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{XVII}{Decomposition, Coarse-Graining, and Robust Relationality}
4 
5 Relationality is always assessed relative to a way of dividing a realization
6 into components. That dependence is not a minor technicality. If every
7 participant, artifact, and channel is merged into one component, the complete
8 workspace becomes local by definition. If a centralized state is recoded into
9 several complementary shares, the same centralized process can be made to look
10 irreducibly distributed. A defensible theory must therefore say which
11 partitions count as admissible, which quantities survive faithful aggregation,
12 and how sensitive a certificate is to alternative descriptions of the same
13 system.
14 
15 \topic{54}{The Decomposition Problem}
16 
17 Let \(\Omega\) be a finite set of primitive carriers at a declared audit
18 resolution. A primitive carrier may be a person, a model instance, a process,
19 a memory store, an instrument, or another independently tracked mechanism.
20 The word \emph{primitive} is relative to the audit. It does not assert a final
21 metaphysical atomization of the system.
22 
23 \begin{definition}[System decomposition]\label{def:system-decomposition}
24 A decomposition of a carrier presentation is a tuple
25 \[
26 \mathcal D
27 =
28 \bigl(
29 \Pi,\mathbf O,G_{\Pi},\mathcal I_{\Pi}
30 \bigr),
31 \]
32 where:
33 \begin{itemize}
34 \item \(\Pi=\{B_\alpha\}_{\alpha\in A}\) is a partition of \(\Omega\);
35 \item \(O_\alpha\) is the declared local-access map for block \(B_\alpha\),
36  producing the local state or history available at that component;
37 \item \(G_{\Pi}\) records the declared communication, transfer, and causal
38  interfaces among the blocks; and
39 \item \(\mathcal I_{\Pi}\) is the family of feasible interventions at that
40  resolution.
41 \end{itemize}
42 The accessible information of component \(\alpha\) is the sigma-field
43 \[
44 \mathscr F_\alpha^{\mathcal D}
45 =
46 \sigma\!\left(O_\alpha(\mathbf H_t)\right).
47 \]
48 Every shared bus, common memory, supervisor, or artifact that can alter more
49 than one local state must appear either as its own carrier or as an explicit
50 channel in \(G_{\Pi}\).
51 \end{definition}
52 
53 The same physical realization can support several decompositions. One may
54 separate a model from its executor, merge them into one computational unit, or
55 treat a persistent artifact as its own component. These alternatives are not
56 mere renamings when they change local access or feasible interventions. Every certificate should therefore display the full specification
57 \[
58 \SRW(W_t;\varsigma),
59 \qquad
60 \varsigma=(\mathcal D,Y^+,\ell,\tau,\mathcal I,\mathcal N,\Theta).
61 \]
62 This part varies the decomposition coordinate while holding the remaining
63 coordinates fixed. Part~XVIII treats the full specification family.
64 
65 \begin{definition}[Refinement and coarsening]\label{def:decomposition-refinement}
66 Let \(\mathcal D_f\) and \(\mathcal D_c\) be decompositions of the same carrier
67 presentation. The fine decomposition refines the coarse decomposition,
68 written
69 \[
70 \mathcal D_f\preceq\mathcal D_c,
71 \]
72 when there is a surjection
73 \[
74 q:V_f\longrightarrow V_c
75 \]
76 such that each coarse component is the union of the fine components in one
77 fiber of \(q\), and its accessible information is generated only from those
78 fine components. The aggregation is \emph{information faithful} when
79 \[
80 \mathscr F_B^{\mathcal D_c}
81 =
82 \bigvee_{i\in q^{-1}(B)}
83 \mathscr F_i^{\mathcal D_f}
84 \qquad(B\in V_c).
85 \]
86 It is \emph{structurally faithful} when it also retains every internal
87 compatibility condition and every boundary transfer condition needed to
88 recover the original global-section problem.
89 \end{definition}
90 
91 Refinement and coarsening are directional. A coarse component may contain
92 information that was spread across several finer nodes. Conversely, a fine
93 description may expose internal channels that disappear when a macro-node is
94 formed. The next results identify what is preserved when the aggregation is
95 faithful.
96 
97 \topic{55}{Faithful Structural Coarse-Graining}
98 
99 Let the vertex set of a core-transfer diagram be partitioned as
100 \[
101 V=V_1\sqcup\cdots\sqcup V_m.
102 \]
103 Write the transfer discrepancy as
104 \[
105 D_H
106 =
107 \begin{pmatrix}
108 D_{\mathrm{int}}\\
109 D_{\partial}
110 \end{pmatrix},
111 \qquad
112 D_{\mathrm{int}}
113 =
114 \bigoplus_{\alpha=1}^{m}D_\alpha,
115 \]
116 where \(D_\alpha\) contains the edge constraints internal to \(V_\alpha\),
117 and \(D_{\partial}\) contains the constraints crossing between blocks. Define
118 the internally coherent macro-state spaces
119 \[
120 W_\alpha=\ker D_\alpha,
121 \qquad
122 W_{\Pi}=\bigoplus_{\alpha=1}^{m}W_\alpha.
123 \]
124 Let
125 \[
126 J_\Pi:W_\Pi\hookrightarrow\mathcal C_V
127 \]
128 be the canonical isometric inclusion, and define the quotient discrepancy
129 \[
130 D_\Pi=D_{\partial}J_\Pi.
131 \]
132 The quotient does not replace a group of nodes by an arbitrary summary. Its
133 macro-state is the complete internal section space of that group, and its
134 boundary operator retains all cross-block compatibility equations.
135 
136 \begin{theorem}[Faithful coarse-graining]\label{thm:faithful-coarse-graining}
137 For every finite partition of the vertex set,
138 \[
139 \boxed{
140 \ker D_H
141 =
142 J_\Pi\ker D_\Pi.
143 }
144 \]
145 Equivalently,
146 \[
147 \boxed{
148 \Gamma(H)
149 \cong
150 \ker D_\Pi
151 =
152 \ker(D_\Pi^*D_\Pi).
153 }
154 \]
155 In particular,
156 \[
157 \dim\Gamma(H)
158 =
159 \dim W_\Pi-\operatorname{rank}(D_\Pi).
160 \]
161 Thus faithful coarse-graining preserves the exact structural workspace even
162 though it changes the number and interpretation of the displayed nodes.
163 \end{theorem}
164 
165 \begin{proof}
166 A vector \(c\in\mathcal C_V\) lies in \(\ker D_H\) exactly when
167 \[
168 D_{\mathrm{int}}c=0
169 \qquad\text{and}\qquad
170 D_{\partial}c=0.
171 \]
172 The first condition is equivalent to \(c=J_\Pi w\) for a unique
173 \(w\in W_\Pi\). Substitution into the second condition gives
174 \[
175 D_\Pi w
176 =
177 D_{\partial}J_\Pi w
178 =0.
179 \]
180 Hence \(c\in\ker D_H\) if and only if
181 \(c=J_\Pi w\) with \(w\in\ker D_\Pi\). The Laplacian identity follows from
182 \(\ker(D_\Pi^*D_\Pi)=\ker D_\Pi\), and the dimension formula is rank-nullity.
183 \end{proof}
184 
185 The theorem supplies a precise sense in which a workspace may be represented
186 at several resolutions without changing its exact core. The preservation
187 fails when the macro-state discards internal section coordinates or when
188 boundary equations are omitted.
189 
190 \begin{corollary}[Two-scale coherence bound]\label{cor:two-scale-decomposition}
191 Let \(P_\Pi\) be the orthogonal projector onto \(J_\Pi W_\Pi\). Let
192 \(\gamma_{\mathrm{int}}>0\) be the smallest positive eigenvalue of
193 \(D_{\mathrm{int}}^*D_{\mathrm{int}}\), and let
194 \(\gamma_\Pi>0\) be the smallest positive eigenvalue of
195 \(D_\Pi^*D_\Pi\). Then every \(c\in\mathcal C_V\) satisfies
196 \[
197 \boxed{
198 \operatorname{dist}(c,\Gamma(H))
199 \leq
200 \frac{\|D_{\mathrm{int}}c\|}{\sqrt{\gamma_{\mathrm{int}}}}
201 +
202 \frac{
203 \|D_\Pi J_\Pi^*P_\Pi c\|
204 }{\sqrt{\gamma_\Pi}}.
205 }
206 \]
207 The first term measures incoherence within macro-components. The second
208 measures incompatibility among their internally coherent states.
209 \end{corollary}
210 
211 \begin{proof}
212 By the triangle inequality,
213 \[
214 \operatorname{dist}(c,\Gamma(H))
215 \leq
216 \|c-P_\Pi c\|
217 +
218 \operatorname{dist}(P_\Pi c,\Gamma(H)).
219 \]
220 The workspace Poincar\'e estimate applied to \(D_{\mathrm{int}}\) bounds the
221 first term. Write \(P_\Pi c=J_\Pi w\). Theorem~\ref{thm:faithful-coarse-graining}
222 and the corresponding estimate for \(D_\Pi\) bound the second term by
223 \(\|D_\Pi w\|/\sqrt{\gamma_\Pi}\). Since \(J_\Pi\) is isometric,
224 \(w=J_\Pi^*P_\Pi c\).
225 \end{proof}
226 
227 This decomposition is useful computationally. Internal blocks can be solved
228 or compressed independently, after which only the boundary discrepancy must
229 be assembled globally. It also gives a diagnostic distinction between a
230 workspace that fails inside its local components and one whose local
231 components are coherent but mutually incompatible.
232 
233 \topic{56}{Predictive Risk Under Aggregation}
234 
235 The structural core can be preserved by faithful coarse-graining, while
236 coalition counts generally are not. Let
237 \[
238 \mathscr F_S^{\mathcal D}
239 =
240 \bigvee_{i\in S}\mathscr F_i^{\mathcal D}
241 \]
242 be the information available to coalition \(S\) under decomposition
243 \(\mathcal D\). For a declared loss \(\ell\), write
244 \[
245 \Risk_{\mathcal D}(S)
246 =
247 \inf_f
248 \mathbb E\!\left[
249 \ell\bigl(Y^+,f(\mathscr F_S^{\mathcal D})\bigr)
250 \right].
251 \]
252 
253 \begin{theorem}[Bayes-risk transport under faithful aggregation]
254 \label{thm:risk-aggregation}
255 Suppose \(\mathcal D_f\preceq\mathcal D_c\) through
256 \(q:V_f\to V_c\), and suppose the aggregation is information faithful. Then
257 for every coarse coalition \(S\subseteq V_c\),
258 \[
259 \boxed{
260 \Risk_{\mathcal D_c}(S)
261 =
262 \Risk_{\mathcal D_f}\bigl(q^{-1}(S)\bigr).
263 }
264 \]
265 Consequently,
266 \[
267 k_\varepsilon(\mathcal D_c)
268 \leq
269 k_\varepsilon(\mathcal D_f),
270 \]
271 where coalition size is counted in displayed nodes.
272 \end{theorem}
273 
274 \begin{proof}
275 Information faithfulness gives
276 \[
277 \mathscr F_S^{\mathcal D_c}
278 =
279 \bigvee_{B\in S}
280 \bigvee_{i\in q^{-1}(B)}
281 \mathscr F_i^{\mathcal D_f}
282 =
283 \mathscr F_{q^{-1}(S)}^{\mathcal D_f}.
284 \]
285 The two Bayes risks optimize over the same measurable decision rules and are
286 therefore equal. If a fine coalition of size \(k\) is sufficient within
287 \(\varepsilon\), the set of coarse blocks meeting that coalition has at most
288 \(k\) elements and contains at least the same information. This proves the
289 coalition-size inequality.
290 \end{proof}
291 
292 The theorem makes the source of a common error explicit. A minimal coalition
293 size of two at one resolution can become one after those two nodes are merged.
294 Node count is therefore a decomposition-relative statistic.
295 
296 A more stable quantity measures primitive carrier cost. Let
297 \(w_\omega>0\) be a declared cost for each \(\omega\in\Omega\), and assign a
298 block the cost
299 \[
300 c(B)=\sum_{\omega\in B}w_\omega.
301 \]
302 Define the sufficient support cost
303 \[
304 \boxed{
305 s_\varepsilon(\mathcal D)
306 =
307 \min_{S\subseteq V_{\mathcal D}}
308 \left\{
309 \sum_{B\in S}c(B):
310 \Risk_{\mathcal D}(S)
311 \leq
312 \Risk_{\mathcal D}(V_{\mathcal D})+\varepsilon
313 \right\}.
314 }
315 \]
316 If \(\mathcal D_f\preceq\mathcal D_c\) is information faithful, then
317 \[
318 \boxed{
319 s_\varepsilon(\mathcal D_f)
320 \leq
321 s_\varepsilon(\mathcal D_c).}
322 \]
323 The fine decomposition permits every union of coarse blocks and may also
324 permit cheaper sub-block coalitions. Equality holds whenever an optimal fine
325 coalition is a union of complete coarse fibers. This weighted support measure
326 does not remove the need to choose primitive carriers, but it prevents a
327 large macro-component from being counted as a single inexpensive unit merely
328 because it was assigned one node label.
329 
330 \topic{57}{Trivialization by Arbitrary Redescription}
331 
332 The dependence on decomposition is unavoidable. Two elementary constructions
333 show why a certificate cannot be required to survive every mathematically
334 possible partition.
335 
336 \begin{proposition}[Coarsening and secret-sharing trivializations]
337 \label{prop:decomposition-trivialization}
338 The following statements hold.
339 \begin{enumerate}
340 \item Any finite realization can be coarsened to a single displayed component.
341  Relative to that decomposition, the full-system state is local and
342  \(k_0\leq1\).
343 \item Let \(Z\) be uniform on a finite abelian group \(\mathsf G\). Let
344  \(K\) be an independent uniform group element and define
345  \[
346  X_1=K,
347  \qquad
348  X_2=Z-K.
349  \]
350  Then
351  \[
352  I(Z;X_1)=I(Z;X_2)=0,
353  \qquad
354  H(Z\mid X_1,X_2)=0.
355  \]
356  Under logarithmic loss,
357  \[
358  \Risk(\{1\})=\Risk(\{2\})=\log|\mathsf G|,
359  \qquad
360  \Risk(\{1,2\})=0,
361  \]
362  so the declared two-node representation has \(k_0=2\) and joint advantage
363  \(\log|\mathsf G|\), even when a single centralized encoder generated both
364  shares.
365 \end{enumerate}
366 \end{proposition}
367 
368 \begin{proof}
369 The first statement follows by taking the indiscrete partition
370 \(\Pi=\{\Omega\}\). For the second, conditioning on any value of \(Z\) leaves
371 \(K\), and hence \(X_1\), uniform. Translation invariance of the uniform law
372 also leaves \(X_2=Z-K\) uniform, so each share is independent of \(Z\). The
373 pair reconstructs \(Z=X_1+X_2\), which gives the entropy and Bayes-risk
374 identities.
375 \end{proof}
376 
377 The secret-sharing example is a valid distributed code. What it does not show
378 is that the process producing or using the code is causally distributed across
379 the declared carriers. If one hidden controller creates both shares, stores
380 the key, or jointly selects their updates, that controller belongs in the
381 causal inventory. Coalition irreducibility and matched predictive nulls remain
382 necessary tests, but their interpretation is conditional on a defensible
383 interface model.
384 
385 This distinction suggests two levels of claim:
386 \begin{description}
387 \item[Encoding-relative relationality.] No declared local view is sufficient.
388 \item[Carrier-relative relationality.] The declared views also correspond to
389 admissible, separately tracked causal interfaces with no omitted common
390 controller.
391 \end{description}
392 The stronger claim requires the decomposition audit developed next.
393 
394 \topic{58}{Admissible Decomposition Families}
395 
396 No purely formal rule can identify the uniquely correct decomposition of every
397 physical or computational system. The practical goal is instead to define a
398 family of decompositions that are defensible for the question being asked and
399 to report how the certificate changes across that family.
400 
401 \begin{definition}[Admissible decomposition family]
402 \label{def:admissible-decomposition-family}
403 An admissible family \(\mathfrak D\) is a predeclared collection of
404 decompositions of the same carrier presentation satisfying the following
405 audit conditions.
406 \begin{enumerate}
407 \item \textbf{Carrier continuity.} Each component corresponds to a process,
408  artifact, or mechanism that can be tracked through the relevant time scale.
409 \item \textbf{Access locality.} The local state contains only information
410  available through the declared component and its recorded incoming channels.
411 \item \textbf{Channel completeness.} Shared memories, buses, supervisors,
412  caches, and synchronized external cues are represented explicitly.
413 \item \textbf{Intervention separability.} At least some component mechanisms
414  or channels can be altered without directly rewriting the entire system.
415 \item \textbf{Target independence.} The decomposition and its alternatives
416  are fixed without using held-out outcomes to manufacture a favorable result.
417 \item \textbf{Resolution relevance.} A proposed split is retained only when
418  it changes access, intervention, reconstruction, or transfer structure at the
419  declared measurement resolution.
420 \item \textbf{Alternative coverage.} The family contains the principal
421  plausible merges, splits, and artifact assignments that a skeptical analyst
422  would consider.
423 \end{enumerate}
424 \end{definition}
425 
426 Let \(m_q(W;\mathcal D)\) be the signed margin of gate \(q\), oriented so that
427 \[
428 m_q(W;\mathcal D)>0
429 \]
430 means that the gate passes after its uncertainty correction. Define the
431 decomposition envelope
432 \[
433 \underline m_q
434 =
435 \inf_{\mathcal D\in\mathfrak D}m_q(W;\mathcal D),
436 \qquad
437 \overline m_q
438 =
439 \sup_{\mathcal D\in\mathfrak D}m_q(W;\mathcal D),
440 \]
441 and its sensitivity width
442 \[
443 \Delta_q^{\mathrm{dec}}
444 =
445 \overline m_q-\underline m_q.
446 \]
447 
448 \begin{definition}[Decomposition-robust certificate]
449 \label{def:decomposition-robust-certificate}
450 A workspace passes the \(\mathfrak D\)-robust certificate at level \(L\) when
451 \[
452 \boxed{
453 \operatorname{Certify}_{L,\mathfrak D}^{\mathrm{rob}}(W)
454 =
455 \bigwedge_{q\in\mathcal J(L)}
456 \left\{
457 \inf_{\mathcal D\in\mathfrak D}
458  m_q(W;\mathcal D)>0
459 \right\}.
460 }
461 \]
462 A pass for one selected decomposition is a \emph{decomposition-specific}
463 claim. A pass throughout \(\mathfrak D\) is a \emph{family-robust} claim. A
464 claim is \emph{decomposition fragile} when at least one required gate changes
465 sign inside the admissible family.
466 \end{definition}
467 
468 Universal invariance over all partitions is neither possible nor desirable,
469 as Proposition~\ref{prop:decomposition-trivialization} shows. The family
470 \(\mathfrak D\) must be broad enough to challenge the favored description and
471 narrow enough to exclude partitions with no operational meaning.
472 
473 \topic{59}{Stability Under Decomposition Transport}
474 
475 Exact faithful aggregation preserves the structural core, but practical
476 alternative decompositions usually introduce approximation. Their certificate
477 can still be controlled by transporting a reference workspace and comparing
478 gate margins.
479 
480 Fix a reference decomposition \(\mathcal D_0\). For each
481 \(\mathcal D\in\mathfrak D\), let
482 \[
483 \Phi_{\mathcal D}:W^{\mathcal D_0}\longrightarrow W^{\mathcal D}
484 \]
485 be a declared workspace correspondence and let
486 \(\delta_{\mathcal D}\) measure its structural and causal identity defect.
487 Assume gate \(q\) has a transport bound
488 \[
489 \left|
490  m_q(\Phi_{\mathcal D}W;\mathcal D)
491  -m_q(W;\mathcal D_0)
492 \right|
493 \leq
494 L_q\delta_{\mathcal D}+b_q(\mathcal D),
495 \]
496 where \(L_q\) is a sensitivity constant and \(b_q\) records model mismatch not
497 captured by the identity distance.
498 
499 \begin{theorem}[Decomposition-transport robustness]
500 \label{thm:decomposition-robustness}
501 If, for every required gate \(q\),
502 \[
503 \boxed{
504  m_q(W;\mathcal D_0)
505 >
506 \sup_{\mathcal D\in\mathfrak D}
507 \left(
508 L_q\delta_{\mathcal D}+b_q(\mathcal D)
509 \right),
510 }
511 \]
512 then \(W\) passes the \(\mathfrak D\)-robust certificate. Conversely, if for
513 some required gate
514 \[
515  m_q(W;\mathcal D_0)
516 +
517 \sup_{\mathcal D\in\mathfrak D}
518 \left(
519 L_q\delta_{\mathcal D}+b_q(\mathcal D)
520 \right)
521 <0,
522 \]
523 then that gate fails throughout the family.
524 \end{theorem}
525 
526 \begin{proof}
527 For every \(\mathcal D\in\mathfrak D\), the transport bound gives
528 \[
529  m_q(\Phi_{\mathcal D}W;\mathcal D)
530 \geq
531 m_q(W;\mathcal D_0)
532 -
533 L_q\delta_{\mathcal D}
534 -
535 b_q(\mathcal D).
536 \]
537 The first hypothesis makes the right-hand side positive uniformly in
538 \(\mathcal D\), which proves robust passage of every required gate. The second
539 statement follows from the corresponding upper bound.
540 \end{proof}
541 
542 When \(b_q\equiv0\), a convenient certificate radius is
543 \[
544 \boxed{
545 r_{\mathrm{dec}}(W)
546 =
547 \min_{q:L_q>0}
548 \frac{m_q(W;\mathcal D_0)}{L_q}.
549 }
550 \]
551 Every admissible family satisfying
552 \[
553 \sup_{\mathcal D\in\mathfrak D}\delta_{\mathcal D}
554 <
555 r_{\mathrm{dec}}(W)
556 \]
557 preserves the sign of all required gate margins. In applications, the
558 transport terms can be bounded using earlier results:
559 \begin{center}
560 \small
561 \begin{tabularx}{\textwidth}{@{}>{\bfseries\raggedright\arraybackslash}p{0.22\textwidth}>{\raggedright\arraybackslash}X@{}}
562 \toprule
563 Gate family & Relevant transport control \\
564 \midrule
565 Structural coherence & Transfer-Laplacian projector drift and spectral gap. \\
566 Predictive alignment & Divergence between transported conditional-law states. \\
567 Causal efficacy & Distance between matched intervention kernels. \\
568 Relationality & Coalition-risk distortion and matched-null preservation error. \\
569 Reconstruction & Perturbation of lower frame bounds and handoff error. \\
570 Persistence and identity & The coordinatewise identity profile from Part~XII. \\
571 \bottomrule
572 \end{tabularx}
573 \end{center}
574 
575 The theorem is intentionally margin based. A result barely above threshold at
576 one decomposition should not be described as robust when a small, defensible
577 change of interface makes it disappear.
578 
579 \topic{60}{Decomposition Audit and Reporting}
580 
581 A complete decomposition audit should proceed in the following order.
582 \begin{enumerate}
583 \item Inventory the primitive carriers at the chosen temporal and physical
584  resolution.
585 \item Record every shared resource and distinguish local state from incoming
586  information.
587 \item Choose a reference decomposition from independently manipulable and
588  temporally trackable interfaces.
589 \item Construct an admissible family containing the principal plausible
590  merges, splits, and artifact assignments.
591 \item For every alternative, specify the correspondence to the reference
592  workspace and validate its manipulation checks.
593 \item Recompute the structural, predictive, causal, coalition, reconstruction,
594  and identity margins.
595 \item Report the full decomposition envelope, not only the most favorable
596  member of the family.
597 \end{enumerate}
598 
599 The report should state:
600 \[
601 \begin{aligned}
602 &\text{reference decomposition and audit resolution},\\
603 &\text{admissible family and reasons for excluded partitions},\\
604 &\text{hidden-resource and common-controller checks},\\
605 &\text{faithful-aggregation maps and identity defects},\\
606 &\text{gatewise minima, maxima, and sensitivity widths},\\
607 &\text{strongest decomposition-specific and family-robust conclusions}.
608 \end{aligned}
609 \]
610 
611 Four controls are especially important:
612 \begin{enumerate}
613 \item merge components connected by an uninterruptible common controller and
614  test whether the relational claim collapses;
615 \item split a known centralized controller into complementary local views and
616  verify that the protocol rejects the resulting secret-sharing appearance of
617  distributedness;
618 \item expose or remove shared caches, external cues, and common memory that
619  were absent from the favored graph; and
620 \item repeat the frozen certificate across the complete admissible family.
621 \end{enumerate}
622 
623 For the motivating human--AI collaboration, this analysis changes the form of
624 the empirical question. It is not enough to ask whether the human, model,
625 executor, and artifact store form a workspace under one natural description.
626 The stronger question is whether the same operative state and its causal role
627 survive plausible alternatives, such as merging model and executor, separating
628 conversation state from persistent artifacts, or making shared orchestration
629 channels explicit. Those measurements have not yet been performed. The case
630 therefore remains decomposition-specific and observational.

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