https://docs.layeredge.io/assets/js/9d227ec4.dab21370.js

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1oin"}),"\n",(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsx)(e.li,{children:"The hash of the root proof, H(\u03c0_root), is included in a Bitcoin transaction"}),"\n",(0,a.jsx)(e.li,{children:"This creates a tamper-evident reference, using Bitcoin's robust security and immutability as a neutral settlement layer"}),"\n"]}),"\n",(0,a.jsx)(e.h2,{id:"light-node-stochastic-sampling-of-proofs",children:"Light Node Stochastic Sampling of Proofs"}),"\n",(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsx)(e.li,{children:"Let M be the total number of nodes (individual and aggregated proofs) in the proof structure"}),"\n",(0,a.jsxs)(e.li,{children:["Each Light Node stochastically selects one node and verifies its proof ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsxs)(e.mrow,{children:[(0,a.jsxs)(e.msup,{children:[(0,a.jsx)(e.mi,{children:"\u03c0"}),(0,a.jsx)(e.mi,{children:"k"})]}),(0,a.jsx)(e.mo,{children:":"}),(0,a.jsx)(e.mi,{children:"V"}),(0,a.jsx)(e.mo,{stretchy:"false",children:"("}),(0,a.jsxs)(e.msup,{children:[(0,a.jsx)(e.mi,{children:"\u03c0"}),(0,a.jsx)(e.mi,{children:"k"})]}),(0,a.jsx)(e.mo,{stretchy:"false",children:")"}),(0,a.jsx)(e.mo,{children:"="}),(0,a.jsx)(e.mi,{children:"T"}),(0,a.jsx)(e.mi,{children:"r"}),(0,a.jsx)(e.mi,{children:"u"}),(0,a.jsx)(e.mi,{children:"e"})]}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"\u03c0^k: V(\u03c0^k) = True "})]})})}),(0,a.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.8491em"}}),(0,a.jsxs)(e.span,{className:"mord",children:[(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"\u03c0"}),(0,a.jsx)(e.span,{className:"msupsub",children:(0,a.jsx)(e.span,{className:"vlist-t",children:(0,a.jsx)(e.span,{className:"vlist-r",children:(0,a.jsx)(e.span,{className:"vlist",style:{height:"0.8491em"},children:(0,a.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,a.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,a.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,a.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.03148em"},children:"k"})})]})})})})})]}),(0,a.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,a.jsx)(e.span,{className:"mrel",children:":"}),(0,a.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"1.0991em",verticalAlign:"-0.25em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.22222em"},children:"V"}),(0,a.jsx)(e.span,{className:"mopen",children:"("}),(0,a.jsxs)(e.span,{className:"mord",children:[(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"\u03c0"}),(0,a.jsx)(e.span,{className:"msupsub",children:(0,a.jsx)(e.span,{className:"vlist-t",children:(0,a.jsx)(e.span,{className:"vlist-r",children:(0,a.jsx)(e.span,{className:"vlist",style:{height:"0.8491em"},children:(0,a.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,a.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,a.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,a.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.03148em"},children:"k"})})]})})})})})]}),(0,a.jsx)(e.span,{className:"mclose",children:")"}),(0,a.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,a.jsx)(e.span,{className:"mrel",children:"="}),(0,a.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"T"}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.02778em"},children:"r"}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"u"}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"e"})]})]})]}

1)," if valid, False if invalid"]}),"\n",(0,a.jsx)(e.li,{children:"If V(\u03c0^k) = False, the Light Node broadcasts an alert, exposing any fraudulent proofs"}),"\n"]}),"\n",(0,a.jsx)(e.h2,{id:"security-through-probability",children:"Security Through Probability"}),"\n",(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsxs)(e.li,{children:["Probability a single Light Node detects a given invalid node: ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsxs)(e.mrow,{children:[(0,a.jsx)(e.mn,{children:"1"}),(0,a.jsx)(e.mi,{mathvariant:"normal",children:"/"}),(0,a.jsx)(e.mi,{children:"M"})]}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"1/M"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,a.jsx)(e.span,{className:"mord",children:"1/"}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"M"})]})})]})]}),"\n",(0,a.jsxs)(e.li,{children:["With L Light Nodes verifying independently: Probability no detection = ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsxs)(e.mrow,{children:[(0,a.jsx)(e.mo,{stretchy:"false",children:"("}),(0,a.jsx)(e.mn,{children:"1"}),(0,a.jsx)(e.mo,{children:"\u2212"}),(0,a.jsx)(e.mn,{children:"1"}),(0,a.jsx)(e.mi,{mathvariant:"normal",children:"/"}),(0,a.jsx)(e.mi,{children:"M"}),(0,a.jsxs)(e.msup,{children:[(0,a.jsx)(e.mo,{stretchy:"false",children:")"}),(0,a.jsx)(e.mi,{children:"L"})]}),(0,a.jsx)(e.mo,{children:"\u2248"}),(0,a.jsxs)(e.msup,{children:[(0,a.jsx)(e.mi,{children:"e"}),(0,a.jsxs)(e.mrow,{children:[(0,a.jsx)(e.mo,{children:"\u2212"}),(0,a.jsx)(e.mi,{children:"L"}),(0,a.jsx)(e.mi,{mathvariant:"normal",children:"/"}),(0,a.jsx)(e.mi,{children:"M"})]})]})]}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"(1 - 1/M)^L \u2248 e^{-L/M}"})]})})}),(0,a.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,a.jsx)(e.span,{className:"mopen",children:"("}),(0,a.jsx)(e.span,{className:"mord",children:"1"}),(0,a.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,a.jsx)(e.span,{className:"mbin",children:"\u2212"}),(0,a.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"1.0913em",verticalAlign:"-0.25em"}}),(0,a.jsx)(e.span,{className:"mord",children:"1/"}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"M"}),(0,a.jsxs)(e.span,{className:"mclose",children:[(0,a.jsx)(e.span,{className:"mclose",children:")"}),(0,a.jsx)(e.span,{className:"msupsub",children:(0,a.jsx)(e.span,{className:"vlist-t",children:(0,a.jsx)(e.span,{className:"vlist-r",children:(0,a.jsx)(e.span,{className:"vlist",style:{height:"0.8413em"},children:(0,a.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,a.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,a.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,a.jsx)(e.span,{className:"mord mathnormal mtight",children:"L"})})]})})})})})]}),(0,a.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,a.jsx)(e.span,{className:"mrel",children:"\u2248"}),(0,a.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.888em"}}),(0,a.jsxs)(e.span,{className:"mord",children:[(0,a.jsx)(e.span,{className:"mord mathnormal",children:"e"}),(0,a.jsx)(e.span,{className:"msupsub",children:(0,a.jsx)(e.span,{className:"vlist-t",children:(0,a.jsx)(e.span,{className:"vlist-r",children:(0,a.jsx)(e.span,{className:"vlist",style:{height:"0.888em"}

1,children:(0,a.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,a.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,a.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,a.jsxs)(e.span,{className:"mord mtight",children:[(0,a.jsx)(e.span,{className:"mord mtight",children:"\u2212"}),(0,a.jsx)(e.span,{className:"mord mathnormal mtight",children:"L"}),(0,a.jsx)(e.span,{className:"mord mtight",children:"/"}),(0,a.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.10903em"},children:"M"})]})})]})})})})})]})]})]})]})]}),"\n",(0,a.jsx)(e.li,{children:"As L increases, the chance of undetected fraud becomes negligible, ensuring a high level of security"}),"\n"]}),"\n",(0,a.jsx)(e.h2,{id:"incentivizing-light-nodes",children:"Incentivizing Light Nodes"}),"\n",(0,a.jsx)(e.p,{children:"Light Nodes provide a valuable verification service. To sustain their efforts:"}),"\n",(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsx)(e.li,{children:"LayerEdge rewards them with its own tokens"}),"\n",(0,a.jsx)(e.li,{children:"Clients of LayerEdge (BTC-L2, DA, AI, DePin, RWA) also contribute tokens as they benefit from reliable verification"}),"\n"]}),"\n",(0,a.jsx)(e.p,{children:"This creates an economic incentive for continuous, honest participation, ensuring the long-term integrity of the network."}),"\n",(0,a.jsx)(e.h2,{id:"key-advantages",children:"Key Advantages"}),"\n",(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsxs)(e.li,{children:[(0,a.jsx)(e.strong,{children:"Scalability:"})," Each Light Node verifies only one randomly chosen proof node, minimizing computational load"]}),"\n",(0,a.jsxs)(e.li,{children:[(0,a.jsx)(e.strong,{children:"Trust Minimization:"})," By relying on stochastic sampling and Bitcoin anchoring, trust in any single entity is reduced"]}),"\n",(0,a.jsxs)(e.li,{children:[(0,a.jsx)(e.strong,{children:"Economic Sustainability:"})," Token incentives ensure a long-term, stable population of verifiers"]}),"\n",(0,a.jsxs)(e.li,{children:[(0,a.jsx)(e.strong,{children:"Interoperability:"})," Compatible with multiple ZK-proof systems and various blockchain ecosystems"]}),"\n"]}),"\n",(0,a.jsx)(e.h2,{id:"conclusion",children:"Conclusion"}),"\n",(0,a.jsx)(e.p,{children:"By combining proof aggregation, Bitcoin anchoring, stochastic sampling of proofs by Light Nodes, and a robust incentive model, LayerEdge achieves a scalable, secure, and economically sustainable verification layer for large sets of ZK proofs. This design ensures broad coverage, strong security guarantees, and continuous incentive-aligned participation, fostering a trustworthy and efficient multi-chain ecosystem."})]})}function m(s={}){const{wrapper:e}={...(0,t.R)(),...s.components};return e?(0,a.jsx)(e,{...s,children:(0,a.jsx)(h,{...s})}):h(s)}},8453:(s,e,n)=>{n.d(e,{R:()=>r,x:()=>l});var i=n(6540);const a={},t=i.createContext(a);function r(s){const e=i.useContext(t);return i.useMemo((function(){return"function"==typeof s?s(e):{...e,...s}}),[e,s])}function l(s){let e;return e=s.disableParentContext?"function"==typeof s.components?s.components(a):s.components||a:r(s.components),i.createElement(t.Provider,{value:e},s.children)}}}]);