ECO/CPO-DAG: A Contradiction-Based Accountability Layer for Adversarial Supply Chains A Domain-Specific Cryptoeconomic Audit Protocol Sebastian Cochinescu University of Bucharest [email protected]
1
arXiv:2607.06804v1 [cs.CR] 7 Jul 2026
Abstract
Introduction
Supply chains are the canonical setting in which parties who do not trust one another must nonetheless rely on one another’s records. A pharmaceutical distributor must trust a carrier’s cold-chain log; an automotive OEM must trust a supplier’s provenance attestation. The economic incentive to misreport is real and well documented, and blockchain-based traceability has been proposed repeatedly as a remedy [28]. Yet recording a claim on a tamper-evident ledger [25] does not make the claim true: the “oracle problem”—that on-chain data is only as trustworthy as the off-chain process that produced it—remains unsolved [30, 31]. A ledger can guarantee that a party said something and cannot later deny it; it cannot guarantee that what the party said corresponds to physical reality. This paper takes a deliberately narrow position. We do not attempt to verify claims against ground truth. Instead we ask a weaker but tractable question:
We present ECO/CPO-DAG, a domain-specific accountability protocol for adversarial supply chains that formalizes contradiction detection as a supplemental validation layer rather than a consensus or truth-establishing mechanism. Participants publish signed Event Claim Objects (ECOs) into a causally ordered, append-only directed acyclic graph (DAG) whose edges encode happenedbefore relations. When two claims about the same subject violate a domain constraint, any observer can compile a Contradiction Proof Object (CPO)—a selfverifying object binding the two signed claims and the violated rule—which, on public verification, triggers economic slashing of a determinately blamed party. We map constraints to GS1 EPCIS 2.0 event semantics (spatial uniqueness, temporal monotonicity, quantity conservation, quality monotonicity, regulatory validity), so detection targets inconsistencies that are meaningful in practice. Selective disclosure via commitment schemes and, optionally, zero-knowledge contradiction proofs lets parties withhold claim contents until a challenge forces the minimal opening. We give an analytical treatment: an independent-observer detection model 1 − (1 − pmin )h (temporally, 1 − e−hλt ), a deterrence condition S > g(1 − p)/(kp) under k-party collusion, and a storage estimate of order 1 GB per participant per year under stated assumptions. We are explicit about the protocol’s boundary: it detects provable contradictions, not consistent lies; a party that never contradicts itself is invisible to it, so the layer complements —and does not replace—source verification and oracle aggregation. A single-machine reference implementation corroborates the detection model—the predicted coverage band overlaps the measured 95% confidence interval at every observer count—and records zero false accusations across the runs; the fully zero-knowledge CPO, multi-party propagation, and adaptive-adversary evasion remain analytical.
How can we economically disincentivize provable contradictions in semi-trusted supply chains through a domain-specific accountability layer? A provable contradiction is a pair of signed claims by identifiable parties that cannot both hold under a domain rule—for example, a lot asserted to originate in two mutually exclusive regions, or a sealed quantity that grows between two custody events. Such contradictions are self-evident: a verifier needs only the two signed claims and the rule, not access to the physical good. This is the accountability primitive that PeerReview established for distributed systems [15] and that the fault-detection literature formalized as detecting deviations from a reference specification [16]. We adapt it to the supply-chain domain and couple it to a cryptoeconomic penalty. Positioning. ECO/CPO-DAG is an audit and accountability layer, not a consensus protocol and not 1
an oracle. It is complementary to oracle aggregation (e.g. DECO’s authenticated TLS feeds [31] and adaptive conformal consensus over multiple oracles [26]), which govern how off-chain data enters the system; our layer governs post-hoc accountability once claims are on the record. It borrows the DAG data structure from recent high-throughput consensus designs (Narwhal/Tusk [10], Bullshark [29], DAG-Rider [17]) but uses the DAG only for causal ordering and detectability, not for agreement: each participant maintains a local view, and no total order is required. Constraints are aligned with GS1 EPCIS 2.0 event semantics [14] so that detection is defined over events practitioners already emit.
claim that conflicts with its own prior claims—produces no CPO and is not penalized. We regard this not as a flaw to be hidden but as the precise boundary of what contradiction-based accountability can offer. A second boundary is narrower still: on-chain slashing fires only where blame is attributable from the contradicting pair alone—self-equivocation or a single-issuer monotone violation (§5); every other contradiction yields a CPO that stands as portable evidence for off-chain adjudication, not an automatic penalty.
2
Related Work
Accountability in distributed systems. PeerReview [15] makes nodes accountable by having each keep a tamper-evident log and having others check it against a reference implementation, exposing any observable deviation. The fault-detection problem [16] formalizes which faults are detectable at all. Non-equivocation— preventing a party from telling different things to different peers—has been enforced with trusted hardware in A2M [8] and TrInc [21], and transparency logs (Certificate Transparency [20], CONIKS [23]) make equivocation over a public log detectable without trusted hardware. Accountable Universal Composability (AUC) [12] gives a composable definition of accountability. Our CPO is in this lineage: it is a portable, self-verifying witness of a specific detectable fault (a domain-rule contradiction), but we add a cryptoeconomic consequence rather than only exposure.
Contributions. 1. A formal model of contradiction-based accountability for supply chains: signed Event Claim Objects (ECOs) in a causally ordered append-only DAG, and Contradiction Proof Objects (CPOs) with stated soundness properties (§3, §4). 2. A mapping of five domain-constraint classes onto EPCIS event types, making the “domain-specific” claim concrete (§4). 3. A cryptoeconomic mechanism whose deterrence condition we derive under rational and k-partycollusion adversaries (§5).
4. A privacy layer using commitment schemes and optional zero-knowledge contradiction proofs, with an explicit disclosure taxonomy and an acknowledgment that some contradiction classes cannot be DAG-structured logs and consensus. Causal checked privately (§6). DAGs underlie modern high-throughput BFT (Nar5. An analytical security and feasibility analysis— whal/Tusk [10], Bullshark [29], DAG-Rider [17]), which detection probability, no-false-accusation, storage— raise the throughput of classical leader-based BFT [6], with every quantitative claim presented as a paand non-blockchain ledgers. We reuse the DAG for rameterized model output, together with a singlehappened-before ordering via hybrid logical clocks [19, machine reference implementation that corroborates 18] but explicitly do not run agreement over it; the the detection model against measurement and redesign goal is auditability, not a total order. ports measured costs and blame outcomes (§7–§8). Oracles. Town Crier [30] and DECO [31] authenticate data as it enters a smart contract; Ekiden [7] adds confidential execution; ACon2 [26] aggregates multiple oracle reports with statistical guarantees. These address ingestion. Our layer is downstream and orthogonal: it operates on claims already recorded and asks whether they are mutually consistent.
Scope and honesty. The paper’s core is analytical: all model numbers are outputs of the stated models under stated parameters, marked as such throughout. A single-machine reference implementation (§8.4) then corroborates the detection model against measurement and reports measured CPO costs, blame outcomes, and storage. We are explicit about what it does not cover—the fully zero-knowledge CPO, a multi-party network, and adaptive-adversary evasion remain analytical—and its commitment/ZK figures are a conservative upper bound (a MODP integer group and a naive Sigma protocol stand in for the paper’s curve-based Bulletproofs). The central limitation is intrinsic: the layer detects contradictions, so a party that lies consistently—never emitting a
Cryptoeconomics. Slashing of staked deposits for provable misbehavior is standard in proof-of-stake finality [4]; the broader study of rational adversaries and extractable value [9] motivates a game-theoretic treatment. We apply the slashing idea to provable domain contradictions rather than protocol-level equivocation. 2
Mechanism PeerReview [15] CT/CONIKS [20, 23] A2M/TrInc [8, 21] PoS slashing [4] Oracle staking This work
3
Detect Blame Slash EPCIS Priv. yes
part.
no
no
no
yes
yes
no
no
no
yes
yes
no
no
no
part. no yes
yes yes yes
yes yes yes
no no yes
no no yes
System Model
Notation. Symbols used in the analysis: κ (constraint class); h (number of honest observers/watchtowers); p, pmin (aggregate and per-observer detection probability); λ (per-observer detection rate); t (detection horizon); S (stake); α (overcollateralization factor); V (maximum single-transaction value); R (history-based risk factor); g (one-shot gain from lying); k (collusion size); D (CPO anti-spam deposit); and f (tolerated Byzantine faults among the n checkpoint participants).
Table 1: Positioning against related mechanisms. Detect=contradiction detection (PeerReview: spec deviation; CT/CONIKS, A2M/TrInc: equivocation; PoS: protocol-level equivocation only; oracle staking: no native cross-event domain-rule detection, as it aggregates independent reports; ours: domain-rule contradictions). Blame=determinate blame (ours bounded to self-equivocation and monotone violations; other contradictions yield ⊥). Slash=economic slashing. EPCIS=domain-specific supply-chain semantics. Priv.=selective-disclosure privacy.
3.1
Objects
Definition 1 (Event Claim Object). An eco is a tuple eco = ⟨id, cm, σ, τ, refs, subj⟩
where cm = Commit(claim, r) is a hiding, binding commitment to the claim payload under randomness r; subj names the subject of the claim (e.g. a GS1 lot or item identifier); τ is a hybrid logical clock timestamp; refs is the set of causal-parent eco identifiers; pk is the issuer’s public key; id = H(dsep ∥ pk ∥ cm ∥ τ ∥ refs ∥ subj) Fraud proofs. Structurally, a CPO is a domain- with a domain-separation tag dsep, so two issuers comspecific fraud proof : a portable, self-verifying witness of mitting to identical fields still mint distinct ids; and an invalid transition that triggers an economic penalty. σ = Sign(sk, id) binds the object to the issuer’s identity. This is the primitive behind optimistic-rollup fault proofs The commitment cm lets an eco be published without and the fraud/data-availability proofs of Al-Bassam, Sonrevealing its payload; the payload is opened only when nino, and Buterin [1], where a single honest party can a challenge requires it (§6). prove an invalid state transition to everyone else. We specialize that idea to GS1 EPCIS domain rules with Definition 2 (Contradiction Proof Object). A cpo is determinate blame: the fraud proved is a supply-chain- a tuple constraint violation by an identifiable issuer, not an cpo = ⟨eco1 , eco2 , κ, π, d, D⟩ invalid rollup state root. asserting that eco1 and eco2 jointly violate constraint κ ∈ {spatial, temporal, quantity, quality, regulatory}. The witness π is either the two openings of cm1 , cm2 together with a check that κ is violated, or a zero-knowledge proof of the same statement (§6). The challenger identity is Cryptographic building blocks and supply chains. d, and D is a refundable anti-spam deposit. We use Pedersen commitments [27], Merkle authentication [24], succinct proofs [13], and CL-style (Camenisch– Lysyanskaya) selective-disclosure credentials [5]. On the domain side, GS1 EPCIS 2.0 [14] supplies the event vocabulary; prior blockchain-for-supply-chain work [28] motivates the setting. Relative to that body of work, our differentiator is native contradiction detection with determinate blame and slashing, defined over EPCIS events, rather than mere immutable recording.
Definition 3 (Supply-Chain DAG). The log is a directed acyclic graph G = (V, E) with V the set of published ecos and E the causal edges induced by refs. The clock invariant is ∀(u → v) ∈ E : τ (u) < τ (v) under the hybrid-logical-clock order [18], giving a partial happenedbefore order [19]. The graph is append-only; there is no global agreement on V , and each participant holds a local view Gi ⊆ G.
Table 1 positions ECO/CPO-DAG against the closest mechanisms: prior accountability logs detect equivocation but attach no economic consequence and carry no domain semantics; staking systems slash but do not detect cross-event domain contradictions. Ours is the only one combining domain-rule contradiction detection, determinate blame, slashing, and selective-disclosure privacy.
Figure 1 illustrates the structure and a same-issuer equivocation witnessed by a CPO.
3.2
Assumptions
We separate the assumption needed to detect a contradiction from the stronger one needed to disseminate the proof reliably. 3
respond to incentives, and may additionally act Byzantine—emitting arbitrary or griefing messages—at a cost. The adversary may equivocate, backdate within clock tolerance, collude in groups of size k, and attempt to spam CPOs. The adversary cannot forge signatures or hash collisions, and cannot suppress messages indefinitely after the global stabilization time under Assumption 2.
4
Protocol Design
4.1
Emitting a claim
A party creates an eco by committing to its claim, timestamping it with the local hybrid logical clock, linking it to its causal parents, and signing the resulting identifier (Algorithm 1). Publishing the commitment rather than the plaintext is what enables selective disclosure: the object is on the record and non-repudiable, but its contents remain hidden until opened.
Figure 1: Signed claims (ECOs) form a causally ordered, append-only DAG whose edges are happened-before relations. A single issuer’s two claims about one subject (lot L) assert incompatible origins; because both carry that issuer’s valid signatures, any observer can compile a CPO—a self-verifying witness that origin(L)=EU ∧ origin(L)=NA |= ⊥. The CPO proves the contradiction unconditionally; it pins blame only Algorithm 1. CreateECO(claim, subj, refs) when §5 resolves determinate fault—here, self-equivocation 1: r ← fresh randomness by one issuer. A contradiction between two different issuers 2: cm ← Commit(claim, r) would be equally provable but need not be attributable, and 3: τ ← HLC.now() may resolve to ⊥. 4: id ← H(dsep∥pk∥cm∥τ ∥refs∥subj) 5: σ ← Sign(sk, id) 6: eco ← ⟨id, cm, σ, τ, refs, subj⟩ Assumption 1 (Detection). At least one honest ob7: Broadcast(eco); store r locally; return eco
server exists with (i) read access to the relevant samesubject ecos (every claim sharing the subject — not only the subject’s declared causal ancestors) and (ii) the ability to broadcast a cpo. Detection requires only this single honest observer; it does not require an honest majority. This is a possibility statement: a bounded-work observer samples only a fraction of candidate pairs, so its per-observer detection probability is pmin < 1 rather than certain; §7 models this and shows how coverage grows with the number of observers h.
4.2
Maintaining the DAG
Each participant appends received ecos to its local view after checking the signature and that all causal parents in refs are present and clock-consistent. There is no ordering vote: the DAG is a shared append-only substrate, and disagreement about membership is tolerated because detection needs only that one honest party sees both sides of a contradiction. Claim emission and conAssumption 2 (Propagation). The network is partially tradiction detection are therefore consensus-free: they synchronous with an eventual but unknown message de- require no agreement on V . Only the optional checkpoint lay bound [11], and a Byzantine reliable broadcast prim- pruning and CPO-finality claims of §7 invoke Byzantine itive [2] is available. For the checkpoint and finality reliable broadcast and the f < n/3 bound (Assumpclaims of §7 we assume at most f < n/3 Byzantine tion 2); a deployment that forgoes pruning and on-chain participants among the n that maintain checkpoints. finality runs the accountability layer with no BFT layer at all. Periodic checkpoints (§7) allow old history to be Assumption 3 (Cryptography). The hash H is pruned to a Merkle root [24]. collision-resistant, the signature scheme is existentially unforgeable, and the commitment Commit is computa4.3 Detecting a contradiction tionally binding and hiding [27].
3.3
On receiving a new eco, an observer indexes claims by subject and tests the new claim against same-subject claims in its local view. To bound work and resist denial of service, refs and radius limits prioritize the same-subject walk under load, and each sender is ratelimited; a candidate CPO carries a refundable deposit (Algorithm 2).
Adversary
Identities are permissioned (each participant holds a certified key) while actions are permissionless (any identity may emit any claim). We consider a hybrid adversary: rational parties maximize expected profit and 4
with h only over tiers (a), (b), and (d) — fields that are public, disclosed-by-policy, or ZK-checkable without 1: if RateExceeded(econew .issuer) then return opening. Where a constraint’s fields stay fully committed 2: A ← SubjectClaims(econew , Gi ) and undisclosed, detection is confined to the parties that 3: for ecoold ∈ A, κ ∈ Constraints do already hold the openings — typically the two counter4: if Violates(econew , ecoold , κ) then 5: D ← LockDeposit() parties to the event — and a ZK-CPO lets such a holder 6: cpo ← MakeCPO(econew , ecoold , κ, D); prove the contradiction to everyone else without revealBroadcast(cpo) ing it. Growing h therefore strengthens detection for the 7: Gi .append(econew ) public and ZK-checkable constraints; it does not conjure openings that no watchtower holds. A deployment picks, per field, how far up the detectability-vs-confidentiality Detection scope (omitted parents). Subject- curve it wants to sit. Claims is not limited to the parents an ECO declares in refs: an observer indexes every ECO in its local view 4.4 Domain constraints over EPCIS by subj and checks a new claim against same-subject claims it holds, not only the declared causal ancestors. The constraint set is where the protocol becomes domainOmitting a known parent to fork a subject into a dis- specific. Table 2 maps each constraint class to the EPconnected timeline therefore does not evade detection; CIS 2.0 event type it is checked against and the rule that two same-subject claims are comparable whether or not defines a violation. These are the predicates Violates refs links them, and a missing-but-expected link is itself evaluates. Each rule is a pairwise predicate over two evidence that can seed a temporal or spatial CPO. The same-subject events, keeping every class inside the tworefs field and the radius limit are an optimization that ECO CPO form for detection (the quality class carries orders and bounds the walk under load; they are not one further qualification for slashing, noted at the end the detection boundary. The bound is not free, however: of this section); the regulatory class in particular pairs a under sustained load an adversary can aim a contradic- compliance assertion with a revocation or expiry record tion at a causally distant same-subject pair the budgeted for the cited certificate, rather than flagging a lone missradius deprioritizes, so completeness over same-subject ing field (a single-event validity check, which sits outside pairs holds only up to the per-observer work budget — the contradiction primitive). For that pair to stay inside that residual is exactly what the sampled per-observer the DAG’s trust base, the certificate lifecycle must itself coverage pmin of §7 models, not a guarantee of exhaustive be represented as ECOs: the revocation signed by the checking. issuing authority acting as a participant, and expiry carried as a validity interval inside the signed certificate What observers can inspect. Detection needs field claim rather than read from a wall clock — otherwise values, yet payloads sit behind commitments, so Vi- the regulatory class alone would import an external olates runs over whatever disclosure tier a subject truth oracle. The temporal rule warrants a note: the exposes: (a) fields published in plaintext, such as many append-time clock check (§4) and the DAG invariant (§3) EPCIS routing fields (location, timestamp, subject id); already force monotone timestamps along every declared (b) fields the issuer selectively discloses under a stand- edge, so a temporal CPO is meaningful only among ing policy or on challenge (§6); (c) fields a watchtower same-subject events that are refs-incomparable (no path — an honest observer that monitors the DAG for con- between them) — it flags a pair whose asserted eventtradictions, in the sense of a Lightning-Network watch- times cannot be reconciled with the happened-before tower [22] — is explicitly authorized to decrypt; or (d) order (backdating), and refs-incomparable concurrent predicates checkable in zero knowledge over the com- events are never a violation. Backdating within the clock mitments (§6) without opening them. A contradiction tolerance granted in §3 is reconcilable by construction, is discoverable exactly when the fields its rule touches so the temporal class is blind up to that tolerance — the fall in one of these tiers. A subject that commits ev- tolerance is a deployment parameter trading detection erything and authorizes nothing is auditable only via sharpness against clock-synchronization strictness. Bethe ZK/disclosure paths discussed in §6 (summarized in cause temporal contradictions across issuers resolve to Table 3), and some classes (such as quality over a chain) ⊥, a spurious one is a false-CPO (spam) risk bounded by then cannot be checked at all without disclosure. This is the deposit D, not a false-slash risk. The quantity rule the concrete privacy/detection tradeoff the paper flags is read the same pairwise way: it pairs an issuer’s inputin §6. quantity claim against its own later output-quantity This resolves an apparent tension with the Detectabil- claim for the subject (the EPCIS TransformationEvent ity theorem (§7), which wants many independent watch- input/output quantity lists), so a mass-balance violation P P towers (large h) while the privacy layer wants few holders outputs > inputs is attributable to that single isof the openings. The two coexist because detection scales suer from the pair. It is deliberately not read off a single Algorithm 2. Detect(econew , Gi ) (rate-limited)
5
AggregationEvent, which in EPCIS 2.0 models reversible containment (packing cases onto a pallet, then disaggregating) where child counts are conserved by definition — there is no input-vs-output balance to violate there. The quality rule needs one qualification the closed classes do not. Detecting a candidate quality contradiction is pairwise — two of the issuer’s own condition claims, one improving on the other — but whether the improvement is illegitimate depends on the absence of an intervening authorized transformation or certification, an existential condition over the chain rather than a function of the two ECOs alone (a partial-view observer missing the authorizing event would see a violation that isn’t one). So the quality class slashes only in its closed form — a self-equivocation on condition, where the two same-issuer claims are jointly impossible regardless of any intervening event (e.g. a continuous-cold-chain assertion contradicted by that same issuer’s own excursion log). A monotone quality improvement that an unobserved authorized transformation could explain is not attributable from the pair alone and resolves to ⊥, exactly like the cross-issuer cases — never an automatic slash. This is what keeps the No-false-accusation guarantee (§7) the quality class; unlike quantity, whose P intact forP outputs > inputs check closes over the two ECOs, quality closes over the pair only in the self-equivocation form.
4.5
Challenging and adjudicating
A published cpo is verified by anyone: check both signatures, check that the openings (or the zero-knowledge proof) are valid, and check that the cited constraint is indeed violated. If verification succeeds and blame is determinate (§5), the blamed party’s stake is slashed and the deposit-backed challenger is rewarded; if verification fails, the challenger forfeits its deposit D. Figure 2 shows the end-to-end flow.
5
Cryptoeconomic Mechanism
5.1
Stake and blame
Constraint
EPCIS event
Violation rule
Spatial
ObjectEvent
Temporal
all events
Quantity
TransformationEvent (input/output quantity lists)
Quality
ObjectEvent (disposition / sensorElementList)
Regulatory
TransactionEvent
Two locations for one subject at one time Backdating: two samesubject events whose asserted times contradict their happenedbefore order (concurrent events are not a violation) P > P outputs inputs across an issuer’s own inputand output-quantity claims for the subject Two same-issuer condition claims for the subject that are jointly impossible (self-equivocation on condition). A monotone improvement without authorization is detectable but resolves to ⊥ — it is not closed over the pair (§4.4) Compliance asserted against a certificate contradicted by a revocation/expiry record
Table 2: Domain constraints mapped to GS1 EPCIS 2.0 event types [14]. A CPO cites exactly one constraint class and the two events whose pairing violates it.
time, two irreconcilable event-times, a jointly-impossible condition—e.g. a continuous-cold-chain assertion against that issuer’s own excursion log—or a compliance assertion against that same issuer’s own revocation/expiry record), blame that issuer; (ii) conservation (monotone) violation—if κ is a conservation constraint whose two claims are each individually satisfiable yet together breach the domain rule (the quantity case: an output exceeding an input the same issuer acknowledged) and the offender is attributable from the pair alone (both events on that one issuer’s self-authored chain), blame that issuer; (iii) otherwise return ⊥ (ambiguous), deferring to off-chain adjudication. A contradiction between two different issuers’ single claims, where neither self-equivocates and no party is attributable from the pair alone, is therefore always ⊥: the protocol does not guess which party lied. In particular, a quantity or quality mismatch that spans two issuers—for example, a sender’s under-reported input against a receiver’s truthful larger reading—is not automatically slashed; lacking attribution from the pair alone it resolves to ⊥, so an honest receiver is never penalized
Each participant i posts a stake Si = α Vi Ri , where Vi is the maximum single-transaction value it can assert, Ri ≥ 1 a history-based risk factor, and α > 1 an overcollateralization factor. Slashing requires determinate blame: a CPO is necessary evidence but not sufficient, because a bare contradiction may not identify which of two parties is at fault. Definition 4 (Blame). Blame(eco1 , eco2 , κ) → {eco1 .issuer, eco2 .issuer, ⊥} resolves fault by: (i) selfequivocation—if a single issuer signed both eco1 and eco2 and the two claims are jointly unsatisfiable (they cannot both be true: two locations for one subject at one 6
is neither jointly unsatisfiable nor a conservation violation — confirming that no authorization exists is a negative over a possibly-partial view — so it resolves to ⊥ (off-chain), never an automatic slash (§4.4). Crossissuer spatial, temporal, and regulatory contradictions, absent self-equivocation, likewise resolve to ⊥: surfaced as evidence for off-chain adjudication, not slashed. The enforceable core is therefore self-equivocation (including on condition) plus single-issuer quantity conservation. We state this plainly because it is arguably a larger practical limit than the consistent-liar blind spot we foreground elsewhere: much of the value lies in creating portable, self-verifying evidence (the CPO) even where on-chain slashing does not fire.
5.2 Figure 2: The accountability layer. Parties emit ECOs against staked bonds; the DAG orders them causally; observers monitor for constraint violations; a CPO challenge is publicly verified and, on determinate blame, slashes the bond. Commitments (green) let claim contents stay hidden until a challenge forces the minimal opening.
Deterrence condition
Consider a party choosing between honest reporting and lying for a one-shot gain g, where g is the gain from lying net of the honest payoff — that payoff is collected either way, so it cancels from the comparison and g is the marginal gain. If detection probability is p and the party is slashed S on detection, its expected utility from lying, relative to reporting honestly, is
for a counterparty’s under-report. A same-issuer quality improvement is likewise ⊥: it is not jointly unsatisfiable— EUlie = (1 − p) g − p S. (1) an authorized transformation could reconcile the two condition claims—and it is not a conservation violation, so Lying is deterred (EUlie < 0) exactly when it satisfies neither (i) nor (ii) (§4.4). Slashing fires only (1 − p) when blame is not ⊥. S> g. (2) p We deliberately reject a last-writer-wins heuristic (blame whichever party wrote later): it would slash For k parties who jointly falsify a single event and split an honest party whose truthful claim merely contra- one gain g/k while each stakes S, the per-party deterdicts a counterparty’s earlier falsehood, violating the rence condition becomes No-false-accusation theorem (§7). Restricting determi(1 − p) S> g. (3) nate blame to the two cases in which fault is attributable kp from the pair alone is what makes that theorem hold; all other contradictions are surfaced as ⊥-blame CPOs for Note the direction of Eq. (3): dividing a fixed gain across off-chain adjudication rather than automatic slashing. more colluders makes each one easier to deter, so this is a best-case reading that applies only to shared-gain Which classes carry economic teeth. It follows joint falsification. It does not model the more dangerthat a slash fires only on (a) self-equivocation — one is- ous collusion in which parties cover for one another and suer signing two jointly-unsatisfiable claims that cannot thereby lower the detection probability p — declining both be true; this covers spatial, temporal, same-issuer to report each other, or coordinating claims so no checkregulatory, and quality (two of that issuer’s own con- able pair ever forms — which raises the stake required dition claims that cannot both hold, e.g. a continuous- and is instead bounded by the detection assumption (a cold-chain assertion contradicted by that issuer’s own single honest observer suffices, Assumption 1) and by excursion log) — or (b) a conservation violation closed the watchtower count h in the Detectability theorem over the pair: the quantity case, one issuer’s own in- (§7). Where each colluder reaps a full gain g rather than put P claim against P its own later output claim, where a shared g/k, Eq. (2) applies per party unchanged. outputs > inputs is a self-contained arithmetic Eq. (1) carries one further assumption worth surfacing: check on two individually-consistent claims. Both are it treats +g and −S as mutually exclusive, i.e., detection the same two-ECO pairing used throughout (§4), at- reverses the gain. In a physical supply chain the fraud tributable to one issuer from the pair alone, not a single is often consummated before a CPO is compiled — the event checked in isolation. A quality improvement that counterfeit part installed, the payment cleared — so the an unobserved authorized transformation could explain liar retains g and only the stake is at risk: EUlie = g−p S, 7
h.
6
Privacy Layer
6.1
Commitment-based claims
The public part of an eco is ⟨id, τ, refs, subj, cm⟩; the payload stays private under the Pedersen commitment cm [27], whose additive homomorphism lets the aggregate of committed quantities be formed without opening them. Because P P a quantity violation is an inequality ( outputs > inputs), not an equality, checking it on committed values requires a zero-knowledge range proof over the homomorphic difference [3], not the homomorphism alone: the homomorphism yields a commitment to the difference, and the range proof certifies its sign without revealing the amounts. An honest party can therefore participate—and be held accountable—without publishing commercially sensitive volumes, prices, or routes.
Figure 3: Cryptoeconomic model outputs (not measurements). Left: the stake-to-gain ratio required for deterrence, S/g > (1 − p)/(kp), versus detection probability p for collusion size k; higher detection lowers the required stake, while larger k lowers it only under the shared-single-gain reading of Eq. (3). Collusion that instead suppresses detection moves the requirement the other way. Right: expected utility of lying from Eq. (1) for several stake multiples S={1, 3, 6}g; lying is deterred where the curve crosses below zero (red line).
6.2
Selective disclosure and ZK contradiction proofs
and deterrence needs S > g/p (per party, S > g/(kp) in the shared-gain case). At p = 0.5 that is roughly twice When a challenge requires it, a party can open exthe stake of Eq. (2). A deployment whose lies are not actly the fields the constraint touches, using CL-style clawed back on detection should size α from the retained- (Camenisch–Lysyanskaya) selective-disclosure credengain condition, which we treat as the conservative design tials [5]: reveal a timestamp while hiding quantity, or prove an aggregate without revealing components. A target. Equations (2)–(3) are the design targets for setting CPO can itself be zero-knowledge: the challenger proves α; Figure 3 plots them. We stress these are model rela- “I know openings of cm1 , cm2 under valid signatures tions under risk-neutral, one-shot assumptions; repeated such that constraint κ is violated” without revealing the play and risk aversion only strengthen deterrence, while claims, via a succinct proof [13]. For Groth16 we report reputational value of g that exceeds a single transaction only the scheme’s published asymptotics (constant-size proof, constant-time verification); we do not report gas weakens it. costs. For the quantity range proof our reference implementation (§8.4) reports measured size and prove/verify 5.3 Slashing and bounty time—but over a MODP integer group with a naive On a valid CPO with determinate blame, the blamed Sigma protocol, so those figures are a conservative upper stake is slashed and redistributed. A concrete split— bound, not the curve-based Bulletproofs a deployment challenger/detector, corroborating reporters, protocol would use. Groth16 also requires a per-circuit trusted treasury—trades off incentivizing detection against dis- setup; a deployment unwilling to run one can substitute couraging frivolous or collusive self-challenges; the de- a transparent-setup system (e.g. a Bulletproofs range posit D on each CPO bounds the cost of spam (§7). We proof for the quantity constraint [3]) at the cost of larger treat the exact split as a governance parameter rather proofs or slower verification. Table 3 gives the disclosure than a fixed constant, since its optimal value depends each constraint class forces. on the deployment’s watchtower economics. That dependence deserves emphasis: monitoring is costly (§8.4 Security Analysis measures Detect() growing super-linearly in subject 7 history) while a given contradiction pays only its first We state three properties. Each is a claim about the reporter, so detection is a public good with a free-rider model under the assumptions of §3; proofs are sketches, structure — rational watchtowers under-invest, and the and we flag where a property is only probabilistic. h that the Detectability theorem takes as given is endogenous to this bounty design. We flag it as an assumption Theorem 1 (Detectability). Let h honest observers each of the same rank as the consistent-liar boundary: the independently detect a given contradiction with probabilanalysis quantifies coverage given h; it does not derive ity at least pmin within horizon t. Then the probability 8
Conflict
Min. disclosure Privacy
Spatial Temporal Quantity
high high medium
location fields timestamps amounts (or ZK aggregate) Quality condition / sensor readings Regulatory certificate / credential (or ZK validity proof)
low medium
Table 3: Disclosure forced by each contradiction class. Some classes (quality degradation over a chain) resist private checking; we state this tradeoff rather than claiming uniform Figure 4: Detection model outputs (not measurements). privacy. Left: coverage 1 − (1 − pmin )h versus honest observers h for several per-observer detection probabilities pmin . Right: temporal detection 1 − e−hλt at λ = 0.05 hr−1 per observer. that at least one detects it is Both are consequences of Theorem 1 under the stated parameters, which we do not claim to have measured.
Pr[∃ detector] ≥ 1 − (1 − pmin )h . If detections arrive as independent Poisson processes with is never the attributable violator on a self-authored conrate at least λmin per observer, then Pr[detected by t] ≥ servation (monotone) chain (per §5), cannot be slashed, except with negligible probability. 1 − e−hλmin t . Proof sketch. By the Blame definition (§5), slashing fires only on self-equivocation or monotonic violation. Self-equivocation requires a verifying CPO whose two ECOs both carry P ’s valid signature; producing such a pair without P having signed both requires a signature forgery or a hash collision, each negligible, so (i) rules it out. Monotonic blame requires P to be attributable as the violator from the pair alone, which (ii) excludes; a cross-party monotone mismatch in which P authored only one event resolves to ⊥. The quality class is the delicate case: a monotone quality improvement is attributable from the pair alone only when the two condition claims are jointly impossible (self-equivocation on condition, covered by (i)); an improvement that an unobserved authorized transformation could explain is not closed over the pair, so a partial-view observer missing P ’s authorizing event obtains a ⊥-blame CPO, not a slash. Signature validity is not the lever here — every signature is genuine — but the Blame rule (§5) routes the existential case to ⊥, so no honest P is slashed by it. Hence no determinate-blame path assigns fault to an honest P .
Proof sketch. The events “observer j fails to detect” are independent with probability at most (1 − pmin ); their conjunction has probability at most (1 − pmin )h , and the complement is the bound. The Poisson form is the minimum of h independent exponentials with rate λmin . The independence of the h per-observer events is an assumption, not a given: observers running identical deterministic checks over identical local views are perfectly correlated (all detect or none do), which collapses the bound to a single Bernoulli trial. We obtain independence from randomized same-subject candidate-pair sampling (§8)—each observer checks an independently drawn fraction of the subject’s candidate pairs—so pmin is the per-observer coverage of one draw and the h draws are independent by construction. For a specific contradiction, moreover, an observer contributes pmin > 0 only if its local view holds both ECOs of the pair and it samples independently; an observer missing either side has pmin = 0 for that pair regardless of h. So h counts the observers that hold both ECOs and draw independent samples — not the raw observer count, and not merely the number of distinct local views. The bound scales in the number of honest observers, not in the number of adversaries—a deliberate feature: adding watchtowers strengthens detection regardless of how many parties misbehave (Figure 4).
Remark (key compromise). The theorem is stated under existential unforgeability; a compromised signing key sits outside it — an attacker holding P ’s key can self-equivocate as P and have P slashed with genuine signatures. Key custody, rotation, and post-compromise recovery belong to the permissioned identity layer (§3), not to the protocol’s guarantees, and a deployment atTheorem 2 (No false accusation). Under the crypto- taching real financial loss to a signature should treat graphic assumptions, an honest party P that (i) never them accordingly. signs two claims that are jointly unsatisfiable, and (ii) 9
Attack
Detected?
Mitigation
Overt equivoca- yes (Thm 1) slash on CPO tion Collusion (k par- shared-gain: scaled stake + ties) yes; sup- watchtowers pression: (§5) partial (§5) Adaptive evasion up to more watchtowsampled ers (h) coverage pmin (§7) Consistent lying no complementary oracle CPO spam n/a deposit D + (DoS) rate limit
8
Analytical Evaluation
This section derives feasibility figures from first principles and states every assumption; §8.4 reports measured values from a single-machine reference implementation alongside the estimates, and finds them consistent.
8.1
Storage
At 104 ECOs/day entering a participant’s local view (the subject subgraphs it retains, not only the objects it authors) and an assumed ≈ 256 B per object (identifier, commitment, signature, a bounded reference set, and timestamp), raw growth is 2.56 MB/day, or ≈ 0.93 GB/year; adding CPOs and metadata gives an Table 4: Qualitative attack posture. “Detected?” is direc- order-of-magnitude estimate of 1 GB per participant per tional, not a measured rate. Consistent lying is out of scope year. Checkpoint pruning to Merkle roots bounds the retained working set below the cumulative total. Pruning by construction. interacts with detection: a contradiction is compilable into a CPO only while both of its ECOs remain in some Theorem 3 (Censorship resistance of proofs). Under honest observer’s unpruned window, so a checkpoint partial synchrony and Byzantine reliable broadcast with must retain a per-subject digest sufficient to seed a CPO f < n/3, every valid CPO broadcast by an honest node is — otherwise a contradiction against a pruned-away claim delivered to all honest nodes after the global stabilization is no longer actionable, and detection is complete only time and is included in the next checkpoint, except with within the unpruned horizon. The deterrence condition inherits this: the p in Eq. (2) is the coverage achieved negligible probability. within the retention horizon, not an asymptotic value, Proof sketch. Delivery is the agreement and validity and keeping a contradiction actionable across a checkproperty of Bracha’s reliable broadcast [2] under f < point requires the digest to retain enough of the opening n/3; inclusion follows because checkpoints commit to all to seed a CPO — a storage cost that partially offsets delivered CPOs, and honest nodes constitute a super- pruning. The per-object size and reference-count assumptions are stated so the estimate can be recomputed; the majority. reference implementation measures 211.9 B/object over ∼2560 objects—slightly below the 256 B assumption— This theorem is where the design admits a bounded de- recomputing it from the actual reference-set distribution pendence on agreement, and we scope it precisely: there (§8.4). is no consensus on the event DAG itself (§4) — emission and detection need none — but finality and pruning 8.2 Detection coverage assume a lightweight BFT checkpoint layer among the n checkpoint participants, i.e. periodic agreement on Coverage follows Theorem 1: it is a function of (pmin , h, t) a Merkle root of delivered CPOs under f < n/3. We only. As an illustration of the tradeoff, lowering the assume rather than construct that layer; any standard same-subject candidate-pair sampling fraction reduces BFT agreement (e.g. PBFT [6]) instantiates it. A deploy- per-object work and storage but lowers pmin , moving a ment that forgoes on-chain finality and pruning drops deployment down the curves of Figure 4. We deliberately this theorem and runs with no agreement at all, keeping do not tabulate “99.99%” detection figures as if observed; the honest statement is that coverage is whatever the detection and portable CPO evidence intact. chosen (pmin , h, t) yield. The reference implementation measures this directly and the model holds: with a Attack surface. Table 4 summarizes the qualitative measured p̂min ≈ 0.50, the predicted 1 − (1 − p̂min )h posture. We give directional detectability—not numeric band overlaps the measured 95% confidence interval at per-attack rates; the one quantitative statement is the every observer count (§8.4). model of Theorem 1, which our reference implementation corroborates against measurement (§8.4). The row that 8.3 Economic viability matters most is the last: a party lying consistently emits no contradiction, so the layer’s detection is none, and For a transaction value Vi and α ≈ 1.5, the stake is only a complementary oracle can catch it. ≈ 1.5 Vi ; its carrying cost is the stake times the cost of 10
capital. Deterrence holds whenever Eq. (2) is satisfied for the deployment’s (p, g), which for moderate detection (p ≳ 0.5) needs S ≳ g — or S ≳ 2g under the retainedgain reading of §5, the conservative target where fraud is consummated before detection. The α ≈ 1.5 illustration therefore assumes the gain from lying is of the same order as the transaction value (g ≈ V ); where a single lie captures downstream, market, or reputational value with g > V (§5), α must be sized from the g/V ratio so that S = αV R still exceeds (1−p) g — it is not a fixed Figure 5: Measured detection coverage vs. the Theorem 1 p ≈ 1.5. Small suppliers for whom S is prohibitive can model (reference implementation, §8.4). Left: measured coverage (black, 95% CI) against honest watchtowers h overpool stake, at the cost of shared slashing risk. h
8.4
Measured reference evaluation
To check the model rather than merely assert it, we built a single-machine reference implementation (Python; Ed25519 signatures, prime-order Pedersen commitments, a zero-knowledge range proof over the homomorphic difference, the five Violates predicates, the Blame resolver of §5, and an N -participant / h-watchtower simulation with independent-seed candidate-pair sampling). Every number below is reproducible from a fixed seed by one command, and the code plus labelled synthetic traces are released (see Reproducibility). It is a reference, not a production build: commitments and the ZK proof run over a 2048-bit MODP integer group with a naive Sigma protocol rather than the paper’s curve-based Bulletproofs, so the ZK size/time figures are a conservative upper bound; hashing is BLAKE2b in place of BLAKE3; and all traces are synthetic with recorded generator parameters.
laid on the model band 1 − (1 − p̂min ) from the measured single-observer p̂min = 0.501; the measurement tracks the band at every h. Right: measured coverage vs. the samesubject candidate-pair sampling fraction at h = 4, showing the work/coverage trade-off the sampling knob controls. Unlike Figure 4, these are measurements, not model outputs.
No false accusation, measured. Across the runs, zero honest parties were slashed; precision was 1.000 (280/280 produced CPOs were true contradictions, no false positives); and a zero-injection control over 600 honest events produced 0 CPOs. Determinate blame broke down as 52 self-equivocation slashes, 7 conservation (quantity) slashes, and 11 ⊥ resolutions routed to offchain adjudication—exercising both slashable branches of §5 and the honest-receiver ⊥ case, with no honest party caught. Precision 1.000 is partly by construction — a verifying CPO is a true contradiction absent implementation bugs — so the informative outcome here is the Blame routing itself: the 11 cross-party cases went to ⊥, not to a slash, and no honest party was ever charged.
Detection: the model is confirmed. We measure single-observer, single-draw coverage directly as p̂min = 0.501 (Wilson 95% CI [0.465, 0.537], n = 736). Costs. Plaintext CPO generation is ≈ 1.5 µs and verPredicting 1 − (1 − p̂min )h from that number alone and ification ≈ 1.1 ms (median, per constraint class). The independently measuring multi-observer coverage, the watchtower Detect() cost per incoming ECO grows predicted band overlaps the measured Wilson CI at every super-linearly with a subject’s history (2.7 µs at history observer count h ∈ {1, 2, 3, 4, 6, 8}—e.g. h = 3 measured 1 to ≈ 3.0 ms at history 100), which is exactly the un0.861 [0.835, 0.885] vs. predicted 0.876 [0.847, 0.901], bounded baseline the radius limit and candidate-pair and h = 8 measured 1.000 [0.995, 1.000] vs. pre- sampling exist to bound. The quantity ZK range proof dicted 0.996 [0.993, 0.998]. The Detectability theorem’s (conservative MODP/Sigma bound) is 28.7 KB with independent-sampling model is thus empirically corrob- ≈ 2.1 s prove and verify at a 16-bit range. orated, not merely assumed; the prediction is not a fit, since p̂min comes from a single-draw measurement and the multi-observer points are a separate one. One caveat keeps the claim honest: the harness constructs Reproducibility. The implementation, its tests, a the independence the theorem assumes (each watch- one-command reproduction (scripts/reproduce.py tower samples with an independently seeded draw), so –seed 0), the raw CSVs, and the generated results live the measurement corroborates the composition law given in the companion repository, archived at 10.5281/zenindependence — it is not field evidence that deployed odo.21114383; the labelled synthetic EPCIS trace set is watchtowers achieve independent coverage. Figure 5 released as a separate citable benchmark at 10.5281/zenoverlays the measurement on the model band. odo.21114601. 11
Scenario
CPO? Blame
Slash?
Limitation
Impact
Falsified shipping record Cold-chain excursion (transporter’s own readings conflict) Counterfeit part (selfinconsistent records) IoT sensor drift Coordinated delay Consistent lie below threshold
yes
issuer (equiv.) transporter (self-equiv.)
yes
misses consistent lies some CPOs undecidable ∼1 GB/yr/party
yes
supplier (self-equiv.)
yes
No ground truth Blame ambiguity Storage growth Pruning vs. detection
no
—
no
yes
ambiguous
no
—
if determinate no
yes
Mitigation
pair with oracles off-chain adjudication checkpoint pruning contradictions retain peragainst pruned subject digests claims unprov- past checkable points pmin calibra- affects coverage watchtower intion centives Stake barrier excludes small stake pooling firms Legal enforce- slash ̸= judg- governance ment ment overlay
yes
Table 6: Limitations and mitigations. None is claimed to be eliminated; each is bounded.
Table 5: Illustrative scenarios traced through detection, blame, and slashing. Coordinated silent deception and consistent lying are the designed-in blind spots. Residual limitations.
Table 6 lists the main ones with mitigations. Blame ambiguity means some real contradictions cannot be adjudicated on-chain; storage 9 Illustrative Scenarios grows without pruning; pmin is a modeling parameter whose real value depends on watchtower participation; Table 5 traces six scenarios through the protocol. They and legal enforceability of a slash sits outside the protoare walked-through illustrations of the mechanism’s col. reach and limits, not experiments. The final two rows are the honest cases: an ambiguous timing dispute that yields a CPO but no determinate blame, and a below- Future directions. Natural extensions include comthreshold consistent lie that produces no contradiction bining the layer with an authenticated-feed oracle to at all. close the consistent-lie gap; learning-based prioritization of which same-subject candidate pairs to check under a fixed sampling budget; cross-domain interoperability 10 Limitations and Discussion across multiple EPCIS deployments; and a governance model for adjudicating ⊥-blame CPOs. The oracle boundary, restated. The protocol detects provable contradictions, which is strictly weaker than verifying truth. A party that is internally consis11 Conclusion tent and lies about the physical world—a supplier whose every record agrees with every other yet all describe a ECO/CPO-DAG formalizes contradiction detection as fiction—emits no CPO. This is not an implementation a supplemental accountability layer for adversarial supgap but the definition of the primitive. It is exactly ply chains. Signed claims in a causally ordered DAG, why we position the layer as complementary to oracle self-verifying contradiction proofs, determinate-blame aggregation [31, 26]: those govern ingestion and can, in slashing, and commitment-based selective disclosure toprinciple, catch consistent lies at the point of entry; ours gether let any observer convert a provable inconsistency governs accountability once claims are on the record. into an economic penalty, without consensus and without revealing more than the contradiction requires. We have Comparison to oracle staking. Chainlink-style ora- been deliberate about scope: the layer does not solve the cle networks aggregate independent reports and can slash oracle problem, it cannot catch a consistent liar, and evnode operators for availability or performance faults, but ery quantitative statement here is a model output rather they do not natively detect causal contradictions across than a measurement. Within those bounds, it adds a events in a domain-specific log. Our contribution is concrete, cryptographically and economically grounded that downstream detection layer, not a replacement for audit primitive that complements existing ingestion-time aggregation. defenses. 12
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