Methodology · v1.0
How are the coefficients calculated?
Seven tier-2 coefficients, each moved only by sourced events, combined with fixed weights into one number between 0 and 1.
1. The formula
ck(t) = clamp( bk + Σe ≤ t Δe,k , 0.001, 0.999 )
G(t) = Σk wk · ck(t)
gap(t) = 1 − G(t)
- ck(t) — the value of tier coefficient k (e.g. gapnium.autonomy) on date t.
- bk — its baseline on 1 January 2020: our estimate of all progress made before the tracked history begins (ImageNet, AlphaGo, the transformer, GPT-2…).
- Δe,k — the add/subtract amount assigned to event e for coefficient k. Every Δ has a written explanation, shown wherever the event appears.
- wk — the tier's weight. Weights sum to exactly 1, so G stays between 0 and 1.
Only published events count. The chart draws a point at each event date and connects the points, like closing prices on a stock chart. Between events the value doesn't change — Gapnium only moves when evidence arrives.
2. The tiers and their weights
| Coefficient | Measures | Weight | Baseline (2020) | Now |
|---|---|---|---|---|
| gapnium.cognition | Reasoning, knowledge and general problem-solving ability. | 0.20 | 0.170 | 0.572 |
| gapnium.autonomy | How long and how independently AI agents can work. | 0.20 | 0.040 | 0.319 |
| gapnium.recursion | AI accelerating the creation of better AI. | 0.20 | 0.030 | 0.164 |
| gapnium.discovery | The rate at which long-standing problems fall. | 0.15 | 0.090 | 0.351 |
| gapnium.automation | Real economic work actually being done by AI. | 0.10 | 0.060 | 0.195 |
| gapnium.compute | The physical substrate: chips, data centres, energy. | 0.10 | 0.140 | 0.263 |
| gapnium.embodiment | AI acting in the physical world. | 0.05 | 0.070 | 0.116 |
| Gapnium Coefficient | 1.00 | 0.085 | 0.315 | |
Why these weights?
Cognition, Autonomy and Recursion carry 0.20 each because the classic definition of the singularity is an intelligence explosion: systems smart enough (cognition) and independent enough (autonomy) to improve themselves (recursion). Discovery (0.15) is the clearest external evidence that capability is real — problems that stood for decades either fall or they don't. Automation and Compute (0.10 each) are enabling and lagging indicators: they matter, but massive deployment or data-centre spending can happen without a singularity. Embodiment (0.05) is weighted lowest because a software-only intelligence explosion is conceivable, but it isn't zero: a singularity that can't touch the physical world is a limited one.
gapnium.cognition — Cognition
How close frontier models are to matching or exceeding the best humans across reasoning, knowledge, mathematics, language and multimodal understanding. Driven mainly by results on hard, uncontaminated benchmarks (GPQA, FrontierMath, Humanity's Last Exam, ARC-AGI), competition performance (IMO, ICPC) and qualitative capability jumps.
Evidence the agent looks for: Frontier benchmark scores (GPQA, HLE, FrontierMath, ARC-AGI) · Olympiad / competition results · New modalities and generalisation · Evidence of benchmark saturation or failure
What 1.0 means: Systems reliably exceed the best human experts in every cognitive domain, including novel problems no benchmark anticipated.
gapnium.autonomy — Autonomy
The length, reliability and independence of agentic work: the duration of tasks an agent can complete unsupervised (METR time horizons), real-world software engineering (SWE-bench), computer use (OSWorld), and long-running deployments. A doubling of reliable task length is treated as a large step.
Evidence the agent looks for: METR 50% / 80% time horizons · SWE-bench, Terminal-Bench, OSWorld · Agent products shipped to users · Hours-to-days unsupervised runs
What 1.0 means: Agents can be handed open-ended, months-long projects and complete them with expert-level reliability and no human in the loop.
gapnium.recursion — Recursion
The degree to which AI systems contribute to AI research and engineering itself: writing the code, kernels and experiments that train their successors, automated ML research, and measurable speed-ups of frontier labs. This is the tier most directly tied to the classic "intelligence explosion" definition of the singularity, so it carries a large weight.
Evidence the agent looks for: Share of lab code written by AI · Automated research agents (AI Scientist, co-scientist) · AI-discovered improvements to training / inference · RE-Bench and ML-engineering evals
What 1.0 means: AI systems do the large majority of frontier AI research, and each generation measurably shortens the time to the next.
gapnium.discovery — Discovery
Genuine new knowledge produced with AI as a principal contributor: solved open problems in mathematics, structural biology, materials, algorithms and physics. Weighted by how long the problem stood open and how independently the AI contributed.
Evidence the agent looks for: Open problems resolved (Erdős, combinatorics, conjectures) · Scientific grand challenges (protein folding, materials) · Peer-reviewed results with AI as a principal contributor · Prizes awarded for AI-driven science
What 1.0 means: AI routinely resolves decades-old problems across fields faster than the human research community can absorb the results.
gapnium.automation — Automation
Adoption and impact in the economy: the share of economically valuable tasks AI performs at expert parity (GDPval), user adoption, enterprise deployment and measured productivity. Negative evidence — failed pilots, productivity studies showing slow-downs — pulls this tier down.
Evidence the agent looks for: GDPval and occupational task evals · User and enterprise adoption · Productivity studies (positive and negative) · Labour-market effects
What 1.0 means: Most economically valuable work can be performed by AI at lower cost than humans and is, in practice, being performed by it.
gapnium.compute — Compute
Training and inference capacity available to frontier AI: accelerator generations, gigawatt-scale data-centre build-outs, capital committed, and algorithmic efficiency gains that make the same hardware go further.
Evidence the agent looks for: New accelerator generations · Committed data-centre capacity (GW, $) · Training-run scale (FLOP) · Algorithmic efficiency results
What 1.0 means: Compute is no longer the binding constraint on AI progress; capacity grows as fast as AI systems can usefully consume it.
gapnium.embodiment — Embodiment
Robotics, autonomous vehicles and world models: general-purpose manipulation, humanoid deployments, driverless services at scale, and models that understand physical dynamics.
Evidence the agent looks for: Driverless deployment scale · Humanoid / general-purpose robot deployments · Vision-language-action models · World models
What 1.0 means: General-purpose robots can perform nearly any physical task a human can, and manufacture more robots.
3. Scoring an event
Each event can move any number of tiers. The sorting agent proposes a Δ per tier using this rubric, and writes one sentence justifying each:
| Δ (typical) | Meaning | Examples |
|---|---|---|
| +0.002 – 0.006 | Notable — incremental, expected progress | A point release; a modest benchmark gain |
| +0.008 – 0.015 | Major — a clear step for that tier | A new frontier model; a validated AI-generated hypothesis |
| +0.02 – 0.035 | Landmark — changes what the field thinks is possible | o1 reasoning; IMO gold; a $500B compute commitment |
| +0.04 – 0.05 | Field-redefining — a grand challenge falls | AlphaFold 2; GPT-4; a celebrated decades-old conjecture |
| −0.003 – 0.012 | Negative evidence — the gap is wider than believed | A hard new benchmark exposing failure; a rigorous study showing slow real-world gains |
Some rules the agent applies:
- Count it once. If several articles report the same development, they become one event with several sources — not several events.
- Primary sources first. Lab announcements, papers and benchmark maintainers outrank secondary coverage. Lab self-reports are scored with caution until independently replicated.
- Negative evidence is mandatory. New benchmarks that frontier models fail, failed replications and sober productivity studies are scored, not ignored.
- Diminishing hype. Demos, roadmaps and funding announcements score far less than shipped, measured capability.
- Re-review with hindsight. Every event is re-reviewed at least every 90 days for its first year. Deltas may be revised; the revision and reason are logged.
4. The extra statistics
- Closing velocity — the change in G over the trailing 12 months (currently +0.0521 per year), with a 3-year average for context.
- Naive crossing — gap ÷ velocity, added to the current year. It assumes linear progress, which is almost certainly wrong in one direction or the other; it's a reference point, not a forecast.
5. Data model
Everything is stored openly in a relational database and served at /api/timeline:
- sites — publishers, their type and a credibility weight.
- articles — each source URL, title and publication date, with a link-health check.
- events — title, short summary, information summary, event date, significance, status, and the date the AI sorting agent last reviewed it (with model and confidence).
- event_impacts — the add/subtract amount per coefficient, with its explanation.
- review_log — an audit trail of every ingest, review and rescore.
6. Known limitations
- The baselines and weights are judgement calls. Changing them shifts the absolute level; the shape of the curve is far more robust.
- News coverage is biased toward big labs and English-language sources. The agent actively looks for academic and international sources, but the bias is real.
- Additive deltas mean that, in principle, enough small events could inflate a tier. Re-review exists partly to correct this.