%% You should probably cite draft-vauban-x402-vpsf-algebra-01 instead of this revision. @techreport{vauban-x402-vpsf-algebra-00, number = {draft-vauban-x402-vpsf-algebra-00}, type = {Internet-Draft}, institution = {Internet Engineering Task Force}, publisher = {Internet Engineering Task Force}, note = {Work in Progress}, url = {https://datatracker.ietf.org/doc/draft-vauban-x402-vpsf-algebra/00/}, author = {Vauban Research}, title = {{VPSF Claim Algebra for x402 Payment Receipts}}, pagetotal = 20, year = 2026, month = may, day = 24, abstract = {The x402 protocol ({[}X402-V2{]}) defines three wire messages for HTTP- native payment flows but provides no composability model for payment receipts. A recipient holding a SettlementReceipt and a DelegationGrant cannot natively express that the settlement satisfies a delegated spending condition, or that a RefundClaim negates an earlier SettlementReceipt, without bespoke facilitator-side logic. As automated payment pipelines grow, the absence of a normative composability layer leads to fragmented, non-interoperable verification surfaces. This document specifies the Vauban Proof Stack Framework (VPSF) Claim Algebra for x402 payment receipts: a grammar of five composition operators (Conjunction, Implication, Aggregation, Selective Disclosure, Revocation; abbreviated ∧, \(\rightarrow\), ⊕, ▷, ¬) applied over the four canonical Payment Claim types (PaymentIntent, SettlementReceipt, RefundClaim, DelegationGrant) defined in {[}LIFECYCLE-FSM{]}. The algebra is chain-agnostic by invariant; the Starknet-based proof system described in {[}STARK-RECEIPTS{]} is the first reference implementation. Composability is grounded in the JCS canonical preimage discipline ({[}RFC8785{]}), ensuring operator results are deterministic and cross-implementation consistent. An open-source Rust implementation is provided in {[}VAUBAN-CRATE{]}.}, }