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