content-addressed, identity-sovereign patch theory system for the cybergraph. treats changes as commutative morphisms instead of snapshots — independent patches apply in any order, conflicts are first-class data, merge is set union

cybergraph embedding

every patch is a signed set of operations over particles and cyberlinks, authored by a neuron, weighted by focus contribution. the three primitives map directly to cyber protocol:

  • patch = cyberlink (signed, timestamped, weighted by Δπ)
  • tracked content = particle (content-addressed node)
  • channel = named view over the global patch DAG
  • repository = neuron-owned subgraph
  • author = neuron (identity + stake + focus vector)

this embedding is literal — cyberpatch repositories ARE cybergraph structures, queryable and rankable by the consensus layer

from patch theory

the mathematical core comes from category theory: repository states are objects, patches are morphisms, composition is sequential application. the key departure from git: a patch is defined by what it changes, independently of the history that produced the source state

three relations between patches:

  • independent (P ⊥ Q) — disjoint regions, patches commute, merge is set union
  • dependent (P → Q) — Q requires P in its dependency closure
  • conflicting (P ⊗ Q) — incompatible changes to the same region, producing a first-class conflict object

the commutativity theorem guarantees that any set of pairwise-independent patches produces the same result regardless of application order. this eliminates phantom conflicts that plague snapshot-based systems

five primitive operations

all mutations over the cybergraph reduce to five atoms:

  • AddParticle — introduce new particle
  • RemoveParticle — remove particle from tracked set
  • AddEdge — link two particles
  • RemoveEdge — remove a link
  • ReplaceParticle — atomic content swap

conflict resolution

conflicts between concurrent patches are algebraic objects with well-defined structure — they can be resolved by further patches, left in state, or arbitrated by consensus. a resolution patch R has both conflicting patches in its dependency closure — once applied, the resolution propagates permanently across all channels

when local resolution is unavailable, the network arbitrates through focus-weighted voting: stake × focus_weight determines voting power, tying version control directly to cyber's economic and epistemic consensus

economics

patches earn rewards proportional to their impact on the knowledge graph:

reward(P) = base_fee + Δπ(P) × reward_coefficient

Δπ measures the change in network focus from applying a patch. patches that increase knowledge coherence earn rewards; patches that fragment or duplicate earn less. this creates economic pressure toward high-quality, well-connected contributions — aligned with collective focus theorem predictions

agent workflows

designed for parallel neuron and agent workflows at planetary scale. multiple agents operate simultaneously — no coordination required to produce patches, only at resolution time. GFlowNet agents propose patches weighted by expected Δπ. active inference agents minimize free energy by adaptively staking on patches

post-quantum cryptography from genesis. hash via Poseidon2-Goldilocks, signatures via the protocol's post-quantum scheme, proofs via STARKs over Goldilocks field

see cyber/patch/spec for the full specification

Local Graph