> For the complete documentation index, see [llms.txt](https://docs.ibis.app/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.ibis.app/reference/glossary.md).

# Glossary and notation

Definitions below use the same terms as the facility pages. Follow the page links for the rules behind each term. The notation reference gives the units and precision used in calculations.

## Terms

| Term                        | Meaning                                                                                                                                                                                                                                        | Page                                                                               |
| --------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------- |
| Admin                       | The facility role named in its agreement that configures terms and rates within platform bounds.                                                                                                                                               | [Roles and responsibilities](/platform/roles-and-permissions.md)                   |
| Approved wallet             | A wallet that Ibis has approved for a facility after identity verification and signature of the facility's Master Lending Agreement. Approval is recorded onchain in the approved-address registry.                                            | [Eligibility, compliance and agreements](/getting-started/compliance-perimeter.md) |
| Approved-address registry   | The platform component that records which addresses are approved to take part in facilities.                                                                                                                                                   | [Eligibility, compliance and agreements](/getting-started/compliance-perimeter.md) |
| APY                         | An annualized yield figure derived from the change in share price over a measured period. It reports yield and does not set what the facility credits.                                                                                         | [Rates and APY](/platform/rate-and-apy-figures.md)                                 |
| Borrower funds              | The borrower's receiving wallet for delivered principal, released withheld principal and returned surplus.                                                                                                                                     | [Roles and responsibilities](/platform/roles-and-permissions.md)                   |
| Borrower ops                | The borrower's published repayment wallet for a facility. Repayment can also come from any other eligible wallet.                                                                                                                              | [Roles and responsibilities](/platform/roles-and-permissions.md)                   |
| Claim                       | A transaction that collects a lender's funded claimable balance. Restricted payouts go to compliance escrow under the lender's address.                                                                                                        | [Withdrawals and claims](/platform/withdrawals-owed-value-and-claims.md)           |
| Claimable                   | A lender's balance of funded withdrawal value, refunds and other credits in a facility, available to collect with a claim. The facility reserves cash for every claimable balance.                                                             | [Withdrawals and claims](/platform/withdrawals-owed-value-and-claims.md)           |
| Claims only                 | The terminal state after migration to a successor facility. No new deposits or withdrawal requests are accepted; claims, pending-deposit refunds and owed-value funding continue. Repayment is capped at the remaining funding shortfall.      | [Facility states and permitted actions](/platform/facility-states.md)              |
| Compliance escrow           | The platform component that holds value owed to restricted addresses under each beneficiary. Its asset balance fully backs held value.                                                                                                         | [Eligibility, compliance and agreements](/getting-started/compliance-perimeter.md) |
| Compliance hold             | The facility credits value owed to a restricted address to the compliance escrow under that address instead of paying it out. Release requires screening the destination again.                                                                | [Eligibility, compliance and agreements](/getting-started/compliance-perimeter.md) |
| Compounding period          | The interval set per Continuous facility at which yield compounds. Accrual within each interval is simple.                                                                                                                                     | [How yield accrues](/platform/yield-accrual.md)                                    |
| Continuous                  | A fixed-rate facility structure that issues shares on deposit and prices withdrawals when executed. Yield compounds once per compounding period.                                                                                               | [Products](/platform/products.md)                                                  |
| Curator                     | The facility role named in its agreement that operates settlement, declares variable yield, executes Continuous withdrawals and funds owed value from facility cash.                                                                           | [Roles and responsibilities](/platform/roles-and-permissions.md)                   |
| Declared yield              | The yield declared for a variable-yield epoch within its locked range. Settlement applies it over the locked epoch length; later settlement adds no yield.                                                                                     | [Rates and APY](/platform/rate-and-apy-figures.md)                                 |
| Delegate                    | An address a lender authorizes to act on its deposits, withdrawal requests and claims. Screening applies at authorization and every use; a delegate can pay only the lender.                                                                   | [Roles and responsibilities](/platform/roles-and-permissions.md)                   |
| Deposit cap                 | The optional facility limit on deposit exposure. Deposits that would exceed it are refused.                                                                                                                                                    | [Deposits and principal delivery](/platform/deposits-and-withheld-principal.md)    |
| Deposit exposure            | The total of a facility's outstanding share value, pending deposits and owed value. The deposit cap limits this total.                                                                                                                         | [Deposits and principal delivery](/platform/deposits-and-withheld-principal.md)    |
| Epoch                       | One period of an Epochs facility, with terms locked at opening and settlement at its end. On the website: 'cycle'.                                                                                                                             | [Epochs and settlement](/platform/epochs-and-settlement.md)                        |
| Epochs                      | A facility structure with consecutive epochs. Deposits and withdrawal requests wait for settlement, which fixes their respective prices once for the epoch.                                                                                    | [Products](/platform/products.md)                                                  |
| Facility                    | One isolated credit line with its own shares, cash and accounting. Facilities pool neither cash nor losses.                                                                                                                                    | [How a facility works](/getting-started/how-a-facility-works.md)                   |
| Facility directory          | The platform component that lists every registered facility. Retiring a listing changes neither facility state nor obligations.                                                                                                                | [How a facility works](/getting-started/how-a-facility-works.md)                   |
| Fixed rate                  | A nominal annual rate set per facility and credited to its share price. Its compounding law depends on the facility structure.                                                                                                                 | [Rates and APY](/platform/rate-and-apy-figures.md)                                 |
| Identity verification       | KYC for an individual or KYB for a business. Approved verification alone grants neither facility access nor wallet approval.                                                                                                                   | [Lending](/getting-started/onboarding.md)                                          |
| In recovery                 | The terminal state following a declared default. Yield accrual has ended, and holders collect from the recovery pot through recovery claims.                                                                                                   | [Facility states and permitted actions](/platform/facility-states.md)              |
| KYB                         | Know your business: verification of a business that takes part in a facility.                                                                                                                                                                  | [Lending](/getting-started/onboarding.md)                                          |
| KYC                         | Know your customer: verification of an individual's identity.                                                                                                                                                                                  | [Lending](/getting-started/onboarding.md)                                          |
| Liquidity sleeve            | A portion of a Continuous facility's principal intended to fund instant redemptions while earning yield in short-term products such as treasury bills. The delivery split sends it to a receiver set per facility that holds no facility role. | [Deposits and principal delivery](/platform/deposits-and-withheld-principal.md)    |
| Master Lending Agreement    | The agreement between lenders and the borrower, signed before participation. A tranched product uses one agreement covering all of its term facilities. A new version requires a new signature.                                                | [Eligibility, compliance and agreements](/getting-started/compliance-perimeter.md) |
| Minimum deposit             | The smallest deposit a facility accepts. A partial pending-deposit cancellation must leave at least this amount, set per facility.                                                                                                             | [Deposits and principal delivery](/platform/deposits-and-withheld-principal.md)    |
| Minimum residual            | The minimum position value left after a partial withdrawal request. Epochs facilities also apply request-size and full-position exceptions.                                                                                                    | [Withdrawals and claims](/platform/withdrawals-owed-value-and-claims.md)           |
| Open                        | The ordinary state of an activated facility. Only Open accepts deposits.                                                                                                                                                                       | [Facility states and permitted actions](/platform/facility-states.md)              |
| Owed value                  | Unfunded withdrawal value fixed at settlement on an Epochs facility. It is never repriced and becomes claimable as cash funds it.                                                                                                              | [Withdrawals and claims](/platform/withdrawals-owed-value-and-claims.md)           |
| Payment-due time            | One settlement window after settlement completes. This disclosure milestone does not itself trigger a default.                                                                                                                                 | [Epochs and settlement](/platform/epochs-and-settlement.md)                        |
| Pending deposit             | An Epochs deposit awaiting conversion into shares at settlement. It can be canceled for a refund except while settlement is in progress.                                                                                                       | [Deposits and principal delivery](/platform/deposits-and-withheld-principal.md)    |
| Position value              | The asset value of a lender's shares in a facility: the number of shares times the share price, rounded down to the asset's smallest unit.                                                                                                     | [Shares and the share price](/platform/shares-and-the-share-price.md)              |
| Private                     | A label the apps show for a facility's participation setting. Participation is set per facility and shown on the facility page.                                                                                                                | [Products](/platform/products.md)                                                  |
| Protected withdrawal window | The period after a protected fixed-rate Epochs settlement when its owed value has funding priority and the next settlement must wait. It ends when that value is fully funded or default is declared.                                          | [Epochs and settlement](/platform/epochs-and-settlement.md)                        |
| Public                      | A label the apps show for a facility's participation setting. Participation is set per facility and shown on the facility page.                                                                                                                | [Products](/platform/products.md)                                                  |
| Queued withdrawal           | A withdrawal request awaiting pricing at settlement on an Epochs facility or at execution on a Continuous facility.                                                                                                                            | [Withdrawals and claims](/platform/withdrawals-owed-value-and-claims.md)           |
| Rate-cut threshold          | The minimum cut from an epoch's opening rate to the next epoch's rate that qualifies settlement for protection. It is set per facility and locked for each epoch.                                                                              | [Epochs and settlement](/platform/epochs-and-settlement.md)                        |
| Recovery claim              | A claim that exchanges shares for recovery units and collects recovery-pot entitlement. Units retain rights to later recoveries.                                                                                                               | [Recovery](/platform/after-a-default.md)                                           |
| Recovery pot                | Cash collected after default and shared pro rata across the shares outstanding at default and the withdrawals unfunded at default.                                                                                                             | [Recovery](/platform/after-a-default.md)                                           |
| Recovery units              | Units recorded when shares are exchanged in recovery, one per share. They retain entitlement to later recoveries against the weight fixed at default.                                                                                          | [Recovery](/platform/after-a-default.md)                                           |
| Redemption operator         | A distinct, screened role that executes queued withdrawals on Continuous facilities.                                                                                                                                                           | [Roles and responsibilities](/platform/roles-and-permissions.md)                   |
| Reserve floor               | The sum of a facility's claimable balances, pending deposits, unclaimed recovery-pot funds and withheld principal. The facility keeps its asset balance at or above the reserve floor.                                                         | [Liquidity accounting](/platform/liquidity-accounting.md)                          |
| Restricted address          | An address that does not pass the facility's current eligibility checks. Its claims, refunds and recovery payouts go to compliance escrow under that address.                                                                                  | [Eligibility, compliance and agreements](/getting-started/compliance-perimeter.md) |
| Safety Operator             | A platform-level role responsible for safety controls.                                                                                                                                                                                         | [Roles and responsibilities](/platform/roles-and-permissions.md)                   |
| Settlement                  | The process that ends an Epochs period, converting pending deposits at the continuing-holder price and fixing withdrawal owed value at the withdrawal price.                                                                                   | [Epochs and settlement](/platform/epochs-and-settlement.md)                        |
| Settlement window           | The epoch-locked interval from settlement completion to payment-due time.                                                                                                                                                                      | [Epochs and settlement](/platform/epochs-and-settlement.md)                        |
| Settling                    | The Epochs state while settlement is in progress. New deposits, withdrawal requests, pending-deposit cancellations and term changes are refused; claims and repayment continue.                                                                | [Facility states and permitted actions](/platform/facility-states.md)              |
| Share                       | A token unit of a position in one facility, with 18 decimals. All its shares use one share price.                                                                                                                                              | [Shares and the share price](/platform/shares-and-the-share-price.md)              |
| Share price                 | The asset value of one share, recorded with 18 decimals. Yield increases it.                                                                                                                                                                   | [Shares and the share price](/platform/shares-and-the-share-price.md)              |
| Term                        | The period length of a separate facility within a tranched product. Each term facility keeps its own shares, cash, share price, epochs and accounting, under the product's shared agreement.                                                   | [Products](/platform/products.md)                                                  |
| Tranched product            | A product that groups several facilities by term under one Master Lending Agreement. Each term has its own share price, epochs, settlement, cap, cash and accounting. Grouping creates no seniority or waterfall.                              | [Products](/platform/products.md)                                                  |
| Variable yield              | An Epochs rate mode with yield declared for each epoch within a range locked at opening. Settlement applies the declared yield to the share price. Variable yield is unavailable on Continuous facilities.                                     | [Rates and APY](/platform/rate-and-apy-figures.md)                                 |
| Winding down                | The state after decommission. New deposits stop, withdrawal requests, claims and repayment continue, and withheld principal becomes ordinary cash.                                                                                             | [Facility states and permitted actions](/platform/facility-states.md)              |
| Withdrawal request          | A request to withdraw shares. The facility holds them until settlement pricing on Epochs or execution on Continuous.                                                                                                                           | [Withdrawals and claims](/platform/withdrawals-owed-value-and-claims.md)           |
| Withheld principal          | Newly funded principal reserved in the facility and not yet delivered to the borrower's receiving wallet. It becomes ordinary cash on entry to Winding down or In recovery.                                                                    | [Deposits and principal delivery](/platform/deposits-and-withheld-principal.md)    |

A withdrawal is funded only when the facility holds cash to fund it, normally from borrower repayment.

## Symbols

| Symbol              | Meaning                                                                                                                                                                               | Unit or scale                            | Notes                                                                          |
| ------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------- | ------------------------------------------------------------------------------ |
| $$B$$               | Facility asset balance: the facility's own balance of its asset                                                                                                                       | assets, 6 decimals                       | Includes every reserved amount                                                 |
| $$C$$               | Claimable value: withdrawal value, refunds and credits that lenders can claim and have not yet claimed, all lenders                                                                   | assets, 6 decimals                       | Part of the reserve floor                                                      |
| $$P$$               | Pending deposits: deposits on an Epochs facility waiting for settlement, all lenders                                                                                                  | assets, 6 decimals                       | Part of the reserve floor                                                      |
| $$W$$               | Withheld principal: newly funded principal reserved in the facility and not yet delivered                                                                                             | assets, 6 decimals                       | Part of the reserve floor; zero in Winding down, Claims only and In recovery   |
| $$D$$               | Recovery-pot funds received and not yet claimed                                                                                                                                       | assets, 6 decimals                       | Part of the reserve floor; zero before a default                               |
| $$D\_{total}$$      | Cumulative recovery funding: every amount the recovery pot has received since the default                                                                                             | assets, 6 decimals                       | Equals $$D$$ plus every amount already claimed from the pot                    |
| $$R$$               | Reserve floor: claimable value plus pending deposits plus unclaimed recovery-pot funds plus withheld principal                                                                        | assets, 6 decimals                       | Derived; see Liquidity accounting                                              |
| $$O$$               | Owed value: withdrawal value fixed at settlement and not yet funded, all lenders                                                                                                      | assets, 6 decimals                       | Outside the reserve floor                                                      |
| $$Q$$               | Priority withdrawal value still outstanding during a protected withdrawal window                                                                                                      | assets, 6 decimals                       | Never more than $$O$$                                                          |
| $$E$$               | Deposit exposure: the value of outstanding shares plus pending deposits plus owed value                                                                                               | assets, 6 decimals                       | Excludes withheld principal; compared with the deposit cap                     |
| $$A$$               | Principal amount of one delivery                                                                                                                                                      | assets, 6 decimals                       | Divided between two receivers only when a liquidity sleeve split is set        |
| $$V$$               | Principal recorded at the settlement of one epoch: the pending deposits converted into shares at that settlement; the weight used by the principal-weighted historical APY            | assets, 6 decimals                       | Epochs only; derived reporting figure                                          |
| $$V\_n$$            | Principal recorded at the settlement of epoch $$n$$                                                                                                                                   | assets, 6 decimals                       | Epochs only; derived reporting figure                                          |
| $$cap$$             | Deposit cap                                                                                                                                                                           | assets, 6 decimals                       | Set per facility; 0 means no cap                                               |
| $$m\_{dep}$$        | Minimum deposit                                                                                                                                                                       | assets, 6 decimals                       | Set per facility                                                               |
| $$m\_{res}$$        | Minimum residual: the smallest position value a partial withdrawal may leave                                                                                                          | assets, 6 decimals                       | Set per facility; never above the minimum deposit                              |
| $$I$$               | Share price: the asset value of one share                                                                                                                                             | assets per share, 18 decimals            | 1.000000000000000000 when a facility is created; yield raises it               |
| $$I\_{live}$$       | Current share price                                                                                                                                                                   | assets per share, 18 decimals            |                                                                                |
| $$I\_{open}$$       | Starting share price for the epoch's yield calculation                                                                                                                                | assets per share, 18 decimals            | Epochs only                                                                    |
| $$I\_{close}$$      | Continuing-holder price pinned at settlement                                                                                                                                          | assets per share, 18 decimals            | Epochs only; pending deposits convert at this price                            |
| $$I\_{exit}$$       | Withdrawal price pinned at settlement                                                                                                                                                 | assets per share, 18 decimals            | Epochs only; equals $$I\_{close}$$ except on a protected settlement            |
| $$I\_{open,n}$$     | Share price recorded for the opening of epoch $$n$$: the continuing-holder price pinned at the settlement of the previous epoch, or the share price at activation for the first epoch | assets per share, 18 decimals            | Epochs only                                                                    |
| $$I\_{close,n}$$    | Continuing-holder price pinned at the settlement of epoch $$n$$                                                                                                                       | assets per share, 18 decimals            | Epochs only                                                                    |
| $$I\_{base}$$       | Share price at the start of the current Continuous accrual run                                                                                                                        | assets per share, 18 decimals            | Continuous only                                                                |
| $$I\_{p}$$          | Share price at the start of the current compounding period                                                                                                                            | assets per share, 18 decimals            | Continuous only                                                                |
| $$I\_{start}$$      | Share price at the start of a measured interval                                                                                                                                       | assets per share, 18 decimals            | Used by the historical figures                                                 |
| $$I\_{end}$$        | Share price at the end of a measured interval                                                                                                                                         | assets per share, 18 decimals            | Used by the historical figures                                                 |
| $$I\_{def}$$        | Recovery conversion price fixed by the facility at default                                                                                                                            | assets per share, 18 decimals            | In recovery only; never changes after the default                              |
| $$s$$               | A quantity of shares                                                                                                                                                                  | shares, 18 decimals                      |                                                                                |
| $$s\_{out}$$        | All outstanding shares of the facility                                                                                                                                                | shares, 18 decimals                      | Facility-wide                                                                  |
| $$s\_{free}$$       | A lender's free shares: shares held and not already in a withdrawal request                                                                                                           | shares, 18 decimals                      |                                                                                |
| $$s\_{req}$$        | Shares in one withdrawal request                                                                                                                                                      | shares, 18 decimals                      |                                                                                |
| $$s\_{max}$$        | Largest partial withdrawal, in shares, that leaves at least the minimum residual                                                                                                      | shares, 18 decimals                      |                                                                                |
| $$s\_{exec}$$       | Shares executed from one withdrawal request                                                                                                                                           | shares, 18 decimals                      | Continuous only                                                                |
| $$s\_{conv}$$       | Minimum number of shares issued when an unpaid withdrawal is converted after a default                                                                                                | shares, 18 decimals                      | In recovery only                                                               |
| $$S$$               | Recovery weight: outstanding shares plus the units that represent owed value unfunded at default                                                                                      | units, 18 decimals                       | Fixed at default                                                               |
| $$u$$               | Recovery units of one holder                                                                                                                                                          | units, 18 decimals                       |                                                                                |
| $$u\_{owed}$$       | Units that represent all owed value unfunded at default                                                                                                                               | units, 18 decimals                       | Part of the recovery weight                                                    |
| $$u\_h$$            | One holder's units in a recovery claim: the shares exchanged in that claim plus the recovery units the holder already has                                                             | units, 18 decimals                       | The subscript $$h$$ denotes one holder                                         |
| $$a$$               | A quantity of assets                                                                                                                                                                  | assets, 6 decimals                       |                                                                                |
| $$a\_{sleeve}$$     | Part of one principal delivery sent to the liquidity sleeve receiver                                                                                                                  | assets, 6 decimals                       | Continuous only                                                                |
| $$a\_{borrower}$$   | Part of one principal delivery sent to the borrower receiving wallet                                                                                                                  | assets, 6 decimals                       |                                                                                |
| $$o$$               | Owed value of one withdrawal request, or, in a conversion after a default, one lender's unpaid owed value across all of its withdrawal requests                                       | assets, 6 decimals                       | Fixed at settlement and never repriced                                         |
| $$f$$               | Amount funded toward one withdrawal                                                                                                                                                   | assets, 6 decimals                       |                                                                                |
| $$e$$               | One holder's cumulative recovery entitlement                                                                                                                                          | assets, 6 decimals                       | In recovery only                                                               |
| $$e\_h$$            | One holder's cumulative recovery entitlement at a claim                                                                                                                               | assets, 6 decimals                       | The subscript $$h$$ denotes one holder                                         |
| $$c$$               | Amount one holder has already claimed from the recovery pot                                                                                                                           | assets, 6 decimals                       | In recovery only                                                               |
| $$c\_h$$            | Amount one holder has claimed from the recovery pot before a claim                                                                                                                    | assets, 6 decimals                       | The subscript $$h$$ denotes one holder                                         |
| $$r$$               | Fixed rate, or the assumed annual rate of the linear yield estimate                                                                                                                   | bps, nominal annual                      | Set per facility as the fixed rate; an assumption in the linear yield estimate |
| $$r\_{open}$$       | Fixed rate in force when the epoch opened                                                                                                                                             | bps, nominal annual                      | Fixed-rate Epochs only                                                         |
| $$r\_{next}$$       | Fixed rate for the next epoch: the staged rate, or the current rate when none is staged                                                                                               | bps, nominal annual                      | Fixed-rate Epochs only                                                         |
| $$y$$               | Declared variable yield for an epoch                                                                                                                                                  | bps, nominal annual                      | Within the variable-yield range locked for the epoch                           |
| $$y\_{min}$$        | Lower end of the variable-yield range locked for the epoch                                                                                                                            | bps, nominal annual                      | Variable-rate Epochs only                                                      |
| $$y\_{max}$$        | Upper end of the variable-yield range locked for the epoch                                                                                                                            | bps, nominal annual                      | Variable-rate Epochs only                                                      |
| $$\theta$$          | Rate-cut threshold                                                                                                                                                                    | bps                                      | Protected withdrawals; fixed-rate Epochs only                                  |
| $$\sigma$$          | Liquidity sleeve split                                                                                                                                                                | bps                                      | Continuous only; 0 by default                                                  |
| $$APY\_n$$          | Realized APY of epoch $$n$$: share-price growth over the epoch, annualized over wall-clock time                                                                                       | bps                                      | Derived reporting figure                                                       |
| $$y\_h$$            | Linear yield estimate for one deposit over the horizon $$h$$                                                                                                                          | assets, 6 decimals                       | An estimate, not credited yield                                                |
| $$h$$               | Horizon of the linear yield estimate                                                                                                                                                  | seconds                                  |                                                                                |
| $$F$$               | Per-period growth factor of a Continuous facility                                                                                                                                     | dimensionless, 18 decimals               | Continuous only                                                                |
| $$r\_f$$            | Rate as a fraction: the rate in bps divided by 10,000                                                                                                                                 | dimensionless                            | Effective annual yield only                                                    |
| $$p$$               | Compounding period as a fraction of a year                                                                                                                                            | dimensionless                            | Effective annual yield only                                                    |
| $$q$$               | Fraction of a year left after $$n$$ complete periods                                                                                                                                  | dimensionless                            | Effective annual yield only                                                    |
| $$EAY$$             | Effective annual yield of a Continuous rate, ignoring rounding                                                                                                                        | dimensionless fraction, shown in percent | Illustrative figure only                                                       |
| $$n$$               | Number of complete periods, or the index of an epoch                                                                                                                                  | count                                    |                                                                                |
| $$Y$$               | One year: 365 days, or 31,536,000 seconds                                                                                                                                             | seconds                                  | Convention                                                                     |
| $$T$$               | Period length: the epoch length on an Epochs facility, the compounding period on a Continuous facility                                                                                | seconds                                  | Set per facility                                                               |
| $$T\_{epoch}$$      | Epoch length                                                                                                                                                                          | seconds                                  | Epochs only                                                                    |
| $$T\_{continuous}$$ | Compounding period                                                                                                                                                                    | seconds                                  | Continuous only                                                                |
| $$T\_w$$            | Settlement window                                                                                                                                                                     | seconds                                  | Epochs only                                                                    |
| $$T\_f$$            | Funding window: the time set for funding priority withdrawal value after a protected settlement                                                                                       | seconds                                  | Fixed-rate Epochs only                                                         |
| $$b$$               | Reaction buffer                                                                                                                                                                       | seconds                                  | Fixed-rate Epochs only; 0 when protected withdrawals are not enabled           |
| $$\Delta t\_a$$     | Time recorded by the facility for yield accrual                                                                                                                                       | seconds                                  | Fixed-rate Epochs and Continuous                                               |
| $$\Delta t\_{a,p}$$ | Accrual time since the start of the current compounding period                                                                                                                        | seconds                                  | Continuous only                                                                |
| $$\Delta t\_s$$     | Elapsed time eligible toward settlement, recorded by the facility                                                                                                                     | seconds                                  | Epochs only                                                                    |
| $$\Delta t\_w$$     | Wall-clock elapsed time, nothing excluded                                                                                                                                             | seconds                                  | Used by the historical figures                                                 |
| $$\Delta t\_{w,n}$$ | Wall-clock time from the opening of epoch $$n$$ to the completion of its settlement                                                                                                   | seconds                                  | Epochs only                                                                    |
| $$t$$               | A point in time                                                                                                                                                                       | UTC timestamp                            | The difference of two times is in seconds                                      |
| $$t\_{open}$$       | Time the epoch opened                                                                                                                                                                 | UTC timestamp                            | Epochs only                                                                    |
| $$t\_{now}$$        | Current time                                                                                                                                                                          | UTC timestamp                            |                                                                                |
| $$t\_{completion}$$ | Time the settlement completed                                                                                                                                                         | UTC timestamp                            | Epochs only                                                                    |
| $$t\_{due}$$        | Payment-due time: the settlement completion time plus the settlement window                                                                                                           | UTC timestamp                            | Disclosure only; it does not by itself trigger a default                       |

## Scales and conventions

Every facility's asset has exactly 6 decimals (bound), so the smallest asset unit is 0.000001. Shares and the share price have 18 decimals. The platform computes in these smallest units.

A year is 365 days, or 31,536,000 seconds. Rates are stated in basis points, and 10,000 bps equals 100%; for example, 850 bps is 8.50%. Every fixed rate and every declared variable yield is a nominal annual rate. The effective annual yield of a Continuous rate and the realized APY figures are derived reporting figures.

Times are in UTC. Durations are measured in seconds.

### Number classes

| Class             | Meaning                                                                          |
| ----------------- | -------------------------------------------------------------------------------- |
| Bound             | A limit the platform enforces                                                    |
| Configured value  | A value set per facility within its bound                                        |
| Per-network value | A value that differs between networks                                            |
| Convention        | A fixed scale or definition; reporting conventions apply only to derived figures |
| Example           | An illustrative figure that matches no live facility                             |

Derived reporting figures do not set what a facility credits. Live facility values come from the chain and the facility's published terms.

### Rounding

The platform rounds down at every step unless a formula shows a ceiling or its page states an exception. In a formula, floor brackets $$\lfloor , \rfloor$$ mean that the result is rounded down to the smallest unit of its quantity, and ceiling brackets $$\lceil , \rceil$$ mean that it is rounded up. An amount lost to rounding down stays in the facility, except where a page states otherwise.

### Subscripts

A subscript narrows a base symbol to one request, one lender or holder, one part of a delivery, one moment or one epoch. A subscripted symbol keeps the unit and scale of its base symbol, except $$y\_h$$, which is an asset amount, and $$r\_f$$, which is a fraction. The subscript $$h$$ has two uses: in $$y\_h$$ it is the horizon $$h$$, and in $$u\_h$$, $$e\_h$$ and $$c\_h$$ it denotes one holder.

## Related

* [Shares and the share price](/platform/shares-and-the-share-price.md)
* [Rates and APY](/platform/rate-and-apy-figures.md)
* [Liquidity accounting](/platform/liquidity-accounting.md)
