[Cryptography] A minimal PoC for ledger-free validation via graph Laplacians

[nouun]

Hi,

This is a small follow-up to the Web4 discussion.

I’ve added a minimal executable PoC that validates one structural claim
of the model: that forged imbalance injections can be rejected without
ledgers or history, using linear algebra alone.

Claim:
Valid negotiated transfers lie in the image of the incidence matrix,
while forged imbalance injections do not.

The PoC constructs a simple graph, computes its incidence matrix B,
and checks whether a proposed Δ-update can be represented as Bf
for some edge flow f.

This is an update-level formulation of the Laplacian equilibrium
condition Lx = 0 described in the whitepaper.

Whitepaper: https://ipfs.io/ipfs/bafkreifjbr6bufuwynktlhh4qkxoa2wswvoaa5jmkro3fa7oarufnlemtm
PoC code: https://github.com/munonun/Web4

The PoC is intentionally minimal and does not include networking,
P2P messaging, or cryptography.

Best,

KIM BYEONGYEON