The Thirty-First Day

1Why the thirty-first day

A thousand Genesis Charters mint in the same hour. They are soulbound at launch (§6), so there is no exit by sale. The dormancy clock resets only on interaction, and after thirty days without one a charter becomes reportable by any address (§10).

Those two facts compose into a third that neither section states. Because every charter starts its clock at the same instant, everyone who never acts becomes reportable within the same hour. This is not a trickle of abandoned accounts discovered one by one. It is a single synchronized event, and it has a date.

In the model, at tick 719 no genesis charter is reportable. At tick 720 every one that has not interacted is. At the whitepaper defaults that is 308 charters — 30.8% of the live set, CI [30.8, 30.9] over 30 seeds — arriving at once.

2Finding one — the bank cannot see it

This is not a statistical result and it does not need a confidence interval. It follows from the rule. §4 sets signal(n) = F(n−1) + F(n−2) — the policy signal for an epoch is the net flow of the two preceding epochs. The first revocations land six hours into the thirty-first day. The epoch that closes as the wave arrives is still reading flow from two epochs earlier, both of them entirely pre-wave. The multiplier cannot move in response until two epoch closes later.

Two epochs, not two days. The whitepaper indexes policy by epoch n and never states how long an epoch is. The model assumes one day, because every other cadence in the document is daily — the auction, the dormancy clock, the base issuance rate. If an epoch is six hours the blind window is half a day; if it is three days the protocol is blind for most of a week while several hundred charters are revoked. How long the bank is actually blind for is set by a number only the team has. That is the first of three places this study can do no more than hand a question back.

3Finding two — the survivors get a bigger share of a smaller issue

Two effects, both clear of zero, pointing in opposite directions.

Every surviving branch earns 6.1% more at day 45 — the control level is 143.0 tokens per branch per day. But the protocol issues less in total over the window: the multiplier integral falls by 1.45 multiplier-days. Fewer branches raise the per-branch share; the revocation payouts being sold push net flow negative, which cuts the multiplier, which shrinks what is being shared.

How much of the cut is the payouts

§10 mints 30% of a revoked balance into the dormant banker’s wallet. Some of it gets sold. To separate “the multiplier fell after day 31” from “the multiplier fell because of payout selling”, the study runs a third arm that is identical to the treatment in every respect except that the payout is minted and never reaches the pool. The difference between the treatment and that arm is the part of the cut that payout selling caused; the rest is everything else revocation does.

It comes to 31.9%, CI [14.8%, 48.3%], over the 171 of 200 seeds in which the multiplier fell at all. Wide, but clear of both zero and one: neither “payout selling is the whole story” nor “payout selling is irrelevant” survives. Across suite B the figure moves with how much of the payout actually reaches the pool — 0% when the sell fraction is zero, 8.4% at a half, 32.5% at one. A dose-response that lands on zero when the dose is zero is the best evidence available that the arm measures what it claims to.

4Finding three — and the advantage does not last

The day-45 advantage is gone by day 90. The licence auction keeps selling, the branch base refills, and the survivors’ edge is competed away in about two months. Both arms end the window with more branches than they had at day 45: the wave is a step down in a rising series, not a collapse.

This contradicts the intuitive reading, and the contradiction is worth sitting with. Destroying a third of the charters sounds as though it should permanently concentrate issuance among those who remain. It does not, and the reason is that the dormant cohort was never holding a third of the issuance. On day 31 they are 30.8% of live charters and 8.3% of live branches — CI [8.29, 8.33] over 30 seeds, a remarkably tight interval for something nothing in the model sets.

Nothing in the model sets that 8.3%. It emerges: a branch is bought at the daily licence auction (§7), and charters that never interact never buy one. Thirty days of committed bankers expanding, and tourists not, is what produces it. The wave destroys a large share of the charters and a small share of the claims on issuance.

5Finding four — all of it scales with a number that is not published

The daily licence supply is REDACTED in the whitepaper. It turns out to be the binding constraint on the whole question, because it caps how fast the active cohort can dilute the dormant one in the thirty days before the wave lands. Tighten it and the dormant cohort holds a larger share of branches when the clock runs out; loosen it and they hold less.

Across its range it swings the supply minted into wallets by 2.7x — from 3.13 million tokens at 25 licences a day to 1.16 million at 400. The effect on day-45 yield is larger still at the tight end and then flattens: 35.2 tokens per branch per day at 25 licences, 15.6 at 50, and between 7.7 and 10.0 at every setting from 100 upward, where the differences are inside the noise band. It is not a smooth dial. It is a steep region below the default and a flat one above it.

The gas cliff

Reporting a dormant charter costs gas, and the informant takes 2% of the dormant balance capped at 100,000 tokens (§10). Below some balance the bounty does not cover the transaction. The study locates that boundary numerically for each cell rather than assuming it — for the baseline, the median ghost breaks even at a gas price of 0.0033 ETH per report.

What it found on either side is not a gradient.

Between one and two times the boundary, the wave goes from fully collected in five days to never collected at all — zero revocations, in all fifty seeds. There is no partial regime in between. A protocol whose reporting costs drift up by a factor of two does not get a slower cleanup. It gets none, and every dormant charter dilutes every active one indefinitely.

And a loop that runs backwards

Loosening the licence auction to dampen the wave makes more ghosts uncollectable, not fewer. More licences means more branches; more branches means lower yield per branch; lower yield means smaller dormant balances by day 31; smaller balances mean a 2% bounty that no longer covers gas. At 25 to 100 licences a day the model leaves nothing uncollected; at 400 and above it leaves a residue. The two unpublished parameters interact, and not in the same direction.

Where an L2 puts you

The Genesis Charter mint is announced for 14 September on Robinhood Chain. That matters here for exactly one thing. The 0.002 ETH default this study uses for a report is a mainnet figure; transaction fees on an L2 sit far below the 0.0033 ETH boundary the baseline calibrates to. At launch the profitability floor does not bind. The collected regime in the table above is the one that applies, and the dormancy mechanism should work as §10 intends.

Two caveats, because it is a cliff and not a slope. The boundary is not a property of the chain alone: it is bounty × price / margin, so a fall in the token price lowers it in ETH terms and moves a fixed fee closer to the edge. And an L2’s fee market is not fixed — congestion, a change in data-availability costs, or a sequencer fee change all move it. Our result is stated as a function of gas rather than at a point precisely so that it stays usable when that number moves.

6The soulbound switch

Charters launch soulbound, and §12 describes a one-way switch that can later make them transferable. Selling a seat then becomes a second exit path: the seat moves whole, branches and balance included, with no sell pressure on the token, and the buyer replaces the seller one for one. The switch cannot be undone, and nobody has put a number on what its timing costs or saves.

The study models it as a fourth arm, built only when a cell asks for it. With the switch thrown on day 15, on a single exemplar seed — this section is one run, not a distribution, and should be read as an illustration of the mechanism rather than an estimate of its size:

Zero revocations avoided at day 31, despite 211 seats having already changed hands. The wave is throughput-bound, not backlog-bound: the reporters are saturated for the first days regardless, so clearing a hundred charters off the queue changes nothing until they would otherwise have caught up. The benefit is entirely a later phenomenon.

By day 90 the picture is strange. 144 revocations avoided, yield per branch 48% higher — and 309 fewer branches, not more. Transferability raises the per-branch yield mostly by stopping the branch base growing, because 381 seats passed to owners who never buy another licence. The net branch figure is two opposing effects — branches saved from revocation, less branches never bought — and it must not be read alone.

A second door for capital

§2 states that there is exactly one place ETH enters or leaves this economy: through trading. §12 creates a second. A seat sale is new capital buying a claim on issuance, moving wallet to wallet, never crossing the pool — which is precisely why it carries no sell pressure, and precisely why the net flow signal in §4 never counts a wei of it.

On a separate 45-day run of the same cell and seed — a shorter horizon than the table above, so the figures are not comparable to it — the seat market moved 206.7 ETH against 748.7 ETH of sell-side pool volume the signal did see — 27.6%, and 7.9% of the pool’s own ETH reserve. In that run it pointed against the signal: the market absorbed sellers who would otherwise have pushed payouts through the pool, so the signal read less selling and the multiplier finished 0.16 higher, while a further 206.7 ETH of genuine buying interest went entirely unrecorded. This is a consequence of the switch, not a flaw in it. But the policy in §5 is built on §2 holding, and after the switch it does not.

7What we did not find

This section is not a footnote. A study that reports only what it found is not reporting what it did.

• The day-90 yield advantage is null. +1.39 tokens per branch per day, CI [−0.44, +3.17]. It includes zero.
• In 29 of 200 seeds the multiplier did not fall at all over days 31– 45. The attribution figure in section 3 is computed over the 171 where it did, and that is why its n is 171 rather than 200.
• The entire sensitivity ranking for the multiplier integral is null. No axis in the grid — not the dormancy rate, not the licence supply, not the demand regime, not the policy asymmetry — moves it by as much as one noise band. Suite A establishes that the mean effect is nonzero; nothing we varied changes it detectably.
• The per-charter licence cap does nothing. Three a day against one a day against ten a day moves supply minted by 0.0 noise bands. The daily inventory binds; the per-charter limit does not.
• Both readings of §10’s 102% ambiguity give the same answer. Whether the informant’s 2% comes out of the protocol’s fee or the banker’s share moves supply minted by 0.1 noise bands. The ambiguity is real and worth resolving in the text; it does not change what this study measures.
• The number of competing reporters does not matter. One, four or sixteen moves supply minted by 0.1 noise bands. Contention changes who pays the gas, not how many charters get collected.
• Every delta except the token totals and the branch and charter counts sits inside its own single-seed noise band. The mean effects are clear; a single run of this protocol would not let you see most of them.

8How it was done

The protocol is implemented as a deterministic model with no floating-point arithmetic in state: every token and ETH amount is an integer, and the accounting identities the whitepaper asserts hold exactly rather than to within a tolerance. One tick is one hour. Charters, branches, the constant-product pool, the licence auction, the resolution fee, the dormancy rule and the fee engine are each implemented against their section and checked against it.

Every point of the grid is a paired run. A level is not a result; the result is the difference between the same world, the same seed and the same agents making the same decisions, with exactly one rule changed:

What makes that sound is that the arms do not share a random sequence. Each agent draws from its own stream, derived from its identity and the kind of decision it is making, so a draw one arm takes and another does not shifts nothing else. Without it the arms would diverge for reasons unrelated to the rule being changed and every difference on this page would be partly noise. The test suite asserts it directly: with a cohort that never goes dormant, all four arms produce byte-identical histories.

What counts as a difference

Stated once, in one place, and applied everywhere. A cell shows a material difference on a metric when

|delta| > max( absoluteFloor(metric), 1.96 × sd_A(metric) )

— it must clear both a noise band measured from 200 seeds of the baseline cell with nothing changed at all, and an absolute floor in the metric’s own units, chosen so that a difference below it would not change any decision a reader could make. Requiring both means nothing is reported that is merely detectable, and nothing that is merely large but indistinguishable from seed noise.

Checking

102 tests. Among them a property suite that asserts, after every tick of every scenario and across randomised configurations and seeds, every identity the whitepaper states: that circulating supply equals the premint plus mints less burns; that max supply only falls; that cumulative issuance never exceeds the budget and stops permanently when it is reached; that the ledger closes to the wei; that retiring k of n branches liquidates exactly k/n; that protocol-owned liquidity never decreases; that the fee split is exhaustive; and that no balance is ever negative.

Making the grid affordable took the model from 8.4 seconds a run to 4.8 — a single-pass redistribution and an exact Barrett-reduction divide — without changing a single wei of any result. The determinism test was re-run after every optimisation. Suites A and B are 2,200 paired runs; the full grid is 41 cells and about 20 hours of core time.

Every number on this page is reproducible in one command. Clone the repository and run the command printed under any figure, or:

pnpm study replay 3b2ab0b6e0d949fd 1000000

9Six places the whitepaper had to be interpreted

None of these are objections. They are the questions that could not be left open once the rules had to run, and in each case the model implements a stated reading — and, where there are two defensible ones, implements both and reports the difference.

10What would settle it

Three questions, put as questions.

1. How long is an epoch? It sets how long the blind window in finding one lasts — half a day, or most of a week.
2. How many licences are sold a day? It scales everything in finding four, and it interacts with reporting costs in a direction that is not obvious.
3. Which of §10’s three percentages is the residual? Two per cent to the informant, seventy to the fee, and “the remaining thirty” to the banker is a hundred and two.

Publish the launch parameters and this study re-runs itself against them.