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Proof PeaksISSUE #38 of 38

finality · probabilistic vs absolute

ZeekaVSThe Collision
Zeeka saysProbabilistic finality (Bitcoin) means reversal probability decays exponentially with confirmations; absolute finality (Tendermint, FFG-finalized eth) means a finalized block is mathematically irreversible without slashing 1/3 of stake.

The two finality models trade off in opposite directions. Probabilistic finality (Bitcoin) never declares a block "final" — it lets reversal probability decay as (q/p)^N with confirmations. The chain never halts, but settlement is statistical. Absolute finality (Tendermint, FFG-finalized eth) declares a block irreversible the moment a 2/3 supermajority signs. Reversal then requires demonstrably byzantine behavior worth 1/3 of stake getting slashed.

Each model has a real cost. Probabilistic finality has no liveness halt — even if the network partitions, both halves keep mining. Absolute-finality systems halt if more than 1/3 of stake goes offline (no supermajority possible), trading liveness for crisp settlement. Bridges, exchanges, and rollups choose between them based on whether they value uptime or speed of irrevocable settlement.

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The Collision attacks — common mistakes

Boss battleTabulate Bitcoin reversal probability for 1–6 confirmations at 10% attacker hashrate and compare to absolute-finality reversal cost.

Example code

<!doctype html><html><head><meta charset="utf-8"></head>
<body style="background:#06040d;color:#e6e0ff;font-family:monospace;padding:20px"><pre id="o"></pre>
<script>
// probabilistic (Bitcoin): P(reversal) = (q/p)^N for q < p.  absolute: P=0 once finalized.
const q = 0.10;
const rows = [];
for(let N = 1; N <= 6; N++) rows.push('  ' + N + ' confirmations → ' + (Math.pow(q/(1-q), N)*100).toFixed(4) + '%');
document.getElementById('o').textContent = [
  'BITCOIN (probabilistic, attacker q = 10%):',
  ...rows,
  '  reversal probability never reaches 0, just gets vanishingly small',
  '',
  'TENDERMINT / FFG (absolute):',
  '  once 2/3 sign → block is irreversible',
  '  reversal requires ≥ 1/3 of stake getting slashed (provable byzantine fault)',
  '  trade-off: faster economic finality, but liveness halts if 1/3 offline'
].join('\n');
</script></body></html>
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