Proof-of-Transit Receipts

• Proof-of-transit receipts are cryptographic artifacts that provide tamper-evident and verifiable logs of digital asset transfers using methods like hash chaining and dual signatures.
• They ensure secure audit trails with properties such as non-repudiation and privacy compatibility across diverse applications like Bitcoin treasuries, supply chains, and interplanetary data relays.
• Implementations leverage blockchain anchoring, zero-knowledge proofs, and succinct receipt batching to uphold integrity, forward security, and efficient verification.

A proof-of-transit receipt (PoT receipt) is a cryptographic artifact that attests, with strong integrity guarantees, that a digital object, asset, or message has been validly transferred, received, or processed at a specific point, under specific policy, and optionally by a proscribed authority. PoT receipts serve as tamper-evident and often privacy-compatible evidence of transit through one or more parties, facilitating verifiable audit trails in domains including institutional Bitcoin treasuries, logistics networks, interplanetary relays, and privacy-respecting electronic payments. Architectures and formal models for PoT receipts span hash-chained and signature-chained logs, receipt batching anchored on blockchains, and zero-knowledge-augmented bulletin boards, all aiming to guarantee authenticity, conservation, non-repudiation, and (where required) indistinguishability.

1. Cryptographic Definition and Core Receipt Structure

At the most abstract level, a PoT receipt comprises a record $rec_k$ that encodes both cryptographic evidence of an event and its sequencing within a tamper-evident log or hash-chain. The precise format is application-specific:

Treasury Proof Ledger (TPL)

For inter-domain digital asset transfers, each event

$e_k = (t_k, d_{src}, d_{dst}, v_k, evid_k, m_k)$

produces a receipt

$$rec_k = (t_k, d_{src}, d_{dst}, v_k, evid_k, m_k, h_k, R_k, \sigma^\text{treas}_k, \sigma^\text{prov}_k)$$

where $h_k = H(evid_k \Vert v_k \Vert m_k)$ and

$$R_k = H(R_{k-1} \Vert h_k \Vert d_{src} \Vert d_{dst} \Vert t_k)$$

Hash-chaining ($R_k$), combined with dual signatures, binds receipt sequence and authorizations, providing forward integrity and non-equivocation (Puente et al., 3 Dec 2025).

Interplanetary Proof-of-Transit Timestamping (PoTT)

For planetary relay of data packets,

$$R_i = (h, \nu, \text{NodeID}_i, t^{(i)}_{in}, t^{(i)}_{out}, prev_i, s_i)$$

with $h = H(P)$, $prev_i = H(R_{i-1}\text{ without }s_{i-1})$, and $s_i$ a Schnorr signature on the full tuple (Puente et al., 28 Aug 2025).

Zero-Knowledge-based Reissuance Systems

In privacy-focused electronic payments, a PoT receipt is the pair $(I, \pi)$, where $I$ is a randomized subset of commitments (burnt asset records), and

$\pi$

is a zero-knowledge proof that a freshly spent asset appears as a valid opening of one of the commitments in $I$—without revealing which one (Friolo et al., 2024).

2. Receipt Generation and Verification Protocols

The protocol for realizing PoT receipts entails distinct phases for generation, verification, and, where necessary, blockchain anchoring. Key protocol steps include:

• Generation: For each transit event, hash the relevant data and metadata to produce a deterministic receipt input; sign the constructed receipt (potentially with multiple keys/roles); update the chain state using a hash function.
• Verification: Check hash-chain or signature consistency, validate digital signatures, confirm correct anchoring commitments (for example, Merkle roots or log hashes against on-chain values), verify zero-knowledge proofs or NP relations as appropriate.
• Anchoring: Periodically, anchor receipt digests or commitments to a public blockchain (e.g., Bitcoin OP_RETURN, Ethereum smart contract) to achieve immutability and independent auditability.

Example: PoT in TPL

Receipt verification includes:

• Hash verification: $h_k \stackrel{?}{=} H(evid_k \Vert v_k \Vert m_k)$
• Chain update check: $$R_k \stackrel{?}{=} H(R_{k-1} \Vert h_k \Vert d_{src} \Vert d_{dst} \Vert t_k)$$
• Signature validation for both treasury and provider
• Ledger prefix hash to on-chain commitment $C_i$ (Puente et al., 3 Dec 2025).

Example: PoTT Chain Verification

• Each $R_i$ is validated for correct signatures, sequence hashes, time monotonicity, and time-beacon cross-checks.
• Administrative-diversity and multi-hop requirements can be enforced at the policy layer (Puente et al., 28 Aug 2025).

Example: Zero-Knowledge Proof-of-Transit

• On receipt, verify signature, non-reuse, and zero-knowledge proof $\pi$ that the asset was generated in accordance with pre-set emission rules (e.g., that $\exists\, (r, i):\, \beta_i = \Com(\vk; r)$ in the audit log) (Friolo et al., 2024).

3. Security Properties and Formal Guarantees

Schemes implementing PoT receipts aim to provide several critical properties:

• Unforgeability: No probabilistic polynomial-time adversary can create a valid receipt chain except through honest protocol execution, even under adaptive corruption or key compromise (Puente et al., 3 Dec 2025, Puente et al., 28 Aug 2025, Watanabe et al., 2020, Friolo et al., 2024).
• Forward Integrity / Non-Repudiation: Once a receipt is anchored, it cannot be removed, replaced, or backdated without detection (collapsing to either hash function or signature unforgeability) (Puente et al., 3 Dec 2025, Watanabe et al., 2020).
• Conservation of Value / Soundness: Especially in treasury and payment contexts, every receipt encodes a value-preserving transition, ruling out hidden minting or burning (Puente et al., 3 Dec 2025, Friolo et al., 2024).
• Privacy Compatibility: In restricted-leakage profiles, simulation arguments show that observable receipts reveal no extra information beyond the intended exposure vector or public auditor view. Zero-knowledge PoTs ensure that asset movement cannot be re-linked to the underlying burn or owner (Puente et al., 3 Dec 2025, Friolo et al., 2024).
• Irrecoverable Audit Trail: Once events are committed on-chain, their existence is provable and their contents, if hash-blinded, remain confidential unless additional information is leaked (Watanabe et al., 2020, Puente et al., 28 Aug 2025).

4. Architecture, Anchoring, and Deployment Variants

The deployment of PoT receipts adapts to system constraints:

System	Receipt Structure	Anchoring / Replay Defense
Treasury Proof Ledger	Hash-chain + dual sig	Bitcoin (OP_RETURN, Taproot)
RFID-Logistics	Tag, reader sig, hash	Ethereum BBcAnchor smart contract + Merkle tree (Watanabe et al., 2020)
Interplanetary Relay	Per-hop Schnorr chain	Delayed anchoring to Bitcoin MTP/DTN beacons (Puente et al., 28 Aug 2025)
ZK Payments	Subset+ZK 1-out-of-n	Merkle-root binding to bulletin board

• Blockchain Anchoring: All surveyed systems publish receipt or log digests as commitments to public blockchains, enforcing immutability and enabling independent replay/audit (Puente et al., 3 Dec 2025, Watanabe et al., 2020, Puente et al., 28 Aug 2025).
• Batching and Succinctness: Receipts are batched in Merkle trees or vector commitments to improve bandwidth and storage efficiency (e.g., Ethereum BBcAnchor batches in logistics; PoR snapshot trees in TPL) (Puente et al., 3 Dec 2025, Watanabe et al., 2020).
• Zero-Knowledge Primitives: In privacy-sensitive settings, PoT receipts are realized via efficient 1-out-of-$n$ proofs (Σ-protocols or SNARKs) applied over Pedersen commitments or authenticated accumulators (Friolo et al., 2024).

5. Illustrative Scenarios and Domain-Specific Instantiations

Concrete implementations validate the generality of PoT receipts across domains:

• Institutional Bitcoin Treasuries: TPL uses PoT receipts to maintain a complete, externally auditable, hash-chained log of intra-org, exchange, and fee movement, guaranteeing solvency and exposure traceability with privacy-compatible policies (Puente et al., 3 Dec 2025).
• Interplanetary Bitcoin Settlement: PoTT receipts guarantee auditability of data propagation over high-latency, custody-transferred relays between Earth and Mars, enabling reliable Lightning HTLC timeouts and pegged sidechain bridging without extending L1 consensus rules (Puente et al., 28 Aug 2025).
• RFID-based Supply Chains: Each checkpoint produces a receipt, blinded for privacy, atomically committed to a public blockchain, thereby guaranteeing package provenance even with cheap, passive tags and potentially untrusted service providers (Watanabe et al., 2020).
• ZK-Verified Reissuance in Digital Cash: A receipt constitutes a zero-knowledge witness that a freshly spent asset was correctly reissued, leveraging a commitment log and NIZKs to preserve payer privacy and prevent value inflation (Friolo et al., 2024).

6. Performance, Scalability, and Deployment Considerations

• Receipt Size: In interplanetary relays, per-receipt size is ≈203 bytes (32 B hash, 16 B nonce, IDs, timestamps, sig) (Puente et al., 28 Aug 2025). In logistics, batching reduces anchor frequency; ZK-PoT proofs can be made constant size (≈200 B) with SNARKs (Friolo et al., 2024).
• Anchoring Overhead: Nationwide RFID logistics achieve public blockchain anchoring (Ethereum) with annual cost ≤6k USD at high frequency, with individual batch anchors costing ~$0.25 (Watanabe et al., 2020).
• Computation: Schnorr signatures and SHA-256 dominate cost (≤1 ms per operation); bandwidth and storage outsize cryptographic operations in logistics and interplanetary contexts (Puente et al., 28 Aug 2025, Watanabe et al., 2020).
• Audit Latency: Public anchoring confirms with blockchain settlement time (seconds to minutes); interplanetary PoTT receipt chains can be validated entirely off-chain with synchronization to beacons (Puente et al., 28 Aug 2025).

7. Security Analysis and Limitations

• Modeling Adversaries: All cited protocols quantify adversaries as PPT actors able to corrupt signatory or anchoring keys, with receipt unforgeability based on cryptographic primitives' security (Puente et al., 3 Dec 2025, Watanabe et al., 2020, Puente et al., 28 Aug 2025, Friolo et al., 2024).
• Irreversibility and Alibi Proofs: Once anchored, historic PoT receipts cannot be redacted, even under late key compromise or certificate expiry, enforcing elapsed-time and anti-fork guarantees (Watanabe et al., 2020, Puente et al., 28 Aug 2025).
• Simulation-based Privacy: For restricted leakage profiles, zero-knowledge simulation shows that receipts reveal no more than permitted by the system policy, bounding passive and active privacy risks (Puente et al., 3 Dec 2025, Friolo et al., 2024).
• Scope Limitations: If all time-beacons or anchoring parties are compromised simultaneously, PoT receipts reduce to administrative assertions; no existing system achieves unconditional guarantees in such settings (Puente et al., 28 Aug 2025). A plausible implication is that diversity in anchoring and quorum policy are essential for strong guarantees across adversarial domains.

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Collectively, proof-of-transit receipts constitute a foundational primitive for accountable, privacy-compatible, and cryptographically verifiable digital asset, data, or information flows in distributed systems, fulfilling roles from financial compliance to physical goods chain-of-custody, and enabling trust-minimized transparency across administrative boundaries.