AI-Driven Coalition-Proof Attestation for Cross-Chain Messaging Systems - Part 2

The CORE Pipeline

In Part 1 we showed why a forged cross-chain message is unprofitable when the cost of corruption (stake at risk, reputation at risk, and chance of being caught) dominates the value at risk. Part 2 turns that idea into a working system that a protocol can run on a schedule: it sets stakes, fees, and watcher bounties; it proves (with finite-sample guarantees) that collusion isn’t worth it; and it publishes a certificate the community can verify.

We’ll refer to the end-to-end procedure described in this blog as the CORE pipeline—Coalition Optimization under Robust Elicitation.

1) The target we enforce (the one inequality that matters)

Everything the CORE pipeline does serves this single statement:

What’s inside.

• $S_i$: slashable stake of operator $i$.
• $R_i$: “franchise value”—the net present value of honest future fees operator $i$ forfeits if caught.
• $c_i$: any internal cost to misbehave (legal, operational, reputational outside the protocol).
• $q$: detection probability (watchers/challengers actually catch and slash).
• $p_i(\Sigma)$: “if I collude, what’s the chance the rest do too?”—the conditional coalition success, which rises with correlation $\Sigma$.
• $V$: value at risk of the message/route.
• $\mathcal C$: minimal collusion sets (LayerZero: ${O,R}$; CCIP: any $t$ of $m$; Across: the relayer).
• $\mathcal U$: the set of “plausible bad days” we prepare for.
• $M^*$: explicit headroom (your safety margin).

Plain English Explanation. The left side is the cheapest success-contingent bribe an attacker must pay, given how correlated operators are that day. We demand this adjusted cost be bigger than the prize $V$ by at least $M^*$, not just on average, but across all plausible worlds.

2) The CORE pipeline at a glance

The pipeline runs in four tightly-coupled phases:

1. Scenario Generation (robust elicitation). Build $\mathcal U$ from data so it includes streaks, fat tails, and correlation spikes—without assuming nice distributions.

2. Robust Feasibility. For each scenario, compute the cheapest coalition and check (R⋆). If any scenario fails, move to the next phase.

3. Parameter Optimization. Raise the cheapest knobs (stake, fees/reputation, bounty/detection) under governance guardrails until all scenarios satisfy (R⋆), with a provable safety margin.

4. Statistical Certification. Use scenario-optimization bounds to turn “we passed N scenarios” into a public, finite-sample guarantee on real-world failure probability. Publish a certificate anyone can recreate from a seed.

We’ll now walk through each phase in detail.

3) Phase 1 — Building “plausible worlds” without wishful thinking

We assemble $\mathcal U$ so it captures three realities of production systems: streakiness, fat tails, and correlation spikes.

Temporal streaks (block bootstrap). Markets and infra fail in runs, not coin flips. We resample blocks of recent days rather than individual points so congestion and outage patterns survive the shuffle. A good default is the automatic block length rule (ABL), which picks a 1–2 week block that preserves long-run variance for common time-series.

Fat tails (peaks-over-threshold EVT). Rare, huge shocks matter disproportionately. We fit a Generalized Pareto to excesses above a data-driven threshold (chosen via a mean-residual-life plot), then inject a fixed share of scenarios from this tail. A quick QQ-plot sanity check keeps the fit honest.

Correlation stress (but stay positive-definite). “Everything fails together” is a regime, not a myth. We push a baseline correlation matrix $\Sigma$ toward a stressed matrix $\Sigma_{\max}$ along the SPD geodesic:

then renormalize diagonals to 1. This path preserves symmetry and positive-definiteness.

Why this is conservative. We are practicing robust optimization: engineer for the worst plausible realization of uncertain inputs. The pipeline deliberately constructs lower bounds (more on $q$ and $R$ in Phase 3) and higher correlations so feasibility today implies feasibility when models are slightly wrong tomorrow.

Plain English Explanation. We fabricate thousands of “hard tomorrows” that look like the nastiest parts of yesterday, then make some of them even nastier in size and synchronicity. Those are the worlds we must pass.

4) Phase 2 — The hard quantity $p_i(\Sigma)$ and the weakest coalition

The term $p_i(\Sigma)=\Pr(\text{others collude}\mid i\text{ does})$ is where correlation bites.

LayerZero (split). Give the Oracle and Relayer high-side acceptance propensities $\theta_O,\theta_R$ (from history). Under correlation $\rho$, a Gaussian copula yields

and similarly for $p_R$. Evaluate at the scenario’s stressed $\rho$.

CCIP (quorum). Model validators as exchangeable Bernoulli with intraclass correlation $\rho_g$ (Beta–Binomial). Positive $\rho_g$ fattens the “many vote yes together” tail. We compute the conditional terms under $\rho_{g,\max}$ for the scenario.

Across (optimistic). One actor suffices; set $p=1$.

Given $p_i$ in a scenario, define each operator’s weight

• Split: sum the two weights.
• Quorum: sum the $t$ smallest weights (partial sort, no combinatorial blow-up).
• Composed routes: build a layered “trust graph” with these weights; if an attacker must corrupt all stages, take a min-cut; if any stage suffices, take the smallest stage sum.

That coalition is the active weak point for that scenario.

Plain English Explanation. Assign every operator a “price tag” that gets cheaper when correlation is high. Then pick the cheapest shopping list that could forge the message in that world.

5) Phase 3 — If (R⋆) fails, how do we fix it cheaply?

Suppose some scenario violates (R⋆). We now raise the cheapest knobs—stake, fees (reputation), and bounty (detection)—under governance guardrails.

Two levers are modeled conservatively as lower-bound envelopes (again, robust optimization by construction):

• Detection from bounty $b$. If watchers arrive according to a Poisson rate $\lambda(b)$ and each detects independently with probability $q_d$ in window $T$, then

  \[\underline q(b)=1-\exp\{-q_d\,\lambda(b)\,T\}\]

  lower-bounds real detection. For the solver we use a piecewise-linear lower envelope of $\underline q$ so constraints stay convex.

• Reputation from fees $F_i$. Let

  \[\underline R_i(F_i)=\eta_i\sum_{t=0}^{T_i}\delta_i^t F_i\]

  with $0<\eta_i\le 1$ a safety factor and $\delta_i$ a discount. This is intentionally smaller than optimistic NPV—again, feasibility underestimates are safer than overestimates.

We then solve a small linear program:

We don’t constrain against all coalitions; we add the currently tight ones (cutting-plane style), re-run the oracle, and iterate. In practice, two or three rounds converge.

Plain English Explanation. Turn the cheapest knobs just enough to get back above the safety line, but never faster than governance allows.

6) Phase 4 — A guarantee you can put your name on

It’s not enough to say “we passed the scenarios.” We want a finite-sample, distribution-free statement of the form:

“With confidence $1-\beta$, the probability that a random future day violates (R⋆) is at most $\alpha$.”

The scenario approach gives this. If you adjusted $d$ effective degrees of freedom (e.g., how many stakes you allowed to move, plus bounty and fee buckets), then choosing

random scenarios and finding a feasible solution implies the bound above. For example, with $d\approx 11$, $\alpha=1\%$, $\beta=5\%$, $N\approx 1030$—small enough to run hourly.

We publish a certificate so others can reproduce the claim from a public seed:

{
  "core_version": "1.0.0",
  "timestamp": "2025-09-18T12:00:00Z",
  "seed": "0x5b3f...e12a",
  "alpha": 0.01,
  "beta": 0.05,
  "N": 1031,
  "dof": 11,
  "margin_target": "1_000_000",
  "achieved_worst_case_margin": "1_084_213",
  "tight_scenarios_hash": "0x3ac9...77cd",
  "param_deltas": {
    "stake_deltas": {"O": 300000, "R": 450000},
    "bounty_delta": 15000,
    "fee_deltas": {"O": 0, "R": 0}
  }
}

Plain English Explanation. Passing $N$ stressful tomorrows lets us quantify how unlikely a failure is tomorrow. This guarantee is powerful, but not magic: it assumes the future is drawn from the same broad process as the past we sampled. That is why we continuously monitor drift and lift the tails and correlations in Phase 1—to defend against “unknown unknowns.”

7) Worked examples you can sanity-check

LayerZero (split). Target margin \(M^\*=\$1.0\)M. Conservative detection $\underline q=0.6$. Reputation \(\underline R_O=\$3.0\)M, \(\underline R_R=\$2.5\)M. Scenario stress yields $p_O=p_R=0.85$. Worst $V=6.0$M.

The condition becomes

With a per-party stake-increase cap of 0.4M/day, two days of adjustments suffice. Alternatively, raising $\underline q$ from 0.6 to 0.7 reduces the required stake by about 20%—sometimes cheaper if bounty dollars are inexpensive.

CCIP (quorum $m=5,t=3$). Stressed per-operator weights (already correlation-inflated) are $[2.75,2.38,2.00,1.50,1.25]$M. The cheapest three sum to $4.75$M, but you need $V+M^*=10$M, so a deficit of $5.25$M. With $\underline q=0.5$ and 1.25x inflation, each 1M of extra stake on a “cheap” validator adds 0.625M to its term; you need about 8.4M spread across the three—unless boosting detection is cheaper under your cost weights, in which case the solver will trade stake for bounty.

8) Backtests, tripwires, and continuous improvement

We replay the past out-of-sample and measure violations of $\text{CoC}-V<M^*$ under the parameters the CORE pipeline would have chosen then. A Kupiec test checks violation frequency ($\approx \alpha$); a Christoffersen test checks independence (no clustering). We watch for drift in the bounty→detection curve and in VaR tails; drift triggers prompt temporary tail-lifting and margin bumps while models retrain. Finally, we regularly inject known exploit patterns into the “digital twin” to ensure the coalition oracle still surfaces the true weak set.

9) What each dollar buys (and when)

Near your current settings, the local “bang per buck” looks like:

• +1 stake on operator $i$ adds roughly $\underline q/p_i$ dollars of CoC.
• +$\Delta q$ detection adds $\Delta q\cdot \sum_{i\in C} S_i/p_i$ to the active coalition’s CoC.
• +$1 of reputation-effective fee for operator $i$ adds $\big(\eta_i\sum_t \delta_i^t\big)/p_i$.

When correlation spikes, $p_i\uparrow$ and stake buys less; in those regimes, detection or reputation are often more capital-efficient. The optimizer makes this trade-off explicit under your cost weights $(\lambda_S,\lambda_F,\lambda_b)$.

10) How this plugs into a protocol (compute off-chain, verify on-chain)

On-chain should stay small, auditable, and gas-light:

• SecurityOracle stores the latest certificate (seed, $\alpha,\beta,N,d$, achieved margin) and emits events.
• ParamGovernor accepts signed deltas (EIP-712) from the off-chain solver, enforces rate limits/timelocks/org caps, and writes updates.
• BountyPool escrows and pays watcher bounties per the chosen schedule.

The heavy lifting—scenario generation, coalition oracle, convex optimization—runs off-chain. This follows the “compute off-chain, verify on-chain” principle that keeps systems both sophisticated and usable.

11) Pseudocode (end-to-end)

INPUT: current S, F, b; safety margin M*; guardrails G;
       scenario seed & knobs; cost weights (λS, λF, λb)

1:  Build scenarios {(Σ^(k), V^(k))}_{k=1..N} with block bootstrap + EVT + correlation stress
2:  For each k: compute p_i^(k)   // via copula/Beta–Binomial or digital twin
3:  W := ∅   // active constraints
4:  repeat
5:      Solve LP: minimize λS||ΔS||_1 + λF||ΔF||_1 + λb|Δb|, s.t. G and constraints in W
6:      new_constraint := false
7:      For each scenario k:
8:          C_k := cheapest_coalition(S+ΔS, F+ΔF, b+Δb, p^(k), V^(k))
9:          if CoC(C_k) < V^(k) + M*:
10:             add inequality for (k, C_k) to W; new_constraint := true
11:     until new_constraint == false
12: Publish certificate (seed, α, β, N, d, worst-case margin, deltas)
13: Submit signed deltas to ParamGovernor; enforce guardrails & timelocks

12) Quick FAQ (myths and answers)

“More validators automatically means more security.” Not if they share risks. Positive correlation makes the cheapest $t$ very cheap. Diversity, caps, and randomized selection matter as much as count.

“Just crank the stake.” Stake shines when $p_i$ is modest. Under high correlation $p_i\to 1$, detection and reputation often buy more CoC per dollar.

“Averages are fine.” The damage lives in tails and sync failures. That’s why we explicitly lift tails and stress $\Sigma$.

“Why not do all this math on-chain?” On-chain must be minimal, verifiable, and gas-efficient. Scenario generation and convex optimization are heavy and data-hungry; they belong off-chain. We adopt “compute off-chain, verify on-chain”: publish seeds, bounds, and deltas; let anyone recompute and challenge.

13) Conclusions

The CORE pipeline is deliberately robust: it uses lower-bound envelopes for detection and reputation, it fattens tails, and it stresses correlations along valid SPD paths. In robust optimization, this is the point—feasibility against the worst plausible inputs buys you safety when models are slightly wrong.

And we don’t just say “trust us.” We (i) fabricate stressful but realistic worlds, (ii) find the true weakest coalition in each, (iii) raise the cheapest knobs under guardrails until every world clears margin $M^*$, and (iv) ship a certificate with a finite-sample guarantee that anyone can regenerate from a seed.

If Part 1 was “why the inequality is right,” Part 2—the CORE pipeline—is “how you keep it true, every day, with receipts.”