UGC/CUR Academic Parallel Edition v0.1

Native Theory × External Academic Correspondence without Canonical Replacement

Version: v0.1
Date: 2026-08-26
作者： Neo.K
機構： EveMissLab／一言諾科技有限公司
Status: Academic parallel edition / correspondence layer
Native baseline: UGC/CUR Canonical Reconciliation + Paper 00–05 + Unified Closure Theory
Evidence lineage: External Academic Reconciliation Round 1–3
Normative rule: External prior art constrains novelty claims and supplies reusable mathematics, but does not silently redefine the Native UGC/CUR ontology.

Abstract

This document establishes the UGC/CUR Academic Parallel Edition (APE) as a permanent parallel layer beside the Native UGC/CUR / Unified Closure Theory (UCT) corpus.

The purpose of APE is not to rewrite Native UCT into the vocabulary of existing academic fields. It instead records typed correspondences between Native claims and external theories while preserving the distinction:

\boxed{ \text{Formal Similarity} \neq \text{Semantic Identity} \neq \text{Ontological Identity}. }

Likewise:

\boxed{ \text{Earlier Publication} \not\Rightarrow \text{More Fundamental} \not\Rightarrow \text{More Correct Outside Its Assumptions}. }

Prior art remains essential. It may show that a claimed mathematical mechanism is already known, supply a special-case theorem, reveal a contradiction, impose a no-go condition, or provide a mature backend implementation. But an external theorem only governs the Native object after an explicit correspondence has been established with sufficient assumption matching.

APE therefore introduces a correspondence relation family, an analogy-stop rule, mapping-strength grades, a no-silent-redefinition policy, and a Native/Academic dual-track publication model. It then applies this framework to the principal UGC/CUR objects: Generative Closure, Unbounded Ontological Extension, First-Cause Sufficiency, Global Ledger, Typed Reachability, Class-Ultimate Reachability, Transformation Closure, Meta-Causal Agency, Bridge Certificates, and the Unified Closure Theory triad.

The resulting architecture is:

\boxed{ \text{Native UCT} \parallel \text{Academic Parallel Edition} }

rather than:

\text{Native UCT} \xrightarrow{\text{external literature}} \text{replacement theory}.

1. Why a Parallel Edition Is Necessary

The external academic audit found many strong formal analogues:

closure-operator lattices and commutative closure composition;
distributive laws, interaction laws and no-go theorems for composition;
Yang–Baxter coherence for iterated distributive laws;
control-theoretic reachability and diffeomorphism controllability;
Dynamic SOS, reflective ASMs and rewriting-logic reflection;
modal and dynamic logics of epistemic action and agency;
provenance semirings, provenance traces and causal provenance;
metaphysical grounding, fundamentality and cosmological-argument literature;
structured/decorated cospans, double categories of open systems and institution theory.

These results matter. They prevent UCT from claiming novelty for mathematical structures that already exist. They also provide reusable theorems and implementation backends.

However, the same audit also revealed a methodological danger: a formal resemblance can tempt the researcher to treat an older vocabulary as an ontological court of appeal.

APE rejects that move.

A closure operator on an algebraic lattice may model one representation of a generative process, but that does not entail:

\operatorname{GenCl} = \text{algebraic closure operator}

without a representation theorem.

A distributive law may instantiate one UCT bridge, but that does not entail:

\mathsf{BridgeCert} = \text{Beck distributive law}.

A foundational-ground account of the cosmos may overlap with First-Cause Sufficiency, but that does not entail:

\mathsf{FCS} = \text{grounding theory}.

The correct research relation is correspondence, not forced identity.

2. Dual-Track Architecture

2.1 Native Track

The Native Track consists of:

Canonical Reconciliation;
Paper 00 — Formal Core Specification;
Paper 01 — Unbounded Ontological Extension;
Paper 02 — Generative Closure and First-Cause Sufficiency;
Paper 03 — Global Ledger and Generative Responsibility Accounting;
Paper 04 — Typed Class-Ultimate Reachability;
Paper 05 — Transformation Closure and Meta-Causal Agency;
Series Synthesis — Unified Closure Theory.

Native definitions may be changed only by Native reasons: internal inconsistency, failed proof obligation, better self-derived formalization, empirical conflict in a domain where the theory makes an empirical claim, or an explicit versioned design decision.

External literature can motivate reconsideration, but does not silently commit the change.

2.2 Academic Parallel Track

APE records:

closest academic analogues;
formal mapping candidates;
theorem reuse candidates;
semantic overlap;
different ontologies;
different assumptions;
contradictions or no-go results;
mapping confidence;
AnalogyStop: the precise point where the comparison ceases to license inference.

2.3 No Silent Redefinition

APE adopts:

\boxed{ \mathsf{AcademicMap}(X,Y) \not\Rightarrow X := Y. }

No relation in APE is a definitional equality unless a Native document explicitly adopts it in a later version.

3. Correspondence Relation Types

APE uses the following non-exclusive relation labels.

3.1 FormalAnalogue

The theories share a mathematical pattern, operation, algebraic law or diagrammatic role, but no semantic identity is asserted.

3.2 PartialEmbedding

A defined subset or representation of the Native object may embed into the external formalism under explicit assumptions.

3.3 SemanticOverlap

The two theories answer some of the same questions or classify some of the same phenomena, but may use different primitives.

3.4 IndependentConvergence

Different research paths independently arrive at a related distinction or structural principle.

3.5 SpecialCase

The external theory provides a rigorous instance of a more general Native pattern, or the Native theory contains a regime that may reduce to the external theory.

3.6 GeneralizationCandidate

The Native framework appears capable of hosting several external formalisms as backends, but a formal generalization theorem has not yet been established.

3.7 DifferentOntology

The mathematical surface may look similar while the objects are intended to mean different kinds of things.

3.8 DifferentFormalization

The target problem overlaps, but the mathematical organization differs materially.

3.9 Contradictory

The claims cannot both hold under a matched assumption set. A contradiction requires assumption alignment; mere vocabulary disagreement is not enough.

3.10 Unknown

The available evidence is insufficient to classify the relation.

4. Mapping Strength

Every correspondence receives a strength grade.

illustrative — useful example only;
heuristic — conceptual analogy;
structural — matching typed roles or formal architecture;
partial-formal — an explicit mapping is available for part of the object;
theorem-level — an external theorem can be imported after stated assumptions are matched;
open — mapping remains unresolved.

No grade automatically upgrades a mapping to ontological identity.

5. The Analogy-Stop Principle

The central APE innovation is not a new mathematical theorem but a research discipline:

\boxed{ \mathsf{AnalogyStop}(X,Y,C) }

means that correspondence between $X$ and $Y$ is licensed only within condition set $C$ . Beyond $C$ , inference must stop unless a new bridge is supplied.

For example, if a control-theoretic theorem establishes that point reachability plus bracket-generating and isotopy conditions permits implementation of a class of diffeomorphisms, then the valid inference is:

\mathsf{Reach}_{\rm control} + C \Rightarrow \mathsf{Transform}_{\rm diffeo}.

It does not license:

\mathsf{Reach} \Rightarrow \operatorname{TransCl}

for generator rewrite, legal authority, cross-layer control, or arbitrary ontological transformation.

6. Native UCT as a Source Theory, Not a Translation Artifact

Native UCT was developed from a sequence of problems:

\text{Generation} \rightarrow \text{Existence} \rightarrow \text{Reachability} \rightarrow \text{Transformation},

with observer, boundary and accounting constraints crossing these layers.

Its source problem was not:

Which established category-theoretic or modal structure should be renamed UCT?

Therefore APE treats external theories as views on Native objects:

\mathsf{View}_i(\mathsf{UCT})

rather than treating UCT as the inverse image of a preselected literature vocabulary.

7. Generative Closure Correspondence

Native Generative Closure is:

\operatorname{GenCl}_{D,T} \left( S\mid\mathfrak E^{\rm gen} \right).

Closure-operator theory is mature. Sets of closure operators on a common lattice can form lattices; their compositions and commutativity have long been studied. This means the following claim is not novel:

There may exist multiple closure operators with nontrivial combination laws.

But the Native GenCl object is source-relative and carries a generative environment, law regime, traces, resource responsibility and target domain.

APE therefore classifies the relation as:

\mathsf{PartialEmbedding} + \mathsf{DifferentOntology}.

A future theorem may prove that a restricted GenCl model induces a closure operator on a chosen poset or lattice. If so, the external closure algebra becomes reusable. Until then, the analogy stops at the shared closure pattern.

8. UOE Correspondence

Paper 01 distinguishes:

\mathsf{open} \not\Rightarrow \mathsf{unbounded} \not\Rightarrow \mathsf{actually\ infinite}.

Many external mathematical fields contain analogous distinctions among extensibility, infinite carrier size, unbounded numerical magnitude, infinite-state behavior, or failure of compactness. None is automatically the UOE ontology.

APE therefore records UOE as a multi-domain mapping problem, not a reduction to one theory of infinity.

The Native local-to-absolute discipline remains independent unless an external epistemic or model-theoretic theorem is explicitly mapped into the relevant UOE claim class.

9. First-Cause Sufficiency Correspondence

Paper 02 separates:

\mathsf{GenSufficiency}, \quad \mathsf{GroundingStatus}, \quad \mathsf{OntologicalPriority}.

The grounding literature contains strong overlaps. Pearce's foundational-ground account of total causal History is especially close to the Native insistence that explaining a total generative structure need not mean prepending one more ordinary causal event.

Yet FCS additionally contains:

Generative Closure;
source/substrate ambiguity;
generative responsibility decomposition;
external resource accounting;
First-Cause Sufficiency grades;
priority-mode distinctions.

APE therefore classifies Pearce and related grounding work as SemanticOverlap + DifferentFormalization, not identity.

9.1 GroundingComplete as a Native Term

Round 3 proposed replacing GroundingComplete with a tuple after encountering Leuenberger and Oberle. APE now reclassifies that proposal.

The Native term remains unchanged in v0.1.

The tuple:

\left \langle \mathsf{CoverageComplete}, \mathsf{RegressStatus}, \mathsf{WellFoundedness}, \mathsf{IndependenceStatus}, \mathsf{GroundingBaseStatus} \right \rangle

is an Academic Parallel Refinement Candidate.

It is useful when publishing into contemporary grounding debates because those debates distinguish all-grounding completeness, ungroundedness, self-grounding, cycles, infinitism and well-foundedness.

But APE explicitly records:

\boxed{ \mathsf{GroundStatus}_{\rm academic} \not\equiv_{\rm def} \mathsf{GroundingComplete}_{\rm Native}. }

10. Global Ledger Correspondence

The external provenance literature strongly overlaps with UCT's insistence on source, derivation, loss, transformation and auditability.

Semiring provenance, provenance traces, workflow provenance and causal provenance are mature. Therefore the following are prior-art-aligned rather than Native novelty claims:

provenance as derivation history;
algebraic propagation of provenance;
trace consistency/fidelity;
causal refinement of provenance.

But Native Global Ledger is defined as a broader accounting layer carrying state/history distinction, law versions, boundary events, generative responsibility, typed reach/transform certificates, unresolved debt and claim gates.

APE therefore treats provenance frameworks as backend mappings.

The key firewall remains:

\boxed{ \mathsf{LedgerComplete} \not\Rightarrow \mathsf{CausallyComplete}. }

Cheney's work supplies a strong domain-specific reason: syntactic provenance reachability can over-approximate actual causality.

11. Typed Reachability Correspondence

Control theory, viability theory, modal logic, epistemic accessibility, open Petri nets and state-transition systems all possess mature reachability notions.

APE does not choose one as canonical.

Instead:

\mathsf{Reach}^{m}_{\Theta,R}(A,x,t)

is treated as a common Native judgement interface whose backends may instantiate different $m$ , $R$ , $\Theta$ , witness and obstruction semantics.

A control-reachable set is therefore a SpecialCase or PartialEmbedding, depending on the model.

A modal accessibility relation is another.

Neither is permitted to silently define every other reach mode.

12. Reach-to-Transform Correspondence

Agrachev–Caponigro and Raginsky provide a particularly strong theorem-level academic mapping.

Point-wise controllability can, under bracket-generating and additional structural conditions, be lifted to implementation of a class of diffeomorphisms.

APE interprets this as a concrete backend for:

\mathsf{BridgeCert}^{\mathsf R\to\mathsf T}.

But the AnalogyStop condition is explicit: the theorem concerns a specific state-space/control setting and transformation class.

It does not prove a universal UCT theorem for rule rewrite, generator rewrite, law rewrite, permission rewrite, semantic rewrite or cross-layer intervention.

13. Class-Ultimate Correspondence

Class-Ultimate is not mapped to one external academic term.

Its closest analogues are distributed across:

maximal controllability or invariant-region analysis;
strategic ability;
epistemic ability;
agency measures;
modal power;
universal or near-universal transformation classes.

This distributed correspondence is itself important.

APE therefore classifies Class-Ultimate as a Candidate Native Concept whose individual axes have known academic ancestors.

This is a stronger and more defensible claim than saying that maximality or controllability is new.

14. Transformation Closure Correspondence

Kleene algebra, dynamic logic, transformation semigroups and rewriting systems provide rich external algebra for action composition.

Native TransCl, however, only admits certified composition under contextual contracts.

Thus a chosen TransCl model may embed into a known action algebra, but only after specifying how Native constraints map to algebraic laws.

In particular, external results showing non-associativity or weak distributivity in concurrent multirelational models warn against assuming free composition.

APE treats such results as specialized algebraic stress tests, not as replacement semantics.

15. Meta-Causal Agency Correspondence

Dynamic SOS, reflective ASMs, Maude reflection and higher-order rewriting provide mature examples in which rules, signatures, static structures or program representations can be changed by a running system.

These are powerful formal witnesses for:

\text{rule rewrite} \neq \text{absolute law transcendence}.

They therefore strongly support the layer-relative reading of:

\mathsf{MC}_0, \ldots, \mathsf{MC}_4.

But they do not define the ontology of meta-causality in Native UCT.

APE classifies them as Domain Models + Independent Convergence.

16. Agency and Intervention as Optional Academic Refinements

Round 3 introduced ActionInterventionCert and AgencyFrame as proposed repairs. In APE these become optional refinements.

16.1 ActionInterventionCert

Jørgensen, Gresele and Weichwald show that a causal model requires an explicit interpretation between real actions and mathematical interventions if interventional validity is to be non-circular and falsifiable.

Therefore, when a UCT paper specifically claims structural-causal intervention power, APE recommends:

\mathsf{ActionInterventionCert} \left( a,do(X=x)\mid\Theta \right).

But Native transformation witnesses outside SCM semantics do not need to be rewritten in this language.

16.2 AgencyFrame

Abel et al. argue that agency attribution depends on choices of boundary, causal variables, goal criterion and adaptation criterion.

APE therefore recommends an optional:

\mathsf{AgencyFrame}

whenever UCT capability is interpreted specifically as agency.

Native capability and transformation remain broader categories.

17. Bridge Theory Correspondence

Bridge Theory is the highest-threat region for academic overlap.

The literature already contains:

distributive laws;
morphisms of distributive laws;
heterogeneous coalgebra interaction laws;
no-go theorems;
Yang–Baxter coherence;
institution morphisms/comorphisms;
conservative translations;
open-system interface functors;
control-theoretic lifting conditions.

Therefore APE rejects any novelty claim of the form:

UCT is the first theory to notice that heterogeneous structures need compatibility maps.

That would be false.

The Native contribution candidate is narrower:

BridgeCert is a cross-domain evidence/audit interface that can host these different mathematical backends while preserving Native source/target typing, obstruction, debt and claim status.

17.1 BridgeDecl as Parallel Academic Refinement

Round 3 proposed:

\mathsf{BridgeDecl}^{X\to Y} = \left \langle \mathsf{SourceType}, \mathsf{TargetType}, \mathsf{Doctrine}, \mathsf{Interface}, \mathsf{Translation}, \mathsf{Preservation}, \mathsf{Reflection}, \mathsf{Coherence}, \mathsf{Debt} \right \rangle.

APE keeps this object as a parallel publication schema, not a replacement for Native BridgeCert.

A future Native v0.2 may choose to adopt some fields independently, but v0.1 identity is preserved.

18. Representation-Relative Collapse

APE strengthens a distinction already emerging in Round 2:

\boxed{ \mathsf{CanonicalNonCollapse} \neq \mathsf{RepresentationRelativeCollapse}. }

Native UCT can maintain different canonical types even if a specialized representation proves an embedding or equivalence.

Example:

A relational program model may encode actions as binary relations and obtain reachability through relational image or modal diamond.

That establishes a useful collapse in that representation.

It does not prove that UCT should erase the conceptual distinction between the question:

Can $A$ reach $x$ ?

and:

Which transformations can $A$ legally realize over a declared class?

The same principle applies throughout APE.

19. Novelty Policy

APE uses the following novelty policy.

19.1 Not Novel by Itself

The following should not be presented as standalone novelty:

multiple closure operators;
closure composition/commutation;
conditional compatibility maps;
distributive-law coherence;
reachability as a formal notion;
controllability as a formal notion;
reflective self-modification;
observer-relative state reduction;
provenance algebra;
non-causal grounding;
completeness-based fundamentality;
intervention semantics;
frame-relative agency;
categorical composition of open systems;
heterogeneous logical translation.

19.2 Candidate Native Contributions

The more defensible candidate contributions are combinations and distinctions whose exact joint architecture has not yet been identified as an existing one-to-one theory:

\boxed{ \begin{aligned} \mathsf{CandidateContribution} = &\;\mathsf{TypedGRTArchitecture} \\ &+\mathsf{CrossDomainBridgeAudit} \\ &+\mathsf{WitnessObstructionDebt} \\ &+\mathsf{GenerativeResponsibilityAccounting} \\ &+\mathsf{FirstCauseClassUltimateSeparation} \\ &+\mathsf{ObserverBoundaryClaimGating}. \end{aligned} }

This remains a candidate, not a publication-level proof of uniqueness.

20. Reuse Without Submission

APE distinguishes reuse from submission.

An external theorem can be reused when:

its objects have an explicit mapping to Native objects;
its assumptions are matched;
its conclusion is translated back without strengthening;
AnalogyStop is declared;
any loss or non-conservativity is recorded.

This permits UCT to benefit from mature mathematics without surrendering Native semantics.

21. Contradiction Protocol

External literature should override a Native claim only when there is a genuine contradiction under matched semantics.

APE requires:

\mathsf{ConflictCert} = \left \langle \mathsf{NativeClaim}, \mathsf{ExternalClaim}, \mathsf{AssumptionMatch}, \mathsf{ObjectMatch}, \mathsf{InferenceConflict}, \mathsf{Scope} \right \rangle.

If object or assumption matching fails, the status is not contradiction but DifferentOntology, DifferentFormalization, or Unknown.

22. Publication Architecture

A future public UGC/CUR release can therefore contain two documents.

A. Native Theory

Presents UCT in its own terminology and derivation lineage.

B. Academic Correspondence Appendix / Parallel Edition

For every major claim, records:

Native claim;
closest known analogues;
RelationType;
MappingStrength;
reusable external theorem;
assumption match;
ontology difference;
AnalogyStop;
novelty implication;
unresolved debt.

This structure is more transparent than either extreme:

pretending no adjacent literature exists;
or rewriting every Native concept as a derivative of the nearest historical term.

23. Machine-Readable Correspondence Record

The canonical parallel record is:

\mathsf{AcademicCorrespondence} = \left \langle id, NativeClaim, NativeObject, ExternalWork, RelationType, MappingStrength, ReusableResult, AssumptionMatch, OntologyDifference, AnalogyStop, NativeStatus, AcademicStatus, Debt \right \rangle.

The accompanying CSV and YAML implement this structure.

24. Round 1–3 Reclassification

The earlier external audit rounds remain valuable evidence, but APE changes their normative interpretation.

Round 1

Broad census and first direct theorem-level mappings remain unchanged as evidence discovery.

Round 2

Novelty reductions remain valid where they concern explicit prior art.

Statements phrased as "UCT must be repaired" are reinterpreted as either:

genuine contradiction findings, if a matched Native claim fails; or
Academic Parallel Refinement candidates, otherwise.

Round 3

The previous canonical repair language is superseded for edition governance by APE.

Objects such as:

GroundStatus;
ActionInterventionCert;
AgencyFrame;
BridgeDecl;

remain valuable, but are now classified as parallel academic refinement candidates unless separately adopted by a Native version decision.

No historical evidence is discarded; only its authority relation to Native UCT is corrected.

25. Native Sovereignty and Academic Accountability

APE is not a license to ignore academic literature.

Native sovereignty means:

\text{we retain our own question and ontology}.

Academic accountability means:

\text{we do not claim as new what is already known, and we confront genuine counterexamples}.

Both are required.

Thus:

\boxed{ \text{Independent Theory} \neq \text{Literature Isolation}. }

and:

\boxed{ \text{Academic Reconciliation} \neq \text{Canonical Submission}. }

26. Current Research Status

After three external audit rounds, APE assigns UCT the provisional status:

\boxed{ \mathsf{PublicationNoveltyStatus} = \mathsf{PlausibleCompositeContributionCandidate}. }

This is intentionally weaker than EstablishedNovelty.

The strongest surviving research question is now:

Does the exact Native combination of typed generation, typed reachability, certified transformation, bridge witness/obstruction/debt, generative responsibility accounting, observer/boundary gating, First-Cause Sufficiency and Class-Ultimate separation have a pre-existing one-to-one formal counterpart?

No such counterpart has been established in the work reviewed so far.

That is a research state, not a proof of absence.

27. Next Research Interface

Future academic work should proceed by adding correspondence records, not by mutating Native source by default.

High-value next targets include:

institution-independent bridge preservation taxonomies;
categorical models of heterogeneous claim/evidence systems;
provenance of theorem reuse across translations;
formal ontology comparison and theory morphisms;
causal abstraction and intervention interpretation;
grounding logics with non-well-founded or plural structures;
fixed-point and closure dynamics for the Native G/R/T triad;
executable verifier for correspondence certificates.

A Native v0.2 remains a separate project decision.

28. Final Position

The Academic Parallel Edition establishes the following permanent research rule:

\boxed{ \text{External Theory} \xleftrightarrow[\text{differences}]{\text{correspondence}} \text{Native UCT}, }

not:

\boxed{ \text{External Theory} \Rightarrow \text{Native UCT must become External Theory}. }

UCT may converge with existing theory, embed into it, generalize it, contradict it, or remain differently ontologized.

The task of APE is to state which case holds, with evidence, and to say exactly where the analogy stops.

Appendix A — Correspondence Matrix

ID	Native object	Relation	Strength	Native status	Academic status
APE-001	GenCl / Reach judgement & ReachEnv / TransCl	IndependentConvergence;SemanticOverlap	structural	UNCHANGED	PARALLEL_MAPPING
APE-002	GenCl	PartialEmbedding;DifferentOntology	partial-formal	UNCHANGED	FORMAL_ANALOGUE
APE-003	UCT triad	FormalAnalogue	theorem-level	UNCHANGED	PRIOR_ART_ALIGNED
APE-004	BridgeCert	SemanticOverlap;GeneralizationCandidate	structural	UNCHANGED	BACKEND_MAPPING
APE-005	BridgeCompCert	FormalAnalogue;SemanticOverlap	theorem-level	UNCHANGED	SPECIAL_CASE
APE-006	Bridge obstruction/debt	IndependentConvergence;FormalAnalogue	theorem-level	UNCHANGED	OBSTRUCTION_BACKEND
APE-007	Reach judgement	SemanticOverlap;IndependentConvergence	structural	UNCHANGED	MULTI_DOMAIN_MAPPING
APE-008	R2T non-collapse	SpecialCase;SemanticOverlap	theorem-level	UNCHANGED	SPECIAL_CASE
APE-009	ReachEnv	DifferentFormalization;FormalAnalogue	structural	UNCHANGED	REPRESENTATION_MAPPING
APE-010	TransCl	SemanticOverlap;FormalAnalogue	structural	UNCHANGED	FORMAL_ANALOGUE
APE-011	MC0–MC4	IndependentConvergence;SemanticOverlap	structural	UNCHANGED	DOMAIN_MODELS
APE-012	ClassUltimate	DifferentOntology;IndependentConvergence	heuristic	UNCHANGED	CANDIDATE_NATIVE_CONCEPT
APE-013	OBRC/SCDT projection interface	IndependentConvergence;SemanticOverlap	theorem-level	UNCHANGED	DOMAIN_SUPPORT
APE-014	Capability mode family	IndependentConvergence;SemanticOverlap	structural	UNCHANGED	CROSS_DOMAIN_MAPPING
APE-015	Action/intervention correspondence (parallel refinement)	SemanticOverlap;IndependentConvergence	theorem-level	UNCHANGED	OPTIONAL_REFINEMENT
APE-016	Agency/control interpretation (parallel refinement)	SemanticOverlap;IndependentConvergence	theorem-level	UNCHANGED	OPTIONAL_REFINEMENT
APE-017	Class-Ultimate / meta-causal evaluation	IndependentConvergence;SemanticOverlap	structural	UNCHANGED	OPTIONAL_REFINEMENT
APE-018	Ledger	SemanticOverlap;IndependentConvergence	structural	UNCHANGED	BACKEND_MAPPING
APE-019	InfoAcct	IndependentConvergence;SemanticOverlap	structural	UNCHANGED	PRIOR_ART_ALIGNED
APE-020	Ledger/causal firewall	SemanticOverlap	theorem-level	UNCHANGED	DOMAIN_SUPPORT
APE-021	FCS	SemanticOverlap;DifferentFormalization	structural	UNCHANGED	PARALLEL_INTERPRETATION
APE-022	GroundingComplete	SemanticOverlap;DifferentOntology	partial-formal	UNCHANGED	PARALLEL_REFINEMENT_ONLY
APE-023	FCS / AbsoluteNothingness firewall	IndependentConvergence;DifferentOntology	heuristic	UNCHANGED	PHILOSOPHICAL_MAPPING
APE-024	UOE taxonomy	SemanticOverlap;DifferentFormalization	structural	UNCHANGED	MULTI_DOMAIN_MAPPING
APE-025	UOE claim ladder / local-to-absolute gate	IndependentConvergence;SemanticOverlap	structural	UNCHANGED	SUPPORTING_ANALOGUE
APE-026	Boundary/channel interface	SemanticOverlap;IndependentConvergence	structural	UNCHANGED	BACKEND_MAPPING
APE-027	Reach/Transform distinction	SpecialCase;FormalAnalogue	theorem-level	UNCHANGED	SPECIAL_CASE
APE-028	UCT typed non-collapse / bridge architecture	IndependentConvergence;SemanticOverlap	structural	UNCHANGED	HIGH_THREAT_PARALLEL
APE-029	Edition architecture	DifferentFormalization	structural	LOCKED	CORE_POLICY
APE-030	Academic correspondence policy	DifferentOntology	structural	LOCKED	CORE_POLICY

For the full claim, academic analogue, reusable result, ontology difference and AnalogyStop fields, use the accompanying CSV/YAML.

Appendix B — Core Academic References

[Jou26] Robin Jourde et al.. Compositionality in Coalgebraic Trace Semantics. 2026. 10.48550/arXiv.2605.18285. Cluster: closure/composition.
[Agr09] A. Agrachev; M. Caponigro. Controllability on the group of diffeomorphisms. 2009. 10.1016/J.ANIHPC.2009.07.003. Cluster: reach/control.
[Rag24] Maxim Raginsky. Some Remarks on Controllability of the Liouville Equation. 2024. https://arxiv.org/abs/2404.14683. Cluster: reach/control.
[Liu22] Zexiang Liu; N. Ozay. On the Convergence of the Backward Reachable Sets of Robust Controlled Invariant Sets For Discrete-time Linear Systems. 2022. 10.1109/CDC51059.2022.9993110. Cluster: reach/control.
[Joh16] Christian Johansen; Olaf Owe. Dynamic Structural Operational Semantics. 2016/2019. 10.1016/J.JLAMP.2019.05.006. Cluster: meta-rewrite.
[Sch20b] K. Schewe; Flavio Ferrarotti. Behavioural Theory of Reflective Algorithms I: Reflective Sequential Algorithms. 2020/2022. 10.1016/j.scico.2022.102864. Cluster: meta-rewrite.
[Cla02] M. Clavel et al.. Maude: specification and programming in rewriting logic. 2002. 10.1016/S0304-3975(01)00359-0. Cluster: meta-rewrite.
[Rov01] Carlo Rovelli. Partial observables. 2001/2002. 10.1103/PhysRevD.65.124013. Cluster: observer.
[Kab19] Oleg Kabernik; Jason Pollack; Ashmeet Singh. Quantum state reduction: Generalized bipartitions from algebras of observables. 2019/2020. 10.1103/PhysRevA.101.032303. Cluster: observer.
[Zan03] P. Zanardi; D. A. Lidar; S. Lloyd. Quantum tensor product structures are observable induced. 2003/2004. 10.1103/PhysRevLett.92.060402. Cluster: observer.
[Mag26] Declan Maguire; Fabio Costa. Causal Order Cannot Be An Observable. 2026. https://arxiv.org/abs/2605.25302. Cluster: observer/causal.
[Che10] James Cheney. Causality and the Semantics of Provenance. 2010. 10.4204/EPTCS.26.6. Cluster: provenance.
[Che08] James Cheney; Umut A. Acar; Amal Ahmed. Provenance Traces. 2008. https://arxiv.org/abs/0812.0564. Cluster: provenance.
[Gre17] Todd J. Green; Val Tannen. The Semiring Framework for Database Provenance. 2017. 10.1145/3034786.3056125. Cluster: provenance.
[Ams11] Yael Amsterdamer; Daniel Deutch; Val Tannen. On the Limitations of Provenance for Queries with Difference. 2011. https://arxiv.org/abs/1105.2255. Cluster: provenance.
[Gra24] Erich Grädel; Val Tannen. Provenance Analysis and Semiring Semantics for First-Order Logic. 2024. 10.48550/arXiv.2412.07986. Cluster: provenance.
[Kil14] M. L. H. Kilpack. The lattice of algebraic closure operators. 2014. https://arxiv.org/abs/1411.6497. Cluster: closure.
[Han53] S. Hanai. On commutative T-closure operators. 1953. 10.2996/KMJ/1138843295. Cluster: closure.
[Tho11] W. Tholen. Closure operators and their middle-interchange law. 2011. 10.1016/J.TOPOL.2011.04.015. Cluster: closure.
[Kon23] Harald König; Uwe Wolter; Tim Kräuter. Structural Operational Semantics for Heterogeneously Typed Coalgebras. 2023. 10.4230/LIPIcs.CALCO.2023.7. Cluster: heterogeneous composition.
[Zwa19] Maaike Zwart; Dan Marsden. No-Go Theorems for Distributive Laws. 2019. 10.1109/LICS.2019.8785707. Cluster: bridge/no-go.
[Goy22] Alexandre Goy. Weakening and Iterating Laws using String Diagrams. 2022. 10.46298/entics.10482. Cluster: bridge/coherence.
[Mol06] B. Möller; G. Struth. Algebras of modal operators and partial correctness. 2006. 10.1016/j.tcs.2005.09.069. Cluster: dynamic algebra.
[Fur14] H. Furusawa; G. Struth. Concurrent Dynamic Algebra. 2014/2015. 10.1145/2785967. Cluster: dynamic algebra.
[Dui20] H. Duijf et al.. Doing Without Action Types. 2020/2021. 10.1017/S1755020320000362. Cluster: agency/epistemic.
[Bal22] A. Baltag; L. Moss; S. Solecki. Logics for Epistemic Actions: Completeness, Decidability, Expressivity. 2022. 10.48550/arXiv.2203.06744. Cluster: epistemic action.
[Leu19] Stephan Leuenberger. The fundamental: Ungrounded or all-grounding?. 2019/2020. 10.1007/s11098-019-01332-x. Cluster: grounding.
[Pea17] Kenneth L. Pearce. Foundational Grounding and the Argument from Contingency. 2017. 10.1093/oso/9780198806967.003.0011. Cluster: grounding/first cause.
[Obe22] Thomas Oberle. Metaphysical Foundationalism and the Principle of Sufficient Reason. 2022. 10.1017/S001221732200018X. Cluster: grounding.
[Ryd18] Henrik Rydéhn. Grounding and ontological dependence. 2018/2021. 10.1007/s11229-018-1818-4. Cluster: grounding.
[Jor25] Frederik H. Jørgensen; Luigi Gresele; Stefan Weichwald. What is causal about causal models and representations?. 2025. 10.48550/arXiv.2501.19335. Cluster: causal intervention.
[Bai21] Christel Baier; Florian Funke; Rupak Majumdar. A Game-Theoretic Account of Responsibility Allocation. 2021. 10.24963/ijcai.2021/244. Cluster: responsibility.
[Car20] Ryan Carey et al.. Incentives for responsiveness, instrumental control and impact. 2020/2025. 10.1016/j.artint.2025.104408. Cluster: agency/control.
[Abe25] David Abel et al.. Agency Is Frame-Dependent. 2025. 10.48550/arXiv.2502.04403. Cluster: agency.
[Cou20] Kenny Courser. Open Systems: A Double Categorical Perspective. 2020. https://arxiv.org/abs/2008.02394. Cluster: open systems.
[Bae18] John C. Baez; Jade Master. Open Petri nets. 2018/2020. 10.1017/S0960129520000043. Cluster: open systems.
[Mye20] David Jaz Myers. Double Categories of Open Dynamical Systems. 2020/2021. 10.4204/EPTCS.333.11. Cluster: open systems.
[Lib25] Sophie Libkind; David Jaz Myers. Towards a double operadic theory of systems. 2025. https://arxiv.org/abs/2505.18329. Cluster: open systems.
[Kli15] Bartek Klin; Beata Nachyła. Presenting Morphisms of Distributive Laws. 2015. 10.4230/LIPIcs.CALCO.2015.190. Cluster: translation.
[Mos05] Till Mossakowski. Heterogeneous Theories and the Heterogeneous Tool Set. 2005. Semantic Scholar record. Cluster: institutions.
[Kut08] Oliver Kutz; Till Mossakowski. Conservativity in Structured and Heterogeneous Ontologies. 2008. Semantic Scholar record. Cluster: institutions.

Appendix C — Edition Governance

APE never edits Native v0.1 source in place.
APE correspondence records may be revised independently as literature knowledge improves.
A Native version may voluntarily adopt an APE refinement only through an explicit Native change record.
A genuine contradiction may trigger a Native review, but only after object and assumption matching are documented.
Formal similarity alone never constitutes a contradiction or definitional identity.

UGC_CUR Academic Parallel Edition v0.1

UGC/CUR Academic Parallel Edition v0.1

Native Theory × External Academic Correspondence without Canonical Replacement

Abstract

1. Why a Parallel Edition Is Necessary

2. Dual-Track Architecture

2.1 Native Track

2.2 Academic Parallel Track

2.3 No Silent Redefinition

3. Correspondence Relation Types

3.1 FormalAnalogue

3.2 PartialEmbedding

3.3 SemanticOverlap

3.4 IndependentConvergence

3.5 SpecialCase

3.6 GeneralizationCandidate

3.7 DifferentOntology

3.8 DifferentFormalization

3.9 Contradictory

3.10 Unknown

4. Mapping Strength

5. The Analogy-Stop Principle

6. Native UCT as a Source Theory, Not a Translation Artifact

7. Generative Closure Correspondence

8. UOE Correspondence

9. First-Cause Sufficiency Correspondence

9.1 GroundingComplete as a Native Term

10. Global Ledger Correspondence

11. Typed Reachability Correspondence

12. Reach-to-Transform Correspondence

13. Class-Ultimate Correspondence

14. Transformation Closure Correspondence

15. Meta-Causal Agency Correspondence

16. Agency and Intervention as Optional Academic Refinements

16.1 ActionInterventionCert

16.2 AgencyFrame

17. Bridge Theory Correspondence

17.1 BridgeDecl as Parallel Academic Refinement

18. Representation-Relative Collapse

19. Novelty Policy

19.1 Not Novel by Itself

19.2 Candidate Native Contributions

20. Reuse Without Submission

21. Contradiction Protocol

22. Publication Architecture

A. Native Theory

B. Academic Correspondence Appendix / Parallel Edition

23. Machine-Readable Correspondence Record

24. Round 1–3 Reclassification

Round 1

Round 2

Round 3

25. Native Sovereignty and Academic Accountability

26. Current Research Status

27. Next Research Interface

28. Final Position

Appendix A — Correspondence Matrix

Appendix B — Core Academic References

Appendix C — Edition Governance