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{XXIII}{Relation to Prior Work}
4 
5 \topic{83}{Scope, Method, and Standards of Priority}
6 
7 \subtopic{83.1 Purpose of the literature review}
8 
9 The preceding parts construct a unified formal theory. Construction alone does
10 not establish priority. This part therefore asks a narrower question:
11 which ingredients are established, which are adaptations to a new domain,
12 which combinations appear to be unusual, and which claims remain open originality candidates?
13 
14 The audit uses five labels:
15 \[
16 \begin{array}{ll}
17 \mathsf{STD} & = \text{established concept, theorem, or technique},\\
18 \mathsf{ADP} & = \text{established machinery adapted to relational workspaces},\\
19 \mathsf{SYN} & = \text{nontrivial synthesis of established components},\\
20 \mathsf{CAN} & = \text{candidate original contribution requiring priority review},\\
21 \mathsf{EMP} & = \text{empirical claim not yet established in an uncontrolled system}.
22 \end{array}
23 \]
24 These labels describe the status of a claim, not its importance. A standard
25 result may be indispensable. A synthesis may be scientifically useful without
26 containing a new theorem. A candidate contribution may later be narrowed or
27 withdrawn when a closer precedent is found.
28 
29 \subtopic{83.2 Search scope and date}
30 
31 This review covers sources available through August 29, 2026. It includes:
32 \begin{itemize}
33 \item extended and distributed cognition, transactive memory, shared
34  intentionality, common knowledge, collective intelligence, and group
35  agency;
36 \item blackboard systems, global-workspace architectures, team cognition,
37  hybrid intelligence, and human--AI cooperation;
38 \item category-theoretic limits, local systems, holonomy, sheaves, \v{C}ech
39  descent, connection and sheaf Laplacians, consensus, and spectral
40  perturbation;
41 \item statistical sufficiency, causal states, information decomposition,
42  structural causal models, system identification, frames, erasure
43  recovery, and probabilistic process equivalence; and
44 \item agency, viability, control, empowerment, damage detection, repair, and
45  self-maintaining systems.
46 \end{itemize}
47 The search combined exact-title queries, component-level queries, backward
48 reference tracing, and comparison with recent formal work. It is a scholarly
49 priority review, not a legal patent search and not a proof that no uncatalogued,
50 unpublished, or differently named precedent exists.
51 
52 \subtopic{83.3 A stronger standard than name uniqueness}
53 
54 Failure to find the phrase ``Stratified Relational Workspace Theory'' in prior
55 literature is weak evidence. Priority is determined by mathematical and
56 operational equivalence, not by terminology. Let \(C\) be a claim in the
57 paper and \(S\) a prior source. Write
58 \[
59 S\preccurlyeq C
60 \]
61 when the main content of \(C\) follows from \(S\) after admissible relabeling,
62 restriction, or direct specialization. A substantive novelty residual exists
63 only when the claim contains content not absorbed by the closure of known
64 sources:
65 \[
66 \operatorname{Res}(C)
67 =
68 C\setminus
69 \operatorname{Cl}
70 \left(
71 \bigcup_{S\in\mathcal L}S
72 \right).
73 \]
74 This is a conceptual audit device rather than a set-theoretic definition of
75 ideas. Its purpose is to force an explicit account of what remains after the
76 standard machinery is removed.
77 
78 \subtopic{83.4 When a synthesis counts as a contribution}
79 
80 A conjunction of known ingredients is not automatically new. The present
81 framework treats a synthesis as a candidate contribution only when it satisfies
82 all three conditions:
83 \begin{enumerate}
84 \item \textbf{Non-redundancy.} Removing one of the joined layers changes the
85  class of systems certified or the predictions made.
86 \item \textbf{Formal integration.} The layers share declared objects,
87  transfer maps, interventions, or invariants rather than appearing as an
88  unconnected checklist.
89 \item \textbf{New discriminations.} The synthesis separates at least one
90  positive case from a matched near miss that the individual components do
91  not separate on their own.
92 \end{enumerate}
93 The anti-centralization, matched-null, non-collapse, provenance, replacement,
94 and repair-replay controls are important precisely because they make the
95 combination testable rather than merely terminological.
96 
97 \subtopic{83.5 Priority claims are coordinatewise}
98 
99 The analysis does not make one global novelty claim. It uses a priority
100 profile
101 \[
102 \boxed{
103 \mathbf p(C)
104 =
105 \left(
106  p_{\mathrm{concept}},
107  p_{\mathrm{object}},
108  p_{\mathrm{theorem}},
109  p_{\mathrm{certificate}},
110  p_{\mathrm{experiment}}
111 \right).
112 }
113 \]
114 For example, the philosophical concept of distributed cognition may be
115 standard while a specific mathematical object is adapted, a theorem is a
116 specialization of known spectral theory, the certificate is a synthesis, and
117 the empirical claim is unresolved. This prevents originality in one
118 coordinate from being used to imply originality in every coordinate.
119 
120 \topic{84}{Philosophical and Cognitive Ancestry}
121 
122 \subtopic{84.1 Extended cognition}
123 
124 The extended-mind tradition argues that external resources can participate in
125 cognitive processes when they are appropriately integrated with an agent's
126 activity \cite{ClarkChalmers1998}. Its critics emphasize that causal coupling
127 alone is too permissive and that cognition requires a principled mark or
128 boundary \cite{AdamsAizawa2001,Rupert2004}. Stratified Relational Workspace
129 Theory inherits the possibility of extracranial realization but changes the
130 question. It does not ask whether a notebook, model, or collaborator literally
131 belongs to one individual's mind. It asks whether a distributed realization
132 contains a persistent, causally operative, jointly reconstructible structure
133 that passes explicit anti-triviality gates.
134 
135 Accordingly,
136 \[
137 \operatorname{ExtendedCognition}
138 \centernot\Longleftrightarrow
139 \operatorname{SRW}.
140 \]
141 An externally scaffolded process may be cognitively extended without being
142 relationally irreducible. Conversely, an institution or multi-agent system may
143 instantiate a certified relational workspace without being an extension of any
144 single person's cognition.
145 
146 \subtopic{84.2 Distributed cognition}
147 
148 Distributed cognition studies cognitive organization across people,
149 representations, artifacts, and environments rather than locating all relevant
150 processing inside one individual \cite{Hutchins1995,HollanEtAl2000}. This is
151 the closest philosophical ancestor of the framework's ontology. It already
152 supports the central observation that the unit of analysis may be a coupled
153 system and that external representations can transform the computations
154 available to that system.
155 
156 The framework should therefore not claim the following ideas as new:
157 \begin{itemize}
158 \item cognition can be distributed across heterogeneous carriers;
159 \item artifacts can be active components of a cognitive process;
160 \item representational transformations can alter system-level performance; and
161 \item the relevant explanatory unit can exceed an individual organism.
162 \end{itemize}
163 The added ambition is mathematical and certifying. The theory specifies local
164 state spaces, transfer maps, compatible sections, causal sufficiency,
165 coalition irreducibility, persistence, replacement identity, formation
166 provenance, and matched nulls. Distributed cognition supplies the ontological
167 motivation. It does not by itself supply this complete formal certificate.
168 
169 \subtopic{84.3 Transactive memory and collective intelligence}
170 
171 Transactive-memory theory models the group-level organization of ``who knows
172 what'' and the processes by which members encode, retrieve, and coordinate
173 specialized knowledge \cite{Wegner1987,Lewis2003}. Collective-intelligence
174 research studies stable differences in group performance that are not reduced
175 to the intelligence of a single member \cite{WoolleyEtAl2010}. Both traditions
176 are directly relevant to the coalition layer.
177 
178 The distinction is:
179 \[
180 \begin{aligned}
181 \text{transactive memory}
182 &\approx
183 \text{distributed indexing and retrieval of expertise},\\
184 \text{collective intelligence}
185 &\approx
186 \text{system-level task capacity},\\
187 \text{relational workspace}
188 &\approx
189 \text{an invariant state plus transfer, causal, and identity structure}.
190 \end{aligned}
191 \]
192 A transactive-memory system may still be centralized by one coordinator. A
193 high-performing group may still be explainable by the best individual member.
194 The certificate therefore requires matched coalition risks and nulls
195 rather than inferring relationality from group success.
196 
197 \subtopic{84.4 Shared intention, common knowledge, and group agency}
198 
199 Common-knowledge theory formalizes nested epistemic conditions required by
200 many distributed protocols \cite{HalpernMoses1990,FaginEtAl1995}. Shared-action
201 accounts analyze jointly intended and mutually responsive activity
202 \cite{Bratman1992}. Group-agency theory asks when a collective can satisfy
203 rational and normative conditions associated with agency
204 \cite{ListPettit2011}.
205 
206 These literatures address questions that the theory deliberately keeps
207 separate:
208 \[
209 \begin{array}{ll}
210 \text{epistemic coordination} & \text{what members know about one another},\\
211 \text{shared intention} & \text{how intentions and plans are jointly organized},\\
212 \text{group agency} & \text{when collective attitudes and actions form an agent},\\
213 \text{SRW structure} & \text{how a distributed operative state exists and persists}.
214 \end{array}
215 \]
216 The workspace-agent predicate in Part~XVI is domain-relative and causal. It is
217 not a general account of corporate personhood, moral responsibility, or
218 collective intentionality.
219 
220 \topic{85}{Workspace Architectures and the Meaning of ``Workspace''}
221 
222 \subtopic{85.1 Global workspace theories}
223 
224 Global workspace theories use widespread availability or broadcast within a
225 cognitive architecture to explain conscious access and flexible control
226 \cite{Baars1988,DehaeneChangeux2011}. The shared word ``workspace'' can create
227 a misleading implication of equivalence. The theory neither assumes a
228 single broadcast hub nor defines consciousness by access to a global channel.
229 Its workspace may be distributed across agents and artifacts, and its
230 existence criterion is a conjunction of structural, predictive, causal,
231 relational, and persistence gates.
232 
233 The relation is therefore analogical rather than identificatory:
234 \[
235 \boxed{
236 \operatorname{SRW}(W)
237 \centernot\Longrightarrow
238 \operatorname{GlobalNeuronalWorkspace}(W)
239 \centernot\Longrightarrow
240 \operatorname{Conscious}(W).
241 }
242 \]
243 The term is retained because it denotes a domain in which jointly
244 available operations can be carried out. Every consciousness claim remains on
245 an explicitly separate axis.
246 
247 \subtopic{85.2 Dialogue and the Shared Workspace Framework}
248 
249 Pickering and Garrod's Shared Workspace Framework treats dialogue as a jointly
250 organized activity in which interlocutors construct, align, and use shared
251 representations, including persistent external artifacts
252 \cite{PickeringGarrod2021}. This is a direct conceptual and terminological
253 predecessor. The theory therefore cannot claim priority for the idea
254 that dialogue or collaboration operates through a shared workspace.
255 
256 The difference is one of formal scope. SRWT permits arbitrary graph-structured
257 human, machine, instrument, and artifact nodes and asks whether their common
258 organization passes typed-transport, coalition, causal, persistence, and
259 replacement gates. A dialogue can instantiate such a workspace, but the
260 shared-workspace account of dialogue does not by itself imply relational
261 irreducibility or persistent identity under carrier replacement.
262 
263 \subtopic{85.3 Blackboard systems}
264 
265 Blackboard architectures coordinate specialized modules through a shared data
266 structure \cite{HayesRoth1985}. They are an important engineering precedent
267 for artifact-mediated collaboration. They also provide a canonical near
268 miss. When the blackboard itself contains the complete operative state and
269 all modules merely read or write it, the system can fail the relational
270 irreducibility gate:
271 \[
272 k_0=1.
273 \]
274 A blackboard implementation can instantiate a relational workspace, but only
275 when no single board or controller is sufficient and when the transfer and
276 coalition tests show genuinely distributed operative capacity.
277 
278 \subtopic{85.4 Consensus and coordination}
279 
280 Network consensus studies how local interactions drive distributed states
281 toward agreement \cite{OlfatiSaberEtAl2007}. Agreement is not the same as a
282 workspace. Consensus often removes heterogeneity by converging all nodes to a
283 common value. Stratified relational workspaces preserve heterogeneous local
284 representations and may require complementary disagreement:
285 \[
286 X_i\not\cong X_j,
287 \qquad
288 E_i c\neq E_j c,
289 \qquad
290 (c_i)_i\in\Gamma(H).
291 \]
292 The global state is compatible, not necessarily copied. This distinction is
293 central to the anti-replication criterion.
294 
295 \subtopic{85.5 Terminological discipline}
296 
297 The phrase ``relational workspace'' is used here in a technical sense:
298 \begin{quote}
299 A state-bearing, operation-supporting organization whose relevant invariants
300 are distributed across declared components and preserved through admissible
301 transfers and time.
302 \end{quote}
303 It does not, by terminology alone, imply a mind, subject, self, institution,
304 shared intention, or conscious broadcast. Those stronger predicates require
305 separate definitions and evidence.
306 
307 \topic{86}{Local-to-Global Mathematics}
308 
309 \subtopic{86.1 Limits, local systems, and holonomy}
310 
311 The exact compatible-section object
312 \[
313 \Gamma(H)=\varprojlim C_i
314 \]
315 is a standard categorical limit construction \cite{MacLane1998}. For
316 invertible transfers on a connected graph, identifying global sections with
317 the fixed subspace of holonomy is standard local-system and bundle mathematics
318 \cite{Hatcher2002,Bredon1997}. Accordingly, Theorem~\(T_1\) is not claimed as
319 a new abstract theorem. Its role is foundational: it translates the workspace
320 question into an exact invariant-subspace question and exposes cycle
321 obstructions.
322 
323 The operation-closure and commutant statements are likewise standard
324 representation-theoretic consequences once the operation algebra and
325 intertwiners are defined. Their contribution is the specification of what
326 counts as a shared operation in the workspace model, not the discovery of
327 commutants.
328 
329 \subtopic{86.2 Cellular sheaves and sheaf Laplacians}
330 
331 Cellular sheaves encode heterogeneous local data and restriction maps, while
332 global sections express consistency across a cell complex. Their Laplacians
333 have kernels equal to spaces of global sections and support spectral analysis
334 of approximate consistency \cite{HansenGhrist2019,Robinson2017}. The transfer
335 Laplacian
336 \[
337 L_H=D_H^*D_H
338 \]
339 is therefore best understood as a workspace-specific sheaf or connection
340 Laplacian. The kernel theorem \(\ker L_H=\Gamma(H)\) is standard once the
341 coboundary operator is constructed.
342 
343 The appropriate priority statement is:
344 \[
345 \begin{aligned}
346 \text{sheaf/Laplacian mechanism} &:\ \mathsf{STD},\\
347 \text{workspace interpretation and gate integration} &:\ \mathsf{ADP}/\mathsf{SYN}.
348 \end{aligned}
349 \]
350 The transfer Laplacian itself is not presented as an
351 unprecedented mathematical object.
352 
353 \subtopic{86.3 Connection Laplacians and gauge covariance}
354 
355 Connection Laplacians compare vector-valued data transported across a graph
356 and naturally transform under local changes of coordinates
357 \cite{SingerWu2012}. The gauge rule
358 \[
359 H_e^g=g_{t(e)}H_eg_{s(e)}^{-1}
360 \]
361 and the conjugacy of holonomy are therefore standard. The theory uses
362 this structure to define realization identity and to prevent raw coordinate
363 matrices from being mistaken for invariant workspace content.
364 
365 This use is an adaptation with conceptual consequences. It makes model or
366 participant replacement a question about transported invariant organization,
367 not token equality. The general mathematics remains prior.
368 
369 \subtopic{86.4 \v{C}ech descent and gluing}
370 
371 Exact gluing, equalizer formulas, and \v{C}ech obstruction theory are standard
372 local-to-global constructions. Sheaf-theoretic contextuality provides a
373 prominent example in which the absence of a global section is itself the
374 substantive phenomenon \cite{AbramskyBrandenburger2011}. Part~XIII adapts this
375 logic to local workspaces and adds an anti-centralization requirement at the
376 meta-level.
377 
378 The exact descent theorems \(T_8\) and \(T_9\) should therefore be presented as
379 specialized consequences of established descent. The candidate contribution
380 is the combination:
381 \[
382 \text{descent}
383 +
384 \text{predictive sufficiency}
385 +
386 \text{causal equivalence}
387 +
388 \text{coalition anti-centralization}.
389 \]
390 Standard gluing alone does not certify an operative workspace of workspaces.
391 
392 \subtopic{86.5 Spectral perturbation}
393 
394 The projector-stability results in Part~IV belong to the classical perturbation
395 theory of invariant subspaces \cite{DavisKahan1970,Kato1995}. Bounds of the
396 form
397 \[
398 \|P-\widetilde P\|
399 \lesssim
400 \frac{\|L-\widetilde L\|}{\text{spectral gap}}
401 \]
402 are not new. Their workspace-specific role is to turn uncertainty in learned
403 transfers into uncertainty about identity, operation closure, and replacement.
404 The novelty, if any, lies in the downstream certificate built on the bound, not
405 in the perturbation inequality.
406 
407 \topic{87}{Predictive, Causal, and Information-Theoretic Precedents}
408 
409 \subtopic{87.1 Minimal predictive states}
410 
411 The conditional-law state
412 \[
413 Z_t=\mathbb P(Y_t^+\in\cdot\mid\mathbf H_t)
414 \]
415 is a canonical sufficient statistic. Computational mechanics develops causal
416 states as equivalence classes of histories with identical future conditional
417 laws and proves their minimal predictive character
418 \cite{ShaliziCrutchfield2001}. Theorem~\(T_{12}\) is therefore an established
419 minimal-sufficiency result specialized to the declared future target and
420 intervention family.
421 
422 The new burden is structural alignment: determining whether the predictive
423 state is recoverable from the low-energy transfer workspace. Predictive
424 sufficiency alone does not identify a distributed workspace.
425 
426 \subtopic{87.2 Statistical experiments and sufficiency}
427 
428 Blackwell's comparison of experiments formalizes when one information source
429 is at least as informative as another for every decision problem
430 \cite{Blackwell1953}. The coalition-risk hierarchy in Part~VII is compatible
431 with this tradition. A coalition can be sufficient even when its internal
432 representation differs from the full-system state.
433 
434 The framework adds a decomposition-relative question:
435 \[
436 \text{what is the smallest coalition whose accessible history is sufficient?}
437 \]
438 The statistic \(k_\varepsilon\) is an adaptation of sufficiency to distributed
439 carrier structure. Its interpretation depends on the declared nodes and
440 accessible encodings.
441 
442 \subtopic{87.3 Synergy and partial information}
443 
444 Partial-information decomposition distinguishes redundant, unique, and
445 synergistic information in multivariate systems, building on standard
446 information-theoretic quantities \cite{CoverThomas2006,WilliamsBeer2010}. The
447 XOR examples in Part~XXII are canonical synergy constructions and are not new.
448 They are used because they provide exact ground truth for relational
449 irreducibility:
450 \[
451 I(Y;X_i)=0
452 \quad\text{for every }i,
453 \qquad
454 I(Y;X_1,\ldots,X_m)>0.
455 \]
456 The matched-predictive-null test is more restrictive than merely
457 reporting synergy. It asks whether local predictive marginals can be held
458 fixed while the relational organization and full-system capacity change.
459 That joint null design is a candidate synthesis, not a claim that XOR or
460 synergy is new.
461 
462 \subtopic{87.4 Structural causal models}
463 
464 Interventions, counterfactuals, mediation, and causal graphs are established
465 machinery \cite{Pearl2009}. The theory adopts the interventionist
466 requirement that a workspace variable can be manipulated only through a
467 feasible implementation intervention. This avoids treating
468 \(\operatorname{do}(W=w)\) as meaningful when no physical or computational
469 operation realizes \(w\).
470 
471 The causal gate is an adaptation:
472 \[
473 \text{SCM intervention theory}
474 \longrightarrow
475 \text{implemented workspace and repair interventions}.
476 \]
477 The potentially distinctive contribution is that causal efficacy is tested
478 jointly with coherence, sufficiency, coalition irreducibility, matched nulls,
479 and identity preservation.
480 
481 \subtopic{87.5 Probabilistic process equivalence}
482 
483 Bisimulation and probabilistic testing compare processes by the observations
484 and experiments they support \cite{LarsenSkou1991}. The causal-identity profile
485 in Part~XII belongs to this broader family of behavioral equivalence notions.
486 It differs by keeping structural transport, operation intertwining,
487 reconstruction, and intervention response as separate coordinates rather than
488 collapsing them into one process equivalence.
489 
490 This is best classified as an integrative adaptation. The existence of
491 behavioral-equivalence theory blocks any claim that replacement identity based
492 on observable behavior is wholly new.
493 
494 \subtopic{87.6 Specification sensitivity, partial identification, and post-selection}
495 
496 A conclusion can depend on analytically reasonable choices even when every
497 individual analysis is internally correct. Sensitivity analysis and
498 specification-curve or multiverse methods make that dependence visible rather
499 than allowing one favorable analysis to stand for an entire scientific claim
500 \cite{Leamer1983,SteegenEtAl2016,SimonsohnEtAl2020}. Partial-identification
501 theory similarly replaces unjustified point conclusions with identified sets
502 when the maintained assumptions and observations determine only bounds
503 \cite{Manski2003,ImbensManski2004}. Post-selection inference addresses the
504 additional error created when a model, target, or specification is selected
505 because it looked favorable on the same data used for reporting
506 \cite{BerkEtAl2013}.
507 
508 These traditions preclude any claim that specification robustness, identified
509 sets, uniform concentration, or selection adjustment are new statistical
510 ideas. The adaptation in Part~XVIII is to apply them jointly to a
511 noncompensatory workspace certificate whose gates span structure, causal
512 operation, coalition irreducibility, identity, provenance, and maintenance.
513 The identified object is therefore not a single regression parameter but the
514 sign profile of an entire relational certificate across a declared family of
515 scientific specifications.
516 
517 \topic{88}{Persistence, Reconstruction, Learning, and Control}
518 
519 \subtopic{88.1 Frames and erasure recovery}
520 
521 Stable reconstruction from distributed encodings is standard frame theory.
522 Lower frame bounds control noise amplification, and frame robustness under
523 erasures is well studied \cite{CasazzaKovacevic2003,Christensen2016}. Theorem
524 \(T_7\) and the node-erasure distance therefore instantiate known recovery
525 logic.
526 
527 The adaptation is to distinguish:
528 \[
529 \overline E_i
530 =
531 \text{complete mathematical chart},
532 \qquad
533 E_i=O_i\overline E_i
534 =
535 \text{locally accessible encoding}.
536 \]
537 This distinction is essential to the anti-centralization gate, but the frame
538 inequalities themselves are standard.
539 
540 \subtopic{88.2 Persistence recurrences}
541 
542 Bounds for recurrences such as
543 \[
544 e_{t+1}\leq\alpha_t e_t+\sigma_t
545 \]
546 are elementary stability results. The persistence theorem is not novel as an
547 inequality. Its conceptual role is to force three independent checks:
548 \begin{enumerate}
549 \item the workspace subspace remains trackable;
550 \item the state remains close to it; and
551 \item the retained workspace content does not collapse to zero.
552 \end{enumerate}
553 The non-collapse gate is a modeling contribution because it rules out a common
554 but misleading form of ``stability.''
555 
556 \subtopic{88.3 System identification and held-out selection}
557 
558 Population least squares, excitation conditions, ridge bias, and empirical
559 model selection are standard system-identification and statistical-learning
560 ideas \cite{Ljung1999}. Theorems \(T_{15}\)--\(T_{17}\) are finite-dimensional
561 specializations. Their workspace-specific content is the demand that transfer
562 maps be compared modulo gauge and that formation, calibration, and
563 certification data remain separated.
564 
565 The provenance layer is not equivalent to identifiability. A transfer can be
566 identified accurately while having been entirely encoded by the scaffold. A
567 structure can be endogenously learned while failing every workspace gate.
568 
569 \subtopic{88.4 Viability, safety, and self-maintenance}
570 
571 Viability theory studies trajectories that remain inside admissible regions
572 \cite{Aubin1991}. Control-barrier methods provide constructive safety
573 certificates \cite{AmesEtAl2017}. Cybernetic and autonomy traditions analyze
574 regulation, adaptive self-production, and operational closure
575 \cite{Ashby1956,MaturanaVarela1980,DiPaolo2005}. Formal accounts of agency
576 emphasize individuality, normativity, asymmetry, and temporally extended action
577 \cite{BarandiaranEtAl2009}. Empowerment measures an agent's potential causal
578 control over future states \cite{KlyubinEtAl2005}.
579 
580 The closed-loop maintenance theorem in Part~XVI uses standard controlled
581 stability. Its candidate contribution is the target of maintenance: not an
582 arbitrary safety set, but the conjunctive workspace certificate, including
583 identity and anti-centralization. The matched no-repair, random-repair,
584 off-workspace-repair, and identity-breaking-reconstruction controls prevent
585 passive robustness or generic recovery from being reported as self-maintenance.
586 
587 \subtopic{88.5 Decision and policy theory}
588 
589 The value-error-to-regret bound in Theorem~\(T_{20}\) is elementary decision
590 theory and aligns with standard reinforcement-learning analysis
591 \cite{SuttonBarto2018}. Its role is evidential. An internal value channel
592 counts only when interventions on that channel alter action selection in the
593 direction predicted by counterfactual value and outperform replay or
594 critic-ablation controls.
595 
596 \topic{89}{Human--AI and Multi-Agent Research}
597 
598 \subtopic{89.1 Hybrid intelligence and AI teammates}
599 
600 Hybrid-intelligence research studies systems in which human and machine
601 capabilities are deliberately combined \cite{DellermannEtAl2019}. Work on
602 machines as teammates emphasizes coordination, trust, communication, shared
603 mental models, and team design \cite{SeeberEtAl2020}. Collective-intelligence
604 research has begun to ask how human--AI groups can produce capacities not
605 reducible to either humans or AI alone \cite{GuptaEtAl2025}.
606 
607 These programs establish that human--AI collectives are a legitimate unit of
608 analysis. They do not by themselves identify an invariant core, prove
609 non-reducibility relative to declared components, or supply a replacement and
610 repair certificate. The theory should be positioned as a formal
611 measurement and falsification layer for such systems, not as the first proposal
612 that humans and AI can form productive teams.
613 
614 \subtopic{89.2 Distributed-cognition analyses of human--AI interaction}
615 
616 Recent work explicitly applies distributed cognition to human--AI cooperation
617 \cite{SidjiEtAl2024,ZhaoHan2026}. This literature is a direct conceptual
618 precedent. It reinforces that representations, artifacts, interface states,
619 and human reasoning can form one analytical system.
620 
621 The framework differs in granularity. It asks for a learned or declared
622 transfer diagram, a spectral or exact structural state, predictive and causal
623 alignment, coalition tests, matched nulls, persistence under handoff, and
624 provenance controls. Those additions may constitute a formal synthesis, but
625 they should not be described as the discovery of distributed human--AI
626 cognition itself.
627 
628 \subtopic{89.3 Cognitive spillover}
629 
630 Randomized evidence now indicates that exposure to AI can causally alter later
631 human--human language, attention, shared mental models, and social cohesion,
632 even outside the immediate human--AI exchange \cite{RiedlEtAl2026}. This is
633 important for the theory because it demonstrates that the interaction graph can
634 have downstream effects that outlast the active model channel.
635 
636 Spillover is not automatically a relational workspace. It may reflect
637 priming, imitation, or one-way influence. A workspace claim additionally
638 requires a jointly sufficient state, matched local nulls, bidirectional or
639 multi-path causal organization, and reconstructive persistence.
640 
641 \subtopic{89.4 Shared neural workspaces}
642 
643 Goyal and collaborators introduced a capacity-limited shared global workspace
644 through which specialized neural modules communicate and compete for access
645 \cite{GoyalEtAl2022}. The architecture directly anticipates the claim that a
646 constrained shared channel can synchronize otherwise specialized components.
647 It is therefore a close machine-learning precedent, not merely a metaphorical
648 relative.
649 
650 SRWT differs by allowing heterogeneous human, model, artifact, and instrument
651 nodes and by withholding the relational label until coalition, matched-null,
652 causal, persistence, and identity gates are passed. A neural shared workspace
653 may satisfy those gates, but task gains and bottlenecked communication alone do
654 not establish them.
655 
656 \subtopic{89.5 Graph-based human--AI artifacts}
657 
658 CoMAP provides a persistent graph-based visual workspace through which
659 educators and AI jointly construct project-based learning designs
660 \cite{LiJiang2026}. It is grounded in distributed cognition and treats the
661 artifact graph as a transparent, revisable collaboration medium. This system
662 is a direct precedent for the claim that human--AI interaction can be organized
663 by a persistent shared graph rather than a linear prompt history.
664 
665 The remaining SRWT question is empirical: whether the graph contains an
666 estimated low-energy compatible state, whether no declared component is
667 sufficient by itself, and whether targeted graph interventions alter later
668 joint behavior in a workspace-specific way.
669 
670 \subtopic{89.6 Controlled shared-workspace synergy}
671 
672 Kotalwar, Das, and Rose study shared-workspace human--AI collaboration across
673 1,482 simulated sessions \cite{KotalwarDasRose2026}. Their results show that
674 adding collaborators can reduce performance when coordination structure is
675 absent, while shared group memory and simulated human-in-the-loop approval
676 gates can improve outcomes. This is a direct empirical predecessor to the
677 manuscript's claim that available capability is not equivalent to coordinated
678 team capacity.
679 
680 The study also constrains priority. SRWT is not the first empirical framework
681 to test whether shared-memory scaffolding changes human--AI team performance.
682 Its candidate increment is the stricter decomposition of that effect into
683 structural coherence, local predictive marginals, relational-null loss,
684 feasible interventions, persistence, and replacement identity.
685 
686 \subtopic{89.7 Active shared context graphs for team science}
687 
688 The closest operational neighbor located in this audit is Mycelium, introduced
689 by Choudhury and collaborators as an active shared workspace connecting
690 researchers and AI agents through an evolving context graph
691 \cite{ChoudhuryEtAl2026}. The system captures observations and hypotheses,
692 relates them to a team's developing knowledge model, and routes them to the
693 person or agent whose next decision they can inform. Its computational account
694 frames networked intelligence as sparse conditional computation over
695 distributed scientific contexts and explicitly asks when a standalone agent is
696 sufficient and when network structure is essential.
697 
698 The overlap is material:
699 \begin{center}
700 \small
701 \begin{tabularx}{0.94\textwidth}{@{}p{0.16\textwidth}X@{}}
702 \toprule
703 Mycelium & Active context graph, routing, team science, and an explicit
704 network-versus-standalone comparison. \\
705 SRWT & Typed transport, invariant core, coalition tests, causal nulls,
706 replacement identity, formation provenance, and maintenance gates. \\
707 \bottomrule
708 \end{tabularx}
709 \end{center}
710 Mycelium rules out any priority claim stated merely as ``an active shared
711 workspace for human--AI science.'' The remaining candidate contribution is the
712 mathematical and empirical certificate applied to such an architecture.
713 
714 \subtopic{89.8 Current multi-agent formalization}
715 
716 Multi-agent research contains extensive models of planning, communication,
717 consensus, epistemic coordination, and decentralized control. The present
718 review did not identify one established framework that jointly uses all of the
719 following as necessary gates:
720 \[
721 \begin{aligned}
722 &\text{heterogeneous core transport and residuals},\\
723 &\text{exact or spectral global-section structure},\\
724 &\text{predictive sufficiency and feasible causal interventions},\\
725 &\text{coalition irreducibility under matched predictive nulls},\\
726 &\text{persistent identity under replacement},\\
727 &\text{formation provenance and leakage controls},\\
728 &\text{goal-conditioned repair of the certificate itself}.
729 \end{aligned}
730 \]
731 This negative search result is provisional. It supports a synthesis claim, not
732 an absolute claim of firstness.
733 
734 \topic{90}{Closest Formal Neighbor: Collective Counterfactual Planning}
735 
736 \subtopic{90.1 Why the comparison matters}
737 
738 Collective Counterfactual Planning (CCP) is a 2026 formal model in which each
739 agent represents an orthogonal projection of a common task space. It separates
740 conception, consent, implementation, and verification, and proves that
741 cross-agent relay can enable plans unavailable to any one-shot individual tree
742 while team-dark task requirements remain unverifiable
743 \cite{Amornbunchornvej2026}. It is the closest current formal neighbor located
744 by this audit because representational geometry, not merely missing
745 information or capability, is the central limitation.
746 
747 \subtopic{90.2 Shared commitments}
748 
749 CCP and the theory share several commitments:
750 \begin{itemize}
751 \item no single member need represent the complete task;
752 \item collective reach may exceed one-shot pooling;
753 \item heterogeneous representation is mathematically explicit;
754 \item validation or certification is distinct from accidental task success;
755 \item subteams and verification roles can be forced by structure; and
756 \item a team's blind subspace creates principled impossibility results.
757 \end{itemize}
758 These overlaps narrow the defensible novelty of this paper. It
759 cannot claim to be the only formal theory of collective action under
760 representational constraints.
761 
762 \subtopic{90.3 Different primary objects}
763 
764 The theories nevertheless address different mathematical objects:
765 \begin{center}
766 \small
767 \begin{tabularx}{\textwidth}{@{}>{\raggedright\arraybackslash}p{0.18\textwidth}>{\raggedright\arraybackslash}X>{\raggedright\arraybackslash}X@{}}
768 \toprule
769 Dimension & Collective Counterfactual Planning & Stratified Relational Workspace Theory \\
770 \midrule
771 Local representation & Orthogonal subspace of one common task space & Heterogeneous local spaces, core--residual decompositions, and transfer maps \\
772 Primary question & Whether a bounded-horizon plan can be conceived, consented to, executed, and validly verified & Whether a persistent distributed operative state exists, acts, survives replacement, and possibly maintains itself \\
773 Global mechanism & Relay closure of projected planning trees & Inverse limits, holonomy, transfer Laplacians, descent, predictive alignment, and causal gates \\
774 Failure object & Dark subspace, consent failure, implementation failure, or missing verifier & Incoherence, local sufficiency, matched-null collapse, causal failure, identity drift, provenance leakage, or repair replay \\
775 Temporal scope & Horizon-bounded task planning & Recurrent dynamics, persistence, handoff, replacement, damage, and repair \\
776 Formation & Representation geometry is part of the declared model & Scaffolded, adaptively learned, or endogenously constituted organization is separately audited \\
777 Agency claim & Cooperative solvability under declared assumptions & Domain-relative workspace agency only after goal, value, action, repair, and distributed-control gates \\
778 \bottomrule
779 \end{tabularx}
780 \end{center}
781 The comparison indicates complementarity rather than subsumption. CCP could
782 serve as a planning layer inside a relational workspace. Conversely, an SRW
783 could exist without solving a CCP instance.
784 
785 \subtopic{90.4 Priority consequence}
786 
787 After Mycelium and the shared-workspace systems above, the novelty residual
788 should not be stated as ``human and AI form an active shared scientific
789 workspace.'' After CCP, it should not be stated as ``groups solve tasks no
790 member can represent.'' Both the operational architecture and a rigorous
791 representational planning model are already present. The narrower candidate residual is:
792 \[
793 \boxed{
794 \begin{aligned}
795 &\text{persistent core--transfer workspace structure}\\
796 &+\text{causal and coalition anti-triviality}\\
797 &+\text{identity under replacement}\\
798 &+\text{formation provenance}\\
799 &+\text{certificate-directed self-maintenance}\\
800 &+\text{robustness across admissible decompositions}.
801 \end{aligned}
802 }
803 \]
804 This is a stronger and more defensible formulation.
805 
806 \topic{91}{Theorem-by-Theorem Dependency and Priority Register}
807 
808 \subtopic{91.1 Register}
809 
810 The following table records the most conservative current classification. A
811 ``candidate'' entry means that the exact integration was not located in the
812 reviewed sources. It does not assert exhaustive global priority.
813 
814 \small
815 \begin{longtable}{@{}>{\raggedright\arraybackslash}p{0.08\textwidth}>{\raggedright\arraybackslash}p{0.25\textwidth}>{\raggedright\arraybackslash}p{0.24\textwidth}>{\raggedright\arraybackslash}p{0.33\textwidth}@{}}
816 \toprule
817 Claim & Present result & Main prior machinery & Current assessment \\
818 \midrule
819 \endfirsthead
820 \toprule
821 Claim & Present result & Main prior machinery & Current assessment \\
822 \midrule
823 \endhead
824 \(T_1\) & Limit--holonomy equivalence & Categorical limits, local systems, holonomy fixed spaces & \(\mathsf{STD}/\mathsf{ADP}\). Standard theorem in workspace notation. \\
825 \(T_2,T_{2a}\) & Operation closure and commutant & Intertwiners and representation commutants & \(\mathsf{STD}/\mathsf{ADP}\). \\
826 \(T_3\) & Transfer-Laplacian kernel & Sheaf and connection Laplacians & \(\mathsf{STD}/\mathsf{ADP}\). \\
827 \(T_4,T_5\) & Spectral stability and gauge covariance & Davis--Kahan, Kato, connection Laplacians & \(\mathsf{STD}/\mathsf{ADP}\). \\
828 \(T_{10},T_{11}\) & Approximate operation closure and path leakage & Spectral projection estimates and telescoping block products & Mostly \(\mathsf{ADP}\). Exact constants may be manuscript-specific, but the method is standard. \\
829 \(T_{12}\) & Minimal predictive state and alignment & Sufficient statistics and computational mechanics & Minimality is \(\mathsf{STD}\). Alignment with a transfer workspace is \(\mathsf{ADP}/\mathsf{SYN}\). \\
830 \(T_{13}\) & Operational relationality & Conditional information, coalition risk, SCM interventions & Individual identities are standard. Their conjunctive matched-null certificate is \(\mathsf{SYN}/\mathsf{CAN}\). \\
831 \(T_6\) & Moving-subspace persistence & Stability recurrences and perturbation theory & \(\mathsf{STD}/\mathsf{ADP}\). The explicit non-collapse gate is a modeling synthesis. \\
832 \(T_7\) & Stable coalition reconstruction & Frame theory and erasure recovery & \(\mathsf{STD}/\mathsf{ADP}\). \\
833 \(T_{14}\) & Replacement invariance profile & Perturbation, process equivalence, causal comparison & Bound ingredients are standard. The coordinatewise structural--causal--reconstructive identity profile is \(\mathsf{SYN}/\mathsf{CAN}\). \\
834 \(T_8,T_9\) & Gluing and hierarchical collapse & Sheaf descent and \v{C}ech theory & Exact results are \(\mathsf{STD}/\mathsf{ADP}\). Descent plus anti-centralization and causal alignment is \(\mathsf{SYN}\). \\
835 \(T_{15}\)--\(T_{17}\) & Transfer learning, selection, boundary recovery & System identification and finite-margin selection & \(\mathsf{STD}/\mathsf{ADP}\). Gauge and leakage audit is integrative. \\
836 \(T_{18}\) & Formation transition example & Standard pitchfork bifurcation & \(\mathsf{STD}\). Included as a solvable benchmark, not a priority claim. \\
837 \(T_{19}\)--\(T_{22}\) & Goal retention, regret, repair, maintenance & Linear systems, decision theory, viability, feedback control & Mathematical bounds are \(\mathsf{STD}/\mathsf{ADP}\). Applying them to certificate repair is \(\mathsf{SYN}\). \\
838 \(T_{23}\) & Workspace-agency synthesis & Agency theory, causal control, viability & The conjunctive domain-relative certificate is \(\mathsf{SYN}/\mathsf{CAN}\). \\
839 \(T_{24}\) & Gatewise false-certification bound & Intersection testing and elementary probability & \(\mathsf{STD}\). The gate architecture is the relevant synthesis. \\
840 \(T_{25}\)--\(T_{27}\) & Faithful coarse-graining, risk transport, and decomposition robustness & Kernel factorization, sigma-field aggregation, and margin stability & Exact identities are \(\mathsf{STD}/\mathsf{ADP}\). Their integration with anti-centralization and certificate envelopes is \(\mathsf{SYN}/\mathsf{CAN}\). \\
841 \(T_{28}\)--\(T_{32}\) & Specification transport, non-identifiability, partial identification, uniform certification, and independent selection & Sensitivity analysis, experimental equivalence, identified sets, uniform concentration, and post-selection inference & The statistical principles are \(\mathsf{STD}/\mathsf{ADP}\). Their gatewise integration with the full relational certificate is \(\mathsf{SYN}/\mathsf{CAN}\). \\
842 Part XXII & Positive cases and near misses & Distributed parity, frames, causal tests & Toy calculations are standard. The common positive/near-miss benchmark architecture is \(\mathsf{SYN}/\mathsf{CAN}\). \\
843 \bottomrule
844 \end{longtable}
845 \normalsize
846 
847 \subtopic{91.2 Standard ingredients that must be cited, not claimed}
848 
849 The following should always be described as inherited machinery:
850 \[
851 \begin{aligned}
852 &\text{inverse limits, global sections, holonomy invariants, commutants},\\
853 &\text{sheaf and connection Laplacians, \v{C}ech gluing, spectral gaps},\\
854 &\text{Davis--Kahan and Kato perturbation, frame reconstruction, erasures},\\
855 &\text{minimal sufficient states, conditional information, SCM interventions},\\
856 &\text{least squares, ridge recovery, finite-margin model selection},\\
857 &\text{sensitivity analysis, partial identification, uniform concentration, post-selection inference},\\
858 &\text{pitchfork bifurcation, feedback stability, viability, policy regret}.
859 \end{aligned}
860 \]
861 Renaming these objects does not create novelty.
862 
863 \subtopic{91.3 Domain adaptations}
864 
865 The following are legitimate adaptations but weak standalone novelty claims:
866 \begin{itemize}
867 \item interpreting local-system sections as shared workspace cores;
868 \item treating the connection or sheaf Laplacian as a transfer-coherence
869  operator;
870 \item using frame bounds to quantify coalition reconstruction;
871 \item using causal states as operational workspace summaries;
872 \item using gauge covariance to compare participant or model realizations;
873 \item using \v{C}ech descent to form workspaces of workspaces;
874 \item applying specification envelopes and identified sets to a conjunctive
875  workspace certificate; and
876 \item applying viability and feedback bounds to workspace-health margins.
877 \end{itemize}
878 Their value depends on the integration they enable.
879 
880 \subtopic{91.4 Strongest candidate synthesis}
881 
882 The strongest current candidate is not a single equation. It is the following
883 conjunctive object:
884 \[
885 \boxed{
886 \mathfrak C_{\mathrm{SRW}}
887 =
888 \left(
889 \begin{array}{c}
890 \text{heterogeneous core--transfer diagram and residuals},\\
891 \text{exact or spectral shared-section state},\\
892 \text{operation and predictive alignment},\\
893 \text{feasible causal interventions},\\
894 \text{coalition irreducibility under matched local-predictive nulls},\\
895 \text{non-collapse, reconstruction, and replacement identity},\\
896 \text{descent across subworkspaces without hidden centralization},\\
897 \text{formation provenance and certification leakage control},\\
898 \text{goal-conditioned action and certificate-directed repair},\\
899 \text{robustness across admissible decompositions and scientific specifications},\\
900 \text{identified-set and uniform finite-sample certification}
901 \end{array}
902 \right).
903 }
904 \]
905 The reviewed sources contain many of these coordinates separately and some in
906 pairs. This audit did not locate a prior source that defines their conjunction
907 as one falsifiable workspace certificate.
908 
909 \subtopic{91.5 Why the conjunction is not arbitrary}
910 
911 Each coordinate excludes a distinct near miss:
912 \[
913 \begin{array}{ll}
914 \text{coherence} & \text{rejects incompatible local states},\\
915 \text{predictive alignment} & \text{rejects inert structure},\\
916 \text{causal efficacy} & \text{rejects correlational epiphenomena},\\
917 \text{coalition irreducibility} & \text{rejects centralized sufficiency},\\
918 \text{matched nulls} & \text{reject local-marginal explanations},\\
919 \text{non-collapse} & \text{rejects convergence to a trivial zero state},\\
920 \text{replacement identity} & \text{rejects task-equivalent but causally different successors},\\
921 \text{provenance} & \text{rejects scaffold-decoded organization},\\
922 \text{repair specificity} & \text{rejects passive robustness and open-loop replay},\\
923 \text{specification robustness} & \text{rejects favorable analytical tuning},\\
924 \text{identifiability} & \text{rejects conclusions unsupported by the experiment family}.
925 \end{array}
926 \]
927 Because the excluded systems differ, the certificate is not equivalent to any
928 one inherited component.
929 
930 \topic{92}{Scope of the Originality Claim}
931 
932 \subtopic{92.1 Defensible thesis}
933 
934 The strongest defensible originality statement is:
935 \begin{quote}
936 Stratified Relational Workspace Theory proposes a unified formal and empirical
937 certificate for persistent operative structures distributed across
938 heterogeneous agents and artifacts. It integrates core--transfer and
939 local-to-global geometry with predictive sufficiency, feasible causal
940 interventions, coalition irreducibility, matched relational nulls,
941 reconstructive identity, formation provenance, certificate-directed
942 self-maintenance, robustness across admissible decompositions and scientific
943 specifications, and identified finite-sample certification. The individual
944 mathematical tools are largely established.
945 The candidate contribution is their noncompensatory integration and the class
946 of near misses it is designed to reject.
947 \end{quote}
948 This statement is narrower than claiming a new theory of cognition in general.
949 It is also stronger than claiming only a metaphor.
950 
951 \subtopic{92.2 Claims excluded by the comparison}
952 
953 The theory does not claim:
954 \begin{enumerate}
955 \item that distributed or extended cognition is newly discovered;
956 \item that global sections, holonomy, sheaf Laplacians, spectral perturbation,
957  frames, causal states, or viability bounds are new mathematics;
958 \item that all human--AI collaboration forms a relational workspace;
959 \item that group performance establishes relational irreducibility;
960 \item that scaffolded organization is unreal;
961 \item that endogenous formation establishes agency;
962 \item that agency establishes consciousness, personhood, or moral status; or
963 \item that the motivating collaboration has already passed the empirical
964  certificate.
965 \end{enumerate}
966 
967 \subtopic{92.3 Claims supported at present}
968 
969 The analysis supports the following claims:
970 \begin{enumerate}
971 \item One coherent formal language can express exact structure, approximate
972  coherence, causal operation, distributed sufficiency, persistence,
973  identity, formation, and repair.
974 \item Under its declared assumptions, the stated mathematical theorems follow.
975 \item The common certificate rejects analytic replicated, centralized,
976  obstructed, externally reloaded, identity-breaking, and replay-based
977  near misses.
978 \item The motivating collaboration is a plausible observational candidate but
979  remains uncertified.
980 \item The synthesis yields concrete experiments whose failure would narrow or
981  falsify the stronger relational claims.
982 \end{enumerate}
983 
984 \subtopic{92.4 Remaining priority risks}
985 
986 The highest-priority remaining searches are:
987 \begin{itemize}
988 \item sheaf-theoretic models of team cognition and organizational knowledge;
989 \item distributed sufficient-statistic and Blackwell-order models with
990  explicit coalition nulls;
991 \item causal representation and multi-agent latent-state identity under
992  replacement;
993 \item formal theories of transactive memory with local-to-global topology;
994 \item organizational cybernetics that couples self-maintenance to the
995  preservation of distributed informational organization; and
996 \item post-August-2026 work that combines representational geometry with
997  persistent human--AI or multi-agent agency;
998 \item formal analysis of active shared context graphs, shared group memory, and
999  artifact-centric graph workspaces under coalition and intervention tests.
1000 \end{itemize}
1001 A specialist review from each adjacent field may uncover precedents not visible
1002 through cross-disciplinary keyword search.
1003 
1004 \subtopic{92.5 Evidence required for a stronger claim}
1005 
1006 Before presenting the synthesis as established rather than proposed, the
1007 following should be completed:
1008 \begin{enumerate}
1009 \item a public, timestamped manuscript and versioned source archive;
1010 \item theorem-level comparison with the closest sheaf, causal-state, group
1011  agency, and CCP formulations;
1012 \item independent mathematical review of the nonstandard claims and constants;
1013 \item preregistered benchmark gates and matched null families;
1014 \item at least one controlled human--AI or multi-agent experiment estimating
1015  the complete certificate vector; and
1016 \item explicit reporting of failures, unidentified quantities, and
1017  decomposition sensitivity.
1018 \end{enumerate}
1019 
1020 \subtopic{92.6 Priority conclusion}
1021 
1022 The literature review narrows rather than weakens the theory. It removes
1023 unnecessary novelty claims from the standard mathematics and leaves a clearer
1024 research object:
1025 \centerbox{\large\bfseries
1026 Not a new Laplacian, sheaf, causal state, or controller, but a candidate
1027 unified certificate for relational workspaces.
1028 }
1029 That is the priority position adopted here.

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