TEPI — Token Energy Parity Index · Methodology

1. Purpose and Scope

The Token Energy Parity Index (TEPI) is a daily index family that places two token-producing uses of electrical energy on a single physical common denominator — gross revenue per kilowatt-hour — and tracks the ratio between them: (i) proof-of-work cryptocurrency mining (currently Bitcoin), interpreted within the Abundantics research programme as defensive dissipation (energy spent to secure claims), and (ii) large-language-model inference, interpreted as productive dissipation (energy spent to produce cognitive output). The interpretive labels are a research lens, not a normative verdict; Section 9 states their intellectual lineage and limits.

TEPI answers a narrow, measurable question: at today's market prices, how much gross revenue does one kilowatt-hour earn in each use, and how large is the gap after adjusting for measured model quality? It does not measure profitability, welfare, or energy consumption shares, and it is not investment advice.

2. The Index Family

Auxiliary published quantities: ε_BTC (embodied energy per mined BTC, GWh), ρ_parity and ρ_market (the two token/BTC exchange rates entering Ω), basket summary statistics, and the chain-linking metadata of Section 6.

3. Notation

4. Data Sources and Sampling

All inputs are free, public, and keyless. The index is computed once per day by an automated pipeline (GitHub Actions, 00:10 UTC) and appended to a public CSV; the pipeline, site generator, and full series are open source.

Two parameters are judgmental and are therefore governed by an explicit review-and-log policy rather than presented as data: η (currently 20.0 J/TH) and the per-model j_i values. Section 7 quantifies the sensitivity of each index to both.

5. Computation

5.1 Mining side

Hashprice (gross mining revenue per PH/s per day) and the daily electricity drawn by one PH/s at fleet-average efficiency give revenue per kWh directly:

Embodied energy per coin is total network energy over coins issued. A useful identity follows by substitution: R_M = k · P_BTC / ε_BTC. Mining revenue per kWh is fully determined by the coin price and the energy embodied in a marginal coin; the difficulty adjustment is the mechanism that keeps this quantity tethered to electricity prices (Section 9.1).

5.2 Inference side

For each basket model, gross revenue per kWh is its output-token price times the tokens one kWh can produce at that model's energy intensity; the index aggregates with normalized usage weights:

If a basket model is missing from the price source on a given day it is dropped and weights are renormalized (missing_model_policy = skip); the event is visible in the run log. Prices are list prices of OpenRouter default endpoints for output tokens; input-token revenue and energy are excluded (limitation L2, Section 7).

5.3 Quality adjustment and standard tokens

Tokens from different models are not homogeneous. TEPI converts raw tokens into standard-token equivalents using quality weights from an external benchmark that is independent of price: q_i = s_i / s_ref, where s_i is the model's Artificial Analysis Intelligence Index score and the reference model defines q = 1. One raw token of model i counts as q_i standard tokens; the quality adjustment therefore acts on the quantity side, not the price side. Standard tokens per joule for model i are t_i = q_i / j_i, and for the basket T = Σ w̃_i t_i.

5.4 Cross-market parity and Ω

Two exchange rates between the two token worlds are compared. The joule-parity rate asks what the energy embodied in one BTC would yield if redirected to quality-adjusted inference; the market-implied rate asks how many standard tokens one BTC buys at market prices:

Interpretation: Ω is the log of a gross-revenue opportunity ratio. Ω = 5.74 (16 Aug 2026, verification run) states that the energy embodied in one bitcoin, if redirected to inference at current quality-adjusted prices, would gross e^5.74 ≈ 311 times the bitcoin's market price. The gross-revenue caveats of Section 7 apply to the level; the informative object is the series.

A decomposition identity, used throughout for verification, separates Ω into the raw ratio and a pure quality term:

5.5 Why price-based quality weights are inadmissible (degeneracy result)

Proposition. If quality weights are defined from prices, q_i = p_i / p_ref, then Ω ≡ ln Λ identically, for every configuration and every day.

Proof. Substituting q_i = p_i/p_ref into T gives T = Σ w̃_i p_i / (p_ref · j_i). Then ρ_parity/ρ_market = ε_BTC · T · p_ref / P_BTC = ε_BTC · Σ w̃_i p_i/j_i / P_BTC. Meanwhile Λ = R_A/R_M = (k Σ w̃_i p_i/j_i) / (k P_BTC/ε_BTC) = ε_BTC · Σ w̃_i p_i/j_i / P_BTC — the same expression. Hence Ω = ln Λ. ∎

Version 0 of this index used price-based weights and exhibited exactly this degeneracy (observed: Ω = 5.457 = ln 234.4 on the launch snapshot). Measuring quality with price and then asking whether price deviates from quality-adjusted parity uses the measured object as its own measuring rod. The v0.1 methodology therefore requires quality scores from a source independent of price; if any basket model lacks a current score, Ω is published as missing rather than computed under the degenerate fallback.

6. Basket Construction and Maintenance

6.1 Selection principles

• Coverage: one high-usage (workhorse, not flagship) model from each major provider family, so that R_A reflects revenue at prices the market actually transacts in volume.
• Priceability: the model must be listed on the price source with a default endpoint.
• Scoreability: the model must carry a current external quality score (Section 6.4); otherwise Ω is suspended, not approximated.
• Parsimony: the basket is deliberately small (currently four models); representativeness is pursued through weights, reviewed against public usage rankings.

6.2 Current basket (version v1, effective 2026-08-16)

Score convention: for each model, the highest effort tier scored by the benchmark provider at review date ('highest-scored tier'). Scores recorded from Artificial Analysis Intelligence Index v4.1.1, retrieved 2026-08-16. The reference model's score (55) lies within the basket's score range (53–56), avoiding a reference at an extreme.

6.3 Chain-linking of Λ

The level of Λ is sensitive to basket composition; model turnover is expected to be frequent. Following consumer-price-index practice (chain-linking; ILO et al. 2020), the published series Λ_chained measures change, not basket level. Each basket configuration carries a version tag (v1, v2, …). A registry file chain_factors.json maps each version to a cumulative linking factor; v1 ≡ 1.0.

On a basket change, old and new configurations are computed side-by-side on the same day (dry run). The new version's factor is set so that Λ_chained is continuous across the splice: factor_new = Λ_chained(old) / Λ_raw(new). Both Λ (raw, current basket) and Λ_chained (spliced) are published; charts and analysis use Λ_chained. Every splice is logged in the changelog with date, models in/out, and the factor.

Ω is not chain-linked in v0.1: its quality-ratio structure removes the first-order basket-level sensitivity, and splice events will be assessed empirically as they occur (open issue O5).

6.4 Quality-score governance

Scores are reviewed quarterly and whenever the basket changes; every adopted change is a changelog line (date, old → new score, benchmark version). Published history is never revised retroactively. The benchmark itself is versioned by its provider (v4.1.1 at adoption) and re-weights over time; the benchmark version in force is part of the record. A benchmark change is treated like a basket splice for documentation purposes.

7. Accounting Boundary and Known Limitations

TEPI is a gross-revenue-per-unit-energy index under an explicitly declared boundary. The declared choices, each with its rationale and direction of bias:

• L1 — Gross revenue, not profit. Electricity is the dominant marginal cost in mining but a minor cost share in inference. The level of Λ therefore cannot be read as a profit arbitrage; economically meaningful objects are the trend, the ratio's response to events, and cross-side comparisons of change. A net-margin variant Λ′ is roadmap item O2.
• L2 — Output tokens only. Inference revenue and energy are computed on output tokens at output prices; input-token revenue and prefill energy are excluded. This understates inference revenue per kWh to the extent input pricing exceeds prefill energy cost. Correcting this requires input/output mix data not publicly available at daily cadence [to be verified].
• L3 — Full-utilization convention. R_A prices every kWh at list-price token output, i.e., assumes 100% billable utilization. Realized fleet utilization is below this, so R_A is an upper bound on realized revenue per kWh; R_M has no comparable wedge. Λ is correspondingly an upper bound.
• L4 — Fleet-average, manually set η. R_M and ε_BTC scale linearly (inversely) in η. η = 20 J/TH is anchored to public fleet estimates and current-generation ASIC specifications, reviewed quarterly. Sensitivity: ±25% in η moves R_M and ln-level of Λ by ∓25% and ±ln(1.25) ≈ ±0.22 respectively.
• L5 — Working j_i values. Per-token full-stack energy (including PUE) is the weakest input: public measurements are scarce, model-specific values are provider-confidential, and the configured values (1.0–3.0 J per output token) are order-of-magnitude working assumptions [to be verified]. A dedicated sensitivity table and sourcing appendix is roadmap item O3.
• L6 — Single chain, single price source. The mining side is Bitcoin only; the inference side prices via one aggregator's default endpoints. Both choices favour reproducibility over completeness and are stated rather than hidden.

8. Data Quality Controls

The sentinel warns but never halts the pipeline; a failed upstream fetch leaves the previous day's published files in place. Each row carries a provenance flag (source = live; backfill reserved for roadmap item O1).

9. Interpretation Guidance

9.1 The mining side is an already-closed arbitrage

Bitcoin's difficulty adjustment forces marginal mining revenue per kWh toward the marginal cost of electricity: excess margin attracts hashrate, which dilutes hashprice. The observed launch value R_M ≈ 0.066 USD/kWh — of the order of common industrial electricity tariffs — is consistent with this mechanism operating as designed. TEPI treats this as its calibration anchor: one side of the ratio is pinned to the energy market by an automatic mechanism.

9.2 Λ as a commoditization distance

On the inference side no such mechanism yet binds: the scarce factors are accelerators, models, and quality premia, not electricity. Λ ≫ 1 therefore measures, in gross-revenue terms, how far inference remains from being priced as an energy commodity. A secular decline of Λ_chained toward unity would indicate inference converging to energy-cost pricing; the capital reallocation channel that would drive such convergence is already observable in the conversion of mining facilities to AI datacentres.

9.3 Productive vs. defensive dissipation

The programme's framing descends from Baumol's (1990) allocation of entrepreneurship between productive and unproductive uses: identical inputs (here, joules) divided between creating claims-worthy output and securing existing claims. The parity apparatus itself is a purchasing-power-parity construction in the sense of Balassa (1964) and Samuelson (1964), with energy as the common currency. These are interpretive commitments of the Abundantics programme; every number in this document is defined and computable without them.

10. Versioning, Revision Policy, Licensing, Citation

Methodology versions are semantic: parameter updates within policy (η, s_i, j_i, basket splices) increment the changelog, not the version; changes to formulas or conventions increment the version. This document is v0.1 (draft); v1.0 will follow external review. Published rows are never retroactively revised. Corrections, if ever required, append a corrected row and a changelog entry.

Series start: 2026-08-16 (basket v1, quality scores adopted same day; Ω enters the published series from 2026-08-17). Data and this methodology: CC-BY 4.0. Reference implementation: open source. A DOI-versioned dataset deposit is roadmap item O4.

The Abundantics preprint collection to which this index belongs (v1.6, 18 August 2026) is deposited on Zenodo: DOI 10.5281/zenodo.21989658.

@misc{tang2026tepi,
  title = {TEPI --- Token Energy Parity Index: Index Methodology v0.1},
  author = {Tang, Huidao},
  year = {2026},
  url = {https://tanghuidao.github.io/token-parity/},
  note = {Abundantics Empirical Module 01. Method v0.1, accessed YYYY-MM-DD}
}

Revision note: 2026-08-19 — mathematical typesetting normalized, authorship finalized, and the preprint DOI cross-link added; no change whatsoever to content or computational conventions, version remains v0.1.

11. Open Issues and Roadmap

• O1 — Backfill. Reconstruct R_M weekly/monthly to the 2010s from public chain and hardware-efficiency data, and R_A to late 2022 from archived price schedules; publish under source = backfill with its own methodology note.
• O2 — Λ′ net-margin variant. Calibrated to public miner and inference-operator financials.
• O3 — j_i sourcing appendix. Full sensitivity tables for η and j_i.
• O4 — DOI deposit. A standalone Zenodo record for TEPI (versioned dataset + this methodology, both language editions), targeted for the 30-day mark of the series.
• O5 — Ω splice behaviour. Assessed on first basket-change occurrence; hedonic refinement of the quality adjustment beyond a single composite score.

Appendix A. Worked Example — 16 August 2026

Reading of the final line: after quality adjustment the measured gap widens by ≈ 33% rather than narrowing — at adoption-date scores the four basket models are nearly quality-equivalent (weights 0.96–1.02) while their prices span a 7.5× range, so the market premium on the reference-side models exceeds what the benchmark attributes to measured capability. This is an observation about one day's cross-section, recorded here as the index's first substantive datapoint, not a stylized fact.

Appendix B. Published CSV Schema (16 columns, in order)

date, btc_price_usd, hashprice_usd_per_ph_day, fleet_efficiency_j_per_th,
epsilon_btc_gwh, basket_price_usd_per_mtok, basket_j_per_token,
R_M, R_A, Lambda, Omega, rho_parity_tok_per_btc, rho_market_tok_per_btc,
source, basket_version, Lambda_chained

Columns are append-only: existing columns are never renamed, removed, or reordered; extensions add columns at the end. Empty string denotes 'not computable under policy' (e.g., Ω before quality-score adoption), never zero.

References

• Balassa, B. (1964). The Purchasing-Power Parity Doctrine: A Reappraisal. Journal of Political Economy, 72(6), 584–596.
• Baumol, W. J. (1990). Entrepreneurship: Productive, Unproductive, and Destructive. Journal of Political Economy, 98(5), 893–921.
• Cambridge Centre for Alternative Finance. Cambridge Blockchain Network Sustainability Index (CBECI). ccaf.io — fleet-efficiency anchor for η.
• ILO, IMF, OECD, Eurostat, UNECE, World Bank (2020). Consumer Price Index Manual: Concepts and Methods. — chain-linking practice.
• Samuelson, P. A. (1964). Theoretical Notes on Trade Problems. Review of Economics and Statistics, 46(2), 145–154.
• Artificial Analysis. Intelligence Index, v4.1.1. artificialanalysis.ai — retrieved 2026-08-16.