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Referential Regimes: Transformation-Invariant Identity for Neutral Substrates

This paper argues that in data systems characterized by persistent disagreement, a neutral substrate must distinguish at least nine transformation-invariant identity regimes—exceeding the six apparent reference kinds—to structurally fix reference without relying on interpretive conventions that cannot withstand ongoing conflict.

Original authors: Denise M. Case

Published 2026-07-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Denise M. Case

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are running a massive, chaotic library where everyone is arguing about what the books mean. One group thinks a book is about its cover art; another thinks it's about the story inside; a third thinks it's about the specific ink used. They can't agree. They can't stop arguing. But they all need to point to the exact same physical object on the shelf and say, "That one," without fighting about its meaning.

This paper is about building the ultimate, unshakeable shelf for that library. The author, Denise M. Case, asks a simple but tricky question: If we can't agree on what things are, how do we make sure we are all talking about the same thing when we move, copy, or rewrite our records?

The answer isn't just "six types of things." It's actually nine.

The Six "Things" We Need to Track

First, the paper says any system that tracks accountability (like who did what, when, and why) needs to keep track of six basic kinds of "stuff":

The Doers: People or groups who can be held responsible (like a company or a person).
The Rules: The laws or instructions that govern the Doers.
The Events: The actual things that happened (like a vote, a filing, or a transaction).
The Scope: The "where" and "who" the rules apply to (like a specific city or a specific group of people).
The Records: The paper, digital file, or note that describes the event (without the system deciding if the note is true).
The Objects: The physical things being acted upon (like a building, a parcel of land, or a machine).

If you just counted these, you'd think you need six different ways to say "this is the same thing." But the paper proves that six is not enough.

The Great Split: Why Six Becomes Nine

Here is where the magic happens. The paper shows that for three of those six types, you can't just have one way to say "it's the same." You need two different ways, because the "same" thing can change depending on how you look at it.

Think of it like a Lego castle.

The Rules Split (Content vs. Structure): Imagine a rulebook.
- View A: It's the same rule if the instructions are the same, even if you rewrite the font or move the paragraphs around.
- View B: It's the same rule only if the layout and page numbers stay exactly the same.
- The Problem: If you "refine" the book (add more details), View A says "It's still the same rule!" but View B says "No! You changed the structure, it's a new rule!" You can't have both views use the same definition. You need two different identity systems for rules.
The Scope Split (The List vs. The Map): Imagine a map of a country's laws.
- View A: The scope is the list of people it covers. If you break the country into smaller districts but the same people are still covered, it's the same scope.
- View B: The scope is the internal map structure. If you redraw the districts, the structure changed, so it's a new scope.
- The Problem: If you "decompose" the country into smaller parts, View A says "Same scope!" but View B says "New scope!" You need two different systems for scopes.
The Object Split (The Spot vs. The Thing): Imagine a parking spot.
- View A: The identity is the spot itself. If a car leaves and a new one parks there, it's still the same "parking spot."
- View B: The identity is the car. If the car leaves, the identity is gone, even if the spot is there.
- The Problem: If you "fork" (split) the timeline, View A might say the spot is the same, but View B says the car is different. You need two different systems for objects.

The Big Reveal: The Nine Regimes

Because of these splits, the paper proves that a neutral system—one that doesn't take sides in the arguments—must have nine distinct ways to track identity, not six.

Doers (1 way)
Events (1 way)
Records (1 way)
Rules (2 ways: Content-based and Structure-based)
Scopes (2 ways: List-based and Structure-based)
Objects (2 ways: Spot-based and Thing-based)

Total: 9 Identity Regimes.

What This Paper Says You Can't Do

The paper is very strict about what doesn't work. It argues against a common shortcut: hiding the difference.

Imagine you try to save space by using only six systems. You decide to say, "Oh, a rule is just a rule," and you use a little flag or a label in your computer code to tell the difference between "content" and "structure" later. The paper says no, that doesn't count.

If you hide the difference in a flag or a label, you aren't actually solving the problem. You've just moved the argument to a different room. If two people disagree about what that flag means, your system breaks. The paper insists that if you want a system that works when people persistently disagree, you must build the nine different ways right into the foundation. You can't sneak the extra three in as "hidden" tricks.

How Sure Are They?

The authors are very confident, but they are also precise. They didn't just guess or simulate this. They used a mathematical proof based on a specific set of rules (like "re-writing," "splitting," and "adding details").

They say: "If you accept our starting rules (that people will keep disagreeing and we need to track these six things), then it is mathematically impossible to get by with fewer than nine identity systems."

They don't claim this is the maximum number of systems you could ever need. They just say it's the minimum floor. If you add more complex operations later, you might need even more than nine. But you can never go below nine without breaking the system.

The Takeaway

In a world where everyone argues about what things mean, you can't just count the types of things. You have to count the different ways those things can stay the same when they change.

If you try to force everything into six boxes, you'll break the system when people try to split, refine, or rewrite their records. To stay neutral and stable, you need nine distinct boxes. It's not about what the things are; it's about how they survive the changes we make to them.

Technical Summary: Referential Regimes: Transformation-Invariant Identity for Neutral Substrates

Problem Statement
Modern accountability and data systems increasingly operate under conditions of persistent legal, political, and analytic disagreement. In such environments, no single interpretive authority can be assumed to resolve causal or normative conflicts. A shared data substrate must therefore provide stable reference to entities, occurrences, and institutional artifacts without forcing agreement on their interpretation. The core problem addressed is the structural requirement for such a "neutral substrate": specifically, what identity conditions are necessary to ensure that reference remains stable as records undergo ordinary transformations (e.g., re-expression, annotation, refinement, decomposition, forking) while the substrate remains neutral regarding causal and normative commitments.

Previous approaches often rely on naming reference kinds (e.g., "rule," "scope") to fix identity. This paper argues that naming kinds is insufficient because different frameworks may require different identity bases for the same kind. If a substrate collapses these distinctions, it either alters the behavior of identity under transformation or hides the distinction in downstream mechanisms (roles, flags, or application logic), which violates the requirement for stable reference under persistent disagreement.

Methodology
The paper employs a formal, algebraic approach to derive a lower bound on the number of identity regimes required. The methodology proceeds as follows:

Formal Setting: The analysis assumes a "neutral substrate" defined by the constraint that it must preserve stable reference without making object-level causal or normative commitments. It operates under the assumption of "persistent disagreement," where extensions may remain incompatible.
Transformation Basis: A finite set of ten representative transformation families ( $F$ ) is fixed, including re-expression (RE), annotation (AN), refinement (RF), aggregation/decomposition (AD), re-contextualization (RC), reassignment (RA), substitution (SU), branching/forking (BF), provenance extension (PV), and state evolution (SE).
Identity as Invariance: Identity is treated as transformation-invariance. An identity regime is defined as a pair consisting of an identity basis (the feature determining sameness) and a classification function that maps each transformation in $F$ to one of four states: Preserving (PRS), Breaking (BRK), Neutral (NEU), or Not Applicable (N/A).
Reference Inventory: A modest inventory of six carrier kinds is established: obligation-bearers, rules, occurrences, scopes, records, and plain referents.
Basis Plurality Analysis: The paper identifies "basis plurality" where admissible frameworks require stable reference to a carrier kind under more than one identity basis. It demonstrates that for three specific kinds (scopes, rules, and plain referents), ordinary transformations separate these bases.
- Scopes: Can be fixed by extension (covered cases) or structure (internal organization). Decomposition (AD) separates these.
- Rules: Can be fixed by content (requirements) or structure (textual organization). Refinement (RF) separates these.
- Plain Referents: Can be fixed by locus (location) or object (the thing occupying the location). Forking (BF) separates these.
Lower Bound Derivation: The paper proves that because these transformations classify the bases differently (one basis is preserved while the other is broken), a single identity regime cannot serve both bases. Therefore, distinct regimes are required for each basis.

Key Contributions

Transformation-Invariant Identity Definition: The paper operationalizes identity not as a static ontological property but as a dynamic profile over a transformation basis. A regime is defined by how it classifies transformations relative to a declared identity basis.
The Nine-Regime Lower Bound: The primary result is a conditional lower bound: a neutral accountability substrate satisfying the stated assumptions requires at least nine distinct identity regimes.
- Three regimes correspond to the non-split carrier kinds: Obligation-Bearer (OBL), Occurrence (OCC), and Record (REC).
- Six regimes correspond to the split carrier kinds:
  - Scope-Extension (SCOPE-E) and Scope-Structure (SCOPE-S).
  - Rule-Content (RULE-C) and Rule-Structure (RULE-S).
  - Plain Referent-Locus (LOC) and Plain Referent-Object (OBJ).
Diagnosis of Hidden Regimes: The paper formally defines "hidden regimes" as distinctions collapsed at the substrate level but recovered via downstream discriminators (flags, roles, workflow states). It argues that under persistent disagreement, hidden regimes are insufficient because they rely on interpretive agreement that cannot be assumed.
Monotonicity: The paper establishes that the lower bound is monotone with respect to the transformation basis. Adding further transformations cannot erase the distinctions witnessed by the current basis; it can only leave the bound unchanged or force further splits.

Results
The analysis yields a classification table (Table 1) demonstrating that the nine core regimes are pairwise distinct.

Carrier Disjointness: Regimes governing different carrier kinds (e.g., OBL vs. OCC) are distinct by definition.
Transformation Witnesses: Regimes governing the same carrier kind but different bases (e.g., SCOPE-E vs. SCOPE-S) are distinct because there exists a transformation (e.g., AD) that preserves identity under one regime but breaks it under the other.
The Count: The inventory of six kinds provides a floor of six regimes. The three witnessed splits (Scope, Rule, Plain Referent) each add one additional regime, raising the minimum requirement to nine.

Significance and Claims
The paper positions itself as a diagnostic structural analysis rather than a prescriptive modeling guide or an upper ontology.

Diagnostic Nature: The result identifies the "identity cost" of the neutral-substrate constraint. It reveals that simply naming reference kinds undercounts the structural complexity required for stable reference when disagreement is persistent.
Constraint Theorem: The nine-regime count is a necessary condition (a lower bound) for any system claiming to be a neutral substrate under the specified assumptions. It does not claim that these nine regimes exhaust all possible identity structures, nor that every deployed system must expose all nine.
Limitations: The result is conditional on the assumptions of persistent disagreement, strong stable reference, and the exclusion of hidden regimes. It does not apply to systems where identity depends on causal/normative commitments or where identity conditions vary by extension.
Relation to Prior Work: The paper builds on the "Neutral Substrates" design constraint (Case 2026) and formal ontology principles regarding identity conditions (Guarino, 1999). It complements FAIR principles by addressing the ontological requirements for data reuse in contested settings where interpretive convergence is absent.

In summary, the paper argues that for a data substrate to remain neutral and stable under persistent disagreement, it must structurally distinguish between at least nine identity regimes, driven by how ordinary record operations affect different identity bases within the same reference kinds.