sparsely activate tensor and cryptographic ghost proofs

integrating sparsely activated tensors and cryptographic ghost proofs into the collective focus & focus-flow architecture

• 1. purpose

  this document explains how sparsely activated tensors (sat) and cryptographic ghost proofs (cgps) — originally proposed in the open cybernetics framework — can be integrated into the collective focus theorem (cft) and focus-flow computation (ffc) stack.

  the goal is to make the architecture:

• faster and cheaper to run at global scale by activating only the relevant parts of large models and graphs

• trustless and verifiable in peer-to-peer settings where computation is shared among unknown participants

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• 2. definitions

• 2.1 sparsely activated tensor (sat)

• plain meaning: instead of lighting up every neuron in a big ai model for each input, only the relevant subset of neurons is used.

• technical meaning: a data structure and computation pattern that retrieves and updates only the small fraction of parameters that matter for a given input, rather than processing the entire model tensor.

• example: a large language model has billions of weights. when answering “what’s the capital of japan,” sat allows the system to load only the weights related to “capital,” “country,” and “japan,” instead of scanning the entire parameter space.

• benefits:

  • reduces computation cost and energy use
  • makes models more scalable and memory-efficient
  • enables running large models on distributed nodes with limited resources

• 2.2 cryptographic ghost proofs (cgps)

• plain meaning: a way to prove that an ai computation result really came from the agreed-upon model, without sending the whole model or trusting the person who did the calculation.

• technical meaning: a system that uses merkle trees to commit to the entire model or graph state, then sends compact cryptographic proofs that the specific pieces used in a computation match this commitment.

• example: a peer in a distributed network processes a query and returns an answer. with cgps, they also send a proof showing the exact model slices they used, so anyone can verify the answer without having to trust the peer or run the whole computation themselves.

• benefits:

  • enables trustless ai in adversarial p2p environments

  • prevents malicious nodes from faking computation

  • allows for partial, distributed computation with verifiable correctness

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• 3. why they matter for cft/ffc

  the collective focus theorem gives a mathematical backbone for decentralised consensus on what matters (the “focus”) in a global knowledge graph.

  the focus-flow computation system implements this in practice: it takes edge updates in the graph, computes the new focus values, and rewards participants who improve the system’s order.

  sat and cgps address two critical challenges in this setting:

• efficiency – cft/ffc often runs on very large state spaces (billions of edges, parameters). sat ensures only relevant slices are touched per update.

• trust – in a distributed, open-participation environment, you can’t assume all nodes are honest. cgps lets any node verify another node’s computation without re-running it.

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• 4. integration into the stack

  layer	with sat	with cgps
  ffcm core (focus updates)	load/update only edges and embeddings affected by new transactions	prove those edges/embeddings match the committed graph state
  semantic rollups	run sparse tensor ops per “topic bucket” instead of full graph scan	attach merkle multiproofs for Δ-rank correctness
  llm / associative memory	load only relevant q/k/v vectors or hopfield memory patterns	prove retrieved vectors are from the committed model root
  ibc supply-rank	send only high-focus bucket updates	include proofs that updates match source network state
  p2p model training	update only parameters touched by local batch	prove updates are valid against model root without leaking whole model

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• 5. operational flow

• context/event triggers a focus-flow update or model inference.

• sat retrieval loads only the k most relevant parameters/edges from the graph or model.

• local computation produces Δ-rank or inference output.

• cgps proof is generated:

  • the retrieved slices are hashed
  • a merkle multiproof shows they belong to the committed global root

• broadcast update + proof over consensus or ibc.

• verification by peers/validators:

  • check proof against known root
  • accept update if valid without running full computation

• commitment: merge updates into global graph/model root.

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• 6. benefits of combined sat + cgps

• lower cost – sat’s sparse ops reduce gpu/memory bandwidth, cgps keeps proof size small.

• global trust – cgps proofs prevent malicious peers from polluting the collective focus or model state.

• scalability – sat lets planetary-scale ai run on a network of mixed-capability nodes.

• open participation – anyone can contribute compute to the system without having to trust or be trusted.

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• 7. next steps

• add sat kernels (wgsl/cuda) to ffcm for graph focus and llm memory ops

• extend merkle commitment scheme to cover sat slices and Δ-rank vectors

• design compact multiproof format optimised for ibc packet size limits

• prototype p2p llm inference where each forward pass is proven with cgps

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  if you want, i can now draft a visual diagram showing how sat and cgps slot into the semantic rollup → ibc supply-rank → ffcm pipeline, so you get a clear architecture view of the integration points.

  do you want me to produce that diagram next?