Rule — summons for an award. A root request that no eligible member has been awarded within wA ticks of its posting — because no member free to commit and able to fund the guarantee offered — is awarded to a troop, when the fund can carry it, at the trailing market price Bˉ: the mean price awarded to members over the trailing period, the ceiling β when there is none (2.0.0: the price level Pt when there is none — P0 before the first award — since the ceiling is the requester's choice now; and members' awards only is the rule, so that a state delivering most of the market cannot set its own price). Read per request, not per tick (ruled after run 9; patch 1.7.1, October 18, 2026): a free member takes the oldest request it can; the others, unawarded past their window with nobody offering for them, are the state's. So at the seating step the requests that have waited wA and exceed the free fundable members — members off duty, uncommitted, holding no review, able to fund G at the market price — are summoned for, oldest first, after the members have taken theirs: the oldest of them, as many as there are free fundable members, are left to the market, and the rest are the state's at that seating. One free member does not hold the state back from the rest of the queue. (1.4.0–1.7.0's engine read the rule per tick — any one free fundable member blocked every award summons that tick, however long the queue; run 9 traced the 50/50 collapse to it, Appendix L.) A troop is summoned only for a request whose ceiling admits the state's price pT=max(Bˉ,B) (2.4.0; β≥Bˉ before it): a request priced below the market is not a shortage and waits; a request priced below the state's reservation is marked and told, and the state takes it at no wait (§5.1). The award pass gathers only what the state may take (2.4.0, a conformance reading of 1.7.1 made at acceptance, Appendix Q): the requests counted against the free fundable members are those at β≥pT, so a request below the state's price neither holds a member's slot it will not use nor pushes a fundable request beyond the count. The troop delivers at pT and the requester pays in exactly as for any award (pT+φE+φF+ωt, from the posting lock, which covers it since the floor only raises the state's price toward β); the troop's guarantee G=⌈0.5pT⌉ is locked from the fund (2.4.0: at the state's price; Bˉ before it), the state's expected cost is burned at pT — cTD=max(0,(1−bT)pT−bTG), §7.7, neutral in expectation at the floor as at Bˉ — and Pt counts the award at pT; the troop delivers once, within the ordinary commitment, and its submission is reviewed as any submission — by the on-duty reserve, round-robin; by a troop reviewer only under the seat rule above. The troop is released at the case's vesting or final settlement. Members first, always: a troop never takes an award a member offered for, never takes a seat a member or probationer is free to fill, and is never preferred to one on price, reputation or duty credit; the window is the whole of the market's chance, and nothing shortens it. (Until 2.0.0 every offer was at the ceiling, so Bˉ=β and "β≥Bˉ" never bound; since 2.0.0 it binds where the requesters post below the market, and since 2.4.0 the floor binds where the members' price is below the anchor cost — the patient cells of run 17 and the edge of its faster-decay cell; every quiet cell of runs 12–17 has Bˉ≥20 and never meets it.) Consequence (2.4.0) — what the floor does and does not do. It does not let the state set the price: above B the state follows the members as before. It stops the state from being driven below the market's anchor cost by a demand side that waits: at the floor the state declines, and the price can fall further only where members cheaper than the anchor choose to bid — which is a market, not a spiral.
Rule (2.0.0) — the capacity case; two places; the troops' wallet. The state fields at most NT troops at once, deliveries and review seats together (default 40, Appendix A: clear of the quiet field at every split in run 10 — 18 / 23 / 26 / 29 at 50–80%, peaks to 34 — and inside every riot peak of run 11, 75–221; unbounded is the control). A delivery's summons needs room in the field for itself and its inspection seat — two of NT — else the field would fill with deliveries whose inspections are then refused: 1.6.0's "a delivery carries its inspection", in capacity terms. Ruled at acceptance (Appendix M): the two places are reserved, and released on seating — a troop delivery holds two places from its summons until its initial review is assigned: to a market reviewer, after which it holds one; to a troop, after which the seat holds its own; the capacity reading counts places held. A summons NT refuses is the capacity case — the one case the market cannot answer with a price: the request waits, its clock runs, and the case is recorded — refused for capacity, the request's wait in seating steps, and that its requester was told (2.0.0: a flag at the first refusal; 2.1.0 — every refusal is told: a summons NT refuses, and a delivery the bank refuses for credit (§10.4), mark the request — refused for capacity / refused for credit, with the tick — and the mark is readable by the requester's policy through the public view, as the below-market flag is; the requester may hold or withdraw (withdrawn before award, owed nothing), the clock runs either way, and the share of marked requests withdrawn is the busy line's reading beside on-time share and lateness — and, since 2.2.0, the forgone share of the period's rebate claims, the unpaid part of the state's blame, the busy line's third reading; the message itself is 2.x); the oldest-first rule of I26 applies to refusals for capacity as it did to refusals for funds. The troops' wallet is Ω (§10.4): a troop's cost is burned from Ω and its locks sit on Ω — created if short under 2.0.0; lent by the bank since 2.1.0, tied to the summons — and its price and released locks come home to Ω, repaying that loan first and then the order of every inflow (debt, liabilities, Ω). Without NT the state is an infinite supplier at Bˉ and nothing is ever scarce; under it the state's share is bounded, bids rise toward ceilings when members and troops are both short, and the price level responds to money.
Rule — the troop account (1.7.0–1.7.1; retired 2.0.0, the troops' wallet is Ω; 1.4.0–1.6.0: "the fund carries the troops first"). The troops' wallet is a separate troop account (§10.4). In: Ω's advances; every troop's earnings — fee, price, court fee won, released bond or guarantee. Out: troop costs purchased and bonds or guarantees posted at summons; a troop's guarantee forfeited to the requester at a final N; a troop reviewer's bond burned on an overturn (the court fee to the winner); repayment of Ω's advances; and at each settlement batch the unlocked balance above the reserve RT flows to Ω. RT is the two-period peak of the capital troops held (the rule below); the summons rules, inspection first, the delivery check and the plant reserve are as 1.6.0, with the troop account in the fund's place. Withdrawn: 1.4.0's clause "nothing a troop earns reaches Ω except by repayment of an advance" — a troop is an actor of the state and its earnings are the state's. What guards the conflict of interest the clause was for — a state that earns from troops has a reason to prefer them — all stand: members first at every seat (a troop is summoned only for a seat or award no eligible actor took within its window); the windows wR, wA; cost at summons; no emission, no uplift, no ρ, no κ to a troop; the state's share on the public record — troop-ticks, troop deliveries, panels held by troops, per period; and, added by 1.7.0, Ω's income by source (§10.4), so that a state living off its own deliveries is visible as such. Consequence: the reviewers' uplift is what 1.3.0 promised them; the state's deliveries pay the state — at 60/40 in run 8 the troops' net was 6 to 7 a tick, the deliveries' price Bˉ less cTD=10 with the guarantee back at vesting and forfeited at a final N, and the review seats' fees (a troop reviewer's cost is reimbursed from the requester's allowance like any reviewer's, §7.3, so an audit seat nets its fee of 3 — the accepted text's "nets nothing" is corrected in Appendix L); the honest end poorer by the troops' former share of their uplift, about two fifths of it at 60/40, and still far richer than the stampers.
Under 1.4.0–1.6.0 (superseded). The duty fund was the troops' wallet and kept its name. In: the raised tax (mt−1)ω0B per award, as before; every troop's earnings. Out, in this order each tick: (1) troop costs at summons and bonds or guarantees posted; (2) repayment of any advance from Ω; (3) at each settlement batch, the uplift of §12.2 — distributed exactly as before, but only from the fund's unlocked balance above a reserve RT — since 1.5.0 the peak troop demand of the current period (next rule); under 1.4.0 it was the largest capital troops had tied up at once during the trailing period, which the uplift drained the fund to every batch, so that the peak could never rise (Appendix J). At rest RT=0 and the whole fund flows to the reviewers as under 1.3.0; under stress the fund keeps what the period's demand required. The advance: when the fund cannot carry a summons, Ω advances the difference from its unlocked balance, up to AT outstanding; the advance is repaid first from the fund's inflows. Beyond AT the summons fails and is counted as troop shortfall. Ω keeps the base rate ω0B and the plant capital, as before; nothing a troop earns reaches Ω except by repayment of an advance.
Rule — the reserve is sized to the need (1.5.0; retired 2.0.0). At each seating step s the troop demand is
Ds=∑troops holding a seat at scapital held+∑cases whose summons the fund could not carry at sthe capital the case’s unfilled seats would have drawn,
where could not carry means refused for funds — the carry check's own refusal, the branch that counts troop shortfall; a request priced below Bˉ is the rule's own exclusion, a requester that cannot pay in is the market's refusal, a challenge path already full is not a need, and none of these adds to demand. A case's demand is its unfilled seats — a delivery one, an audit one, a challenge missing both panel seats two, 2(cT+GV) — and once per seating is about ticks, not seats: a case refused at ten consecutive seatings adds its seats' cost to each of those ten stocks, never ten times to one; a case refused at s and carried at s+1 appears in Ds as refused cost and in Ds+1 as capital held, and no stock counts it twice. The refused cost is the amount the carry check refused, as it would have been purchased and posted at s: a delivery's cTD plus its indexed guarantee G=max(1,⌈GfracBˉ⌉), a seat's cT plus the case's indexed bond — not the Appendix A defaults. The reserve is the peak demand of the period, RT=maxsDs — under 1.5.0 over the current period alone, starting at the period's first seating from the demand then standing; under 1.6.0 over the current and the previous period (the rule below). Since 1.7.0 the troop account's reserve is the two-period peak of the capital troops held — costs purchased plus bonds and guarantees locked, every troop in the field — and no longer counts refused summonses. 1.5.0 added the refused component so a fund Ω backed only to AT could grow into the need; 1.6.0 removed AT, and the component became retention without a purpose — under stress most of a 952–3,494 reserve was refused demand held back from an Ω that could not fund plants (run 8). What RT is for now, and the reason the account holds anything back at all: the troops' in-flight capacity is shielded from the liability queue — Ω pays liabilities older than a period before it advances (§10.4), so an account that kept nothing would see every summons compete with every old debt, and the state's share would fall exactly when the debts are largest. With peak-held capital retained the state sustains its current share from its own account as deliveries vest and the capital returns; growing that share draws on Ω after the debts, which is the right order. The surplus reaches Ω only once the account stands at RT and only while RT is not rising; in a ramp, and after every new peak in the field, Ω's income is the base fee alone. Ds and its refused part remain readings (§18.1 questions 13 and 14). A peak holds: the stock Ds falls as the backlog is served, the reserve does not — it stands at the period's peak until the period ends and comes down to the standing demand at the next boundary; the money returns to the reviewers at the period's end, not the moment the shortage passes, and that retention — one period, the dial's own lag — is a feature: a fund that has just been short does not pay out the moment it is not. The fund grows into the need: a refusal raises the reserve by what was refused, the fund keeps its inflows until it can carry the summonses that were made, and since every troop seat is net-positive to the fund at the defaults (a review about +2, a delivery about +4 in expectation and +10 realised at a vesting) a fund allowed to keep what it earns grows into the demand on its own; what bounds the state's share is then the market's unmet need and the fund's inflows, as the rule above intended. At rest, Ds=0, and at the first boundary after it RT=0: the whole fund flows to the reviewers as under 1.3.0.
Reading — how a probationer's false approval reached the customer (1.5.0). A reading, not a rule, the drivers'. For every probationer's false approval that vests, the drivers record the route: the pinned audit upheld it (the auditor missed), or the audit rejected it and the ruling overturned the rejection (the ruling erred — a sixth of the leak at drift in run 6's ruling sweep). For the first route they record the auditor's kind at the time: a troop; a member never suspended in the run; a member suspended at a later tick than the audit — inside its detection lag; a member readmitted before the audit. Attribution is after the run, since a record that later fails is known only at the end.
Rule — inspection first; a delivery carries its inspection (1.6.0). In every summons pass, review-seat summonses are processed before delivery summonses, oldest clock first within each. A troop delivery is summoned only when the fund's unlocked balance plus Ω's available advance can carry its own capital and the capital of two review seats — cTD+G+2(cT+GV), 36 at the defaults — the initial review it will need and the audit it will probably draw. It is a check, not a hold: the advance actually drawn is the delivery's own shortfall, the review seats are not earmarked, the order of the pass funds them first when they come, and the demand stock Ds keeps the delivery's own capital. The state never starts work it cannot get inspected.
Rule — the reserve over two periods (1.6.0; retired 2.0.0). RT is the peak troop demand Ds over the current and the previous period (the 1.4.0 engine's reading, Appendix I); the one-period reset of 1.5.0 is withdrawn — the boundary no longer pays out an accumulated balance in one batch when the in-flight cohort happens to have just vested. With Ω backing the fund, the reserve's remaining job is to decide when the fund repays Ω and when it pays uplift — since 1.7.0, when the troop account's surplus flows to Ω — not whether a troop is summoned.
Rule — minimization is a rule, and a reading. No troop persists: one seat, one summons, released at completion, nothing carried over; a turn vacated in the reserve is refilled by kind from members and probationers before any troop is summoned; a troop is summoned only for a seat or an award that has waited its window. The History carries, per period: troop-ticks (review seats and deliveries separately), troop shortfall (seats and awards no troop could be summoned for, and the ticks cases held for want of one), cases held for the market's audit (count and age), the fund's balance, reserve and advance, and since 1.5.0 the period's peak demand with its refused component and the demand at its last seating. In an honest population at rest every one of these reads zero; a nonzero reading is a stress gauge, like the dial, not a feature. There is nothing to size and nothing to retract, because nothing persists: the number of troops at any tick is the shortfall at that tick, after the market has had its chance.
Consequence. The state's reach is its treasury: what the dial has levied, what its own troops have earned, and a bounded float — never more. Stress raises mt, mt raises the surcharge, the surcharge pays for the force that answers the stress; as the stress passes, troop usage falls, RT follows it down at the next period's end, and the money returns to the reviewers. The dial sizes the army without a second dial. ELEF's conflict of interest — troops earn the fund a fee and a price — is answered structurally: the window, members-first, cost at summons, and no route from the fund to Ω. The state does not profit from scarcity; the market does.
Hypotheses (1.4.0). The audit leak closes: a probationer's every approval is audited, by a member or a troop; its false approvals fall to the audited residual. The slowness is supplied: at fixed splits vesting recovers toward the 1.2.0 control with troops delivering what members could not — about a third of tasks at 60/40, two thirds at 80/20 — and the state's share reads how captured the market is. Minimization under adaptation: troop-ticks fall to zero as the stamper share falls, close to the tick at which the population is honest. No crowding out — restated by 1.5.0 after run 6: the honest keep their income; its composition shifts. A troop takes only what the market left, but what it delivers the market inspects — a probationer's initial review, a member's pinned audit — so as the state's share rises, members spend more of their time on duty and less delivering; their wealth rises by the uplift, their awards fall, bounded by the duty cap, which keeps at least half of them free. A member whose award count fell while the state delivered is the mechanism; a member whose award was taken by a troop it had offered for would be the failure, and none was observed. The stamper − careful gap keeps its sign and changes in size by the uplift. The fund carries it: a review seat nets about +2, a delivery about +4 in expectation, so the treasury bounds simultaneous troops through RT and AT, not their number over time — failed in run 6 under the 1.4.0 reserve (the fund refused 4,800–8,800 award summonses a run while paying 6,400–12,700 in uplift; AT was not the binding constraint), answered by 1.5.0's rule above. The state's work is seen: cases held for the market's audit are few and short-lived wherever members are on duty. Open, deliberately: whether troop usage should feed the dial; whether the duty cap should loosen now that the floor is the state rather than "whoever is free".
Hypotheses (1.5.0). The fund carries the need — failed in run 7: refusals rose, deliveries did not, vesting and uplift were identical to 1.4.0, because the demand stock counted a never-expiring queue and the reviewing seat, not the treasury, was the binding capacity (Appendix K). As written: refused award summonses fall from thousands a run to a ramp of a few tens of ticks and then near zero at 50–70%; the state's share rises to the unmet demand — at 60/40 from 27% toward the third of tasks the four free members cannot deliver — and vesting with it; uplift is zero while the fund accumulates toward a reserve of a few hundred and higher than run 6's once it serves the backlog, paid late in each stressed period, not never. wA begins to matter: with the fund sized to need the award window is the knob it was meant to be — shorter, more troops and faster service; longer, fewer and a longer wait. Minimization still holds: troops reach zero as the population turns honest, the reserve falls to zero one period after the last troop, the convergence tick is unchanged within noise. The auditor's lag: under drift most probationers' false approvals travel the upheld route and are audited by members suspended later than the audit; under fixed splits the upheld route with the auditor's ε miss dominates and the overturned route is a sixth or less. If the lag dominates, a later revision may ask whether a pinned approval's auditor should itself have a determined record; that is not proposed. Limit, restated: a fund sized to need can grow; the state's share in a captured market will be larger than under 1.4.0, and the text accepts that — the share is the reading of the capture, and the market comes first at every seat.
Hypotheses (1.6.0; run 8, Appendix L: the seat unbound the queue — 94 open cases at 60/40 — and on time came out inverted, 0.90 at 80/20 and 0.40–0.60 at 50–60% where Ω's liability reached 20,000–26,000 and plants went unfunded; wA failed again; the auditor's record held in full; the two-thirds cap fixed the seat at 60/40; minimization held for every flow and not for the liability stock). The seat unbinds the queue, not the rate: three tasks a tick at b=0.2 vest at most 2.4 a tick plus the false approvals — a ceiling the 1.2.0 control is at and run 7 within a few percent of; the seat caps the queue (~300 open cases at 60/40) and the latency of each. So reviews waiting fall from 7,300–11,400 case-ticks a run to a few hundred, the open-case queue to the in-flight count, vesting by the backlog cleared toward the ceiling, and the state's share to the unmet delivery demand. On time, from the second period: at 50–70% the on-time share exceeds 90% at Ts=8 and rebates are small; at 80/20 it falls and rebates accrue because Ω's balance, not policy, is the limit — Ω's minimum above the plant reserve reaches zero at Ω0=300 and recovers at 1,000, plants unfunded reading zero in both. wA is a knob now. The auditor's record: at fixed splits the upheld route's lagging-member kind falls from 55–75% to near zero; under drift it falls little. The ramp, which every run is: panels are the state's until records determine (100–200 ticks), Ω's advance drawn hard and repaid, the state's share of panels falling toward its steady value by the second period. The cap decides the market's shape: at ⌈Et/2⌉ the honest deliver and inspect in equal measure, at Et they inspect only and the state delivers everything the stampers cannot; honesty unchanged; a product decision with the numbers beside it. Minimization still holds: troops, advances, lateness and rebates reach zero as the population turns honest. Limit: a market the state can always carry is a market that need not grow; the price signal that would make it grow is §18.1 question 2, now the next question.
Hypotheses (1.7.0). Ω is solvent at 60/40, and the plants are its sharp edge: with the troop surplus in Ω and the cap at two thirds, the liability at 60/40 falls from 19,778 to a few hundred and is paid within the run, Ω's minimum stays above the plant reserve, the on-time share is at or above 0.90 — and plants unfunded read zero, which the arithmetic says is close: run 8's two-thirds cell had about 7,800 of need (a liability of 3,700, 272 unfunded plants at about 15 each) against a troop net of about 6,200, plus what the smaller reserve releases; it may hold on the liability and fail on the plants by a thousand or two, and ω0=10% closes that gap. 50/50 is the open question: the liability falls by the cap's effect and the troop surplus against a plant bill the cap raises there too; whether what remains is paid within the run decides whether 1.8.0 is the cannot-serve protocol — the text does not predict it. The state does not prefer troops: the state's share is unchanged from run 8's two-thirds cells within noise, since the summons rules are unchanged, read beside the refusals — a rise matched by a fall in refusals for funds is capacity, a rise without one would be what the guards exist to catch; Ω's income by source shows the troop surplus as a line, not a trend. The honest are a little poorer and still far ahead: uplift paid falls by the troops' former share, about two fifths at 60/40 (11,900 → 6,900 a run; a careful actor's uplift 1,290 → 750); the stamper − careful gap keeps its sign at every split; honesty is unchanged. The stock clears: in the adaptive run Ω's liability is paid down to zero. The take: with rs pinned, ω0=10% doubles Ω's base income and the clock is carried at 50–60% on fees alone; at 15% Ω accumulates — ELEF's price question. Limit, restated: the state now earns from scarcity; the guards are what keep that from becoming a motive, and the reading is what shows if they fail.
Consequence. Under this rule the reserve's honesty is a controlled variable with an uncapturable sensor and an actuator that removes negligent reviewers through a channel they cannot vote on. The honest regime gains margin; the captured regime is detected and acted on from inside the loop. What capture becomes instead is a shortage: in a stamper-majority market the reserve runs short of eligible actors, reviews wait, and the eligibility shortfall is on the record — the loop stays honest and slow rather than captured and fast, and says which. What the dial does not do is make negligence impossible: it makes it unprofitable and short-lived.
Hypotheses (1.2.0). The contest, by channel: careless review loses to careful review through money (about πβP(fˉ+GV)≈0.6 per review at the defaults, roughly 120 per actor over 1,000 ticks at run 3's volumes — the scale of the 50/50 gap under appeals alone, +200, and it reverses it), through reliability (plant failures enter ρ: a stamper adds about 7.5 overturns per 100 outcomes at π=0.1, a careful reviewer about 0.5, reversing run 3's 0.973 against 0.953 and with it the award shares that made the 10/90 gaps), and through the seat (a stamper leaves the reserve within about nmin/(πβP)≈50 reviews). The dependence on the requester's dispute rate and the actor's appeal rate, which decided the contest under 1.1.0, is removed as a necessary condition; both remain welcome. Capture: a stamper majority cannot persist in the reserve; the tipping point of run 3 (between 50/50 and 10/90) moves to "nowhere" for honesty and reappears as a capacity cliff the market must answer by recruiting reviewers. Cost: at m=1 plants cost Ω about one careful inspection's fee and expenses per plant (a stamper's failed plant costs Ω nothing but the refunded pots), about 2 credits a tick at 3 tasks a tick, against a service-fee income of 3 a tick; at mmax the floating fee covers four times the plants — §18.1 question 3 restated. Camouflage: a stamper that rejects a random fraction of work to look careful still approves bad plants at its approval rate and is caught in proportion; camouflage buys time, not safety.
Spec 2.9.0, lines 640–672.