Data and methods

Frozen acquisition and version identity

The analysis uses the downloadable Epoch AI model CSVs, retrieved on 6 September 2026 UTC. The all-model snapshot contains 3,601 records and 57 original fields. The primary 2020–6 September 2026 study contains 2,749 dated records. Weight accessibility is known for 2,334: 1,269 open-weight and 1,065 closed-weight records; 415 remain unknown. No original field or original CSV byte is overwritten.

Epoch did not expose a semantic version number or a Last-Modified header for these CSV responses. The dataset version used here is the timestamped, SHA-256-identified snapshot below, not an invented database release number. The source page described the all-model data as updated 6 September; subset snapshots displayed 3 September. Do not assume the five files were generated atomically. Preserve each receipt and original response separately.

The ECI supplement is a separate Epoch data product. Its 927 version/configuration rows contain 657 scored rows, which collapse to 250 model groups with identical group scores. Six groups have unknown accessibility. Two unreleased closed groups are excluded from the public capability race, leaving 242 groups (128 open, 114 closed). There are 216 exact group-to-main-CSV name matches before those exclusions and 211 after them. Unmatched capability groups retain their ECI-side metadata, but missing model-CSV fields stay missing. There is no fuzzy match or external license enrichment.

Taxonomy and universes

1. Frontier closed/proprietary: Epoch Frontier model flag true and weight accessibility API, hosted without API, or unreleased.
2. Frontier open-weight: same flag and any Epoch category beginning “Open weights”.
3. Non-frontier open-weight: open weights and no positive flag; this is operationally “not flagged”, not proof of non-frontier capability.
4. Non-frontier closed: closed weights and no positive flag, with the same qualification.

Unknown accessibility is a fifth audit stratum, excluded from binary contrasts. Closed does not necessarily mean a for-profit proprietor: the organization field separately identifies industry, academia and other combinations. Unreleased records are included in the broad metadata/compute census but excluded from the public ECI race. “Open weights (unrestricted)”, “Open weights (restricted use)” and “Open weights (non-commercial)” remain distinguishable. Downloadable weights are never equated with open source. The main CSV provides training-code accessibility but no structured complete-model open-source, recipe, training-data-license or reproducibility census. Dataset size is not data disclosure. License categories are descriptive Epoch metadata, not legal verification.

Epoch’s flag is a compute-frontier proxy, not a benchmark ranking. It marks 49 records in this study: seven open and 42 closed. No 2026 record is flagged. We therefore separately define capability-relevant as within five ECI points of the best publicly accessible score on the recorded release date (sensitivity: three and ten points). This is an analyst threshold, not an Epoch designation. A reconstructed known-compute top-ten screen ranks each dated record against all earlier or same-day records with known compute across the full historical CSV; ties are included. It is coverage-dependent and is never called a capability score.

Capability, chronology and uncertainty

Only the current fitted Epoch Capabilities Index is used for cross-family capability comparisons. ECI combines benchmark information statistically; it is a modeled indicator, not an observed universal ability. Its scale is not a percentage, economic productivity unit or human-intelligence scale. We do not merge older ECI fits, incompatible benchmark results, or parameter counts into it. Benchmark choice, evaluation harnesses, inference configurations, contamination, group-level pooling and missing evaluations all limit interpretation. The earliest scored group is dated 24 February 2023; there is no support for a comparable capability-lag estimate in 2020–22.

For each group, the primary availability date is the later of Publication date and the earliest dated Version release date in the current benchmark file. This prevents public-announcement dates from placing o3 ahead of its April 2025 release and avoids assigning September 2024 Gemini versions to February. The latest-version-date sensitivity instead uses the latest recorded version in the group. Neither correction reconstructs when every evaluation was performed or when weights first became downloadable. Accessibility is a present snapshot, not a historical license panel. Later-opened models can still be backdated; this remains a limitation.

At each day, the closed/open frontier is the maximum ECI among released, known-access groups in that class. The overall frontier is the maximum of both. Gap = overall maximum minus open maximum. The “backward clock” measures elapsed time since the closed frontier first strictly exceeded the current open point score. A tie is considered reached. Daily dates imply one-day resolution; 30.4375 days define one month. This is distinct from the forward delay of a fixed threshold. If the earliest observed closed model already exceeds the open score, the backward clock is left-censored; those early lower bounds are omitted from the lag chart. Annual lag summaries before July 2024 must not be interpreted as exact averages. Annual capability gaps are daily weighted, with 2023 and 2026 partial years.

The download supplies marginal 90% ECI intervals. These are shown for selected models. Subtracting interval endpoints produces a descriptive envelope, not a joint confidence interval for the gap or an interval for the selected maximum. The latest envelope is 4.72–18.96 ECI. Paired bootstrap score draws and their covariance are not supplied here; therefore we cannot reproduce Epoch’s paired-bootstrap tie rule or assign a confidence interval to our month estimate. A May 2026 Epoch essay reported a shorter lag under another cutoff and statistical rule. That figure is not a contradiction of this September strict point-score clock and is not silently reused.

Diffusion and release events

For ECI thresholds 130, 135, 140, 145, 150, 155 and 160, find the first dated closed group, first open group, and first open group with known total parameters ≤40 billion. The earlier 120/125 thresholds are retained only in audit tables because closed first crossing is left-censored. Unreached thresholds are right-censored at 6 September 2026 and shown with lower bounds, never assigned a synthetic completion date. The 65 qualifying smaller groups provide a size screen only: we do not claim a specific consumer GPU, inference price or availability to every user. Total rather than active mixture-of-experts parameters avoids pretending inactive weights occupy no memory. No supported cheap-model cost series is available.

Rank breakthroughs by the positive jump in the open record, measured against the same-day overall frontier. The first observed open record has no prior comparator and no jump rank. Equal scores are not new records. Seven jumps are at least two ECI points; five largest account for 48.3% of total observed open-record improvements after the first observation. Because maxima are step functions by construction, step-shaped plots alone do not prove a burst mechanism. The useful evidence is the size of particular contractions, reopenings in the following 90 days, and the non-monotonic annual mean gap. We make no causal claim about secrecy, releases or commercial strategy.

Compute, cost, parameters, data and power

Training FLOP are taken from Epoch with original estimation-method, confidence, notes, lower and upper bounds retained. There are 1,077 positive compute entries among 2,749 study records; 986 have known weight accessibility. “Reported” is a strict single-category screen: 55 records, 48 with known accessibility. Developer reported does not mean independently observed or metered. Mixed “Reported” plus estimation categories do not pass the strict screen. Missingness is never imputed. Neither Epoch’s confidence label nor the presence of an exact-looking number converts an estimate into a measurement.

For each year and class, annual release statistics include median, pandas linear-interpolated 90th percentile, maximum and non-missing N. Additional rows restrict to frontier-flagged records. Separate cumulative maximum tables show the known compute record up to year-end, with the model and release date. The proprietary/open ratio divides those two cumulative maxima within the selected universe; annual ratios are also available from annual maxima. A carried maximum stays visible as an old observation. Log scales handle orders of magnitude. The true undisclosed frontier may be higher. Epoch lower/upper compute bounds are retained, but no comparable comprehensive uncertainty distribution is assumed.

Training cost is Epoch’s estimated training compute cost in constant 2023 USD. All 165 populated cost entries are treated as modeled estimates; none is rebranded observed expenditure. We do not infer costs for missing models, count inference or post-training budgets as pretraining compute, or equate estimated training cost with total R&D. Recent estimates are particularly sparse: nine in 2024, nine in 2025 and one in 2026. Parameters and training power are reported alongside source notes where present. Architecture is operationalized only by the Approach field. Dataset-size availability is comparable as metadata; dataset-size magnitudes are not pooled across tokens, images and other domains.

Concentration and recurrent producers

Normalize the documented organization aliases, then split one release credit equally across its listed unique organizations. Countries are handled separately and fractionally. A model therefore contributes one total credit to each attributed level. Missing attribution is excluded from that denominator and counted. HHI = 10,000 × sum of squared credit shares. Report top-three, top-five, top-ten shares and all organization/country shares by year and pooled window. Alphabetical ties do not affect summed shares. Parent-group aliases are a sensitivity choice: organization-level concentration can change with co-development conventions and corporate restructuring. Country refers to the organization’s recorded country, not the training datacenter, employee nationality or origin of all inputs.

Two frontier universes are reported, with their very different denominators. The top-three open share is 71.4% among seven Epoch-flagged releases and 85.7% among fourteen groups within five ECI of the release-date frontier. The corresponding closed shares are 59.5% among 42 flags and 92.9% among 56 comparable near-frontier groups. Such counts are database-release shares, not model usage, revenue, market power, innovation rates or a representative census. The five-point screen produces no open entrant in 2026: this is a threshold result, not disappearance of the ecosystem.

Recurrent high-compute open producers are counted among records with known training compute ≥10^24 FLOP. Counts measure included model records and may include variants or derivative training; they do not identify independent from-scratch training investments.

Logistic regression and disclosure

Estimate unpenalized logistic regressions for current open weights on log10 training compute, log10 parameters, linear publication year, organization type and country. Fit compute-only, parameter-only and joint specifications within all, notable, Epoch-frontier, reported-compute, capability-complete, known-compute-top-ten and Language subsets. Categorical organization types: industry-only, academia-only (reference), mixed/other. Countries: China (reference), USA, other/multinational. Rows missing any required variable are excluded and enumerated; there is no imputation. Organization clustering uses the normalized full co-organization set. This groups identical collaborators rather than creating fractional regression observations.

The joint all-model specification uses 897 complete cases and 364 clusters, excluding 1,852 study records. Maximum likelihood is solved with analytic gradient; a Hessian condition number above 10^12 or absolute coefficient above 30 blocks the fit. Fewer than 70 complete cases or fewer than 15 observations in either accessibility class blocks estimation. We retain convergence diagnostics, counts and exclusions for every attempted fit. Coefficient 95% intervals use organization-cluster sandwich covariance and finite-sample correction. Average marginal effects use sample-averaged derivatives for continuous covariates and discrete changes for indicators; delta-method intervals include covariance. These are conditional associations in a selected sample. Reporting selection, organization practices, release strategy, domain and correlated compute/parameter scale prevent causal interpretation. The Language restriction is a sensitivity check, not a comprehensive task or architecture adjustment.

Transparency is the eight-field unweighted metadata-availability score described in disclosure.md. Estimates count as available data; code marked Unreleased counts as a known code status. Separate reported-compute and actual code-available rates avoid confusing a known negative status with access. A field’s absence means missing here, not necessarily secrecy by its producer. The composite is not a full open-source score.

Sensitivity and failure boundaries

All 242 public ECI groups, 101 notable groups and 211 exact metadata-matched groups give the same current leading models and 11.61-point gap. The ten-point release-relevance screen (148 groups) does too. The five-point screen (70 groups) and three-point screen (48 groups) exclude later open releases that arrive farther from the frontier, and mechanically enlarge the current subset gap to 23.44 and 30.24. The flag-only ECI universe has just fourteen groups and stale leaders; it is unsuitable as a correction to the current capability frontier. The four strictly reported-compute ECI groups cannot support a two-sided comparison. This failure is itself substantive disclosure evidence.

Latest-version dating yields annual average gaps of 5.90 ECI in 2024, 5.78 in 2025 and 9.18 in 2026 to date, compared with 5.94, 5.82 and 9.18 under the primary date rule. The current 11.61-point gap and 6.08-month clock are unchanged. This date sensitivity retains the episodic interpretation without combining scores from different index fits. The three/five/ten-point screens test how the definition of relevance affects concentration. Availability sensitivity excludes restricted and non-commercial weights. Compute analyses include the strict reported-only sample, all models, notable models, flags, reconstructed top ten and complete capability/accessibility cases; all cell denominators are exported. The 2026 compute and cost observations do not support a strong contemporaneous capital-divergence conclusion.

The central supported statement is descriptive: several large open releases materially narrowed the modeled capability distance, followed by renewed widening. Continuous catch-up is not supported over the observed 2023–26 window. Nor does this establish permanent divergence. Historical coverage changes, survivorship, selection into Epoch, differential benchmark inclusion, statistical model fitting, licensing changes and missing high-end compute remain material. Raw release counts are never interpreted as innovation rates.

Major models

The early years use known training compute as a relevance screen, not a capability ranking. Later years use the best comparable ECI scores. Missing values remain missing.

Closed comparison releases

Ranked open-weight breakthroughs

Ranking criterion: largest reduction in the same-day point-estimate gap when an open record was released. It measures an ECI contraction, not broader historical importance.

Concentration

Each model receives one fractional release credit, divided equally between listed organizations or countries after documented alias normalization. These are shares of selected database releases, not market shares. Empty denominators are missing, not zero. HHI is on a 0–10,000 scale.

Descriptive logistic regression

All-model joint specification: 897 complete cases; 1,852 exclusions from 2,749 dated records; 364 organization clusters. The response is current open-weight status. Continuous scale variables are log10, centred over the fitted sample. The year coefficient is linear since 2020. Reference categories are academia-only organizations and China. Intervals are 95%, based on a finite-sample corrected cluster sandwich covariance. Binary-factor effects are average discrete changes; continuous effects are average derivatives.

The main model has no domain controls; the Language sensitivity limits the domain and reports a separate fit. Joint scale effects should not be read as unadjusted group differences or as causal effects.

Sample accounting

Metadata availability and disclosure

The eight-field score is the unweighted mean of non-missing indicators for parameters, training compute, dataset size, cost estimate, approach, hardware, power estimate and code status. A known unreleased-code status contributes to metadata availability but not code availability. Estimates count as populated fields, not developer disclosure. No training-data or recipe disclosure is inferred from the dataset-size number.

Mean score: open weights 45.35/100; closed weights 31.64; unknown access 18.40. Equal weights are a transparent convention, not a validated latent openness index. The separate field rates carry more meaning than the composite.