Field notes

Notes From the Architecture Boundary

Writing about crypto-to-fiat settlement without turning unmeasured design targets into product claims: pricing, fees, custody, bank evidence, privacy, tax boundaries, and failure exposure.

Mathematical Foundations

• Petri Nets: A Small Machine for Resources That Must Not Duplicate

  Places hold resources, transitions consume and create them, and illegal moves simply do not exist.

• CALM: Coordinate Only Where “Not Already Taken” Matters

  Most vault facts only accumulate; the one negative fact—a competing claim does not exist—forces coordination.

• Curry–Howard: A Theorem Is a Type, and Its Proof Is a Program

  “And” becomes a pair, “or” a tagged choice, implication a function, and constructive existence an algorithm with evidence attached.

• Language Classes: Ask What the Checker Must Remember

  Finite state remembers a summary, a stack remembers nesting, and a tape supports revisitable semantic facts.

• Session Types: One Settlement Story, Three Local Views

  A resource transition says what is conserved; a choreography says which participant must send or receive each message next.

Vault Architecture

• UTXOs, Notes, and Resources: Value as Something You Consume Once

  A balance is one view of value; a set of uniquely consumable objects gives privacy and local rules a different foundation.

• Account Abstraction: Make Authority a Programmable Resource Rule

  Every account validates through a kind; asset logic executes the authorized effect.

• Logic as Owner: The Offer Predicate Is the Escrow

  Ownership can name a rule instead of a person, collapsing escrow and state-machine authority into one relation.

• EIP-3009: A Signed USDC Deposit, With a Public On-Ramp

  Authorization removes an allowance transaction; it does not make the L1 funding address or amount private.

Cryptographic Primitives

• Stwo Circle-STARKs Over Mersenne-31, From Trace to Proof

  A local transition table becomes one succinct proof, with field choice shaping every lookup, hash, and non-native operation.

• Poseidon2-M31: One Field-Native Sponge, Many Separated Meanings

  Hashing inside a proof is arithmetic, so the permutation, capacity, encoding, and separators become protocol law.

• Mangrove: Folding Many Private Actions Into One Public Settlement

  Each proof certifies a local transition and carries the data needed for the next proof to combine it safely.

• Indexed Merkle Trees: Proving a Nullifier Is Not Already There

  Membership proves a value exists; private double-spend prevention needs a succinct proof that it does not.

• LogUp Completeness: Proving Nothing Was Quietly Left Out

  Validating every supplied item is weaker than proving that the supplied items are the complete set.

• Post-Quantum Where, Exactly?

  The settlement core avoids curves; the mailbox, notary signature, and bank TLS do not.

Protocol Economics

• Fees for Liveness: First Price, a Posted Reserve, and No Native Token

  The universal rule is deliberately thin: every Action funds exactly one positive, approved aggregator fee.

• One Epoch Leader From a Bonded Set—Selected by iVRF, Not a VDF

  Rotation must be unpredictable, stake-weighted, curve-free, event-driven, and compatible with the vault's stated security boundary.

PayMoney Protocol

• TLSNotary: Prove the Bank Response Without Publishing It

  Fiat never enters the vault; an authenticated, template-parsed bank fact authorizes one resource transition.

Crypto to Fiat Withdrawal & Conversion

• What a Crypto-to-Fiat Conversion Really Costs

  Compare the full route without mistaking an unmeasured protocol design for a live quote.