Stablecoin Beat S0/S1/S2 Monetary Aggregates

Abstract

This paper specifies the S0/S1/S2 stablecoin monetary aggregates, a three-tier classification of fiat-denominated stablecoin claims expressed in United States dollars at official reference exchange rates. The tiers are ordered by claim form: primary claims, representations of those claims in other settlement environments, and other transferable claims derived from them. For each admitted instrument, the specification also records claim distance, defined as the number of redemption steps between the token held and the base instrument's redemption endpoint. That endpoint may be an issuer redemption obligation or a protocol redemption mechanism. S0 measures base stablecoin supply: native primary stablecoin claims intended to redeem at or track par. S1 measures represented supply by adding tokenized representations of S0 claims created in other settlement environments. S2 measures extended claims by adding transferable instruments whose principal exposure can be traced to an S0 asset. S1 and S2 are each defined on a net basis, which deduplicates backing relationships, and a gross basis, which counts every token layer circulating at the same time.

The ratio of gross extended claims to base supply, termed the representation multiplier, measures the amount of claim structure built on each unit of base supply. The specification defines the equations, constituent admission policy, and edge-case rules for bridge designs, wrapper chains, tranches, rebasing designs, issuer treasury balances, tokenized securities, and claims issued in excess of backing held. It also establishes the versioning and revisions policy. The aggregates are published as a maintained daily series.

Keywords: stablecoins, monetary aggregates, tokenized money, claim structure, statistical methodology. JEL: E41, E42, G23.

Status of this document

This document is Specification 1.1. It is normative. The numbered rules in sections 2 through 5 determine how the published S0/S1/S2 series is compiled, and every figure labeled S0, S1, or S2 by Stablecoin Beat is compiled under an identified version of this specification. Section 7 governs version changes and revisions to published values. Definitions use the present indicative; the phrases "is included" and "is excluded" have normative force.

Version note. Specification 1.1 is a minor version under section 7.1. The tier ordering, tier boundaries, net and gross conventions, and treatment of claim layers are unchanged. No value published under Specification 1.0 is revised.

Version 1.1 makes the following changes. It states explicitly that tier ordering is based on claim form and that claim distance is recorded as an instrument property, consistent with the definitions in sections 2.3 and 2.4 since version 1.0. It specifies the parameters of the par test that version 1.0 expressed as a principle, changes the test statistic to the median absolute deviation from parity, and defines the information set used for a verdict. It separates the definition of the base universe from compilation coverage, incorporates the covered sets into the equations, and commits to daily publication of coverage using a vocabulary of coverage and classification statuses alongside the exclusion vocabulary in section 5.4. It extends U from dollar par claims to par claims in any fiat unit of account, valued at official reference rates, as anticipated by section 7.5 of version 1.0, and publishes changes in S0 at constant exchange rates alongside the exchange-rate effect. It compiles S0 over every member carried by the issuance record, instead of limiting the compilation to members for which a per-environment decomposition is collected, an approach permitted by version 1.0 but not applied by its compiler. It restates rule R9 so that the excess and admitted wrapper value each use a single valuation basis, which makes the ordering of the two multipliers hold by construction. It specifies the completeness gate and netting tolerance as a published set and a numerical threshold. It removes shares in pools that lend the base coin onward from the wrapper set and reports them as an adjacent segment. It also states the relationship between the two supply figures published by the platform.

No value published under version 1.0 is restated. The series compiled under that version remains as published, and its vintages remain available. The series published under version 1.1 covers the same dates on the 1.1 basis. As a result, the 1.1 series contains historical levels that differ from those compiled under version 1.0. Section 7.4 states the period covered by the backcast. Several changes in this version alter the population, the coverage, or the valuation of the compilation and therefore the level compiled under version 1.1: the change of test statistic bears on a small number of instruments, the extension to non-dollar claims and the compilation over every member of the issuance record add members, membership is resolved per instrument rather than per ticker, and base units are valued at par under rule R8 where the version 1.0 compiler had summed the issuance record's market-valued figure. The change in the par-test statistic produces a constituent change for each affected instrument, recorded in the constituent-change log. Three further constituent changes are recorded with their windows. The first is the removal of lending-pool shares from the wrapper set, which lowers S2 gross by $1.545 billion and the multiplier by 0.0052 at the effective date, with S0 and S1 unchanged. It enforces the stablecoin-lineage boundary that rule R6 already draws and leaves the definition of the wrapper layer unchanged, which is why it is a constituent change under a minor version and not a redefinition of a layer under section 7.1. The second is the removal from S0 of a representation that the version 1.0 compiler had counted alongside its base coin, $0.468 billion, 0.16 percent of S0. The third is the resolution of membership per instrument: the version 1.0 compiler identified members by ticker, so two instruments sharing a ticker were one member carrying one verdict, and a verdict formed on one instrument's prices admitted another. Under version 1.1 each instrument in the issuance record is a member in its own right, its verdict is the verdict of the coin whose prices formed it, and an instrument whose coin holds no verdict is a candidate under section 5.6. At the effective date this moves $0.50 billion from S0 to the candidate set, of which $0.18 billion is a single instrument whose par verdict rested on no price the platform holds. The backcast of section 7.4 carries every level effect through the window it covers. The corrections to rule R9 move no value, because no documented excess exists at the effective date.

Figures compiled under version 1.1 carry its version label from 16 September 2026. A backcast of the series under version 1.1 is published as a separate vintage over 27 September 2018 to 18 September 2026. Every value published under version 1.0 remains retrievable under its identifier and is not restated.

1. Introduction and motivation

Every monetary statistic begins with a choice about ordering. Central-bank fiat monetary aggregates, including the monetary base and the M1 and M2 money stock measures, order claims on the banking system by liquidity. Currency and transaction deposits come first, followed by instruments that take progressively more time or cost to convert into means of payment. That ordering reflects the question those aggregates are designed to answer: how much spending capacity exists.

Stablecoin supply raises a different measurement problem. With few exceptions, these instruments are transferable on demand and settle within seconds, so a liquidity ordering distinguishes little among them. A savings wrapper and the base token it wraps may both be liquid and may trade in the same venues within the same block. The relevant distinction is what stands between the token held and the point at which redemption is ultimately satisfied. That point is the redemption endpoint. Depending on the design, it may be an issuer's redemption obligation or a protocol redemption mechanism. A base-token holder has a direct claim. A holder of a bridge-issued representation has a claim on the representation issuer, which holds the base token immobilized one for one, effectively relocating the same claim to another settlement environment. A holder of a savings wrapper has a claim on an arrangement that holds base tokens and pays out of them, creating a different claim derived from the base. A holder of a savings wrapper over a representation is one further step removed.

The S0/S1/S2 aggregates retain the familiar three-tier form while using a different ordering principle. Fiat monetary hierarchies order money by liquidity. This hierarchy orders claims by form: primary claims first, representations of those claims in other environments second, and other claims derived from them third. The specification also records claim distance for every instrument, defined as the number of redemption steps between the token held and the base instrument's redemption endpoint, with the base unit assigned a distance of zero. Claim distance is a published property of an instrument but does not determine its tier. A representation and a direct wrapper, for example, both stand one step from the base unit but belong to different tiers because their claims differ in form. The analogy with the monetary base, M1, and M2 serves only as a mnemonic for the nesting of the tiers in constituent scope, under which S0 ≤ S1_gross ≤ S2_gross. It does not map economic functions across the two systems. S1 does not correspond to a stablecoin version of M1.

Three properties motivate the design.

Aggregation without double counting requires an explicit layer convention. The total value observable across settlement environments exceeds the total of base claims outstanding because a single base claim may support a representation on another chain and a wrapper over that representation, with each layer carrying an observable outstanding value. Treating the observable total as supply overstates the base claims outstanding. Restricting the measure to base claims omits information about the claim structure built on them. The aggregates report both quantities on a common base and connect them through an identity.

Claim structure is itself an object of measurement. Layering per unit of base supply changes over time and cannot be recovered from any single supply measure. Section 4 reports it as a series through the representation multiplier.

The boundary must be specified in advance. Yield-bearing wrappers, structured tranches, and tokenized securities settled in stablecoins sit at the outer edge of the hierarchy. They are also among the fastest-growing parts of the segment and among the instruments most easily aggregated incorrectly. Section 5 therefore adopts an admission policy under which exclusion is the default, while section 3 specifies the rules on which that policy depends.

The rest of the paper proceeds as follows. Section 2 defines the tiers and their net and gross variants. Section 3 presents the edge-case rules. Section 4 defines the representation multiplier and gives equal attention to the inferences the measure does not support. Section 5 sets out the constituent admission policy. Section 6 documents the measurement framework and source classes. Section 7 defines the versioning and revisions policy. Section 8 places the framework in relation to prior work on stablecoins and money. Section 9 provides citation forms.

2. Definitions

2.1 Notation

Symbols are set in a fixed-width face. A subscript follows an underscore; a compound subscript is braced, as in FX_{c(i)}(t). S0, S1 and S2 are names, not subscripted symbols.

The exception terms x_i and ℓ_j have the same structure. Each measures claims outstanding at one layer in excess of the backing held against them at the layer immediately below. Because the terms are layer-local, they can be added without double counting. They are also the only terms through which the net measures can differ from S0.

Base and representation quantities are measured at par in the coin's peg currency and translated into United States dollars using the official reference rate specified in section 6.4.2. For a dollar-par coin, this translation is the identity. Wrapper layers are measured at outstanding market value. Rule R8 states and governs this deliberate valuation asymmetry. Because non-dollar members enter at a reference rate, S0 is a United States dollar-equivalent aggregate and may move even when no unit is issued or redeemed. Sections 4.2 and 6.4.6 state the implication and its treatment. The published series includes a decomposition of S0 by peg currency so that issuance effects can be separated from exchange-rate effects.

2.2 S0, base stablecoin supply

S0 is the total of native primary stablecoin claims intended to redeem at or track par, as recognized by the issuing arrangement. It excludes unreleased issuer treasury balances and is consolidated across settlement environments so that each claim is counted once regardless of the number of environments in which it circulates.

S0(t) = Σ_{i ∈ U_0(t)} n_i(t)

S0 is the base measure in the hierarchy. It is a different compilation from the platform's market value figure; section 6.7 defines their relationship. An S0 holder has a claim at claim distance zero. The unit held is itself the redemption endpoint, with no intermediate claim between the holder and that endpoint.

Consolidation across settlement environments is embedded in n_i, rather than applied as a separate adjustment. When issuance is recorded by environment, the native measure for each environment excludes units issued against base units immobilized elsewhere. Representation flows therefore cancel within the sum, making S0 net by construction.

A redemption endpoint has one of two forms. Throughout the specification, the term "claim" is used broadly enough to encompass both. An instrument is eligible for S0 when it satisfies either form.

The first form is an identifiable redemption obligation, whether legal or technical. A fiat-backed stablecoin whose issuer undertakes to redeem at par meets the condition legally. A design whose redemption is enforced by contract code meets it technically. The relevant requirement is an identifiable counterparty or mechanism supporting redemption at par.

The second form is primary par issuance in which the redemption path is mediated by a protocol rather than embodied in a legal person. A collateralized design that allows any holder to retire units against collateral through an open mechanism has no obligor in the legal sense, yet still qualifies as a base instrument. Units are issued at par against value, and the route back to that value is defined and open.

The base universe U is determined exclusively by the following criteria. Criterion 3 is evaluated as provided in section 6.4.1, including through the proxy used for dates preceding the collection of daily prices. An instrument belongs to U when all four conditions hold:

1. it is a primary issued claim: units are created against value at issuance and the unit held is itself the redemption endpoint (claim distance zero), under either form described above;
2. it is designed to maintain parity with one fiat unit of account;
3. it maintains that parity in practice under the par test in section 6.4.1; and
4. it is neither a representation of another claim (section 2.3) nor a wrapper (section 2.4), preventing any unit of underlying value from being counted twice.

Membership is an attribute of the instrument. It is independent of the source that lists the instrument, the platform's current ability to observe it, and the platform's technical capacity on any given day. Those factors concern compilation coverage and are treated in section 6.4.4. When criterion 3 cannot yet be evaluated, membership remains unresolved rather than being assigned either member or non-member status. Section 5.6 records that state. The constituent registry also records which of the two redemption-endpoint forms admits each base instrument.

2.3 S1, represented stablecoin supply

S1 adds tokenized representations of S0 claims. These are units issued in one settlement environment against base units held or immobilized in another, with a redemption path that passes through the representation issuer before reaching the base redemption endpoint. S1 is reported in two variants.

S1_gross(t) = S0(t) + Σ_{i ∈ U_b} b_i(t)
S1_net(t)   = S0(t) + Σ_{i ∈ U_b} x_i(t)

The gross variant counts every token layer simultaneously in circulation. The net variant removes duplication arising from the backing relationship. Immobilizing one base unit to issue one representation creates no additional base claim, so the two layers reduce to one in the net measure.

When all representations are fully backed, the net identity becomes S1_net(t) = S0(t), which is the normal state. The shortfall term x_i is nonzero only under the circumstances specified by rule R2. This is the sole case in which net represented supply departs from base supply.

2.4 S2, extended stablecoin claims

S2 adds transferable instruments whose principal economic exposure can be traced to a claim on an S0 asset, including savings receipts, staking receipts, and tranches over those claims. Shares in pools that lend the base coin onward belong to the adjacent segment defined in rule R7. Admission requires a documented redemption path that resolves to exactly one base coin, as specified in section 5.

ρ_j(t)      = 1 − ℓ_j(t) / C_j(t),   with ρ_j(t) = 1 where C_j(t) = 0
v_j(t)      = ρ_j(t) · ṽ_j(t)
S2_gross(t) = S1_gross(t) + Σ_{j ∈ W_c} v_j(t)
S2_net(t)   = S1_net(t) + e(t),   where e(t) = Σ_{j ∈ W_c} ℓ_j(t)

The gross variant counts every circulating layer that constitutes a claim on the base. Claims issued by a wrapper beyond the backing it holds, ℓ_j, do not constitute claims on that base. Rule R9 therefore admits only the backed share of the wrapper's market value, ρ_j · ṽ_j. A market premium or discount scales the admitted value without altering the excess, and admitted wrapper value cannot be negative. The excess itself is measured at par and enters the net identity through e. S2 includes every admitted derived claim regardless of claim distance. A wrapper directly over a base coin stands one step from it, while a wrapper over a representation or another wrapper stands farther away; all belong to the wrapper layer under rule R3. The sums run over W_c, the admitted wrappers whose base coin is covered on the observation day, so criterion A2 enters the equation directly. The gross measures therefore sum represented claims on the base without including every observable item of value in the segment.

The net measures represent deduplicated claims within the hierarchy. Placing a base unit into a wrapper creates no additional claim on the base coin, so wrapper layers net out and only e(t) remains. This term records documented claims created at the wrapper layer in excess of the backing held there. Those excess claims are obligations of the arrangement that issued them and do not constitute base claims. When no documented excess exists, S2_net(t) = S1_net(t) = S0(t).

This specification publishes S0, S1 gross, S2 gross, and the multipliers defined in section 4 as measured series. S1 net and S2 net are conditional accounting identities. They depend on the full-backing assumption that section 6.5 states is not independently verified. The exception terms x_i and ℓ_j are recognized only when documented evidence reaches the compiler under rules R2 and R9; otherwise they are set to zero. The absence of a measured exception term does not establish that no exception exists. The net measures are therefore identities that hold when the backing they assume is in fact present.

2.5 Layers, tiers and the non-overlap requirement

The specification distinguishes between two concepts that can otherwise be conflated.

A claim layer classifies an instrument by the form of its claim. Each admitted instrument belongs to exactly one layer: base units belong to the base layer, cross-environment representations of base units to the representation layer, and all other admitted derived claims to the wrapper layer. Claim distance is recorded separately and does not determine layer assignment. A bridged representation and a wrapper held directly over the base coin, for example, are both one redemption step from the base unit but occupy different layers because their claims have different forms.

A tier is an aggregate containing all layers through its boundary. The tiers are therefore nested in constituent scope, so that S0 ≤ S1_gross ≤ S2_gross, while assignment to the underlying layers is mutually exclusive. An instrument contributes once to every tier at or beyond its own layer. The wrapper layer has no upper bound on claim distance: a wrapper over another wrapper remains in the wrapper layer under rule R3.

R0. Non-overlap with the base record. A representation or wrapper is admitted only when its units are absent from the base coin's native issuance record. If the issuer's own reporting consolidates a variant token into the circulating supply of the base coin, the variant belongs to S0 and is classified as neither a representation nor a wrapper, regardless of its technical design.

Rationale. Layer counting requires a base that is measured once. R0 assigns the compiler responsibility for checking the base record before admitting another layer.

2.6 Worked example: one base unit through three tiers

Consider 100 issued and outstanding units of a base coin. Thirty are immobilized in a lock-and-mint bridge, against which 30 representation units circulate in a second settlement environment. A savings vault holds 21 units, consisting of 20 units deposited by holders and 1 unit received as yield paid in the base coin. Wrapper shares with a value of 21 units circulate against those vault holdings. The resulting tiers are:

S0 includes the 30 immobilized base units, while S1 gross also includes their representations. S0 likewise includes the 21 units held by the vault, while S2 gross also includes the wrapper shares issued against them. This duplication is the intended consequence of layer counting. Gross measures capture claim structure; net measures capture deduplicated claims, which in this example equal base supply.

The additional unit of yield illustrates rule R9. When yield is paid in the base coin, an already outstanding unit moves into the vault. Vault holdings and wrapper value rise by the same amount. Wrapper claims of 21 are backed by 21 base units, leaving the net measures at S0. Accrued yield increases S2 gross and the multiplier without entering e.

3. Edge-case rules

Every rule in this section is normative. Each rule is stated first, followed by its rationale and, where the treatment requires an observable decision criterion, the relevant observable.

4. The representation multiplier

4.1 Definition

m(t)   = S2_gross(t) / S0(t)
m_1(t) = S1_gross(t) / S0(t)

m(t) is the representation multiplier, defined as the total value of circulating stablecoin claim layers per unit of base stablecoin supply. Wrapper layers enter at market value under rule R8, making the measured quantity market-valued claim layering. m_1(t) is the bridge-only multiplier. It isolates the representation layer from the wrapper layer and is published alongside m because the two layers differ in coverage and observability.

By construction, m(t) ≥ m_1(t) ≥ 1: every b_i is non-negative, and every admitted wrapper value v_j = ρ_j · ṽ_j is non-negative under rule R9. A value of 1.0 indicates that no representation or wrapper value is outstanding within the measured coverage of those layers. Values above 1.0 indicate the amount of claim structure accumulated on the same base. m_1 is observed over U_b, the members whose bridges are tracked by the record, so its scope is bounded by that coverage and does not estimate representation value across all of U.

m is published only for observation days with wrapper-layer coverage. When wrapper coverage is absent, m is withheld and m_1, which depends only on the representation layer, is published separately. The two multipliers can therefore span different windows. Any comparison identifies the window used for each figure.

4.2 Interpretation

The multiplier measures claim layering: the value of admitted representations and derived claims outstanding per unit of base supply, within the stated coverage of each layer.

An increase means that representation or wrapper value has grown faster than base supply, leaving more claim layers outstanding per unit of base supply. A decline means the converse. The level expresses circulating claim value per unit of base and, correspondingly, the amount of observable segment value that a simple sum across all tokens would count more than once.

With a multi-currency U, changes in a peg currency's reference rate can also move m when coins denominated in that currency have a different layering ratio from the rest of the base. This is a composition effect and does not represent a change in claim structure. When a movement in m spans a period of reference-rate change, its description states the per-currency decomposition of S0 required by section 6.4.6.

The multiplier has an additive decomposition into the two channels that generate it:

m(t) = 1 + [ Σ_{i ∈ U_b} b_i(t) / S0(t) ] + [ Σ_{j ∈ W_c} v_j(t) / S0(t) ]
              representation channel           wrapper channel

The identity is exact, so the two channels account for every movement in m without a residual. m_1 consists of the first two terms. The decomposition is published with the series.

The decomposition identifies the channel through which a movement occurs but does not establish its cause. Rule R1 shows that a change in bridge design can move the representation channel without changing the base claims outstanding. Rule R3 shows that adding a layer over existing claims can move the wrapper channel. Commentary on a movement in m therefore identifies the channel that changed and the relevant coverage boundary without assigning a cause.

4.3 What the multiplier does not measure

The multiplier shares the form of a fiat money multiplier, but the resemblance does not extend to interpretation. The following limitations are part of the specification.

No solvency or reserve-adequacy inference. A high multiplier is compatible with full backing at every layer. A multiplier of 1.0 is also compatible with impaired reserves at the base coin. The measure is compiled from outstanding quantities and contains no information about the quality of an issuer's reserves. No value of m is defined or published as a warning threshold.

No leverage measure. Rule R9 excludes from the S2 gross wrapper total value created through leverage within a wrapper structure and recognizes that value separately. In the normal case, the layers counted by the multiplier are fully backed claims on the same base, meaning the same obligation represented more than once rather than an obligation borrowed against more than once.

No measure of liquidity or velocity. None of the components is a transaction measure. Two segments with the same multiplier can have arbitrarily different turnover.

No measure of money creation. Under the net identities in section 2, the layers counted by the multiplier add no claim on the base coin. The documented exceptions under rules R2 and R9 are claims on the representation issuer or the wrapper arrangement that created them. They are not base claims, and the net measures record them accordingly. Deposit creation changes the aggregate quantity of claims. Representation and wrapping change the number of tokens through which an unchanged quantity of claims is held.

No redemption-value measure. Wrapper layers enter at market value under rule R8. A wrapper that trades away from the value of its underlying claim can therefore move the multiplier even when claim structure is unchanged. The specified statistic is market-valued claim layering. A redemption-valued version would be a separate statistic, recorded in section 7.5 as a candidate rather than a restatement of the present measure.

Comparability requires a common coverage boundary. A change in the coverage of either measure changes the ratio. Daily coverage is published under section 6.4.4, so a reader comparing m across two dates can identify the coverage on each date. Coverage changes are not constituent changes and therefore do not enter the constituent-change log described in section 7.2.

4.4 Worked example: the published series

The following example is taken from the published series at the vintage of 16 September 2026, the vintage on which every figure in this document is stated. Every figure is reproducible from the downloadable series of that vintage for the same date. A later vintage may restate this date under section 7.3; the vintage used here remains retrievable.

Observation date 16 September 2026.

For this observation date, the decomposition in section 4.2 is:

m = 1 + 0.066668 + 0.021425 = 1.088093

The components are reported to six decimal places so that the identity closes at the stated precision. The published series reports the multiplier to four decimal places, 1.0881, while retaining the three levels without rounding. A reader can therefore reproduce every number in the table from the download.

Under the interpretation in section 4.3, the figure reports the amount of market-valued claim structure circulating per unit of base supply. It contains no information about the backing quality of any layer.

For this vintage, the two published forms of the series, the downloadable artifact and the daily table, are written by one compilation and agree for this date. Both apply the constituent rules in force under this version, instead of those in force on the observation date: constituent map version 3, membership keyed by instrument identifier under section 6.2, valuation at par under rule R8 where a token count is recorded, the exclusion of lending-pool shares under rule R7, and coverage-consistent S2 admission under criterion A2.

5. Constituent admission policy

5.1 Exclusion as the default

An instrument does not enter S2 merely because it is denominated in a fiat unit, bears yield, or resembles an admitted instrument economically.

Admission requires an explicit entry in the maintained constituent map. Any instrument absent from the map is excluded. That absence records the state of the compilation and does not constitute a judgment about the instrument itself.

A1. Documented redemption path. Admission requires a redemption path to exactly one base coin, documented by the issuing arrangement. The path must resolve through a finite sequence of steps, each independently documented. Admission follows from the documented path, not from price correlation with a base coin.

A2. Single-base attribution and base coverage. Each entry records the base coin to which its claim resolves. The instrument enters S2 only for vintages in which that base coin is within S0 coverage. An admitted entry whose base falls outside coverage on a given day contributes nothing to S2 for that day. Otherwise, its value would increase the multiplier's numerator while its base contributed nothing to the denominator. The condition is evaluated for each vintage and published for each entry. Once the base becomes covered, the entry enters the compilation without reopening the admission decision.

A3. Finite chain. Every step in the claim chain must be documented, and the chain must terminate in a base coin. Rule R3 governs multi-step chains and tranches.

5.2 Relation vocabulary

Each admitted entry records its claim form using a controlled vocabulary. The vocabulary forms part of the specification. Any addition to it constitutes a version change under section 7.

Instruments reported alongside the hierarchy but excluded from it carry an adjacent-segment code outside the admission vocabulary: adjacent-lending for shares in pools that lend the base coin onward under rule R7, adjacent-tokenized-security for instruments excluded under rule R6, and adjacent-commodity for tokenized commodity claims. Adjacent-segment codes are separate from relation codes, and an instrument assigned one belongs to no tier.

A stated waiting period for redemption does not affect admission or tier assignment, because the hierarchy is ordered by claim form rather than liquidity. Waiting periods are recorded on the entry.

5.3 Confidence vocabulary

Every admitted entry also carries a confidence grade. The grade governs permissible use of the entry rather than its inclusion in the compilation. All admitted entries are compiled. Allowing constituents to vary with an internal judgment would prevent the series from being reproduced from the published map.

A medium grade cannot persist indefinitely. Section 7 requires every entry carrying a re-verification flag to be resolved or removed at each specification revision.

5.4 Exclusion vocabulary

Excluded instruments are assigned a reason so that the boundary remains auditable.

An exclusion recorded as unclear-lineage reflects the state of the documentation. It is reconsidered when the documentation improves, and any resulting change is recorded under section 7.

The exclusion vocabulary applies to instruments outside U by definition or by the par test. Instruments that belong to U but are not reached by a particular compilation are described instead by one of the statuses in section 5.6.

5.5 Coverage boundary

Both the base universe and the admitted wrapper set have explicit boundaries, and those boundaries are stated wherever the aggregates are reported. For each compilation, section 6.4.4 records the share of U that is covered and the status of every member that is not.

A compilation day is accepted only when every member of a published required set has reported for that date. The required set identifies the base coins whose absence would leave the day's level unrepresentative of the segment. It is carried in the constituent map, so a change to the set is a constituent change under section 7.2 and does not require a specification version change. The required set in force is USDT and USDC, together 86.42 percent of S0 at 16 September 2026. A day with incomplete reporting is withheld because a coverage gap in a level series cannot be distinguished from a contraction in supply. The rule is a completeness gate; it does not interpolate missing observations. Missing days remain missing.

5.6 Coverage and classification status vocabulary

Every instrument observed by the platform has one status for each compilation and observation day. The statuses fall into three groups: covered members, uncovered members, and unresolved candidates. Instruments outside U carry one of the exclusion reasons in section 5.4.

An uncovered status describes a limitation of the compilation and does not characterize the instrument itself. A status may change as source coverage changes. Such changes are treated as coverage movements under section 6.4.4 and do not constitute constituent changes under section 7.2.

6. Measurement and data sources

6.1 Source classes and authority

The compilation follows a single authority principle. One source owns each data type, one source supplies each instrument within a given series, and no series changes source partway through its history. When a series must combine different data types, the combination occurs across instruments rather than within a single instrument and is documented as a composite. Section 6.6 identifies the composites used in the aggregates.

Official exchange reference rates are the only reference-series input to the aggregates. All other reference series are used solely for comparison. A dollar-par coin is unaffected by the exchange-rate input, whereas the dollar-equivalent level of a non-dollar member changes with that input. Section 6.6 records the resulting limitation.

6.2 Identifier resolution

Constituents are keyed by persistent instrument identifiers rather than ticker symbols, and the constituent map is joined to the observation record using that identifier. Ticker symbols are not unique. A symbol-keyed join can merge two instruments that share a ticker into one record or silently omit one of them. The wrapper join used to compile S2 is identifier-keyed.

Renames and migrations do not alter instrument identity because identity follows the persistent identifier rather than the display name. A change in an instrument's recorded identifier is treated as a constituent change under section 7.2.

The data store used for the base and representation layers retains the source identifier alongside the instrument symbol. Moving those joins to identifier-only keying, so that the principle in the first paragraph applies at every join rather than only to the wrapper join, is recorded as compilation work.

6.3 Observation frequency, timing and latency

Observations are daily and carry a UTC calendar date. Within each daily collection cycle, the base and representation layers are collected first, followed by the wrapper layer within the same cycle.

If a collection cycle is incomplete at the cutoff, the wrapper layer may lag the base layer by one day. In that case, the latest published S2 and m values correspond to the most recent date on which wrapper coverage is complete. That date is shown with the figure and is not represented as the current day. S0, S1, and m_1 are still published for the current day because they do not depend on the wrapper layer.

The completeness gate in section 5.5 applies to the base layer. If the constituents of the required set of section 5.5 have not reported for a day, no observation is published for that day.

6.4 Definition, test and coverage

6.4.1 The par test and its parameters

Base coins qualify through a par test rather than self-description. An instrument qualifies when it is designed to maintain parity with its reference unit and does so in practice. The decision to test observed par behavior rather than rely on a design label follows Kosse et al. (2023), who examined 68 stablecoins and found that none had maintained parity with its peg at all times. That finding motivates the existence of the test; the statistic and parameters specified below are specific to this methodology.

For each coin i and observation day t, the par ratio is

q_i(t) = P_i(t) / FX_{c(i)}(t)

where P_i(t) is the coin's observed daily price in United States dollars and FX_{c(i)}(t) is the official reference rate of its peg currency, expressed as dollars per unit, under section 6.4.2. For a dollar-par coin, FX = 1. Parity is q = 1 in every currency. A claim on one euro, one yen, or one real is therefore evaluated in the same way as a claim on one dollar.

The test statistic is the median absolute deviation from parity over the coin's entire observed history:

D_i = median_t | q_i(t) − 1 |

A coin passes when D_i ≤ 0.025. Absolute deviation prevents movements above and below parity from canceling. A coin alternating between 0.90 and 1.10 has a median price of one but a median distance from parity of 10 percent, and the latter quantity is the one measured by the test. The 1.0 compiler applied the same band to the signed median median_t q_i(t). Compared across the population the test can judge at the effective date, the two statistics disagree on 11 small instruments, $50.4 million in total; their stored verdicts stand under section 7.2 until reopened, and no instrument above one billion dollars is within a tenth of the band under either statistic.

A verdict is stored only after the coin has at least 30 valid daily observations and only after the primary market-data price has been checked against a second independent price under section 6.1. Until both requirements are met, the coin is unclassified under section 5.6. Its membership remains unresolved, and it stays outside every compilation. The 1.0 compiler stored an initial verdict after three valid daily observations from a single source.

The median is preferred to the mean or the most recent price because a bounded episode should not determine membership. A coin that traded at 87 cents for two days within a 500-day history remains a base coin. The episode is recorded in the peg-stability series and the coin's depeg record. The 2.5 percent band is a classification parameter rather than a measure of peg quality; peg deviations are measured separately in the platform's peg-stability series.

Information set and precedence. A coin's verdict is formed from the observations available on the day the verdict is stored. Later observations do not alter it, and the whole-history statistic is not reapplied after the verdict has been frozen. A frozen verdict can be reopened only by the review trigger in section 6.5 or through a logged constituent change under section 7.2. Any resulting change applies prospectively. A backcast compiled under this version applies the verdicts in force on its compilation date throughout the backcast window, and the vintage note discloses that treatment.

Proxy for dates before daily prices. For observation days preceding the platform's collection of daily prices for an instrument, criterion 3 of section 2.2 is evaluated by proxy. The instrument is treated as maintaining parity when the issuance record classifies it as a par claim on a fiat unit, and those days carry the status proxy_verdict. An instrument is not removed from a historical observation solely because no computed verdict exists for that date. The proxy is never applied to a day on which the par test can be run. For dates eligible for the proxy, the proxy takes precedence over the backcast treatment of the preceding paragraph.

Verdicts are frozen by vintage under section 7.2. Once frozen, a verdict changes only through a logged constituent change stating the reason. Because a whole-history statistic can respond slowly to a permanent collapse, section 6.5 defines a review trigger that surfaces such a case while preserving the rule.

6.4.2 Reference rates

A par claim denominated in a non-dollar unit is valued in dollars, and its par ratio is formed, using an official reference rate. The applicable rate for a given day is chosen mechanically according to the following hierarchy:

1. the European Central Bank's daily euro reference rate for the currency, crossed into dollars per unit through the same day's euro reference rate for the dollar;
2. otherwise, the official exchange rate for the currency published by its issuing central bank, stated or crossed into dollars per unit through that bank's same-day official dollar rate;
3. otherwise, no rate.

Commercial and venue-derived exchange rates are excluded from both valuation and the par ratio at every step. When no rate is published on a given day, the most recently published rate is carried forward for at most seven calendar days. After that period, the rate is stale and the coin is assigned reference_rate_stale until publication resumes.

If no rate exists under this hierarchy for a currency, its coins remain inside U but outside the compilation with status no_official_reference_rate. As of 16 September 2026, the platform holds reference rates for 17 currencies under step 1; the first rate admitted under step 2 took effect on 17 September 2026. The rouble is the material case for the second step: the European Central Bank suspended its rouble reference rate on 2 March 2022, and the issuing central bank publishes a daily official rate, which is applied under step 2.

6.4.3 Definition and coverage are separate statements

The definition of U is kept separate from the coverage achieved by a particular compilation, consistent with monetary-statistics practice. An aggregate's definition does not change when a reporting institution is absent, and compilers state the share of the defined population reached by their collection. The International Monetary Fund's Monetary and Financial Statistics Manual and Compilation Guide (2016) states an institutional coverage boundary as part of compilation practice. The European Central Bank defines the population of monetary financial institutions and allows derogations for small institutions whose combined share of the national balance sheet does not exceed 5 percent (Regulation (EU) 2021/379, Article 9(1)). Its compilation manual refers to those derogated institutions as the reporting tail and requires collection of the size of that tail so it can be monitored (European Central Bank 2024, section 2.7.1). The base universe is handled on the same principle: the tail remains within the definition, its size is measured, and its share is reported as coverage. No gross-up is performed, and no level in this specification is estimated for an uncovered member.

6.4.4 Coverage, stated daily

Every daily S0 compilation reports:

• the share of U covered, both by count and by value;
• each member of U that is omitted, with one status from section 5.6; and
• unresolved candidates, listed separately and excluded from the coverage denominator.

Coverage for higher tiers is reported separately whenever assignment to a tier requires information beyond the base level. A base claim may be fully measured in S0 while its units are only partly attributed across settlement environments for S1. Missing environment attribution therefore limits representation-layer coverage without reducing S0.

Value coverage requires a value for members that the compilation itself cannot value. For this purpose, coverage is measured against a coverage benchmark: the broadest independently observable United States dollar value for each confirmed member of U on the day, taken from market data. The benchmark is diagnostic only. It never enters S0 or any higher tier, is not valued at official reference rates, and does not imply the level the compilation would carry for the member. Count coverage requires no benchmark and is published alongside value coverage. A confirmed member of U with neither an issuance value nor an independently observable market-data value counts in coverage by count, is listed as unvalued, and is outside the value denominator, so the value share remains defined. In the machine-readable coverage record the share is labelled value coverage among value-observable members of U; the prose of this specification calls it value coverage.

Coverage increases when collection improves and decreases when a source withdraws. Neither movement changes the definition, neither constitutes a revision under section 7.3, and neither is announced instrument by instrument. The movement is visible in the coverage figure, while the daily list identifies its source.

6.4.5 The compilation in force

S0 includes every member of U for which the platform has both a qualifying issuance record under section 6.1 and, when the peg currency is not the dollar, an official reference rate under section 6.4.2. Membership in U, coverage of a member, and the quantity measured for that member are distinct statements and are kept separate by the specification. For each instrument, the circulating figure carried by the record is its issuance net of units immobilized against representations elsewhere. S0 is therefore net by construction for every covered member, whether or not a per-environment decomposition has been collected. On 16 September 2026 S0 covers 99.91 percent of U by benchmark value and 70.22 percent by count, over 158 instruments. Uncovered members by status: no_issuance_record $0.24 billion, no_official_reference_rate $0.02 billion. Unresolved candidates: 205 instruments, $2.31 billion by benchmark value; of these, 150 are instruments in the issuance record whose market-data identity the platform cannot yet establish, and the remainder are instruments whose coin holds no verdict.

The representation layer b_i is measured from the per-environment decomposition specified in section 2.2, which the record carries for members whose bridges it tracks. The decomposition is sought for every S0 member. A member for which no bridged units are tracked receives the status no_bridge_record, contributes its full circulating figure to S0, remains outside U_b, and is excluded from representation-layer coverage. The representation sum in section 2.3 therefore runs over U_b and not over all of S0. An untracked bridge is absent from the sum and is never assigned a value of zero. On 16 September 2026 the representation layer is measured for members constituting 99.44 percent of S0 by value, 137 of 158. Version 1.0 stated the same rule, but its compiler did not apply it. S0 was summed only across members with a collected decomposition, 18 instruments on the final day compiled under that version, while the rest of U appeared only in the coverage denominator. Under version 1.1, those remaining members enter S0. The level therefore rises on the effective date by the share previously outside compilation coverage. Section 6.4.4 classifies the increase as a coverage movement, and section 7.4 carries it through the backcast. The increase is not treated as a revision.

The issuance record is a compiled source rather than the primary source. Primary issuance is recorded on chain, and the platform's program of reading issuer contracts directly is expected to increase coverage over the life of this version without requiring a version change.

6.4.6 Changes at constant exchange rates

Because non-dollar members are converted at reference rates, the change in S0 between two dates has two components. The constant-exchange-rate quantity effect measures the change in outstanding units within each peg currency at the earlier day's exchange rate. The exchange-rate effect measures the change in rates applied to the later day's outstanding units.

ΔS0 = Σ_c FX_c(t−1) · [ Q_c(t) − Q_c(t−1) ]  +  Σ_c Q_c(t) · [ FX_c(t) − FX_c(t−1) ]
        constant-exchange-rate quantity effect          exchange-rate effect

The quantity effect includes more than issuance and redemption. It also captures members entering or leaving coverage under section 6.4.4 and constituent changes under section 7.2. Where a further decomposition is published, the quantity effect is divided between changes in members present on both dates, representing issuance and redemption, and changes associated with members present on only one date, representing coverage and constituent movements. Both components are published with the series. Statements about growth in S0 or a higher tier use the quantity effect, or its continuing-member component where available, because exchange-rate movements are holding gains or losses on outstanding positions. This follows the distinction used in monetary statistics when transactions are derived from changes in outstanding amounts (European Central Bank 2024, section 5.8). The same decomposition is published for the components of the multiplier so that movements in m, as described in section 4.2, can be evaluated net of currency composition.

6.4.7 Further rules in force

New instruments. The base universe and the wrapper set use opposite defaults. Admission to W requires an explicit entry, so an instrument not yet ruled on is excluded from S2 under section 5.1. When the issuance record first begins to carry an instrument, that instrument enters as a candidate. It remains unclassified until the par test in section 6.4.1 produces a stored verdict, and it enters S0 on the first vintage with a passing verdict. Section 6.5 lists candidates awaiting adjudication.

Adjacent segments. Tokenized commodity claims fall outside the hierarchy because their parity is to a commodity rather than a currency. Tokenized securities fall outside under rule R6, and shares in pools that lend the base coin onward fall outside under rule R7. None of the three is added to any tier; each is reported beside the hierarchy where the platform tracks it.

Minted-only instruments under rule R5. If the issuance record contains a minted quantity but no circulating quantity for an instrument, rule R5 excludes the instrument from n_i. A minted quantity alone does not establish that units are externally held. At the observation date of 16 September 2026, no instrument in coverage is in this state.

Entries outside base coverage under criterion A2. An admitted wrapper is excluded from the compilation for any vintage on which its base coin is not covered by S0, whether because the base is outside U or because it is a member that S0 does not cover. This condition preserves the literal meaning of the multiplier in section 4: every instrument in the numerator has its base represented in the denominator, so m compares claim layers with the base of the same population. The condition is a coverage state rather than an admission error, because each affected entry still satisfies A1. Those entries remain admitted, are disclosed for each vintage through a published base-coverage flag, and enter the compilation on the first vintage in which their base is covered. The flag is calculated for each vintage rather than stored in the map and therefore applies only to the day being compiled.

6.5 Reconciliation and monitoring checks

The compilation is subject to deterministic checks that run daily and feed an operational digest. The following checks are in force.

Completeness. The section 5.5 gate withholds any day on which a member of the required set has not reported.

Cross-source agreement. When an instrument appears in both the issuance record and market data, the two measures of outstanding value are compared. A widening difference indicates that one source has moved away from its stated measurement basis.

Series continuity. Published series are checked for discontinuities at points where an input changes in coverage or vintage.

Market value comparison. S0 is compared daily with the market value figure in section 6.7. Because the two populations differ by construction, the difference is published as information rather than treated as a defect signal. Movements in the difference are read against the daily coverage statement and changes within the market category itself. When the market value figure is unavailable, the value is recorded as absent rather than carried forward.

Netting. For every member with a collected per-environment decomposition, the instrument-level circulating figure in the record is compared with the sum of native circulating figures across environments. Agreement within 1 percent confirms that the instrument-level figure is net of bridged units for that member. A difference beyond 1 percent constitutes a finding about the record. At 18 September 2026, the compilation day of the release run, 135 members were compared and 13 differed by more than 1 percent; the differences total $0.108 billion, 0.036 percent of the value compared, and the largest is 5.1 percent. Under version 1.0 the comparison ran on market-valued figures and reported differences that were movements in price rather than in units; under rule R8 both sides are unit counts.

Reference-rate availability. For every peg currency represented in U, the check reports the age of the most recent official reference rate under section 6.4.2 and the coins affected when the carry-forward limit has been exceeded.

Constituent review trigger. For every member with a stored par verdict, the compiler calculates the median absolute deviation from parity over the latest 30 valid observations. A value above 0.025 does not change membership. It assigns the member under_review under section 5.6 and sends the case to a reviewer. Any resulting membership change is prospective and is logged under section 7.2. Each flag records whether the two price sources agree on the member's last observed price, so that a venue-data error is read as a data question before it is read as a peg question. At 16 September 2026 the trigger stands on 32 members totalling $0.27 billion; for 12 of them both sources agree, for one they differ, and 19 carry a single price. The whole-history statistic would have flagged 15 of the 32. Every one is a pending constituent decision under section 7.2; none had been ruled on at the release date.

Coverage. The compilation itself calculates the coverage share in section 6.4 and publishes it with the series it qualifies. This prevents the coverage statement and the associated levels from referring to different vintages or constructions.

Unclassified instruments. Symbols present on the latest day of the issuance record that are neither classified as par members nor excluded under section 6.4 are listed for adjudication. A newly listed instrument therefore reaches a reviewer within one day rather than entering S0 without an explicit decision.

Neither x_i under rule R2 nor ℓ_j under rule R9 can be inferred mechanically from the data used to compile the aggregates. Both require documented evidence about the relationship between claims outstanding and backing held. Section 6.6 states the consequence.

6.6 Known limitations of the measurement

The aggregates combine source classes. S2 combines base and representation values from issuance records with wrapper values from market data. The combination occurs across instruments, which is permitted by the authority principle in section 6.1.

Valuation differs across layers. Rule R8 measures base and representation layers at par and wrapper layers at market value. The multiplier is consequently a ratio in which a market-valued component appears in the numerator but not in the denominator.

Accrued yield enters S2 gross. Under rule R4, wrapper value rises with accrued yield even if no new deposit is made. No principal-only variant is published.

The exception terms are not measured. x_i under rule R2 and ℓ_j under rule R9 are recognized when documented evidence is available, but no current monitoring check detects either term. The net measures are therefore conditional accounting identities and are not measured quantities. They hold under full backing, which the compilation does not independently verify. This is the most consequential limitation in this section and explains why section 2.4 identifies the gross measures as the measured series.

Representation-layer coverage is bounded. The native and bridged decomposition is published only for the coins it covers, and the bridge-design effect in rule R1 operates within that boundary.

Survivorship affects snapshot-derived inputs. When an input series is reconstructed backward from the instruments present at reconstruction time, instruments that ceased to exist earlier are absent from the reconstructed window. The base layer is drawn from issuance records that retain instruments after circulation ends, whereas the wrapper layer comes from market data that does not. The wrapper layer is therefore the affected component, and its coverage begins in April 2025. Wrappers that ceased circulating before that date are absent from the compiled wrapper total. For the earliest part of the window, this makes S2 gross and the multiplier lower than they would otherwise be, rather than higher.

The base and representation layers extend further back than the wrapper layer. For that reason, m_1 is published over a longer window than m, as specified in section 4.1. A comparison of m across the date on which wrapper coverage begins crosses a coverage boundary and therefore does not compare claim layering on a like-for-like basis.

Structural breaks can arise at input boundaries. When an input's coverage expands on a known date, series derived from that input contain a break reflecting the coverage change rather than a change in the segment. Section 7.4 marks the affected windows.

A small share of the record is valued at the source's figure. Rule R8 values a base unit at par in its peg currency at the official reference rate, which requires the unit count for each instrument and day. The issuance record supplies that count for 316,311 of 317,304 instrument-days in the compiled series; for the remaining 993, 0.31 percent, the source carries no count and the compilation uses the source's own dollar figure for that day, which is a market-valued quantity. At 16 September 2026 nine instruments in S0 are valued this way, $0.89 billion. The share is published with the series and falls as the record is completed. Version 1.0 valued every member at the source's dollar figure; the difference at the effective date is 0.08 percent of S0.

Non-dollar members are translated at official reference rates. The dollar-equivalent level of a non-dollar member changes with its reference rate. Exchange rates are an input under section 6.1 and can move the level without any issuance. The per-currency decomposition and constant-rate change reported under section 6.4.6 permit the two effects to be separated. No level is published for a currency without a qualifying rate.

Value coverage depends on a market-data benchmark. The value-coverage share in section 6.4.4 uses a market-data benchmark for members absent from the issuance record. The benchmark diagnoses compilation coverage and does not measure the segment itself.

Bridge tracking bounds representation-layer coverage. b_i is observable only for instruments whose bridges are tracked by the issuance record. A member without a bridged figure receives no_bridge_record; no zero value is assigned. Representation-layer coverage is therefore the share of S0 for which bridge tracking exists. This replaces the version 1.0 statement that the representation layer covered all of S0, which followed from that compilation's restriction of S0 to members with a decomposition.

The par test reaches only dates for which daily prices exist. Computed verdicts are available only for the period covered by the daily price history. Earlier days use the proxy rule in section 6.4.1 and are identified accordingly. Those observations carry the issuance record's classification and do not represent results of the par test.

6.7 Relation to the platform's other supply figure

The platform publishes two supply figures that may appear on the same day. They measure different populations and therefore produce different totals. Wherever either appears, its universe, source class, and coverage are stated. The two figures are never presented as a single measure.

Tracked stablecoin market value. The market value of the population identified as stablecoins by a market-data category, after subtracting representations and instruments flagged as yield-bearing. This is a descriptive market statistic over a category that the platform does not define. It applies no par test and does not compile U.

S0, base stablecoin supply. The supply of every member of U carried by the issuance record, across all currencies for which an official reference rate is available, valued under section 6.4.2 and compiled under this specification. It is the series underlying the platform's supply charts and the base of the hierarchy. No third supply measure sits between these two.

Their relationship is descriptive rather than normative. The market-value population will usually contain U and be larger because it includes instruments rejected by the par test, but a market category can also omit a member of U just as it can include a non-member.

Comparison. Reconciliation between the two totals is neither expected nor required because their populations, valuation methods, and purposes differ. The daily difference is calculated and published under section 6.5 for information. It is not treated as a defect signal, and a legitimate change in the category defining the first figure can move the difference. At 16 September 2026 the difference is 1.52 percent of the market value figure, $302.09 billion against $297.50 billion. The larger part is valuation: the market value figure prices every member at its market price while S0 counts units at par, and the two differ on the members they share. The remainder is population: instruments in the market category that are outside U or unresolved, and members of U the issuance record does not carry, $0.24 billion. Version 1.0 treated the difference as a reconciliation subject to thresholds. Specification 1.1 withdraws those thresholds and uses the coverage statement in section 6.4.4 as the compilation's defect signal.

7. Versioning and revisions

Canonical status depends on the way a series changes after publication, not on the way it is first defined.

7.1 Specification versions

The specification uses a two-part version number. A minor version change, such as 1.0 to 1.1, adds a rule, adds an item to a controlled vocabulary, or clarifies an existing rule while preserving the definitional core of the tiers. A major version change, such as 1.x to 2.0, redefines a tier, changes the ordering principle, or changes the treatment of a layer in a way that alters the object measured by the aggregate.

Each version has a dated document of record and a persistent identifier. Superseded versions remain retrievable. Every figure labeled S0, S1, or S2 states the version under which it was compiled.

7.2 Constituent changes

The constituent map is dated, versioned, and published. Every change appears in a constituent-change log stating the effective date, the instrument, the direction of the change, and the governing rule or admission criterion. Logged changes include additions to the admitted set, removals, changes in the recorded base coin, changes in relation, changes in confidence grade, and changes in exclusion reason.

A constituent change alters the definition of the series for the days it affects and is handled accordingly under section 7.3.

A change in a member's coverage status under section 5.6 is a coverage change rather than a constituent change. It appears in the daily coverage statement under section 6.4.4 and does not enter the constituent-change log. A change in the par-test verdict, including one resulting from the section 6.5 review trigger, is a constituent change and is logged.

The log is published with the constituent map and begins before this specification was frozen. Its first entry records a correction to the base universe. Claims on securities, which rule R6 excludes from the hierarchy, had been entering S0 because the universe rule was not fully enforced at compilation. The source data themselves had not reported those instruments incorrectly. The entry records the change, affected window, effect on the published level, and revision classification.

7.3 Revisions

Published values are never restated silently. A value changes only through a dated revision accompanied by a note identifying the affected series and window. Earlier series vintages remain retrievable.

Revisions are classified as follows.

Constituent revisions arise from a change recorded under section 7.2. The affected window is stated.

Source revisions arise from a restatement in an input record.

Compilation revisions arise from a correction to the compilation process itself.

Routine updates to the current observation within the same day do not constitute a revision.

A change in coverage under section 6.4.4 is also outside the revision framework. No published value is being changed, the defined population remains the same, and only the share of that population reached by the compilation has changed.

7.4 Vintage notes

When a series is revised, the affected window carries a vintage note. The note states what changed and when, using neutral language, without explaining why the underlying data changed.

Permitted forms:

Figures for [window] were revised on [date]. The revision reflects a constituent change recorded in the constituent-change log for [effective date]. The previous vintage remains available.

Figures for [window] were revised on [date] following a restatement in an input record. The previous vintage remains available.

No observation is published for [date]. Constituent reporting for that day did not meet the completeness requirement of section 5.5.

Figures under Specification [1.1] for [window] were compiled on [date] as a backcast. Figures for the same window under Specification [1.0] remain retrievable and are not restated.

Vintage notes do not characterize or attribute the cause of an input restatement and do not describe its effect as material or immaterial.

7.5 Candidate additions to a future minor version

The following candidates are recorded to make the boundary of version 1.1 explicit: a redemption-valued variant of the hierarchy under rule R8, to be introduced if instrument conversion rates enter collection; publication of e as a measured term rather than a definitional term; and a per-base-coin multiplier alongside the segment aggregate. A compiled issuance record read directly from issuer contracts is excluded from this list because it constitutes a coverage improvement under section 6.4.4 and requires no version change.

8. Related work and provenance

8.1 Prior work

Policy and academic literature has long compared stablecoins with forms of money. This specification makes no claim to originating that comparison.

Central-bank and standard-setting work evaluates stablecoins against the functions and requirements of monetary and settlement systems. The Bank for International Settlements (2023, 2025) considers whether privately issued tokenized monies preserve the singleness of money and assesses stablecoins against the criteria of singleness, elasticity, and integrity. The Committee on Payments and Market Infrastructures and IOSCO (2022) apply financial-market-infrastructure standards to systemically important stablecoin arrangements that perform a transfer function. The Financial Stability Board (2023) provides high-level recommendations for the regulation, supervision, and oversight of global stablecoin arrangements. Arner, Auer, and Frost (2020) set out principles for stablecoin regulation and the associated risks, including financial stability, market integrity, and consumer protection.

Two studies provide classification frameworks for the field. Adrian and Mancini-Griffoli (2019) classify means of payment along four dimensions: type, meaning claim or object; value, meaning fixed or variable at redemption; backstop, meaning government or private; and technology, meaning centralized or decentralized settlement. Their framework explicitly excludes issuer identity. Bullmann, Klemm, and Pinna (2019) classify stablecoin designs according to issuer accountability, decentralization of responsibilities, and the source underpinning the asset's value, producing a taxonomy organized primarily around the stabilization mechanism.

The closest antecedents apply a hierarchy of claims directly to this asset class. Aldasoro, Mehrling, and Neilson (2023) analyze stablecoins through the money view, which places monetary instruments at different levels according to the settlement claims they represent. They identify a second layer in the stablecoin hierarchy in which one stablecoin is collateralized by another and treat cross-chain bridge protocols as foreign-exchange dealers linking two ledgers. Wu (2026) applies the same perspective to decentralized finance more broadly, assigning tokens to tiers according to their derivation from base assets and defining a layering multiplier as the ratio of total mapped claims to base-tier value, explicitly by analogy with the money multiplier.

Section 8.2 states the relationship between those works and this specification.

The literature treating stablecoins as private money is also well established. Gorton and Zhang (2023) compare stablecoins with the historical experience of privately issued bank notes trading at time-varying discounts from par. A separate strand examines the redemption and arbitrage mechanism directly, including Ma, Zeng, and Zhang (2026) on the concentration of redemption rights among a small group of authorized participants and Lyons and Viswanath-Natraj (2023) on arbitrage that sustains the peg. Related work addresses run dynamics (Liu, Makarov, and Schoar, 2026) and the design conditions under which a peg can be maintained, including the credibility of a repurchase commitment (d'Avernas, Maurin, and Vandeweyer, 2026).

On aggregate construction, the closest methodological antecedents lie in monetary statistics rather than the digital-asset literature. The International Monetary Fund's Monetary and Financial Statistics Manual and Compilation Guide (2016) provides the methodological basis for several practices adopted here: consolidation, exclusion of issuer-held balances, explicit statement of an institutional coverage boundary, and a formal revisions policy. The distinction in this specification between the definition of U and the coverage of a particular compilation follows the same body of practice. The European Central Bank defines the reporting population of monetary financial institutions, permits derogations for small institutions within a stated share of the national balance sheet (Regulation (EU) 2021/379, Article 9(1)), and requires the size of that reporting tail to be collected and monitored (European Central Bank 2024, section 2.7.1). The same manual distinguishes transactions from exchange-rate valuation effects, the distinction applied in section 6.4.6 (section 5.8). Federal Reserve money-stock measures apply comparable practices in a published series. Section 3's exclusion rule has a direct parallel in that system: M1 counts currency outside the Treasury, the Federal Reserve Banks, and the vaults of depository institutions, excluding units held by the issuing authority from the aggregate. Friedman and Schwartz (1970) and Barnett (1980) argue that constructing a monetary aggregate requires choices about which instruments to admit and how their quantities should be combined, choices that require justification rather than being natural facts. Friedman and Schwartz state the point directly: the choice "cannot be made by any single set of hard and fast rules", and "the test of the choice is in the results". Section 1 begins from that premise.

A recent Federal Reserve staff note, Payne and Styczynski (2026), considers whether payment stablecoins belong in the United States monetary aggregates. It approaches the question in the manner of the existing fiat aggregates, examining whether an instrument is used for transactions or saving, and identifies a potential double-counting problem when a stablecoin is backed by a bank deposit already included in M2. This specification addresses a different measurement question. It classifies stablecoin claims by form, records their distance from the redemption endpoint, and counts the claim layers built on a common base. Its double-counting concern arises when multiple token layers represent the same base unit, while the Federal Reserve note considers overlap between a stablecoin and the deposit backing it. The two approaches are complementary. The note also observes that reliable and timely circulation data are a prerequisite for inclusion in monetary aggregates, a measurement gap that the series compiled under this specification is designed to address.

8.2 What is claimed and what is not

The distinction is stated narrowly because the value of the priority record depends on claims that can be defended precisely.

Outside the claim. The literature already contains the propositions that stablecoins resemble money and that stablecoin claims can be arranged in tiers. This specification claims neither. Two antecedents are identified because they are the closest. Aldasoro, Mehrling, and Neilson (2023) apply a hierarchy of claims to stablecoins and identify a layer in which one stablecoin is collateralized by another. Wu (2026) assigns tokens to tiers according to derivation and defines a layering multiplier, the ratio of mapped claims to base-tier value, by analogy with the money multiplier. Accordingly, this specification makes no priority claim over either the application of a hierarchy to the asset class or the ratio of layered claims to a base.

Claimed contribution. The claimed contribution is the operationalization: the S0, S1, and S2 tier boundaries defined in section 2 and restricted to claims rooted in stablecoins rather than tokens generally; the application of net and gross variants to S1 and S2, including explicit net identities and exception terms; the constituent admission policy under which exclusion is the default; the edge-case rules in section 3, including the bridge-design rule and the separation of valuation effects from quantity effects; and the compilation of the entire framework as a maintained daily series governed by a versioned specification, a constituent-change log, and a revisions policy.

Provenance. Stablecoin Beat introduced the S0/S1/S2 stablecoin monetary aggregates in 2026: labeled three-tier boundaries restricted to stablecoin-rooted claims, net and gross variants of S1 and S2, an admission policy that defaults to exclusion, and a maintained daily compilation governed by a versioned specification.

8.3 Reuse

The specification and series may be reused under the terms stated in section 9. Reuse of the framework, including the tier names, multiplier, and admission policy, is encouraged with citation of this document as the source of the definitions, under the same conventions used for published statistical methodologies.

9. Citation

9.1 Citing the specification

Silenzi, M. and Stablecoin Beat Research (2026): "Stablecoin Beat S0/S1/S2 monetary aggregates: specification 1.1", SB Methodology Papers, No 1, September. DOI: 10.5281/zenodo.22744683

Specification 1.0 (August 2026) remains retrievable under DOI 10.5281/zenodo.21861584 and governs every figure compiled before 16 September 2026.

9.2 Citing the series

A series citation identifies the aggregate, observation date or window, and vintage because section 7 permits revisions to the series.

Stablecoin Beat Research: S0/S1/S2 stablecoin monetary aggregates, [series and window], vintage [vintage date], compiled under SB Methodology Papers No 1, specification version 1.1. https://stablecoinbeat.com/charts/aggregates/, accessed [access date].

The citing reader supplies all bracketed fields except the vintage, which is a property of the download and is embedded in the series artifact. An access date without a vintage does not identify the quoted values because, under section 7.3, a published value may differ across vintages.

9.3 Data availability and terms

The published series, constituent record, and constituent-change log are available at stable addresses. The complete series can be downloaded rather than accessed only as displayed values. Each download carries its vintage, allowing any quoted figure to be identified later under section 7.3.

The specification and series are published under the Creative Commons Attribution 4.0 International license. Reuse, including commercial reuse and the construction of derived aggregates, requires attribution to this document as the source of the definitions and to the series as the source of any figures.

The series is not deposited separately. Because it is revised daily under section 7.3, it is identified by its stable address together with the vintage embedded in the download, which is the citation convention specified in section 9.2. Depositing a snapshot would freeze a single vintage and encourage citation of a version that the maintained series may already have superseded.

The constituent record places the admitted set, exclusions and their reasons, and the change log on a single page, with a machine-readable version at the address above. The series download includes the coverage block and per-entry base-coverage flag specified in section 6.4. A reader can therefore reproduce the coverage share, the structural difference described in section 6.7, and the criterion A2 effect without rerunning the compilation.

Appendix A. Index of rules and criteria

The table below lists every normative statement in the specification together with the section in which it appears. An implementation of the aggregates can be built from this table and the equations in section 2.

The controlled vocabularies are relation in section 5.2, confidence in section 5.3, exclusion reason in section 5.4, and coverage and classification status in section 5.6. Adding an item to any of the four constitutes a version change under section 7.1.

Appendix B. Summary of identities

S0(t)       = Σ_{i ∈ U_0} n_i(t)
S1_gross(t) = S0(t) + Σ_{i ∈ U_b} b_i(t)
S1_net(t)   = S0(t) + Σ_{i ∈ U_b} x_i(t)
ρ_j(t)      = 1 − ℓ_j(t) / C_j(t),     ρ_j(t) = 1 where C_j(t) = 0
v_j(t)      = ρ_j(t) · ṽ_j(t)
S2_gross(t) = S1_gross(t) + Σ_{j ∈ W_c} v_j(t)
S2_net(t)   = S1_net(t) + e(t),        e(t) = Σ_{j ∈ W_c} ℓ_j(t)
                                        U_b(t) ⊆ U_0(t) ⊆ U(t),  W_c(t) ⊆ W(t)
m(t)        = S2_gross(t) / S0(t)
m_1(t)      = S1_gross(t) / S0(t)
m(t)        = 1 + [Σ_{i ∈ U_b} b_i(t) / S0(t)] + [Σ_{j ∈ W_c} v_j(t) / S0(t)]

Under normal conditions, x_i = 0 and ℓ_j = 0 for every constituent. In that case, ρ_j = 1, each wrapper enters the gross measure at its full market value, and S1_net(t) = S2_net(t) = S0(t). S1 net and S2 net remain conditional accounting identities because they depend on the full-backing assumption described in section 6.5, which the compilation does not independently verify. The exception terms are layer-local and therefore additive. Each is recognized only when documented evidence becomes available under rule R2 or rule R9, respectively.

Appendix C. Fields of the published constituent map

The map is the machine-readable implementation of section 5. It is published, versioned, and dated so that any published figure can be reproduced using the map version in force when the figure was compiled.

The excluded list is published beside the admitted set. An instrument appearing in neither list has not yet been ruled on, and section 6.5 lists such instruments for adjudication. An instrument appearing in the coverage list as unclassified is a candidate awaiting either the observations or the second price required by the par test. That status is distinct from an instrument on which no ruling has yet been made.