Sustained Participation as a Security Resource: The Bounded Participation Channel

1. Introduction

• Existing defenses often price admission rather than continued participation, leaving no guaranteed recurring cost for sustaining admitted identities.CAPTCHAs are one-shot; Proof-of-Personhood systems, raise ceremony costs but do not continuously price participation.Source: §1 · pp. 1–2
• BPC produces an independently re-established, verifiable participation bit for each identity and window, rather than accumulating participation into a score or reputation.Higher-level systems may interpret the time-indexed proofs for their own purposes.Source: §1 · p. 2
• BPC’s four properties—identity binding, freshness, real-time response, and bounded per-channel throughput—prevent solutions from being shared across identities, replayed across windows, or produced beyond channel capacity.The guarantee depends on channel throughput, not on humans outperforming machines.Source: §1 · p. 2
• Across 600 trials with GPT-4o, Gemini 2.5 Flash, and Claude Sonnet 4.5, near-perfect perceptual-task success did not remove the evaluated channels’ throughput bound.The paper reports that solvability does not imply unlimited throughput.Source: §1 · p. 2
• The paper specifies BPC as an Event/Claim/Proof pattern with Prove and Verify operations, then gives a hash-based realization and four admissible challenge families.The construction supports publicly verifiable participation proofs under standard cryptographic assumptions.Source: §1 · p. 2
• Under Assumption 1, the properties force C(s, T) = Ω(sT), exporting participation as time-indexed proofs rather than an accumulated score.The cost theorem requires the channel-capacity assumption in addition to the other properties.Source: §1 · p. 2

2. Related Work

• Graph-based defenses constrain adversarial identity counts, while CAPTCHAs and Proof-of-Personhood, price admission; none guarantees per-identity recurring cost over time.CAPTCHA’s perceptual gap is eroding –, and token-binding extensions do not supply fresh per-window challenges or a composable cost theorem.Source: §2 · pp. 2–3
• Behavioral authentication is continuous but passive, lacks identity-specific time-bound challenges, and provides no exportable, verifiable per-window proof.Its output is an internal risk score consumed by a provider.Source: §2 · p. 3
• Trusted hardware can instantiate channel serialization, but BPC also allows software-only enforcement; storage-time proofs concern one prover and file, not many identities under a joint channel ceiling.Resource-based mechanisms such as Proof-of-Work and Proof-of-Stake are parallelizable, and their economic cost over time depends on separate assumptions [12].Source: §2 · p. 3
• Signatures, timestamps, and VRFs do not alone enforce the real-time channel-throughput constraint: offline computations can be produced at leisure or batch-evaluated.Remote attestation can support properties of BPC but does not itself formalize multi-identity throughput cost.Source: §2 · p. 4
• BPC combines persistence, per-identity rate-limiting, solver-agnosticism, and joint cost scaling, exporting a public per-window proof with a C(s, T) ≥ sT/τh lower bound.Figure 1 depicts fresh challenges bound to identity and window, responses under a deadline, and the channel-level throughput cap.Source: §2 · p. 4, Figure 1 · p. 4

3.1. Primitive Interface

• BPC defines Prove and Verify over a qualifying event, a verifier-checkable claim, and a publicly verifiable proof.Each valid proof establishes that identity v performed the qualifying action during context d; the proof requires no long-term participant-data storage or trust in the issuer.Source: §3.1 · pp. 4–5

3.2. Security Properties

• The four properties separate identity binding and non-precomputability objectives, a bounded temporal context, and a channel-throughput assumption needed for the multi-identity cost theorem.H4 is not enforced by the cryptographic construction and is needed for the cost theorem, not for an individual proof to be meaningful.Source: §3.2 · p. 5
• Given the channel-throughput assumption, sustaining s active identities for T windows requires at least sT/τh independent channel-windows, regardless of solver type.The cost counts channel-windows, not economic expenditure.Source: §3.2 · p. 6

3.3. On Property (H4) and Solver Identity

• H4 can arise from human cognitive serialization or engineered channel serialization, and channels may serve identities sequentially up to the response-time bound.Serialization bounds concurrent service; τh counts the sequential round trips possible before the deadline.Source: §3.3 · p. 6

3.4. Channel Semantics and Enforcement Models

• A deployment must define what counts as a channel; enforcement models change τh, while the formal cost theorem applies to any model satisfying H4.The Section 9 API-solver measurements do not automatically calibrate device-bound or UI-occupancy deployments.Source: §3.4 · pp. 6–7, Table 2 · p. 7

3.5. Separability and Composability

• BPC’s guarantees depend on H1–H4 rather than application-level interfaces or challenge formats, allowing higher-level protocols to set policies over exported participation proofs.BPC itself does not interpret or aggregate participation across windows.Source: §3.1 · p. 5, §3.5 · p. 7

3.6. Delegation and Key Sharing

• BPC binds proofs to a registered key, not to the person or process using it, so delegated solving or shared signing access remains within scope.Deployments needing non-delegation must compose BPC with an external key-custody mechanism.Source: §3.6 · p. 7

4. A Hash-Based Realization

• The hash-based realization satisfies H1–H3 under the random oracle and signature-unforgeability assumptions, but H4 remains a separate channel constraint.The construction is self-contained and requires no trusted hardware.Source: §4 · p. 7, §4.4 · pp. 8–9

4.3. Response and Verification

• A valid response must arrive before the deadline, solve the challenge, and be cryptographically bound to the identity, window, and challenge index.Verification checks the deadline, signature, binding tag, and task solution.Source: §4 · p. 7, §4.3 · p. 8

4.1. Setup

• Each identity has a registered public key, and each window begins with a publicly broadcast nonce that is unpredictable beforehand.Registration is external to BPC and need not make identity creation costly; admission cost is additive to recurring participation cost.Source: §4.1 · pp. 7–8

4.2. Challenge Generation

• The binding tag and challenge payload derive from the same window-fresh seed, preventing payload precomputation before the window opens.The challenge-family generator is deterministic given that seed, and verification publicly checks the submitted response against the payload.Source: §4.2 · p. 8

4.4. Security of the Construction

• H1 and H2 rely on cryptographic assumptions, H3 holds unconditionally, and H4 depends on a deployment-specific lower bound on channel round-trip time.That bound limits responses per window to τh = floor(∆resp/δrtt); the construction itself does not enforce H4.Source: §4.4 · pp. 8–9

5.1. System Model

• For each fixed-duration window, BPC exports whether an identity performed at least one valid qualifying action, without storing or aggregating participation across windows.Verification is deterministic and public, and requires no long-term participant-data storage.Source: §5.1 · p. 9

5.2. Adversary Model

• The cryptographic properties address a PPT adversary, while the cost results hold against a computationally unbounded adversary given the channel-throughput assumption.The structural adversary may create and coordinate arbitrary identities and use multiple channels, outsourcing, relays, or AI automation.Source: §5.2 · p. 9

5.3. Adversarial Cost Function

• The cost function counts independent channel-windows, and the throughput assumption requires a deployment-specific round-trip lower bound that holds against the fastest admitted channel.τh depends on the capacity regime: it can count sequential round trips before a response deadline, service over a full window, or an exclusive-channel limit of one identity per window.Source: §5.3 · p. 9

• Each channel produces at most τh valid responses per window, and identity binding prevents one response from covering multiple identities.Freshness and real-time response reject precomputed or late responses.Source: §6 · p. 10
• C(s, 1) ≥ s/τh = s · δrtt/∆resp, so sustaining s identities in one window requires a linear number of independent participation channels.Source: Figure 3 · p. 10, §6 · p. 10
• The proof is a counting argument: the contribution is establishing that H1–H4 suffice and identifying how their combination yields the bound.The authors do not claim that these properties are individually necessary.Source: §6 · pp. 10–11
• No adversary can sustain s identities with o(s) channels per window, regardless of the value of τh.Source: §6 · p. 11
• The theorem bounds channel counts, not dollar costs; bulk pricing or labor-market economies of scale could still reduce per-channel cost as an adversary grows.An economic floor requires the separate Assumption 2.Source: §6 · p. 11

• In every window d, the number of active identities is bounded by sd ≤ md · τh; effort in one window cannot carry into the next.Source: §7 · p. 11
• C(s, T) ≥ sT/τh: sustaining s identities over T windows requires at least this many channel-windows under the stated properties and Assumption 1.Fresh responses cannot carry forward from one window to the next.Source: §7 · p. 11
• The bound counts channel-windows, not currency; an economic floor additionally assumes a positive per-channel operating cost independent of s and T.Bulk pricing or scale-dependent labor costs could violate that assumption.Source: §7 · p. 11
• With ∆resp = 8 s and δrtt ≈ 2.7 s, τh = 2 gives C(s, T) ≥ sT/2; tighter deadlines strengthen the per-channel-window guarantee but increase interaction burden.A reasoning deployment with ∆resp = 12 s and δrtt ≈ 1.4 s has τh = 8.Source: §7 · p. 11
• Concentrating effort in bursts does not reduce the linear cost in total channel-windows, regardless of temporal concentration.Source: §7 · p. 11

8.1. Abstract Admissibility Requirements

• 8.1. Abstract Admissibility Requirements: A family must use unpredictable, window-fresh instances, publicly verifiable responses, identity-bound proofs, and an interaction latency that caps throughput.The construction supplies H1–H3; whether H4 holds depends on the task family's latency.Source: §8.1 · pp. 11–12

8.2. Admissible Families

• 8.2. Admissible Families: Four families are described—perceptual visual matching, interactive reasoning, biometric-light response, and attention-based interaction—with latency bounding channel throughput.The account does not require tasks to be unsolvable: multi-image inference, multi-step reasoning, real-time signal synthesis, or sustained tracking can impose latency.Source: §8.2 · p. 12

8.3. Deployment Example: Relaxed Window Sizes

• 8.3. Deployment Example: Relaxed Window Sizes: Device-bound daily login with τh = 1 yields C(s, T) = Ω(sT), provided channel binding is enforced.Relaxed windows reduce user burden, while tighter deadlines strengthen near-real-time resistance at higher usability cost.Source: §8.3 · p. 12

8.4. Rotation and Composability

• 8.4. Rotation and Composability: Systems may rotate or combine admissible families while preserving the guarantees of Theorems 2 and 3.The stated basis is that security depends on H1–H4 rather than on any single family.Source: §8.4 · p. 12

9. Empirical Evaluation

• The evaluation measures solver throughput and contextualizes it against published human-performance findings to assess whether τh remains small under deployment-realistic deadlines.The authors use literature ranges rather than a new controlled human study, explicitly treating them as contextualization rather than a substitute for human-subject data.Source: §9 · p. 12, §9.1 · p. 13

9.1. Methodology

• The deployed challenges used 8 s perceptual and 12 s reasoning deadlines, with 100 trials per solver–family pair and no access to private verification targets.Perceptual trials used transformed geometric-image matching; reasoning trials used four-element numeric sequences.Source: §9.1 · p. 13

9.2. Results

• Perceptual trials achieved 97–100% correctness but τh ∈{2, 3}, while reasoning trials achieved 75–78% correctness with τh ∈{6, 7, 12}.Across all three models, perceptual failures were concentrated in latency and reasoning failures in correctness; these mean-latency values are illustrative, not conservative bounds.Source: §9.2 · p. 13, Figure 4 · p. 14, Table 3 · p. 14
• Perceptual channels are latency-bound, whereas reasoning channels are correctness-bound; either pattern preserves linear adversarial cost in identities and time windows.Reasoning’s roughly one-in-four incorrect responses require accepting more rejections or spending additional channel-windows to compensate.Source: §9.2 · pp. 13–14
• Using 10th-percentile latency raises reasoning τh estimates, while discounting by success rate yields effective throughput and leaves the qualitative bounded-throughput conclusion unchanged.The p10-based reasoning τh rises most sharply for GPT-4o, from 12 to 22; deployments facing tail-racing should use success-discounted effective throughput.Source: §9.2 · p. 15, Table 4 · p. 15
• Published human response times on structurally comparable tasks are of the same order as measured automated latencies, but the comparison is not a controlled paired test.The underlying task presentations differ, and the authors make no statistical-significance claim about a human-versus-automated gap.Source: §9.2 · p. 15

Automation

• Automated solvers preserve linear scaling in identities, shifting participation cost from human labor to API credits or hardware.Under the channel model, sustaining s identities requires Ω(s) independent channels.Source: §10 · p. 15

Channel parallelism

• Sustaining 1,000 perceptual identities at τh ≈3 requires 334 independent solver instances per window, each with its own request and marginal inference cost.The analysis contrasts channel-parallelism, which is priced linearly by the model, with reusable resources whose marginal economics may vary.Source: §10 · p. 15

Economic cost of channel provisioning

• Under Assumption 2, recurring provisioning requirements imply Cecon(s, T) ≥ cop · C(s, T) = Ω(sT), although scale economies in cop remain an empirical question.The 1,000-identity example requires 334 simultaneously active instances per window, recurring across T windows.Source: §10 · p. 16

Adversarial strategies

• Human outsourcing converts labor into wages but still requires Ω(s) workers; relaying adds network latency, while replay and precomputation are constrained by binding and freshness.Batch solving more than τh challenges within a window exceeds the channel’s round-trip latency budget.Source: §10 · p. 16

Synthetic media and privacy

• For biometric-light challenges, freshness prevents offline synthesis, while privacy-preserving unlinkability across windows remains an open direction.The described verification stores no raw biometric data or behavioral record.Source: §10 · p. 16

Scope of the guarantees

• The linear cost guarantee depends on Assumption 1 (H4); faster channels or additional channels can weaken its multiplier, so deployments must reassess latency and provisioning costs.A tenfold increase in τh weakens the channel-window lower bound by a factor of ten without removing linear scaling in s and T.Source: §11 · p. 16

Economic assumptions

• The cost bound is structural, but the economic floor also assumes per-channel operating costs do not fall with scale.Bulk-rate API pricing or labor-market economies could make Cecon(s, T) grow more slowly; the paper does not resolve this for a given deployment.Source: §11 · p. 17

Empirical scope

• Automated-solver results are first-party, but human performance is literature-calibrated rather than measured in a controlled study of the paper’s challenges.The automated evaluation also leaves task-specific fine-tuned models, custom inference hardware, and organized human–AI hybrid pipelines for future work.Source: §11 · p. 17

Future work

• The paper leaves difficulty-calibrated challenge design for human channels as an open problem; current evaluation measures solve rates post hoc for fixed challenges.Source: §11 · p. 17

Accessibility and inclusivity

• Challenge families requiring visual, auditory, or motor interaction may exclude participants with relevant impairments, so deployments need alternative modalities and accessibility-aware selection.Source: §11 · p. 17

Parameter sensitivity and theoretical scope

• Although the guarantees hold for any Δresp > 0, concrete parameters require measuring τh and honest-participant success rates in the target environment.The theoretical results assume (H1)–(H3) and Assumption 1 (H4); partial H4 failures yield intermediate scaling, with larger τh.Source: §11 · p. 17

Conclusion

• Under (H1)–(H4), sustaining s identities over T windows requires Ω(sT) independent channel-windows, regardless of whether channels are human-operated, automated, or hybrid.BPC exports independently verifiable, time-indexed proofs rather than accumulating participation into a score or reputation.Source: §12 · p. 17
• All three evaluated vision-language models exhibit throughput ceilings under strict deadlines, bounded by latency on perceptual tasks and correctness on reasoning tasks.The paper presents a hash-based construction for (H1)–(H3), identifies four challenge families, and evaluates three independently developed models.Source: §12 · p. 17
• BPC makes fresh, per-window verification unavoidable without assuming any particular resource class is intrinsically expensive to sustain.Source: §12 · p. 17
• BPC verifies each window’s participation bit but leaves downstream systems to decide whether and how to aggregate those bits into policy.Domains such as consensus, governance, and reputation may aggregate the same per-window bits differently, or not at all.Source: §12 · p. 18

Future work

• Future work includes a controlled human study, challenge-difficulty calibration, privacy-preserving delivery, composability analysis, and adaptive challenge rotation.Source: §12 · p. 18

Ethics Considerations

• The paper reports no human-subject research, personal-data collection, or vulnerability disclosure.Source: Ethics Considerations · p. 18
• The automated evaluation used API calls to three commercial vision-language models on synthetic challenges, without human participants or personally identifiable information.Source: Ethics Considerations · p. 18
• The described web application is intended for future human-subject evaluation under appropriate institutional oversight.Source: Ethics Considerations · p. 18

Generative AI Usage Considerations

• Generative AI assisted with phrasing, consistency checking, and structural revision of draft sections.Source: Generative AI Usage Considerations · p. 18
• The authors state that they developed, executed, and verified the technical content, formal definitions, proofs, experimental design, and results.Source: Generative AI Usage Considerations · p. 18
• The authors report inspecting all AI outputs for accuracy and originality and state that no AI-generated ideas or results appear without independent development and validation.Source: Generative AI Usage Considerations · p. 18