Indexing the archive…
Your Universe of Digital Possibilities
Strangers who trust nobody keep one ledger by racing to solve a lottery. A liar with less than half the hashing power can rewrite history, but the odds of catching up fall exponentially with every block. Count the blocks, and come back to the net that had no centre.
The attacker’s progress over the z confirmations taken as Poisson at the average pace, then the gambler’s ruin from wherever he is. 0.0009137 at q = 0.1, z = 5 — The Chain’s engine rebuilds the whole printed table. Run as an exact Poisson race the count is negative-binomial, and Rosenfeld’s form gives 0.00178 there.
A random walk that steps toward the attacker with chance q and away with chance p ever closes a gap of z with probability (q/p)z — the gambler’s ruin. Below half the hash power the odds fall exponentially with every block; at half or above the attacker always catches up.
A pool of share α, winning γ of the honest miners in a tie, earns more than its share by withholding blocks inside this range: above ⅓ when ties go against it, ¼ when they split, any size when they all go its way. The Chain simulates the state machine and lands on the revenue formula to the third decimal.
After a strike, the share of surviving station pairs that can still reach each other: ck are the sizes of the surviving components, ns the survivors. Baran’s own criterion is its cousin — the share of survivors still in the largest group. Both are counted by breadth-first search, which no station can run.
The Packet began the edition with Baran’s question — can a net with no centre survive the loss of most of its nodes? — and The Chain ends it with Nakamoto’s: can strangers with no owner keep one ledger? The answer is the same shape: count, do not trust. The Generals counted a third; the miners count blocks, and the liar’s odds fall like a gambler’s ruin. And the ledger rides the very net Baran drew — The Packet’s sweep, re-run on the miners, is the last curve on the rack. Where the money goes once it is kept is The Ledger’s story.