The computable theory of group organizations: paradigm evolution from Shannon efficiency to Bitcoin consensus Introduction: Reconstruction of Communication Dimension The core of traditional information theory (Shannon paradigm) lies in solving the symbol transmission efficiency of point-to-point communication, while the Bitcoin protocol reveals the data consensus law of peer-to-peer groups. This transformation marks the shift of computational theory from "precise restoration of information" to "stable emergence of meaning". This article aims to define the logical gap between individual certainty and group stability through two major conjectures of the computability theory of group organizations. --- 2. Core conjecture: the logical hierarchy of abstraction and emergence Assumption 1: Abstract existence is a native attribute of a group At the individual level, data is only manifested as physical symbols or meaningless fragments of information. Only when individuals enter group organizations through non exchange interactions can abstract existences such as "meaning," "value," or "consensus" be generated. >Inference: Any attempt to define "value" within a single node or isolated Turing machine is logically incomplete. Conjecture 2: Theoretical stratification arises from differences in the emergence of objects Theoretical stratification is essentially due to the emergence of group attributes through the interaction of individual attributes. Due to the different scales of the research subjects (individuals or groups), their presented attributes are different, which in turn determines the transition of underlying theoretical tools. ** * Object differences * *: As the research object shifts from "individual" to "group", the underlying logic evolves from determinacy to probabilism. ** * Attribute Transition * *: Group attributes are not simply the sum of individuals, but rather new dimensions generated through nonlinear interactions. --- 3. The computability trait of group organizations There are essential differences between group organization computation and individual Turing computation in terms of objective function and implementation path: 3.1 Certainty and Consistency (Individual Side) The pursuit of individual level computation is * * certainty * *, which comes from * * consistency * *. ** * Logical Model * *: Following the computability theory of Turing machines. ** * Result * *: Generate deterministic and repeatable operations. However, this consistency often expresses fragmented information that is highly reduced but lacks macroscopic significance. 3.2 Stability and completeness (group side) The calculation at the group level pursues stability, rather than absolute certainty. ** * Logical model * *: isomorphic to Darwin's theory of evolution. *Implementation path: Prioritize completeness. The more complete the group structure, the more stable it is, which can carry abstract existence such as "meaning" and "consensus". *Fault tolerance mechanism: The stability of group structure inevitably requires individual "inconsistency" to provide fault tolerance space. --- 4. Logical Comparison: The Game of Consistency and Fault Tolerance |Dimension | Individual | Bitcoin Consensus Group| | :--- | :--- | :--- | |* * Logical Core * * | Consistency $\ rightarrow $Certainty | Inconsistency $\ rightarrow $Stability| |* * Primary goal * * | Pursuing consistency | Pursuing completeness| |* * Communication mode * * | Peer to Peer (P2P) | Peer to Group (P2G)| |* * Data Characteristics * * | Compressed Symbols (Pursuing Efficiency) | Non Compressed Data (Pursuing Consensus)| |* * Output attribute * * | Deterministic meaningless information | Abstract consensus/value/meaning| |Evolutionary Logic | Mechanical Repetition | Darwinian Isomorphism of Evolution| --- 5. Conclusion: The Birth of Meaning The computable theory of group organizations states that certainty comes from mechanical consistency, while vitality comes from stable inconsistency. ** Although individual certainty provides reliable instrumental attributes, it is "meaningless" at the macro level. The true 'meaning' and 'consensus' must be rooted in a stable group structure with fault tolerance. In this framework, Bitcoin's non compressed network is no longer seen as a sacrifice of efficiency, but rather as a completeness cost that must be paid in order to build an extremely stable group structure and carry "abstract value". This theory provides a rigorous logical foundation for understanding the evolution of complex social systems from quantum entanglement to Bitcoin consensus.