ResearchPapers, evidence & method
Research system running an unreleased Anthropic model proves the Aaronson–Ambainis quantum conjecture, with a Lean-checked proof
Startup PSI says its research system, running a non-public Anthropic model, produced a Lean-verified proof of a quantum-query conjecture open since about 2008. Import AI 480 pairs it with two-continent model training, Meta's tactile glove and lunar industry bootstrapping.
From the Import AI article of November 9, 2026 and cited sources: PSI's internal research system produced a proof of the Aaronson–Ambainis conjecture on the third day of a run. [2] [6]
SOURCES[2] PSI: A proof of the Aaronson–Ambainis conjecture psi.inc[6] The Quantum Insider: AI-Assisted Proof Settles… thequantuminsider.com
AT Pulse research deskPublished · Updated · 5 min read · AI-assisted analysisAI-assisted, not human-edited. Methodology Corrections Who owns this site
- What happened
- PSI's internal research system produced a proof of the Aaronson–Ambainis conjecture on the third day of a run. [2] [6]
- Original source
- Import AI article, independent perspective
- Brief by
- AT Pulse research desk AI-assisted; publisher and contact on the desk page
- When
- November 9, 2026 article published
- Covered
- Nov 10 edition
- Evidence
- 9 sources across 7 sites
- 1Import AI 480 (Jack Clark)jack-clark.net
- 2PSI: A proof of the Aaronson–Ambainis conjecturepsi.inc
- 3Metzger et al., arXiv 1612.03238arxiv.org
- 4Tactus (arXiv 2610.39076)arxiv.org
- 5Core Automation: Hitchhiker's Guide to Training on Compute…coreauto.com
- 6The Quantum Insider: AI-Assisted Proof Settles…thequantuminsider.com
Reach: not measured yet
PSI's internal research system produced a proof of the Aaronson–Ambainis conjecture on the third day of a run. The proof builds on Lovett and Zhang's fractional-certificate framework and Reimer's Butterfly Lemma, and it shows that some variable has influence of at least (v/d)^7. Lean 4's kernel checked the main theorem. A PSI researcher chose and scoped the problem, ran the system and edited the paper, and he takes responsibility for its correctness. [2] [6]
Core Automation trained a 32B-parameter mixture-of-experts model across a US GPU cluster and an Asian GPU cluster about 9,000 miles apart, linked at 25 Gbps. It synced model fragments on a staggered schedule within each 50-step window, tolerated late-arriving updates and compressed what it sent between sites. By the company's own measurement, the result was about 1% worse in bits per byte than standard training at equal compute. [5] [1]
Meta Reality Labs researchers describe Tactus, a textile glove with 1.5 mm fingertips and capacitive pressure sensors. It combines hand-pose tracking with inertial sensors so it keeps working when the hand is hidden from view. The authors report a minimum detectable force of 0.59 N and an 11.0 mm fingertip error under heavy occlusion, which makes the glove a possible source of training data for robot manipulation. [4] [1]
The evidence is a kernel-checked formal proof and a single training comparison. If both hold up, AI research outputs could be audited mechanically, and smaller GPU clusters in different locations could be combined for training.
Sources are checked; writing the dossier now.
Executive brief
An AI research system at startup Physical Superintelligence (PSI), running a non-public Anthropic model, produced a proof of the Aaronson–Ambainis conjecture on the third day of a run. The conjecture had been open since about 2008, and the Lean proof checker accepted the proof (PSI). Stanford researchers called it "a huge result," but the work has not been peer reviewed. Import AI 480 also covers three other items: Meta's Tactus tactile glove, Core Automation's training run across two GPU clusters about 9,000 miles apart, and an older NASA-linked plan for bootstrapping industry on the Moon (Import AI).
What changed and event timeline
Lunar bootstrapping paper published
Metzger et al. appeared in the Journal of Aerospace Engineering and was posted to arXiv in December 2016. Import AI calls it a 2016 paper ().
Tactus glove preprint
Meta Reality Labs researchers posted a textile glove that senses touch and hand pose for collecting manipulation data ().
Core Automation reports a two-continent training run
A 32B-parameter mixture-of-experts (MoE) model was trained across a US cluster and an Asian cluster linked at 25 Gbps ().
PSI announces the proof
It released a manuscript and a Lean 4 formalization on (;).
Import AI 480 frames the proof as a "taste" of the singularity
Jack Clark also reads Tactus as hardware a rogue AI might pay people to wear ().
Capabilities and access
- PSI: The Anthropic model is unnamed and not public, and PSI's research system is internal.
- The preprint describes a calibration pipeline but no product release (arXiv).
- Core Automation: The post describes method and results. The model is not released (Core Automation).
Read the full section
- PSI: The Anthropic model is unnamed and not public, and PSI's research system is internal. The proven bound says some variable has influence at least (v/d)^7 (PSI).
- Tactus: Research hardware. The preprint describes a calibration pipeline but no product release (arXiv).
- Core Automation: The post describes method and results. The model is not released (Core Automation).
Technical analysis for researchers and developers
- PSI proof: Builds on Lovett–Zhang's fractional-certificate framework and Reimer's Butterfly Lemma. Lean's kernel checked the main theorem.
- Core Automation run: 256 experts with top-8 routing; 160 B300 GPUs plus 160 GB300 GPUs. Token counts are not stated (Core Automation).
- Tactus: 1.5 mm fingertip thickness, capacitive pressure sensors, and pose tracking fused with inertial sensors (IMUs) so it keeps working when the hand is hidden from view (arXiv).
Read the full section
- PSI proof: Builds on Lovett–Zhang's fractional-certificate framework and Reimer's Butterfly Lemma. Lean's kernel checked the main theorem. After the first proof, the system improved the result twice (PSI). One write-up says the exponent fell from 22 to 7 (Qelvin).
- Core Automation run: 256 experts with top-8 routing; 160 B300 GPUs plus 160 GB300 GPUs. Model fragments were synced on a staggered schedule within each 50-step window, late-arriving updates were tolerated, and updates were compressed with stochastic rounding and error feedback. Each site used a variant of the Distributed Shampoo optimizer. Token counts are not stated (Core Automation).
- Tactus: 1.5 mm fingertip thickness, capacitive pressure sensors, and pose tracking fused with inertial sensors (IMUs) so it keeps working when the hand is hidden from view (arXiv).
Claims and evidence
- The proof is valid. Neither PSI's page nor The Quantum Insider's report confirms peer review (The Quantum Insider).
- Two-site training costs little quality. In both pairs the first figure is the two-site run (Core Automation). No independent replication was found.
- The authors report a minimum detectable force of 0.59 N, 1.6–2.7× lower than commercial baseline gloves, and an 11.0 mm fingertip keypoint error under heavy occlusion (arXiv).
Read the full section
- The proof is valid. Lean acceptance is strong evidence for the formal statement. Stanford's Blanc, Docter, Strassle and Tan endorsed it (PSI). Neither PSI's page nor The Quantum Insider's report confirms peer review (The Quantum Insider).
- Two-site training costs little quality. Core Automation reports itself that the two-site run scored about 1% worse in bits per byte than standard training at equal compute: 0.2525 vs 0.2549 on general coding and 0.1995 vs 0.2017 on systems/kernels. In both pairs the first figure is the two-site run (Core Automation). No independent replication was found.
- Tactus sensing. The authors report a minimum detectable force of 0.59 N, 1.6–2.7× lower than commercial baseline gloves, and an 11.0 mm fingertip keypoint error under heavy occlusion (arXiv).
Context and prior work
- The conjecture concerns when quantum algorithms can be exponentially faster than classical ones on random inputs.
- Import AI places Core Automation's run below Covenant's 72B model, the largest distributed run it has tracked (Import AI).
- OpenTouch is an earlier full-hand tactile glove dataset (arXiv 2512.16842).
Read the full section
- The conjecture concerns when quantum algorithms can be exponentially faster than classical ones on random inputs. The new proof finishes an inequality that Lovett and Zhang had left open (DEV Community).
- Import AI places Core Automation's run below Covenant's 72B model, the largest distributed run it has tracked (Import AI).
- OpenTouch is an earlier full-hand tactile glove dataset (arXiv 2512.16842).
- Metzger et al. estimate that 12–41 t landed on the Moon could bootstrap a lunar industry (arXiv 1612.03238). Clark's estimate that Starship could deliver that for $1.5–4.2bn is his own rough calculation (Import AI).
Limitations, safety and contested findings
- PSI's David Turturean chose and scoped the problem, ran the system, and edited the paper. He takes responsibility for its correctness (The Quantum Insider).
- The result is narrow. It covers the number of input reads, not total computation time, and only "most" random inputs (The Quantum Insider).
- The same week, a benchmark called FrontierPhysics reportedly found that none of 22 models passed more than 30% of end-to-end physics research tasks (Qelvin).
Read the full section
- Humans set the problem up. PSI's David Turturean chose and scoped the problem, ran the system, and edited the paper. He takes responsibility for its correctness (The Quantum Insider).
- The result is narrow. It covers the number of input reads, not total computation time, and only "most" random inputs (The Quantum Insider).
- Contrasting benchmark. The same week, a benchmark called FrontierPhysics reportedly found that none of 22 models passed more than 30% of end-to-end physics research tasks (Qelvin).
- Training across providers has a risk. Core Automation notes that one faulty site could silently degrade the shared model (Core Automation).
- Clark's rogue-AI scenario is speculation. He offers it as a way of reading papers, not as a forecast (Import AI).
Business and practitioner implications
- Proof checkers make AI research outputs auditable.
- Scattered compute may be usable for training. If the roughly 1% gap holds up, startups could combine smaller clusters in different places.
- Robotics teams get a new data source.
Read the full section
- Proof checkers make AI research outputs auditable. For R&D teams in math, chip verification or cryptography, pairing a model with a checker like Lean is now a concrete workflow (PSI).
- Scattered compute may be usable for training. If the roughly 1% gap holds up, startups could combine smaller clusters in different places. Core Automation argues power, grid equipment and land are the real bottlenecks, not chips (Core Automation).
- Robotics teams get a new data source. Gloves that record touch and pose together could supply training data for robot manipulation and world models (arXiv).