Worked Formula Examples

These compact vectors are for hand audit. Inputs are abbreviated but use the exact public semantics; domain specs define the full plain-data shapes and trace fields.

Twelve representative cross-domain vectors are also stored as plain data in WORKED-EXAMPLES.json and executed by the formula-manual contract test. The table remains the complete 49-function human index; the JSON set protects high-risk arithmetic examples from documentation drift.

Public function	Hand-checkable example
canonicalizeDecimalString	001.2300 → 1.23; every spelling of signed zero becomes 0.
quantizePrice	Perp 103436.7, szDecimals=0, down: the normal candidate is 103430, integer candidate is 103436, so the tight result is 103436.
quantizeSize	1.239 at two size decimals becomes floor(123.9)/100 = 1.23.
deriveCanonicalAssetKey	mainnet perp first-party dex (null), index 0 becomes hl:mainnet:perp::0.
encodeAssetId	Outcome 1, side 1: 100000000 + 10×1 + 1 = 100000011.
decodeAssetId	100000011 − 100000000 = 11, so outcome is floor(11/10)=1 and side is 1.
calculateOutcomeDualPrice	Price 0.37 has merged-book dual 1−0.37 = 0.63.
calculateOutcomeSettlement	No token, settle fraction 0.8, size 10, entry 0.63: payout fraction 0.2, value 2, notional 6.3, gross PnL -4.3.
evaluateRecurringOutcome	Marks 100@t0 and 110@t1, settled halfway: interpolated mark 105; binary target equality settles Yes.
calculateBookMetrics	bid 99, ask 101: mid 100, spread 2, spread bps 2/100×10000 = 200.
simulateBookFill	Buy 1.5 from asks 1@100, 1@110: fills 1@100 + 0.5@110, total notional 155, VWAP 155/1.5.
calculateTradeFee	price=100, size=2, rate=0.001: notional 200, fee 0.2, account delta -0.2.
calculateWeightedFeeVolume	Perps 100 and Spot 50: 100 + 2×50 = 200.
selectFeeTier	Threshold 100 is inactive at volume 100 and active at 100.0001 because comparison is strict >.
calculatePerpUnrealizedPnl	Long 2@100 marked 110: 2×(110−100) = 20.
projectPerpFill	Long 5@100 plus buy 1@160: new size 6, entry (5×100+1×160)/6 = 110.
projectPerpFillSequence	The preceding 6@110 followed by sell 6@120 ends flat with gross realized PnL 6×10 = 60.
calculatePerpBreakEvenPrice	Long 2@100 with cumulative cost 4: 100 + 4/2 = 102.
calculateFundingPremiumIndex	Impact bid 110, ask 90, oracle 100: (10−10)/100 = 0.
calculateFundingRate	Premium 0, interest 0.0001, eight-hour interval, no cap hit: hourly rate 0.0001/8 = 0.0000125.
calculateFundingPayment	Long size 2, oracle 100, rate 0.001: payment 0.2, account delta -0.2.
annualizeFundingRate	Simple 0.001 for 365 periods gives 0.365; compound uses (1.001)^365−1.
calculatePerpInitialMargin	2×100=200 notional at 5×: initial 40; transfer requirement max(40,20)=40.
calculatePerpMaintenanceMargin	Notional 200, max leverage 10: rate 1/(2×10)=0.05, maintenance 10, backstop threshold 20/3.
evaluatePerpAccountMargin	Cross account value 1000 with the preceding position: maintenance availability 990, initial availability 960.
calculateUnifiedAccountRatio	Cross maintenance 5, isolated usage 1.5, spot total 11.5: available 10, token and account ratio 0.5.
calculatePerpLiquidationPrice	Isolated long q=1, mark 100, value 20, rate 0.05, deduction 0: x=(−20+100)/(1−0.05)=80/0.95.
simulatePerpAccountScenario	A complete fill buy 1@100 action from flat is folded first; margin and liquidation are then recomputed from that projected state, never from a prefix after failure.
validatePerpOrder	price=100, size=0.1, minimum notional 10, band 90..110: notional 10; both inclusive constraints pass.
calculatePerpMaxOrderSize	Collateral 100, leverage 5, reference 100, long 2 selling non-reduce-only: opening 5 plus reducible 2 gives local bound 7.
evaluatePerpReduceOnly	Long 2, sell 3: only 2 is reducible, so the request is would-flip and the check is violated.
calculatePerpSlippagePrice	Buy reference 100 with 50 bps: raw boundary 100×1.005 = 100.5, then quantize down.
classifyPerpTrigger	Long position, sell order, mark 100, trigger 110: correct closing side and take-profit.
derivePerpTriggerPrice	Long 2@100, target gross PnL 20, no cost: 100 + 20/2 = 110.
buildPerpScaleLadder	Linear 90..110, size 1, three legs, two size decimals: prices 90,100,110; sizes 0.33,0.33,0.34.
calculatePerpTwapExecutionTarget	Size 6, duration 90,000 ms, elapsed 45,000 ms: cumulative target 6×45,000/90,000 = 3.
replayPerpAccountEvents	Cash 100; open long 1@100, then sell 1@110 with fee 1: gross 10, net cash delta 9, final cash 109.
reconcilePerpAccountSnapshot	Projected cash 109, observed 109.01, tolerance 0.02: residual 0.01, check satisfied.
convertSpotTokenUnits	Human 0.5 with weiDecimals=5 becomes 0.5×10^5 = 50000 minimal units.
calculateSpotOrderDeltas	Buy base 2 at price 3: notional 6, base delta +2, quote delta -6.
projectSpotPositionEvent	Flat plus buy 2@3 with quote fee 0.1: position 2@3, gross PnL 0, closed PnL -0.1.
calculateSpotPortfolioValue	Balance 2, entry 3, mark 4: value 8, entry notional 6, unrealized PnL 2.
evaluateSpotDustEligibility	Balance 0.5, lot 1, mid 0.07, threshold 1: below lot and notional 0.035≤1, so eligible.
projectSpotDustAllocation	Aggregate size 10, proceeds 5, user size 2, lot 1: ratio 0.2, user proceeds 1.
validateHip1Deployment	weiDecimals=8, szDecimals=3: lot is 10^(8−3)=100000; userGenesis+anchorGenesis must equal max supply.
evaluateHip1AnchorGenesisEligibility	Holder 2, max supply 1,000,000: threshold 1, weight max(2−1,0)=1.
resolveHip3CollateralSource	Deprecated DEX abstraction with collateral index equal to validator-perp USDC index resolves to the validator-perp USDC balance.
evaluateHip3MarginMode	assetMarginMode=noCross, requested cross: locally unsupported with a violated support check.
calculateHip3FeeRates	Maker 0.001, taker 0.002, deployer scale 0.5, no discount/growth/alignment: HIP-3 scale 1.5, effective rates 0.0015 and 0.003.

The examples intentionally do not hide missing evidence. Where server behavior is not an executable oracle, the corresponding formula remains a local deterministic contract and the oracle registry says not-supported.