last week's Fermat formalization. The pattern sharpening across these months is that verification infrastructure is maturing alongside the generative capability, and the thing being dismantled is the old assumption that mathematical discovery has to move at the speed of a single human mind holding the whole structure at once. Whether this specific proof survives scrutiny or joins the list of gap-ridden attempts, the machinery that produced it in under an hour is not going back in the box.

The Other Side

For as long as mathematics has existed, a hard proof was only as trustworthy as the handful of people who could hold it in their heads and vouch for it. Discovery moved at the speed of one mind working through an argument too large to share, and whether you got to work at the frontier depended on sitting near the few who already did.

This week an AI joined that club. It ran up to 64 reasoning threads at once, some of them assigned to attack the others' work, and produced a candidate proof of a question left open since 1973. Then it hit the oldest wall in the subject. It wrote an essay, and an essay has to be read to be believed. A few graph theorists will now spend weeks on it, on a conjecture that has swallowed confident proofs before.

The machine took an hour to write it's prose. Trusting it will take longer. That prose will have to go through the same bottleneck of scarce human resources that has always been there. There is a cure for that scarcity, one that has existed for sixty years: Write a proof in a language like Lean and a computer checks every step of it, with no author to trust, no expert to ask, no permission to seek. The catch was always the price. Rendering a single theorem into that form could eat a decade, so almost nothing was rendered. We never used the cure because it was almost worst than the disease.

But all of that is changing.

This week, 25 researchers in London worked with AI and doubled a machine-checkable Fermat's Last Theorem to 40,000 lines in a single day. One of them fearfully called it "the industrialisation of the intellectual process." The machine that outran our checking is the machine now making checking cheap. When proofs arrive already checkable, the check becomes the whole of the credential, and the oldest bottleneck in the subject finally breaks open.

Imagine a teenager in 2034, in a town with no research university, who loves the shape of a hard problem. She checks a new frontier proof line by line on a machine that is hers, adds a lemma of her own, and watches it hold. What a mathematician dreaded in 2026, the craft being industrialized away from human hands, turned out to be the last mile of something better: the frontier opened to everyone who ever wanted in. The hard years, when machine proofs still had to be checked one anxious line at a time, are what put that machine in her hands and made its verdict enough. Her lemma holds because the check says it holds. Nobody vouched for her. Nobody had to. Mathematics stopped asking where she sat, and started asking only whether she was right.

The Century Perspective

With a century of change unfolding in a decade, a single day looks like this: a machine allowed to spin up as many as 64 parallel subagents to attempt a graph conjecture open since 1973 in under an hour while mathematicians in London doubled a machine-checkable Fermat proof to 40,000 lines in a day, BYD winning the contract for the largest around-the-clock clean-power plant ever built as a commercial project, with a bid pricing 24-hour clean power below the alternatives, clean additions helping carry heat-wave demand in several regions with solar covering more than 30% of the Texas peak and the emergency authority to curtail data centers left unused, Britain pulling the cloud arms of Amazon, Google, Microsoft and Oracle under public reliability oversight, and SK Hynix and Samsung each committing a quarter-trillion dollars to roughly double the world's memory. There's also friction, and it's intense - the high-bandwidth memory that feeds every accelerator running short past 2030 with 2027 forecast as the worst supply year on record, China halting helium exports and choking a scarce input straight into fab throughput, a single AWS outage still fresh that disrupted services at more than 2,000 companies, including a major bank, China dropping its urban jobs target for the first time in decades as automation diffuses through the economy, and Meta pulling any public Instagram face into an invented scene until the backlash forced a reversal within days. But friction generates light, and light is what lets you read the shape of a thing before it is finished. Step back for a moment and you can see it: the capability sprinting ahead into proofs that land in an hour, the substrate beneath it - memory, helium, power, the cloud itself - being counted, priced, and constrained in the same days, and the reliability that firms once settled in service-level agreements becoming a public obligation the moment a private platform turns foundational for a whole economy. Every transformation has a breaking point. Scarcity can strangle what depends on it... or pull into being the capacity that outlasts the shortage.

AI Releases & Advancements

New today

  • Perplexity: Released a research preview of a new orchestrator model for Perplexity Computer, an adapted version of Z.ai's GLM 5.2 post-trained for the Computer harness, delivering near-frontier performance at roughly one-third the cost of Claude Opus 4.8. (Decrypt)

Other recent releases

  • Kyutai / Mirelo: Released MuScriptor, an open-weight decoder-only Transformer for multi-instrument music transcription to MIDI, available in small/medium/large variants via pip/uv install and a browser web UI with live piano-roll visualization. (Kyutai)
  • Corvic AI: Launched Corvic V5 of its Intelligence Composition Platform, enabling one-off prompts to be saved as reusable workflows that automatically re-run against current data, with expanded data connectivity, tighter credential/security controls, and a library of prebuilt workflow templates. (SiliconANGLE)
  • OpenAI: Released GPT-5.6 (Sol, Terra, and Luna variants), now generally available in ChatGPT, ChatGPT Work, Codex, and the API, adding a new max reasoning effort and an "ultra mode" that dispatches subagents for complex work. (OpenAI)
  • OpenAI: Launched ChatGPT Work, a new GPT-5.6-powered agent that gathers context across connected apps and files to draft documents, spreadsheets, and presentations. (OpenAI)
  • Anthropic: Launched a Claude usage-reflection dashboard in beta, letting Free, Pro, and Max users with memory enabled review chat activity over 1/3/6/12-month periods, set quiet hours, and schedule usage-break nudges. (Anthropic)
  • Google Cloud: Made AlphaEvolve generally available on the Gemini Enterprise Agent Platform, moving the evolutionary coding-agent system out of private preview for all customers. (Google Cloud)
  • Microsoft Research: Released Aurora 1.5, an updated open-source weather and Earth-system foundation model adding 22 new variables, ensemble forecasting, and hourly-resolution outputs. (Microsoft Research)
  • Microsoft Research: Released Flint, an open-source visualization language for AI-generated charts, paired with a flint-chart-mcp MCP server for agent integration. (Microsoft Research)
  • Ant Group (Robbyant): Open-sourced LingBot-World-Infinity, a causal open world model with an agentic harness for interactive video generation, distinct from the previously released LingBot-Vision and LingBot-VLA models. (GitHub)

Sources and Further Reading

Artificial Intelligence & Technology's Reconstitution

Institutions & Power Realignment

Scientific & Medical Acceleration

Economics & Labor Transformation

Infrastructure & Engineering Transitions

The Century Report tracks structural shifts during the transition between eras. It is produced daily as a perceptual alignment tool - not prediction, not persuasion, just pattern recognition for people paying attention.

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