01 / EXECUTION-COST INVERSION
Why Replicated Consensus Fails on Non-Deterministic & Computationally Expensive Workloads
Standard blockchains require deterministic state transition functions (STFs). Non-deterministic computations yield divergent state roots, halting consensus. Computationally expensive STFs exceeding block times induce liveness failures.
Root Cause: Hardware Non-Reproducibility and Computationally Expensive Execution
GPUs optimize for heavily parallel workloads, but floating-point math is non-associative. Different GPU architectures schedule threads differently, causing bit-level divergence that breaks consensus.
02 / EXECUTION SUPERPOSITION
Superposition of Execution Models via Decoupling Asynchronous Workloads from the Critical Path
Symphony keeps deterministic replication on the critical path while delegating expensive or non-deterministic execution to async enshrined nodes with proof-based settlement.
Preserving Blockchain Guarantees
Critical-path consensus remains non-blocking while expensive execution is delegated asynchronously. Settlement requires integrity proofs (Zero-Knowledge Proofs or Trusted Execution Environments), preserving safety and liveness guarantees.
03 / DUAL SAFETY
The Product Lattice: Introducing Dual Safety
Applications declare safety requirements as upsets across heterogeneous proof systems (TEE and ZKP).
Flexible Security Requirements
Symphony lets applications choose their trade-off frontier without changing global safety semantics. Latency-sensitive flows can finalize early, while high-value flows require dual-verification depth.
Monotonic State Advancement
Results move strictly upward in the lattice as proofs arrive from independent systems. If a proof fails, ascent is interrupted and the leader is slashed before top-state admission.
04 / SCALABLE PROVING
Exploiting Structure and Symmetry: Special-Purpose ZK for LLMs
Symphony scales proof generation and verification by composing heterogeneous proof systems across architecture-specific boundaries in the transformer computational graph.
Distributed Proof Generation and Verification
Shard-specialized provers parallelize proof creation while preserving deterministic settlement semantics.
Exploiting Symmetry and Structure in the LLM Computational Graph
Instead of monolithic proving, we distribute proving and verification across specialized network roles. Optimal partitioning over narrow and fat boundaries overfits the proving stack to true compute topology.
05 / SYMMETRY & STRUCTURE
Exploiting Structure by Proxy of Tree Reduction for Aggregation
Unlike sequential aggregation, Symphony exploits sublinear tree reduction to recursively aggregate heterogeneous proofs and align proving workload with network topology.
Symmetry & Structure
Proofs of dense inner compute and narrow boundary states are recursively aggregated by tree reduction. Subtrees and leaves can be broadcast directly to validators, bypassing monolithic aggregation bottlenecks.
06 / EXTENDED VALIDITY
Extended External Validity: Constraining the Proposer
Proposed blocks must satisfy an extended set of validation predicates to enforce protocol-level constraints at inclusion, exclusion, and ordering boundaries.
Extended External Validity
Symphony augments standard blockchain validity rules by enforcing inclusion, exclusion, and ordering predicates. Blocks violating these predicates are rejected at the consensus level.
07 / UFI & AOUFE
Protocol-Enforced Inclusion and Exclusion
User-Forced Inclusion (UFI) and Application-Ordered User-Forced Exclusion (AOUFE) provide programmable censorship-resistance and scheduled inclusion constraints. When predicates conflict, UFI supersedes AOUFE to preserve user-forced inclusion guarantees.
Programmable Censorship-Resistance and Scheduled Inclusion
Users can invoke UFI for mandatory scheduled inclusion; apps/users can invoke AOUFE for mandatory exclusion. When predicates conflict, UFI strictly supersedes AOUFE to preserve censorship-resistance guarantees.
08 / ACE ORDERING
ACE: Application-Defined Ordering Constraints
Smart contracts can assert Application-Controlled Execution (ACE) predicates to enforce strict transaction sequencing and mitigate toxic Maximal Extractable Value (MEV) extraction.
Eliminating Toxic MEV
Instead of proposer-controlled sequencing, ACE lets applications cryptographically enforce ordering constraints. Violations (for example, executing a Trade before a Cancel) deterministically trigger block rejection.