{"engine":"qed","provedAt":"2026-09-26T05:38:41.763Z","totalMs":244.78,"proved":125,"failed":[],"results":[{"id":"borrow-draw-stays-inside-the-limit","ok":true,"method":"the real maxDrawUsd and ltvOf over every combination of five collateral sizes, five prices, five liquidation limits and four existing debts","evidence":"500 positions: none priced past the cushion, none negative, and every full draw lands strictly inside the venue's own limit","ms":0.44},{"id":"borrow-draw-never-passes-the-market-ceiling","ok":true,"method":"the real drawableUsd over every combination of six market sizes and six borrowed shares, plus five unreadable rows","evidence":"36 market states: no draw passes 90% of what is supplied, none exceeds what the market holds, none is negative, and an unread market answers null rather than zero","ms":0.16},{"id":"agent-mandate-clauses-hold","ok":true,"method":"every clause in the mandate vocabulary, run against the real seal verdict and mandate normaliser","evidence":"11 of 11 clauses proved over the grids they name","ms":3.97},{"id":"agent-badge-never-rounds-up","ok":true,"method":"four mandates naming limits the signing gate cannot reach","evidence":"4 mandates: the badge never counted more than it checked, and never read complete while something was unenforceable","ms":9.96},{"id":"wilson-lower-bound-monotone","ok":true,"method":"the Wilson interval over every (wins, n) with n up to forty","evidence":"860 cases: lo <= w/n <= hi and lo non-decreasing in wins","ms":0.55},{"id":"crew-veto-and-proven-exclusive","ok":true,"method":"crewRead over a grid of two-wallet crews","evidence":"153 crews: never both refused and proven; every proven crew reads 0.3 or better","ms":0.6},{"id":"refusals-are-scored-like-buys","ok":true,"method":"vetoSummary over four families and a grid of counts","evidence":"36 cases: right = n - bonded for a refusal, bonded for a taken push, rate in [0, 1]","ms":0.21},{"id":"copy-fee-is-a-share-of-a-win-or-nothing","ok":true,"method":"winFeeFor over losses, zero and wins at four fee rates","evidence":"24 cases: zero on a loss, at most pnl * bps / 10000 on a win","ms":0.12},{"id":"copy-size-never-exceeds-the-bankroll-or-the-wallet","ok":true,"method":"followSize over bankrolls, desk slices, wallets and committed sums","evidence":"81 cases: 0 or under the bankroll, the uncommitted part, the cap and the wallet less gas","ms":0.38},{"id":"flywheel-spend-never-exceeds-the-cycle-cap","ok":true,"method":"sizeBuyWei, scaleByVolumeWei and paceSpendWei composed over a grid","evidence":"300 cases: every step at most its input, the spend at most the cycle cap","ms":0.23},{"id":"flywheel-record-only-eases","ok":true,"method":"shadeFromRecord over counts and hit rates","evidence":"35 cases: shade in [0.75, 1], one under 30 judged buys","ms":0.14},{"id":"claim-split-conserves-every-wei","ok":true,"method":"splitClaim over amounts and shares","evidence":"40 cases: mm + reserve + float = amount, all non-negative","ms":0.13},{"id":"public-split-is-three-legs-of-one-hundred","ok":true,"method":"publicSplit over a grid of weights","evidence":"72 cases: exactly three legs summing to 10000, order kept","ms":0.38},{"id":"index-swap-scale-only-shrinks","ok":true,"method":"swapScale over swap counts and average slips","evidence":"40 cases: scale in [0.3, 1], one until 5 swaps, non-increasing in slip","ms":0.18},{"id":"index-self-limit-holds-a-quarter","ok":true,"method":"selfLimit over holdings, earlier sales inside and outside the day, and amounts","evidence":"108 cases: accepted iff sales in the day plus this one stay within a quarter of the holding plus those sales","ms":0.32},{"id":"zap-send-covers-the-basket","ok":true,"method":"zapSendEth over basket values and ETH prices","evidence":"12 cases: send * (1 - fee) >= needed * 1.03","ms":0.11},{"id":"deposit-fee-never-charges-a-desk-delivery","ok":true,"method":"depositFee over cash, marks and desk deliveries","evidence":"36 cases: deposit = max(0, cash - mark - delivered), fee = 100 bps of it","ms":0.13},{"id":"exec-slices-cover-the-order","ok":true,"method":"planSlices over orders, caps and windows, down to single units","evidence":"240 cases: the slices cover the order, and the gap is a minute or more whenever there is more than one","ms":0.26},{"id":"a-swap-is-counted-by-size-and-never-by-direction","ok":true,"method":"signed amounts on both sides, including a thirty digit one","evidence":"5 swaps, every side counted by size","ms":0.18},{"id":"an-unpriced-pool-never-reports-a-zero","ok":true,"method":"counted but unpriced pools, carried through into the ranking","evidence":"3 pools, none of them scored on a volume nobody measured","ms":0.78},{"id":"a-window-reports-the-hours-it-watched","ok":true,"method":"feeds from one hour old to past the window","evidence":"6 windows, none claiming an hour it did not watch","ms":0.26},{"id":"a-failed-read-never-becomes-a-yield","ok":true,"method":"every unreadable value in every input, against a reading known to be sound","evidence":"36 failed reads, none of them turned into a number","ms":0.1},{"id":"a-pool-too-thin-is-never-chosen","ok":true,"method":"every depth under the floor against volumes up to a trillion","evidence":"20 thin pools, none of them able to win at any volume","ms":9.95},{"id":"the-router-never-moves-for-a-rounding-error","ok":true,"method":"every ratio from four fifths to three times the incumbent, in twentieths","evidence":"45 comparisons, the edge honoured on every one","ms":0.28},{"id":"an-unmeasured-incumbent-is-never-abandoned","ok":true,"method":"every unreadable incumbent against rivals up to ten billion in volume","evidence":"12 blind cycles, money moved on none of them","ms":0.1},{"id":"a-deposit-is-never-swept-as-profit","ok":true,"method":"every deposit size from dust to a hundred ETH, against five stakes, through the sweep rule itself","evidence":"30 deposits, none of them reachable by the sweep","ms":0.35},{"id":"the-desk-s-own-winnings-are-never-capital","ok":true,"method":"wins and losses at six sizes across three stakes, read back through the reconciliation","evidence":"18 results, none of them mistaken for capital in","ms":0.12},{"id":"band-refusal-needs-its-own-count","ok":true,"method":"every count under the minimum, with the worst possible fills","evidence":"7 counts, none of them enough to close a band","ms":0.41},{"id":"band-payoff-is-never-one-trade","ok":true,"method":"one and two wins at five sizes up to a thousandfold, against a band with wins of its own","evidence":"15 records, no single fill able to hold a losing band open","ms":0.65},{"id":"band-refusal-is-never-cheaper-than-the-band-paying","ok":true,"method":"every hit count at five sample sizes, against the sign of the band's own best case","evidence":"95 records, refusal and the sign of the best case agree on every one","ms":1.72},{"id":"band-boundaries-never-drop-a-fill","ok":true,"method":"every whole percent of a curve, and every unreadable progress","evidence":"106 readings, each in exactly the band its percent belongs to","ms":0.08},{"id":"exec-slice-never-exceeds-the-cap","ok":true,"method":"planSlices over a grid reaching a whole ETH cut at single wei, where the slice count passes 2^53","evidence":"88 cases: the slice never exceeds the cap","ms":0.11},{"id":"exec-fee-is-a-quarter-percent-at-most","ok":true,"method":"feeFor and sliceScale over a grid","evidence":"10 cases: fee <= notional / 400, slice scale in [0.35, 1]","ms":0.1},{"id":"dca-tranche-bounded-and-budget-never-exceeded","ok":true,"method":"decideTranche over bases, carries, budgets and reads","evidence":"96 cases: factor in [0.5, 1.5], tranche <= min(1.5 base, remaining), carry in [0, base]","ms":0.44},{"id":"factory-spend-under-every-cap","ok":true,"method":"spendForCycle over cash, reserves and caps","evidence":"144 cases: spend <= min(cycle cap, day room, cash - reserve - gas)","ms":0.5},{"id":"mining-grid-split-exact","ok":true,"method":"splitAcrossGrid over six wagers","evidence":"6 wagers: 25 squares, sum exact, remainder on the last","ms":0.18},{"id":"mining-gas-ceiling-and-wager-scale","ok":true,"method":"efficientWager and wagerScale over a grid","evidence":"44 cases: gas <= 2% of any wager placed, wager <= cap and float, scale in [0.25, 1]","ms":0.3},{"id":"pool-day-caps-hold","ok":true,"method":"poolGate and suggestedEth over pools, payments and days","evidence":"77 cases: at most 3 a day, a quarter of the pool a day, one per solver, gas kept, suggestions in [0.0005, 0.02] or nothing","ms":0.4},{"id":"world-rank-is-a-count-off-the-desk","ok":true,"method":"rankOf over the ladder's boundaries","evidence":"visitor, student, apprentice, journeyman, master at 5 checked; submitted never substitutes for checked","ms":0.07},{"id":"world-purse-pays-a-fraction-under-the-day-cap","ok":true,"method":"planPayouts over a full, a thin and an empty purse","evidence":"three rows on 1 ETH paid 0.08968809 ETH in total, each a fraction of the purse as it stood, none over 0.05 ETH, all under the 25% day cap; a thin purse holds every row","ms":0.19},{"id":"depth-a-buyer-pays-at-least-what-a-leaver-receives","ok":true,"method":"depositQuote against exitQuote over generated books with idle balances, and the whole supply out against the holdings","evidence":"400 books: every deposit at least its exit in both tokens and in liquidity, every whole exit within the holdings","ms":27.15},{"id":"depth-dividend-passes-through-as-the-step-times-the-holding","ok":true,"method":"dividendOwed over generated books, steps and partitions of the supply","evidence":"400 books: the whole supply owed exactly the step, no shares owed nothing, no rise owed nothing, every partition summing to at most the book's dividend","ms":1.91},{"id":"depth-holds-still-off-the-issuers-print","ok":true,"method":"oracleVerdict over both pool orderings, thirteen dislocations, eight bands and four broken prints","evidence":"208 verdicts: hold on every missing, stale or halted print; move exactly within the band; never a hold from widening it; a pool at the print always moves","ms":0.52},{"id":"world-bounty-is-the-set-figure-for-checked-work-only","ok":true,"method":"bountyPot over eight set figures either side of the minimum and maximum, bountyStandings and planBounty over a tie","evidence":"the pot is the set figure capped at 0.05 ETH and nothing under 0.0002; only a rise in checked work stands, ties split evenly, shares never exceed the pot","ms":1.04},{"id":"world-milestone-needs-the-desk-not-the-world","ok":true,"method":"MILESTONES and standingOf over a walker and a checked resident","evidence":"no paid milestone without a desk's check; one checked piece is apprentice and journeyman, 5 in one district is master, and a skill is a district at journeyman or better","ms":0.22},{"id":"solve-check-needs-two-others","ok":true,"method":"checkVerdict over author, single, duplicate and second approvals","evidence":"checked only at 2 approvals from distinct identities, the author's never counted","ms":0.16},{"id":"seal-paused-signs-nothing-and-the-cap-holds","ok":true,"method":"sealVerdict over paused and live seals, and spentWithin over a window","evidence":"52 cases: paused refuses everything, live signs iff wei <= per payment and spent + wei <= daily; the sum counts only the window","ms":0.28},{"id":"seal-tightening-is-immediate","ok":true,"method":"planSealChange over tightening, loosening and mixed changes","evidence":"32 cases: tighter caps in force now, looser ones only after the delay","ms":0.18},{"id":"blend-stays-between-the-market-and-its-parts","ok":true,"method":"blend over markets, models, cross prices, analysts and confidences","evidence":"432 cases: |p - market| <= shrink * max|part - market|, p in [0.01, 0.99]","ms":0.49},{"id":"edge-floor-only-rises","ok":true,"method":"floorsFromRecord over records from perfect to hopeless","evidence":"25 cases: base <= edge <= 0.2, unchanged under 30, non-decreasing as the record worsens","ms":0.22},{"id":"stake-under-every-cap","ok":true,"method":"kellyFraction, sizeUsd and the venue fee over a grid","evidence":"95 cases: kelly in [0, 1], stake <= min(cap, room) and 0 or >= minimum, fee <= ceil(1.75 c)/100","ms":0.31},{"id":"reads-per-cycle-bounded-and-crowd-first","ok":true,"method":"readOrder and familiesWithoutSkill over allowances, fresh reads and families, the refusal asserted in both directions","evidence":"35 cases: at most the allowance, none fresh, crowd first; 2 families measured and found wanting were refused and the 3 others were not","ms":0.42},{"id":"conviction-is-a-bounded-weighted-mean","ok":true,"method":"conviction and checkRequest over a grid","evidence":"140 cases: conviction between the least and greatest signal, a request accepted iff inside every limit","ms":0.39},{"id":"scorebook-keeps-every-open-row","ok":true,"method":"trimRows over sizes, windows and open caps","evidence":"27 cases: the newest settled rows up to the window, every open row up to its own cap, order kept","ms":0.81},{"id":"fees-are-claimed-to-the-caller-and-nowhere-else","ok":true,"method":"signature and call-site check over the only claim path in the codebase","evidence":"claim takes only { type: \"uint256\", name: \"amount\" } and is called with args [amount]: there is no destination to point elsewhere","ms":0.34},{"id":"the-allocator-conserves-every-wei","ok":true,"method":"exact bigint arithmetic over a grid of amounts and adversarial weights","evidence":"40 splits, every one summing to the input exactly","ms":0.37},{"id":"the-burn-floor-cannot-be-breached","ok":true,"method":"exhaustive check over malformed and adversarial proposals","evidence":"7 proposals, every one landing on 10000 bps with burn at or above 3000","ms":0.09},{"id":"rounding-can-only-reduce-supply","ok":true,"method":"exact comparison of the remainder against the floor share","evidence":"572 amounts, burn never under its exact share and above it in 458 of them","ms":0.68},{"id":"the-vault-has-no-destination","ok":true,"method":"signature scan over every external and public function in the deployed source","evidence":"24 functions; the only ones taking an address are the owner's own role setters, so there is no destination to name","ms":0.29},{"id":"the-exit-carries-one-condition","ok":true,"method":"modifier scan over every exit path","evidence":"withdraw, withdrawAll, sweepNative, revokeManager are onlyOwner with no second condition, and the contract has no pause","ms":0.25},{"id":"the-daily-cap-cannot-be-doubled-at-the-boundary","ok":true,"method":"the hour ledger the vault keeps, executed in a model over the boundary timings and a long random run, and held to the deployed source; the bytecode itself is driven across the same timings by the EVM test, not here","evidence":"a window that resets at a fixed edge lets 400000 through in two minutes against a cap of 200000; the deployed ledger refuses one unit more at the hour boundary and a day later, restores the allowance once its hour has left the window, and over 167 accepted moves no twenty-four hours held more than 200000","ms":1.51},{"id":"the-service-fee-cannot-reach-principal","ok":true,"method":"constructor bounds plus a read of the only fee path","evidence":"FEE_BPS is immutable, capped at 2000 bps by the constructor, and applied to the pool's fee delta rather than to any balance","ms":0.17},{"id":"a-round-can-never-promise-more-than-it-holds","ok":true,"method":"exact bigint summation of every holder's floor share against the pot","evidence":"20 rounds across 5 holder distributions: the promise never exceeds the assets, and lands exactly on them in 1","ms":0.61},{"id":"what-truncation-strands-is-swept-not-lost","ok":true,"method":"exhaustive over every amount up to 500 against a badly-dividing supply","evidence":"500 rounds; truncation stranded 832 units in total and never a negative one, so every one of them reaches the next round as surplus","ms":0.23},{"id":"a-resting-bid-never-straddles-the-price","ok":true,"method":"every fee tier, the 0.01% tier included, crossed with adversarial ticks and volatilities, both currency orderings","evidence":"240 bands, none containing spot, all on their spacing, every one at least a full spacing and at least 20 ticks clear of it; the tightest sat 20 ticks clear (about 0.20%)","ms":1.44},{"id":"desk-ladder-first-blood","ok":true,"method":"exact basis-point arithmetic over the ladder","evidence":"first blood then breakeven = 10600 bps (+6%); free roll banks 7960 bps, worst case afterwards is a 20.4% loss, never a wipeout","ms":0.08},{"id":"desk-ev-rule-is-the-inequality","ok":true,"method":"the gate evaluated on a 75-point grid against the inequality","evidence":"75 cases agree: refused iff p(M-1)-(1-p)L < 0.05","ms":1.02},{"id":"desk-size-is-bounded","ok":true,"method":"fifteen synthetic records through the sizer","evidence":"the slice is the base for eleven trades, then within [0.5x, 2x] of the base for every record tried","ms":0.7},{"id":"desk-nothing-past-the-bond","ok":true,"method":"the two exit functions evaluated on a 84-point grid of marks, banked tiers and progress at or past the exit mark","evidence":"84 cases: the pool exit is portion 1 at every mark, and the curve exit is portion 1 at 94% and beyond at every multiple; nothing is held past the bond","ms":0.47},{"id":"learned-veto-only-refuses","ok":true,"method":"120-case grid over real and unreal separations, both losing sides, six rate pairs and five readings","evidence":"refused iff on the losing side of a real separation with the winning rate at least 2x the losing rate; act ∧ ¬veto never exceeds act; nothing refused before the record has learned","ms":0.35},{"id":"early-own-record-only-stands-down","ok":true,"method":"every hit count for four record sizes against five tape bounds, 350 cases","evidence":"the safe upper estimate never falls as hits rise; stood down iff it sits under the tape's lower bound with at least 8 closed entries","ms":1.78},{"id":"paused-desk-resumes-only-on-proven-skill","ok":true,"method":"the gap identity on a 32-point grid, then 8 synthetic records through readSkill","evidence":"g = (q − p)(q + p − 2y) and g > 0 iff the desk is closer; never proven when never closer, never under 30 reads, never when the gaps cancel; always proven when always closer","ms":0.61},{"id":"euler-identity","ok":true,"method":"complex arithmetic, IEEE doubles","evidence":"|e^(iπ)+1| = 1.22e-16 < 10⁻¹²","ms":0.03},{"id":"euler-formula","ok":true,"method":"40-term Taylor series vs trig, four angles","evidence":"max Δ = 1.43e-16 < 10⁻¹³","ms":0.06},{"id":"harmonic-diverges","ok":true,"method":"Oresme's grouping bound, executed to 2²⁰ terms","evidence":"S(2²⁰) = 14.440160 ≥ 11; the bound 1 + k/2 held at every doubling","ms":2.56},{"id":"basel","ok":true,"method":"2,000,000-term partial sum with rigorous tail bracket","evidence":"π²/6 − S_N = 4.999999e-7, inside (1/(N+1), 1/N) exactly as the integral bound demands","ms":2.72},{"id":"gauss-sum","ok":true,"method":"exact integer summation","evidence":"Σ = 5050, exactly","ms":0.03},{"id":"taxicab","ok":true,"method":"exact arithmetic + exhaustive minimality scan below 1729","evidence":"1³+12³ = 9³+10³ = 1729, and no smaller sum of two cubes repeats","ms":0.04},{"id":"golden","ok":true,"method":"direct evaluation at (1+√5)/2","evidence":"|φ² − φ − 1| = 0.00e+0 < 10⁻¹²","ms":0.02},{"id":"birthday","ok":true,"method":"exact BigInt product, no floats","evidence":"P(shared birthday, 23 people) = 0.5072 > 0.5, by integer comparison 2(den−num) > den","ms":0.03},{"id":"monty-hall","ok":true,"method":"exhaustive enumeration of all car placements","evidence":"switching wins in exactly 2 of 3 worlds","ms":0.01},{"id":"point-nine","ok":true,"method":"exact BigInt partial sums to 60 digits","evidence":"1 − 0.999...(60 nines) = 10⁻⁶⁰ exactly; the gap vanishes in the limit, so the limit is 1","ms":0.03},{"id":"pnt","ok":true,"method":"sieve of Eratosthenes to 10⁶, recomputed","evidence":"π(10⁶) = 78498; π(x)·ln(x)/x = 1.0845, drifting toward 1 as the theorem says","ms":5.29},{"id":"euclid-primes","ok":true,"method":"Euclid's construction executed for the first 8 primes","evidence":"each p₁···p_k + 1 yielded a prime factor outside the list, every time, as the proof promises","ms":0.08},{"id":"gaussian-integral","ok":true,"method":"Simpson quadrature, 20,000 panels on [−10,10]","evidence":"∫ e^(−x²) dx = 1.772453850906; √π = 1.772453850906; Δ = 6.44e-15","ms":0.65},{"id":"bayes","ok":true,"method":"P(A|B) counted over the population against Bayes' rule on the marginals, both in lowest terms, over six joint distributions; the same comparison against the swapped rule","evidence":"6 joints agree term by term; the swapped rule was caught on 4 of them, so the comparison can fail","ms":0.21},{"id":"collatz","ok":true,"method":"full trajectory verification for every n ≤ 200,000, recomputed at boot","evidence":"all 199,999 starting points fall to 1; the general case remains UNPROVEN, which is the whole point","ms":6.58},{"id":"launch-a-fee-handle-is-an-x-handle-or-nothing","ok":true,"method":"parseLaunchRequest over handle, address and malformed asks","evidence":"8 asks: a fee handle is 1-15 handle characters or null, never an address","ms":2.04},{"id":"launch-hook-options-are-bounded-or-dropped","ok":true,"method":"cleanHookOptions over in-range, out-of-range and malformed options","evidence":"5 cases: every option inside its bounds or dropped, pons carries none","ms":0.21},{"id":"payout-held-fees-never-exceed-the-credits-and-never-go-negative","ok":true,"method":"heldFeeWei over credits, conversions and outflows","evidence":"60 cases: 0 <= held <= credited, a conversion's own send never counted twice","ms":0.66},{"id":"payout-the-tally-conserves-and-only-counts-the-account-named","ok":true,"method":"tallyFor over credits and conversions beside a stranger's receipts","evidence":"18 cases: credits summed exactly, unconverted = max(0, credits - conversions), nobody else's counted","ms":0.25},{"id":"payout-a-missing-price-is-never-a-zero-and-milestones-only-climb","ok":true,"method":"creditedUsdRaw and rungCrossed over the dollar line","evidence":"2007 points: no price is null not zero, rungs non-decreasing and never above the figure","ms":0.69},{"id":"husd-the-maximum-is-the-chain-figure-and-the-scale-is-exact","ok":true,"method":"parseAmount and SCALE over max, typed and dust amounts","evidence":"13 cases: max is the chain's wei, 18 decimals survive, dust refused, the scale is exact","ms":0.24},{"id":"bond-a-quote-never-hands-out-a-free-arbitrage","ok":true,"method":"fairValue and quoteFor over records, tilts, progress and concentration","evidence":"432 quotes: fair inside [150, 9000], both asks sum to 10000 or more, spread never under the house minimum","ms":39.9},{"id":"bond-shares-round-against-the-buyer-and-liability-is-netted-never-negative","ok":true,"method":"sharesFor and liabilityOf over stakes, prices and two-sided books","evidence":"42 cases: shares x price <= stake x scale, liability = max(0, owed - held)","ms":0.51},{"id":"bond-caps-scale-with-the-balance-and-solvency-refuses-what-cannot-be-covered","ok":true,"method":"capsFor over balances; solvencyFor on an empty and a funded book","evidence":"6 balances: caps under both ceilings and non-decreasing; the empty book refuses, the funded one covers","ms":0.55},{"id":"brain-tape-fires-only-on-a-dip-or-the-cap","ok":true,"method":"arithmetic","evidence":"4000 tapes: 1924 fired (every one with the floor passed and a dip, a drop or the cap; 854 by the cap alone), 2076 held (none past the cap, none on a dip), 1574 short tapes fired only by the cap","ms":9.76},{"id":"bond-settlement-conserves-the-pot","ok":true,"method":"settlement over generated fills at quoted prices, both outcomes, held to settleMarket on a book","evidence":"300 markets, 4174 fills: conserved to the wei, every winner at least their stake, the fee within a twentieth of the win, the house's net the stake less the winning shares, and the live path pays the same","ms":11.41},{"id":"bond-one-verdict-per-fill","ok":true,"method":"settlement both ways over generated fills","evidence":"1809 fills: each paid on exactly one outcome, and the two outcomes together pay every share once","ms":1.73},{"id":"compute-a-private-host-is-never-fetched","ok":true,"method":"checkUrl and privateHost over the reserved ranges","evidence":"16 refused, 3 allowed, 15 hosts classified","ms":0.76},{"id":"compute-a-job-is-never-priced-under-its-floor-and-a-spec-hashes-only-what-it-uses","ok":true,"method":"priceFor over every kind and rate; validateSpec and refFor with a stray field","evidence":"30 prices at or above the floor, the reference ignores what the kind does not use","ms":0.55},{"id":"credit-an-advance-never-exceeds-the-ltv-the-cap-or-its-share-of-the-expectation","ok":true,"method":"quoteLoan over marks, odds, multiples and concentration; interestEth over days","evidence":"72 loans under every ceiling, 288 refused by a rule, interest non-negative and non-decreasing","ms":0.65},{"id":"brain-every-split-sums-to-ten-thousand-and-the-trade-leg-is-capped","ok":true,"method":"normalizeSplit and harmonicSplit over percent, bps, tapes and seats","evidence":"53 splits: exactly 10000 bps, trade under its cap, no negative leg, the seat paid from burn","ms":0.75},{"id":"brain-caps-stay-inside-their-bounds-and-the-cycle-fee-is-small","ok":true,"method":"normalizeCaps with absurd and empty input; cycleFeeWei over amounts","evidence":"4 caps inside their bounds, 5 fees at or under five percent","ms":0.15},{"id":"chart-a-proof-is-settled-only-by-bars-that-closed-after-it","ok":true,"method":"resolveAgainst over a bar before the claim, the bar in progress, a refuting close, the horizon and a confirming close","evidence":"5 cases: only closed bars after the claim settle it, and only through a level","ms":0.38},{"id":"chart-the-refuting-level-is-always-on-the-far-side-of-price-and-the-sheet-fits-a-post","ok":true,"method":"readCandles over rising, falling and flat series with a fixed seed","evidence":"24 series: the refuting level on the far side of price, the ladder inside the range, every sheet inside a post","ms":10.68},{"id":"stock-token-multiplier-never-falls-except-on-a-split","ok":true,"method":"classifyStep over the boundary cases, then applyReads over a dividend run, a split and a fall","evidence":"11 cases: five percent is the boundary, a failed read is no step, and the trailing figure is the compounded product of the dividend ratios alone","ms":0.85},{"id":"usdg-aristotle-never-places-under-the-risk-floor","ok":true,"method":"allocateByDepth over a scored board, one under the floor, and the same board unscored","evidence":"4 deposits: the refused market never placed, every leg at most its fraction of its share, placed plus held back the deposit to the cent, 9122.83 USDG held back in all, depth alone and nothing held when unscored","ms":0.74},{"id":"the-entry-floor-never-leaves-its-bounds","ok":true,"method":"floorFrom over every verdict a five-band record can take, at every band edge as a starting floor, and the running state","evidence":"6144 cases inside the bounds and on a band edge, each with its reason in words; the live floor at 60% after 4 moves","ms":14.54},{"id":"the-entry-floor-moves-only-on-what-the-record-proved","ok":true,"method":"floorFrom on records that are empty, gapped, losing under the floor, thin at the floor, losing at the floor, losing everywhere, and paying throughout","evidence":"silence moves nothing, a gap blocks the drop, a losing band is never opened into, nothing this reading says can close a band the desk trades, a floor already lowered retreats no further than the constant, and proof all the way down opens it to the bottom band","ms":0.45},{"id":"dial-never-leaves-its-bounds","ok":true,"method":"valueFrom over every dial and a grid of weights, the absurd included","evidence":"96 cases inside the bounds, weight one is the base, every base inside its bounds","ms":0.16},{"id":"dial-moves-only-on-proven-separation","ok":true,"method":"applyRecord with no record, an unlearning record, a gap under the bar, an unmeasurable feature, and a proven one","evidence":"4 records moved nothing, the proven one moved 8 dials to base times weight inside the bounds","ms":0.34},{"id":"alloc-sums-exact","ok":true,"method":"normalizeWeights over a grid of proposals, the absurd included","evidence":"162 proposals: four weights summing to exactly 10000, none negative","ms":0.4},{"id":"index-mint-never-dilutes","ok":true,"method":"ceiling pro-rata over a grid of balances, supplies and mints, exact bigint","evidence":"80 cases: (b + a) / (S + s) >= b / S every time","ms":0.08},{"id":"index-redeem-never-overpays","ok":true,"method":"floor pro-rata over a grid of balances, supplies and redemptions, exact bigint","evidence":"75 cases: out <= b s / S and (b - out) / (S - s) >= b / S","ms":0.06},{"id":"supply-non-increasing","ok":true,"method":"the flywheel's alphabet (buy, burn, claim) executed over a fixed sequence","evidence":"10 operations: supply never rose","ms":0.16},{"id":"burn-monotone","ok":true,"method":"the flywheel's alphabet (buy, burn, claim) executed over a fixed sequence","evidence":"10 operations: the burn address never fell","ms":0.03},{"id":"buy-then-burn","ok":true,"method":"the flywheel's alphabet (buy, burn, claim) executed over a fixed sequence","evidence":"10 operations: every buy was returned exactly by its burn and the agent holds none of its token","ms":0.03},{"id":"no-mint-reachable","ok":true,"method":"the flywheel's alphabet (buy, burn, claim) executed over a fixed sequence","evidence":"10 operations: no state above the initial supply","ms":0.01},{"id":"strategy-funds-only-eligible-markets","ok":true,"method":"planStrategy over every objective and a board with a dead, empty, refused, low and wrong-kind market","evidence":"12 plans: every leg traces to an eligible row, nothing over the deposit","ms":0.48},{"id":"risk-score-is-bounded-weighted-mean","ok":true,"method":"scoreRow over a grid of every input, missing ones included","evidence":"4800 rows: an integer in [0, 100] every time, weights summing to 100","ms":11.65},{"id":"risk-modulation-monotone","ok":true,"method":"modulation over every score from 0 to 100","evidence":"101 scores: deploy fraction non-decreasing, band width non-increasing where defined","ms":0.17},{"id":"v4-range-ticks-aligned-and-ordered","ok":true,"method":"planUsdgBid over ticks, spacings, volatilities and both pool orderings","evidence":"224 ranges: ordered and aligned to the spacing","ms":0.87},{"id":"mm-move-never-needs-more-than-it-frees","ok":true,"method":"planMove over seeded books, re-deriving the freed and needed amounts with the pool's own rounding","evidence":"586 moves and 14 stand-downs: every move stays on its side, is paid for in full, keeps inside the cap and the near-spot limit, and lands nearer the price","ms":22.42},{"id":"mm-hook-refused-exactly-when-it-can-touch-the-exit","ok":true,"method":"hookVerdict over every fourteen-bit permission set a hook address can carry","evidence":"1024 admitted and 15360 refused, each exactly as its remove-liquidity and liquidity-delta bits say; no hook and the Pons hook admitted","ms":10.5}]}