The following extracts from the paper’s Appendix help illustrate how the proposed coordinates trigger LLM instant “conceptual collapse” toward a shared grammar.
But please beware that:
The framework provides a “universal dictionary”, the LLM is simply following the instructions to “port” its existing knowledge into the new labels. So, while this “collapse” feels like a profound proof to a human, for an LLM, it is actually a standard feature of how LLM process data, not necessarily a confirmation of a new law of the universe.
A.3 Domain instantiations (clean “dictionary table”)
Each row below is an example of a consistent adapter. The point is not that these domains are the same, but that the roles in the equations can be mapped consistently.
| Domain | ρ(x,t) (what spreads) | J(x,t) (how it moves) | Π(x,t) / constraints | γ (domain-lock) | τ (agitation) | Ô / P_Ô (discrete events) |
|---|---|---|---|---|---|---|
| Non-eq. physics / transport | particle/mass density | drift + diffusion flux | stress / boundary geometry | confinement strength | temperature/noise | measurement protocol / boundary switch |
| Chemistry / reaction–diffusion | concentration fields | diffusion + advective flux | reaction network constraints | compartmentalization | thermal/chemical noise | catalyst insertion / phase change trigger |
| Ecology / epidemiology | population/infection density | migration/contact flux | network structure, habitat borders | quarantine / barriers | environmental variability | policy interventions / testing regime |
| Economics / macro-flow | capital/liquidity density | trade/credit flows | regulations, friction, market microstructure | capital controls / margin rules | volatility/shocks | rule changes / accounting reclassification |
| Organizations / ops | task/queue density | handoff/throughput flux | org chart, bottlenecks, approvals | SOP rigidity / access control | interruptions/context switching | reorg / new KPI / workflow redesign |
| Cognition / awareness | attention/belief density | associative/inferential flow | cognitive constraints, priors | fixation / schema lock | distraction/noise | reframing / “label change” update |
| AGI / LLM systems | probability mass over hypotheses | message passing / inference flow | architecture, memory gates, safety constraints | alignment constraints, tool permissions | sampling temperature, noise, distribution shift | policy update, prompt spec change, tool enable/disable |
| Legal / governance | norm/precedent density | propagation via cases/decisions | jurisdiction boundaries, procedures | doctrine rigidity | societal turbulence | statutory change / landmark ruling |