Stratified Relational Workspace Theory

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1 % This file is part of the modular source for Stratified Relational Workspace Theory.
2 % !TeX root = ../Stratified_Relational_Workspace_Theory.tex
3 \theorypart{XXIV}{Theory Hierarchy}
4 
5 \topic{93}{Levels of Organization}
6 
7 \subtopic{Level 0: Archive}
8 \[
9 \delta_{\mathrm{coh}}\text{ may be low},
10 \qquad
11 \eta_{\mathrm{causal}}=0.
12 \]
13 
14 \subtopic{Level 1: Shared representation}
15 \[
16 d_\varepsilon>0,
17 \qquad
18 \delta_{\mathrm{coh}}\leq\varepsilon.
19 \]
20 
21 \subtopic{Level 2: Coordinated operational workspace}
22 \[
23 \delta_{\mathrm{align}}^{\mathcal I}\leq\varepsilon,
24 \qquad
25 \eta_{\mathrm{causal}}^\nu>0.
26 \]
27 
28 \subtopic{Level 3: Relational workspace}
29 \[
30 k_\varepsilon\geq2,
31 \qquad
32 \Delta_{\mathrm{joint}}^\ell>0,
33 \qquad
34 \Delta_{\mathrm{tr}}^{\min}(\mathcal Q)>0.
35 \]
36 
37 \subtopic{Level 4: Persistent relational workspace}
38 \[
39 d_{\mathrm{id}}(W_t,W_{t+\tau})
40 \leq\varepsilon.
41 \]
42 
43 \subtopic{Level 5: Self-maintaining workspace}
44 \[
45 \eta_{D\to M}>0,
46 \qquad
47 \eta_{M\to R}>0,
48 \qquad
49 \eta_{R\to v}>0,
50 \qquad
51 \Delta_{\mathrm{repair}}^{\mathrm{spec}}>0,
52 \qquad
53 \sup_t e_t\leq e_{\max}.
54 \]
55 
56 \subtopic{Level 6: Workspace agent}
57 \[
58 \begin{aligned}
59 &\eta_{G\to A}>0,
60 \qquad
61 \eta_{W\to A}>0,
62 \qquad
63 \delta_Q\leq\varepsilon_Q,\\
64 &\operatorname{Reg}_t(\pi)
65  \leq2\varepsilon_Q+\delta_{\mathrm{opt}},
66 \qquad
67 k_{\mathrm{ctl},\varepsilon}\geq2,
68 \qquad
69 \operatorname{SelfMaintenance}.
70 \end{aligned}
71 \]
72 
73 \subtopic{Orthogonal formation-provenance axis}
74 \[
75 \operatorname{Scaffolded}
76 \longrightarrow
77 \operatorname{AdaptivelyParameterised}
78 \longrightarrow
79 \operatorname{StructurallyAdaptive}
80 \longrightarrow
81 \operatorname{EndogenouslyConstituted}.
82 \]
83 This axis is independent of Levels~0--6. A scaffolded system can instantiate a
84 high-level relational workspace, while an endogenously learned organization
85 can fail every operational workspace gate.
86 
87 \subtopic{Decomposition-robustness qualifier}
88 
89 Every level is first defined relative to a decomposition \(\mathcal D\). A
90 family-robust version carries the additional requirement
91 \[
92 \inf_{\mathcal D\in\mathfrak D}
93  m_q(W;\mathcal D)>0
94 \qquad
95 \text{for every gate required at that level}.
96 \]
97 This is a robustness qualifier rather than a higher agency level. A system can
98 be highly agentive under one fixed interface while remaining decomposition
99 fragile.
100 
101 \subtopic{Specification-robustness and identification qualifier}
102 
103 Every level is also relative to a complete scientific specification
104 \(\varsigma\). A specification-robust version requires
105 \[
106 \inf_{\varsigma\in\mathfrak S}
107  m_q(W;\varsigma)>0
108 \qquad
109 \text{for every gate required at that level}.
110 \]
111 An identified version additionally requires the sign of each required lower
112 envelope to be constant across the realization set compatible with the
113 available experiment family. An empirical claim must finally subtract the
114 uniform finite-sample error radius before declaring the lower envelope
115 positive. These are epistemic qualifiers, not additional agency levels.
116 
117 \subtopic{Separate, unresolved axis}
118 \[
119 \operatorname{PhenomenalConsciousness}.
120 \]

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