Glossary

Comprehensive terminology for the XPower Banq protocol suite — the consolidated References & Glossary paper ported into web form. Entries marked with a dagger (†) are specific to the bad-debt risk analysis in the simulations paper.

Where a term names a governable parameter, contract, or feature, the entry links out to its dedicated page rather than restating values. Numeric ranges and per-cycle bounds live in Parameters and the governance parameter catalog.

A

Accrual. The periodic update of the global index to reflect newly earned interest. In the multiplicative form, accrual multiplies the index by $\exp (r)$; in the log-space form, it adds $r$ to the index.

Accrual Path. The code path executed during a reindex event. Also called the write path, since it mutates the stored index.

Acma. Access manager — wrapper around OpenZeppelin's AccessManager; manages three-tier roles per capability — the bare function-caller role (e.g. SET_TARGET), its _ADMIN (grants/revokes the caller role), and its _GUARD (emergency revoke). Role IDs are derived via keccak256 of the role name and a domain string in the Roles library. See role hierarchy and architecture overview.

$A(n)$ †. Absorption fraction — the share of the log-space deviation absorbed after $n$ oracle refreshes: $A(n)=1-{\alpha }^{n-1}$ for $n\ge 2$, with $A(0)=A(1)=0$ due to the one-refresh delay.

Annualised Rate ($r_{\text{annual}}$). The interest rate expressed per year in WAD. Converted to per-period yield via $r_{\text{annual}}\times \mathrm{\Delta }t/\text{year}$.

$\alpha$ †. EMA decay parameter of the log-space TWAP oracle. Governs tracking speed: $\alpha ={0.5}^{1/\text{HL}}$ where HL is the half-life in refreshes. Default $\alpha \approx 0.944$ (12 refreshes; with the default 1-hour refresh interval enforced by PowLimited(1 hours) in Oracle, this is a 12-hour half-life). Stored on-chain as the DECAY parameter.

AMM. Automated Market Maker — decentralized exchange architecture using liquidity pools and mathematical formulas for price discovery.

APY Differential. Difference in annual percentage yield between locked and unlocked positions; with spread $s$, supplier differential is $\mathrm{\Delta }r\approx 0.09\times r_{\text{base}}$.

Asymptotic Transition. Parameter change mechanism where values approach targets gradually via time-weighted mean rather than discrete jumps. See lethargic governance and transition curves.

B

Bad Debt. Uncollectable debt arising when a position's collateral value falls below its debt value; protocol absorbs the loss. See bad debt scenarios and the simulations paper.

Bitmap. 16-bit mask tracking which slots contain active locks. Stored in the lower 16 bits of cache. See ring-lock.

${\text{BD}}_{\text{inst}}$ †. Bad debt under instant (zero-delay) liquidation. The baseline shortfall when a position's true collateral value $H_0(1-\delta )$ falls below LTV.

${\text{BD}}_{max}$ †. Conservative upper bound on bad debt, incorporating the oracle delay penalty: ${\text{BD}}_{max}\le {\text{BD}}_{\text{inst}}\cdot (1+W_{max}{\sigma }_h/\delta )$.

Beta Cap. Position limit following $12\lambda (1-\lambda {)}^2$ distribution where $\lambda$ is the user's fraction of total supply; peaks at $\lambda =1/3$ and vanishes at boundaries. See position caps and how caps grow.

Bid/Ask. Price quotes for selling (bid) vs. buying (ask) an asset; spread provides manipulation resistance.

Block Stuffing. Attack filling blocks with transactions to delay or censor others; prevented by PoW requirements.

Breakeven Period. Minimum holding period $T^{\ast }$ for lock adoption to be profitable; approximately $T^{\ast }\approx D/\mathrm{\Delta }r$ where $D$ is secondary market discount and $\mathrm{\Delta }r$ is APY differential.

Borrow Position. ERC20 token representing debt obligation; uses inverted transfer semantics where transfer pulls debt. See positions as tokens and ERC20 semantics.

Borrow Rate. The interest rate charged to borrowers, computed as $r_{\text{base}}\times (1+s)$ where $s$ is the spread parameter. Capped at $2\times (1+s)\times {10}^{18}$. See interest rates.

Break-Even Ratio ($R$). The on-chain read/write ratio at which the log-space transformation is gas-neutral. Computed as $R=\mathrm{1,200}/\mathrm{1,100}\approx 1.09$.

C

Calculator. Library providing overflow-safe ${\log }_2$ and ${\exp }_2$ operations for the oracle pipeline, wrapping PRBMath's UD60x18 functions. Defines the bias constant LOG2_ONE $={\log }_2({10}^{18})\approx 59.79$ (internal private constant, scaled $\times {10}^{18}$ as a UD60x18 value), used to convert between raw uint256 values and UD60x18 fixed-point representation in the paired functions Log2() / Exp2().

Cap Floor. Minimum position cap ensuring users can enter even when $\lambda \to 0$; prevents cold start problem. See new user allocation.

Capital Efficiency. Borrowing power per unit of collateral; higher LTV ratios provide greater capital efficiency.

Cascade Amplification. Ratio of actual liquidations to initial shock-induced liquidations; measures feedback loop severity. See bad debt risk.

Cascade Attenuation. Reduction of liquidation-cascade depth by factor $(1-\varphi )$, where $\varphi$ is the locked fraction of the position; the central result of the cascade theorem in the theory paper. See cascade protection.

Circuit Breaker. Mechanism halting cascading failures; locked positions act as circuit breakers during market stress.

Cold Start. Problem where the first depositor faces zero or minimal cap due to $\lambda \to 0$; solved by cap floor mechanism.

Collateral. Assets deposited to back borrowed positions; must exceed borrow value by the over-collateralization ratio.

Compounding Index. A global accumulator tracking cumulative interest. Multiplicative form: $I=I_0\prod \exp (r_i)$. Log-space form: $L=\sum r_i$. See log-space index paper.

Conservation. The invariant that totalOf(u) $=p_u\cdot \exp (L-L_u)$ holds for all users at all times, exact up to WAD rounding.

Constant Product. AMM pricing formula ($x\cdot y=k$) used to derive bid/ask quotes from reserve balances.

Coordination Game. Strategic interaction where player payoffs depend on aggregate choices; lock adoption exhibits coordination dynamics where seniority value decreases as adoption increases. See the theory paper.

$\text{CVaR}(99\mathrm{\%})$ †. Conditional Value-at-Risk at the 99th percentile — the expected bad debt in the worst 1% of simulated paths.

D

Debt Assumption. Liquidation model where the liquidator assumes the victim's debt rather than repaying it; enables capital-efficient liquidation without requiring liquid capital. See debt-assumption liquidation overview.

Decay Factor. EMA smoothing parameter $\alpha$ — the on-chain DECAY parameter; controls how quickly older price observations lose influence. See oracle parameters and half-life.

$\delta$ †. Crash fraction. An instantaneous price drop from $p_0$ to $p_0(1-\delta )$; e.g. $\delta =0.50$ is a 50% crash.

Depth ($\mathrm{\Sigma }$). Cached epoch-weighted sum $\sum v_i(e_i+1)$ enabling $O(1)$ token-second reconstruction. See ring-buffer locks paper.

Depth Identity. The algebraic identity $D=\mathrm{\Sigma }Q-Tt+pL$ that converts the $O(k)$ token-seconds sum into an $O(1)$ cached computation. Stated as a theorem in the ring-buffer locks paper.

Difficulty. PoW puzzle hardness parameter; governance-adjustable per operation type to tune spam resistance. See PoW-gated public mode.

Dual Approval. Transfer model requiring approval from both sender and receiver; used for borrow position transfers. See ERC20 semantics.

Dust Extraction. A theoretical attack exploiting rounding errors to extract small token amounts. Bounded at $\le 2$ wei per totalOf query in the log-space form.

E

E-fold. One unit of natural-logarithmic growth; a factor of $e\approx 2.718$. The RAY index has $\sim 115$ e-folds before overflow.

Enlisting. Governance-approved process to add new tokens to a pool; subject to time delays for existing feed modifications. The relevant role is POOL_ENLIST_ROLE (with companion admin/guard).

EMA. Exponential Moving Average — smoothing technique giving exponentially decreasing weight to older observations. Applied in log-space for the TWAP oracle.

Entry Fee. Deposit fee charged when supplying assets to a vault; accrues to existing depositors. The on-chain FEE_ENTRY parameter — see vault parameters.

Epoch. Absolute quarter index $e=\lfloor t/Q\rfloor$. Each epoch spans exactly $Q$ seconds.

ERC20. Ethereum token standard defining transfer, approve, and balance interfaces; basis for position tokens. See ERC20 semantics.

ERC4626. Tokenized vault standard extending ERC20 with deposit/withdraw mechanics; basis for the XPower Banq Vault. See ERC4626 vaults. Position tokens themselves are ERC20Permit, not ERC4626.

Exit Fee. Withdrawal fee charged when redeeming assets from a vault; discourages short-term liquidity cycling. The on-chain FEE_EXIT parameter — see vault parameters.

F

Fixed Token List. Architecture requiring predetermined token sets per pool; ensures predictable collateral requirements.

Flash Loan. Uncollateralized loan that must be repaid within the same transaction.

Formal Verification. Mathematical proof of smart contract correctness; provides stronger guarantees than testing alone. See audits and reviews for current status.

Front-running. Inserting a transaction before a known pending transaction to profit from its price impact.

G

Gas. Ethereum transaction execution cost; measured in gas units multiplied by gas price. See gas costs.

Geomean Spread. Bidirectional geometric mean of relative spreads from forward and reverse AMM queries; stored in log-space as ${\log }_2(1+s_{\text{geo}})$. Provides symmetric, manipulation-resistant spread estimation. See spread and slippage.

Governance Cycle. Single parameter change period with minimum duration (e.g., monthly); bounds rate of protocol changes. See parameter bounds.

Growth Factor. The ratio $G=\exp (L-L_u)$ by which a user's principal has grown since their last snapshot.

H

$H_0$ †. Initial health factor of a position: $H_0=(\text{supply}\times w_s)/(\text{borrow}\times w_b)$. Liquidation triggers when the oracle-observed health $H_{\text{oracle}}<100\mathrm{\%}$.

Half-Life. Time for EMA weight to decay to 50%; determines TWAP responsiveness to new price observations.

Hash Rate. Computational power for PoW puzzle solving, measured in hashes per second; determines solve time.

Health Check. Validation performed after operations ensuring health factor $H\ge 100\mathrm{\%}$; reverts if violated.

Health Factor. Ratio of weighted supply value to weighted borrow value: $H=\sum w_s{V}_s/\sum w_b{V}_b$, expressed as a percentage. Liquidation occurs when $H<100\mathrm{\%}$. See health factor and monitoring health.

Holder-Count Scaling. Sybil resistance mechanism using the $\sqrt{n+2}$ divisor; creating accounts increases $n$, reducing per-account cap gains. See position caps.

Holder Floor. Governable lower bound on the effective holder count used in the cap divisor; largeHolders() $=max(\text{real\_holders},n_{min})$, with $n_{min}$ a lethargic governance parameter capped at Constant.MIN_HOLDERS = ${10}^{18}$. See position parameters for MIN_HOLDERS.

I

Index. Logarithmic accumulated-rate index stored in WAD (18 decimals) inside the packed state word; per-user balance growth is $\exp (I_{\text{global}}-I_{\text{user}})$, the exponential of the log-space delta. See the log-space index paper.

Initial Lock Period. Mandatory delay before first parameter change after deployment; prevents immediate manipulation. See change-rate constraints.

Integrator. Library computing $\mathrm{\Delta }$-stamp weighted arithmetic means over (timestamp, value) tuples; accumulates area $\sum v_i\cdot \mathrm{\Delta }{t}_i$ and divides by elapsed time. Used by the Parameterized base contract to implement asymptotic parameter transitions in lethargic governance.

Interest Rate Model. Utilization-based formula determining borrow/supply APY; slope increases sharply above the kink. Formalized in the theory paper. See interest rates.

Inverted Transfer. Borrow position transfer semantics where transfer(from, amount) pulls debt FROM the first parameter rather than pushing to it. See ERC20 semantics and transferring positions.

Iteration Cap. Maximum capacity gain per governance-defined period (e.g., per week); bounds accumulation rate. See how caps grow.

K

Kink. Utilization threshold (e.g., 90%) where interest rate slope increases; incentivizes liquidity retention. See interest rates.

L

Lambda ($\lambda$). Balance fraction $B/S$; user's holdings divided by total supply.

Large Holder. Account holding $\ge 1$ full token unit; tracked for cap calculations.

Leading Zeros. PoW validation metric counting zero nibbles at start of hash; determines if difficulty threshold is met. See PoW-gated public mode.

Lethargic Governance. Governance model with time-delayed, bounded parameter transitions. Values approach targets asymptotically, bounded to $0.5\times$–$2\times$ per governance cycle. See lethargic governance overview.

Liquidation. Forced closure of an unhealthy position ($H<100\mathrm{\%}$); XPower Banq uses the debt assumption model. See liquidation.

Liquidation Cascade. Destructive feedback loop where forced sales depress prices, triggering further liquidations. Modeled in the simulations paper.

Liquidation Seniority. Priority in liquidation order; locked positions gain de facto seniority because liquidators prefer unlocked positions for immediate liquidity.

Liquidation-Recovery Haircut ($\kappa$) †. Fraction of collateral value lost to slippage and gas during liquidation; applied to the partial-liquidation recovery model.

Liquidity Buffer. Reserve of unutilized assets available for withdrawals; maintained via optimal utilization targeting.

Lock Adoption. Aggregate fraction $\overline{\rho }$ of positions that are locked across the protocol; equilibrium adoption varies with utilization regime. Analyzed in the theory paper.

Lock Bonus. Additional interest earned by locked suppliers; percentage of interest accrued, bounded by spread. The on-chain LOCK_BONUS parameter — see position parameters and bonus and malus.

Lock Depth. The weighted sum $\sum v_i\times (e_i+1)$ across a user's time-locked positions, where $v_i$ is the locked value and $e_i$ is the epoch. Used in lock bonus/malus computation.

Lock Malus. Interest reduction for locked borrowers; percentage of interest owed, bounded by spread. The on-chain LOCK_MALUS parameter — see position parameters and bonus and malus.

Lock Ratio ($\rho$). Fraction of position that is locked; $\rho =\text{lock}/\text{balance}\in [0,1]$.

Lock Yield. The rate $\times$ depth $\times (\exp (\mathrm{\Delta }L)-1)/({10}^{18}\times$ LOCK_TIME$)$ bonus or malus applied to locked positions, where LOCK_TIME is the maximum lock horizon in seconds (16 quarterly slots = 48 months $\approx 1.26\times {10}^8$ s; defined in the Lock library).

LOCK_TERM ($Q$). One quarter $\approx 91.3$ days — the epoch duration and ring-buffer granularity.

LOCK_TIME ($L$). $16\times Q\approx 48$ months — maximum lock duration and permanent lock depth cap.

Log-Normal Distribution. Statistical distribution where logarithm is normally distributed; used to model position sizes in simulations.

Log-Space Index ($L$). The cumulative sum of per-period WAD yields, stored in uint256. Initialised to 0. Grows linearly (additively). See log-space index paper.

Log-Space Oracle. Oracle architecture storing prices as ${\log }_2(\text{price})$ and spreads as ${\log }_2(1+s)$; enables EMA smoothing as geometric-mean temporal averaging.

Log-Sum-Exp. The numerical identity $\sum \log x_i=\log \prod x_i$, used classically to avoid overflow in iterated products. The theoretical basis for the log-space index.

LTV. Loan-to-Value ratio — maximum borrowing power as fraction of collateral value. Not a stored on-chain parameter; derived from the supply/borrow weights as $w_s/w_b$. Default $170/255\approx 66.67\mathrm{\%}$. See pool parameters for the underlying weights.

M

Market Depth. Total volume that can be traded before significantly moving price; inverse of market impact coefficient.

Market Impact. Price change from selling assets; coefficient $k$ relates volume to price depression.

Market Impact Coefficient. Constant $k$ in linear price impact model $\mathrm{\Delta }p=k\cdot V$; relates sell volume to price depression. Used in cascade simulation.

Memory Decay. Weight ${\lambda }^n$ retained by historical price observations in EMA after $n$ refresh periods; after half-life $h$ periods, weight decays to 50%.

Mempool. Transaction waiting area before block inclusion; PoW prevents flooding attacks against mempool.

Merton Jump-Diffusion. Asset-price model with continuous Brownian motion plus a Poisson-driven jump component; basis for the Monte Carlo bad-debt simulation. See Merton 1976.

MEV. Maximal Extractable Value — profit available from transaction ordering, insertion, or censorship.

Modular Arithmetic. Solidity's unchecked arithmetic where values wrap at $2^{256}$. The additive log-index is compatible with modular subtraction for computing $\mathrm{\Delta }L$.

Monotonicity. The property that $L(t)$ is non-decreasing: each accrual adds a non-negative yield, so the index never decreases.

Monte Carlo Simulation. Randomized numerical method using many simulated paths to estimate statistical distributions; used for bad-debt risk quantification and TWAP analysis.

Multiplicative Bounds. Constraint limiting parameter changes to $0.5\times$–$2\times$ per governance cycle; prevents rapid manipulation. See parameter bounds.

Multiplicative Index ($I$). The running product of exponential growth factors, stored at RAY (${10}^{27}$) precision. Grows exponentially.

N

Nash Equilibrium. Stable strategic state where no player can improve their payoff by unilaterally changing strategy; lock adoption exhibits utilization-dependent equilibria. Analyzed in the theory paper.

Nonce. Random value in PoW puzzle; combined with transaction data must hash below difficulty target.

O

Observation Window. Time available for detecting suspicious activity during gradual capacity accumulation; enabled by iteration caps.

Optimal Utilization. Target utilization $U^{\ast }$ (e.g., 90%) where interest rate curve has its kink; balances efficiency and liquidity. The on-chain UTIL parameter — see position parameters.

Oracle Aggregation. Combining prices from multiple feeds (TraderJoe, Chainlink) using log-space EMA smoothing with bidirectional geomean spread computation.

Overflow Horizon. The time until a stored value exceeds $2^{256}$. For the multiplicative RAY index: $\sim 29$–$\mathrm{1,154}$ years depending on rate. For the log-space WAD index: $\sim {10}^{58}$ years.

Over-collateralization. Requirement that collateral value exceed borrow value; enforced via health factor $H>100\mathrm{\%}$.

P

Partial Liquidation. Liquidation of $2^{-e}$ fraction of positions rather than full liquidation. The exponent $e$ is the per-call partial_exp argument to liquidate() — see pool parameters and how liquidations work.

$p_{\text{crit}}$ †. Critical oracle price ratio that triggers liquidation: $p_{\text{crit}}=1/H_0$. The oracle fires when $\hat{p}(n)/p_0<p_{\text{crit}}$.

Permanent Lock. Irrevocable lock with dt_term $=2^{256}-1$. Stored in the upper 120 bits of cache (cache.perma), not in a ring slot. Contributes $p\cdot L$ to token-seconds at query time. See timed vs permanent.

Phantom-healthy †. A position state where the oracle reports $H_{\text{oracle}}\ge 1$ (solvent) but the true health $H_{\text{true}}<1$ (underwater). Arises from oracle staleness during crashes. See oracle staleness.

Pool. Main lending/borrowing contract managing supply, borrow, settle, and redeem operations with health checks. See architecture overview and contract addresses.

Pool-to-Depth Ratio. Pool size as fraction of market depth; determines cascade severity under price shocks.

Position Lock. Fraction $\varphi$ of a position restricted from redemption or sale; prevents liquidation cascades. See locked positions and locking positions.

Position Transfer. Movement of supply or borrow position tokens between accounts. Supply uses standard ERC20 push; borrow uses inverted pull semantics. See transferring positions.

PoW. Proof-of-Work — computational puzzle required for certain operations to prevent spam. See PoW-gated public mode.

PRBMath. A Solidity library providing fixed-point exp(), ln(), mul(), and related functions at WAD (${10}^{18}$) precision. The exp() function reverts when its input exceeds $133.08\times {10}^{18}$. See PRBMath.

Price Feed. External data source providing asset prices; XPower Banq supports TraderJoe and Chainlink feeds.

Price Shock. Sudden price change used to test TWAP responsiveness; EMA smoothing dampens shock impact based on half-life configuration.

Principal. Base position amount before interest accrual; multiplied by index ratio to get current balance.

Protocol Margin. Revenue retained by protocol from interest spread; $M(\overline{\rho })=2s(1-\overline{\rho })$ where $s$ is spread and $\overline{\rho }$ is lock adoption rate.

Protocol Parameters. Governable constants (weights, decay, spread, rates, caps) that control protocol behavior; each transitions lethargically. See parameter catalog for a one-stop list and the per-contract pages under Parameters.

Q

Quote / TWAP packed word. Log-space price representation packed into a uint256 word with four fields: mid (${\log }_2(\text{price}\times {10}^{18})$, biased by LOG2_ONE), rel (${\log }_2(1+s_{\text{geo}})$ where $s_{\text{geo}}$ is the bidirectional geomean spread), utc (timestamp), and dec (decimal-pair packed as (dec_source << 8) | dec_target for unit normalisation). The containing struct is TWAP { uint256 last; uint256 mean; } with two such words per pair: last for the most recent observation and mean for the EWMA running mean. Replaces linear bid/ask pairs with a compact log-space encoding suitable for EMA smoothing.

R

Rate Limit. Token-bucket mechanism bounding operation frequency; configured per pool with capacity and regeneration rate. See MAX_SUPPLY / MIN_SUPPLY / MAX_BORROW / MIN_BORROW in pool parameters.

Ray. Fixed-point representation with 27 decimal places (${10}^{27}$). Defined in the Constant library.

Read Path. The code path executed when querying a user's balance via totalOf. In the log-space form, this is where exp() is called.

Reentrancy Guard. Protection preventing a contract from being called recursively during execution; uses transient storage.

Reindex. Interest compounding mechanism that updates the global log-space index and snapshots per-user indices. The functions _reindex and _reindexWith advance the global log-space index; lock bonus/malus is applied per-user via _spreadDiff consumed by the IR model when computing the position rate. Per-user balance growth is $\exp (I_{\text{global}}-I_{\text{user}})$.

Reserves. Token balances held in AMM liquidity pools; used to calculate bid/ask quotes via constant product formula.

Ring-Lock. Base mechanism: ring buffer + bitmap + cached total. 9 words per user. See ring-buffer locks paper.

Role Guard. Contract restricting which addresses can execute role-gated functions; part of access control system. See role hierarchy.

S

Sandwich Attack. MEV attack bracketing a victim transaction with front-run and back-run to extract value.

Secondary Market Discount. Price reduction $D$ (typically 3–10%) for locked position tokens relative to NAV; reflects inability to redeem for underlying assets. See secondary market risk and transfers and exits.

Self-Healing. more() correcting stale slot contributions during overwrite, maintaining total and depth consistency per-slot. Stated as a theorem in the ring-buffer locks paper.

$\sigma$, ${\sigma }_h$ †. Annualized and hourly volatility of the collateral asset. ${\sigma }_h=\sigma /\sqrt{8760}$. ETH calibration: $\sigma =90\mathrm{\%}$, ${\sigma }_h\approx 0.96\mathrm{\%}$/hour.

Slippage. Price deviation from executing a trade against AMM reserves; increases with trade size relative to reserves. See spread and slippage.

Solvency Boundary. Parameter constraint ensuring protocol can meet all obligations; default configuration satisfies $r_{\text{bonus}}+r_{\text{malus}}=2s$, maintaining solvency for any lock adoption rate.

Spread. (1) Oracle: bidirectional geomean of relative spreads from both AMM query directions, stored as ${\log }_2(1+s_{\text{geo}})$; wider spreads indicate lower liquidity or higher manipulation resistance. (2) IRM: symmetric half-spread parameter (e.g., 10%) applied to base rate; borrow rate = base $\times (1+s)$, supply rate = base $\times (1-s)$. The IRM half-spread is the on-chain SPREAD parameter — see position parameters.

Spread Scaling. Logarithmic widening of bid/ask spreads for large positions via $\mu ={\log }_2(x+1)+1$ where $x=\text{center}\cdot s$ is the notional spread (equivalently ${\log }_2(2x+2)$); reflects market impact without governance parameters.

Square. Restricted-access liquidation function executing debt assumption: for a given exponent $e$, atomically transfers $\lfloor \text{borrow}/2^e\rfloor$ and $\lfloor \text{supply}/2^e\rfloor$ from victim to liquidator via bit-shift. Reverts if the victim is healthy (wnav_supply >= wnav_borrow, equivalently $H\ge 1$, treating the boundary as solvent) or the liquidator's post-transfer health is insufficient. The public entry point is Pool.liquidate(victim, partial_exp), which (after role/PoW checks) calls Pool.square(msg.sender, victim, partial_exp). The square() selector is gated by POOL_SQUARE_ROLE. See debt assumption and partial liquidation.

Staleness. Age of price data from an oracle; stale prices beyond threshold are rejected to prevent exploitation. See oracle staleness.

Supply Position. ERC20 token representing deposited collateral; uses standard transfer semantics. See positions as tokens.

Supply Rate. The interest rate earned by suppliers, computed as $r_{\text{base}}\times (1-s)$ where $s$ is the spread. Always less than or equal to the base rate.

Sybil Attack. Creating multiple accounts to gain unfair advantage; XPower Banq defends against rapid capacity monopolization via holder-count scaling.

Sybil Resistance. Protection against Sybil attacks; in XPower Banq, bounds accumulation rate via holder-count scaling, not equilibrium share.

T

Time-lock. Mandatory delay between proposing and executing governance parameter changes; prevents sudden malicious updates. See proposing changes.

Time-Lock (Lock Extension). Extension of Ring-Lock adding the depth mapping for token-seconds. 10 words per user.

Time-Weighted Mean. Integration technique averaging parameter values over time; enables smooth transitions without discrete jumps. See transition curves.

Token Bucket. Rate limiting mechanism with capacity $C$, regeneration rate, and per-operation cost; operation allowed iff $C\ge 0$.

Token-Seconds. $\sum v_i\times \text{remaining time}$ — integral of locked amount over remaining time. The depth metric that drives graduated commitment.

Truncation Bias. The systematic negative error introduced by fixed-point truncation (rounding toward zero). In the multiplicative form, this bias compounds over $N$ accrual steps ($\le 2N$ ULP). The log-space form has zero truncation during accrual.

TVL †. Total Value Locked — the aggregate collateral value in the lending pool. All bad-debt metrics in bad-debt risk are reported as a percentage of TVL.

tx.origin. Transaction originator address included in PoW hash; prevents front-runners from reusing others' solutions. See PoW-gated public mode.

TWAP. Time-Weighted Average Price — price smoothed over time via log-space EMA (geometric mean temporal averaging) to resist manipulation. See TWAP oracle overview.

U

UD60x18. PRBMath's unsigned 60.18-decimal fixed-point type. 60 integer digits and 18 fractional digits, fitting in uint256. Used for exp(), mul(), and ln() operations.

uint256. Solidity's 256-bit unsigned integer type, holding values from 0 to $2^{256}-1\approx 1.16\times {10}^{77}$. The storage type for both the multiplicative and log-space indices.

ULP. Unit in the Last Place — the smallest representable increment at a given precision. At WAD: 1 ULP $=1$ wei $={10}^{-18}$.

User Snapshot ($L_u$). The value of $L$ at the user's last state transition, stored in _userIndex[user].

Utilization. Ratio of borrowed assets to supplied assets in a vault; drives interest rates via a piecewise-linear model with a kink at optimal utilization. See interest rates.

V

$\text{VaR}(99\mathrm{\%})$ †. Value-at-Risk at the 99th percentile — the bad debt level exceeded in only 1% of simulated paths.

Vault. ERC4626-compliant custody contract holding deposited assets; tracks utilization for the interest rate model. Distinct from a Position — Position tokens are plain ERC20Permit. See ERC4626 vaults.

W

$W$ †. Phantom-healthy window — the number of oracle refreshes during which a position remains phantom-healthy after a crash.

WAD. Fixed-point representation with 18 decimal places (${10}^{18}$). Defined in the Constant library.

Weight. Multiplier applied to asset values in health calculations; determines effective LTV. Defaults: $w_s=170$, $w_b=255$. See WEIGHT_SUPPLY and WEIGHT_BORROW in pool parameters.

Write Path. The code path executed during index accrual (_reindex). In the log-space form, this is a single addition; in the multiplicative form, it calls exp() and mul().

Where to go next

• Bibliography — citations referenced throughout the glossary.
• FAQ — short answers to common questions.
• Comparison table — XPower Banq vs other protocols.
• Parameter catalog — every governable parameter with ranges.