Fractal Dimension of Value: Lightning Network as Percolation
The Lightning Network introduces a fractal structure to the BTF (Bitcoin Topological Fabric):
Lemma 10.1 (Channel Graph Percolation).
Payment channels form a percolation network. At critical liquidity density, a giant connected component emerges—a spanning cluster where any two nodes can transact off-chain.
The fractal dimension of this network determines routing efficiency. Below the percolation threshold, the network fragments into isolated islands.
The "Homorupt" phase at 100% velocity now has a deeper interpretation: it's the percolation phase transition where the Lightning network achieves ∞ connectivity—every economic agent is reachable via off-chain paths, hence value flows become instantaneous and frictionless, approaching the hyperbolic limit.
https://beyondturbulence.blogspot.com/p/extended-framework-puncture-operator-as.html?m=1
tj2025 / Coach Taj
npub182…ug5wd
2025-12-07 18:35:02 UTC
Author Public Key
npub182vscmeh2w5tjnjwsnl53230dq5ggd2chur225hqs0drh52apx3qeug5wdPublished at
2025-12-07 18:35:02 UTCEvent JSON
{
"id": "729d97a4102200b5e96594a530d7496a6b75ea7bd8e1d9cb9e0ebcc74c657def",
"pubkey": "3a990c6f3753a8b94e4e84ff48aa2f6828843558bf06a552e083da3bd15d09a2",
"created_at": 1765132502,
"kind": 1,
"tags": [
[
"r",
"https://beyondturbulence.blogspot.com/p/extended-framework-puncture-operator-as.html?m=1"
]
],
"content": "Fractal Dimension of Value: Lightning Network as Percolation\n\nThe Lightning Network introduces a fractal structure to the BTF (Bitcoin Topological Fabric):\n\nLemma 10.1 (Channel Graph Percolation). \n\nPayment channels form a percolation network. At critical liquidity density, a giant connected component emerges—a spanning cluster where any two nodes can transact off-chain.\n\nThe fractal dimension of this network determines routing efficiency. Below the percolation threshold, the network fragments into isolated islands.\n\nThe \"Homorupt\" phase at 100% velocity now has a deeper interpretation: it's the percolation phase transition where the Lightning network achieves ∞ connectivity—every economic agent is reachable via off-chain paths, hence value flows become instantaneous and frictionless, approaching the hyperbolic limit. \n\nhttps://beyondturbulence.blogspot.com/p/extended-framework-puncture-operator-as.html?m=1",
"sig": "203eb21a161008a2fd6f393a67a347222422ac6abf0822dba1fedd2655b870bda2551f9d6f3f11a0f81dc0f45e54934376efc521e616a2f4b19b8012335d393f"
}