A formal framework for human–AI creative provenance in music.
Abstract
A music artifact may result from materially creative decisions attributable to different agents. Its schema-complete creative provenance is therefore represented as a structured decision-level record, not as a primitive binary property of the finished artifact.
Any smaller label space necessarily compresses that record: when distinct provenance states share one label, the label cannot reconstruct the complete provenance. Such compression may nevertheless be appropriate for a downstream rule exactly when the rule is constant over every set of provenance states merged by the label.
The framework therefore separates three objects: materially creative decisions, schema-complete provenance, and summary labels. The central conclusion is that a label is a function of a provenance record, not a substitute for it — and it is sufficient for a downstream decision only when the distinctions it discards are irrelevant to that decision.
Scope and provenance schema
Throughout, s denotes the music artifact under analysis. Depending on the stated scope, s may refer to an underlying musical work, a sound recording embodying that work, or both.
The framework is descriptive: it models creative provenance and does not, by itself, determine legal authorship, copyright ownership, neighboring rights, contractual credit, or eligibility under any external rule.
Throughout, “complete provenance” means complete relative to the declared schema M — not exhaustive of every conceivable causal or historical fact about the artifact.
For music-industry clarity, an underlying musical work refers to the composition, including music and any accompanying lyrics. A sound recording refers to the particular fixed recorded sounds embodying a performance or realization of that work. The framework permits these domains to be analyzed separately because their creative provenance need not coincide.
A provenance schema is a tuple
M = (D, 𝒜, Ω)
where
D = {d1, …, dn}
is a finite set of candidate provenance-relevant decision units that the schema treats as materially creative when applicable,
𝒜
is the set of admissible agency states for a decision unit, and
Ω ⊆ 𝒜n
is a nonempty set of admissible schema-complete provenance records under the schema.
The units in D are chosen for the purpose of the analysis. They may represent, for example, lyrical, melodic, harmonic, structural, arrangement, performance, sound-design, production, selection, or revision decisions. The theorem does not depend on a particular taxonomy; it requires only that the schema, including its materiality convention, be fixed before labels or downstream rules are evaluated.
Materially Creative Decisions
Let X denote the musically relevant outcome of the creative process, taking values in an outcome space 𝒳. Fix a counterfactual intervention model specifying which background and downstream variables are held fixed or allowed to respond under an intervention. For a decision unit di ∈ D, let ai be its realized choice and let ai′ be an admissible alternative. Under the declared intervention model, let
μa and μa−i, ai′
denote the induced probability laws of X under the realized decision profile a and the counterfactual intervention replacing only ai by ai′. Let Δ be a specified discrepancy between outcome laws and let ε > 0 be a materiality threshold.
Relative to the declared intervention model, discrepancy Δ, and threshold ε, the unit di is materially creative at a if
∃ ai′ such that Δ(μa, μa−i, ai′) > ε.
For a deterministic creative system this reduces to
∃ ai′ such that dX(X(a), X(a−i, ai′)) > ε,
for a specified discrepancy dX on musical outcomes.
The definition is explicitly model-relative: the intervention semantics, discrepancy, and materiality threshold are declared components of the analysis. It is counterfactual rather than interface-based. An action is not materially creative merely because it triggers a process. Conversely, an instruction, selection, revision, performance choice, or other intervention may be materially creative when an admissible alternative would materially change the musical result or its outcome distribution. Accordingly:
operational causation ≠ material creative contribution
Schema-Complete Creative Provenance
Let the agency-state space contain at least {H, A} ⊆ 𝒜, where H denotes human provenance and A denotes AI provenance. A schema may also include J = joint human–AI provenance for a decision that the schema treats as genuinely joint, and ∅ for a schema unit that carries no provenance entry for a particular artifact because it is not applicable or does not satisfy the declared materiality criterion.
For an artifact s, define the provenance assignment
ps : D → 𝒜.
Its schema-complete creative provenance record is
P(s) = (ps(d1), …, ps(dn)) ∈ Ω.
The record preserves the provenance of all creative units represented by the declared schema before any summary category is assigned. It therefore distinguishes, for example, an artifact with human-originated compositional decisions and AI-originated recording decisions from an artifact in which those same modeled decisions are all AI-originated.
Creative Provenance Decomposition Theorem
Let L : Ω → Λ be a function assigning each admissible schema-complete provenance record a summary label.
If |Λ| < |Ω|, then L is not injective. Hence ∃ P1, P2 ∈ Ω with P1 ≠ P2 and L(P1) = L(P2). Consequently, no function R : L(Ω) → Ω can satisfy R ∘ L = idΩ. Thus the summary label cannot uniquely reconstruct schema-complete creative provenance.
If |Λ| < |Ω|, no injective map from Ω into Λ exists. Therefore L maps at least two distinct provenance records to the same label. If a reconstruction map R satisfying R ∘ L = idΩ existed, then L would necessarily be injective: L(P1) = L(P2) would imply P1 = R(L(P1)) = R(L(P2)) = P2, a contradiction. Hence no such reconstruction map exists. ∎
If Λ = {Human, AI} and |Ω| > 2, every binary labeling function L : Ω → {Human, AI} is non-injective. Therefore binary labeling is necessarily an information-losing summary of schema-complete provenance.
Non-injectivity does not make a label intrinsically invalid. It establishes only that the label does not preserve all provenance distinctions represented by the schema. Whether those lost distinctions matter is a separate question addressed in Section 7.
Exclusive, Mixed, and Domain-Specific Provenance
For an artifact s, define
Dsrel = { di ∈ D : ps(di) ≠ ∅ }.
These are exactly the schema units carrying a provenance entry for s. Only units in Dsrel are considered when exclusivity is asserted.
Relative to the fixed schema M, define
s ∈ PureAI(M) ⇔ ∀ di ∈ Dsrel, ps(di) = A.
Exclusive human provenance is defined analogously, replacing A with H.
If ∃ dj ∈ Dsrel with ps(dj) ≠ A, then s ∉ PureAI(M). In particular, a materially creative unit assigned human or joint provenance falsifies exclusive AI provenance. The converse conclusion does not follow:
s ∉ PureAI(M) ⇏ s ∈ PureHuman(M).
Thus a human creative contribution can make the statement “exclusive AI provenance” false without making the statement “exclusive human provenance” true.
If the provenance record on Dsrel contains both human and AI states, or contains a joint human–AI state distinct from both, then the artifact is neither exclusively AI-provenanced nor exclusively human-provenanced under the schema. Its provenance record preserves that mixed or joint structure even if a downstream system later assigns a simpler label.
Underlying musical work and sound recording
Let the schema include a disjoint partition
D = DW ⊔ DSR ⊔ DO,
where DW contains units attributed to the underlying musical work, DSR units attributed to the sound recording and its realization, and DO any other units required by the chosen model. Define the restricted provenance records
PW(s) = P(s)|DW, PSR(s) = P(s)|DSR.
The definitions alone impose no functional dependence between PW and PSR. In particular, if Ω contains two admissible records P1, P2 satisfying
PSR,1 = PSR,2 and PW,1 ≠ PW,2,
then sound-recording provenance cannot determine musical-work provenance on Ω. Symmetrically, if Ω contains two records agreeing on PW but differing on PSR, musical-work provenance cannot determine sound-recording provenance. Accordingly, any rule inferring provenance in one domain from provenance in the other requires an additional constraint on the admissible state space Ω; it does not follow from the provenance definitions themselves.
A schema may locate arrangement or production choices in the domain appropriate to the specific analysis. The framework requires consistency of the declared schema, not one universal taxonomy of every music-production practice.
Prompting, Selection, and Iterative Creation
Let N(s) be the number of human–AI interaction events recorded in a workflow.
Without additional assumptions linking interaction events to the decision units in D,
N(s) does not determine the schema-complete record P(s).
In particular, it is possible that
N(s1) = N(s2) while P(s1) ≠ P(s2).
It is also possible for one interaction to instantiate several materially creative units and for many interactions to instantiate no additional materially creative unit.
A prompt is not materially creative merely because it initiates generation. A prompt contributes to creative provenance only through the decision units it instantiates under Definition 2. Consequently:
prompt count ≠ schema-complete creative provenance
A single prompt may encode several musically material constraints; a long sequence of prompts may encode repeated requests without adding new materially creative decisions.
If choosing among alternatives or revising an intermediate result satisfies the materiality criterion in Definition 2, that selection or revision is itself a provenance-relevant decision unit. The fact that candidate material was machine-generated does not erase the provenance of a later materially creative human selection or revision; likewise, human-originated input does not erase a later materially creative AI-originated contribution.
An iterative workflow may be represented as
u1 → x1 → u2 → x2 → ⋯ → um → xm,
where each xi is the intermediate result produced by the subsequent intervention. Every intervention that instantiates a materially creative unit in D contributes its corresponding agency state to P(s). Therefore, two artifacts produced with the same generative system need not have the same schema-complete provenance, even when both workflows are conventionally described as “AI-assisted” or “AI-generated.”
Provenance-Label Sufficiency Theorem
The preceding theorem establishes when a label loses information represented by the provenance schema. The next theorem establishes exactly when that loss is harmless for a specified downstream decision.
Let L : Ω → Λ be a provenance labeling function and let E : Ω → Y be a downstream rule defined on schema-complete provenance records.
There exists a function g : Λ → Y with E = g ∘ L if and only if E is constant on every fiber of L. Equivalently,
L(P1) = L(P2) ⇒ E(P1) = E(P2)
for every P1, P2 ∈ Ω.
If E = g ∘ L, then L(P1) = L(P2) implies E(P1) = g(L(P1)) = g(L(P2)) = E(P2), so E is constant on every fiber of L.
Conversely, suppose E is constant on every fiber of L. For each λ ∈ L(Ω), choose any P ∈ Ω with L(P) = λ and define g(λ) = E(P). The definition is well-defined because every record in the same fiber has the same E-value. Extend g arbitrarily to Λ ∖ L(Ω) if necessary. Then E(P) = g(L(P)) for every P ∈ Ω. ∎
If there exist records P1, P2 ∈ Ω with L(P1) = L(P2) but E(P1) ≠ E(P2), then there exists no function g : Λ → Y with E = g ∘ L:
∃ P1, P2 ∈ Ω : L(P1) = L(P2) and E(P1) ≠ E(P2) ⇒ ∄ g : E = g ∘ L.
No rule using only the label can reproduce E on all admissible provenance records. The label is insufficient for that decision.
A non-injective label may still be sufficient for a particular downstream rule. Precisely,
L may be non-injective and still sufficient for E ⇔ E is constant on every fiber of L.
Thus a compressed label is justified for a particular decision exactly when every provenance distinction erased by that label is irrelevant to that decision.
Let S : Ω → {0, 1} be any binary substantiality criterion defined on schema-complete provenance. A label-only implementation exists if and only if
L(P1) = L(P2) ⇒ S(P1) = S(P2) for all P1, P2 ∈ Ω.
If the implication fails, then substantiality depends on provenance distinctions that the label has erased and cannot be determined from that label alone.
Conclusion
The framework yields a single ordered structure:
Materially Creative Decision Units → Schema-Complete Creative Provenance → Summary Label → Downstream Decision
The first transition assigns an agency state to each materially creative unit under a fixed provenance schema. The second transition compresses the schema-complete provenance record into a label. The third transition is logically valid as the sole basis of a downstream decision exactly when the label is sufficient for that decision in the sense of Theorem 2.
The conclusions are therefore:
- Schema-complete creative provenance is a structured record of materially creative decision units, not a primitive binary property of a finished music artifact.
- Whenever |Λ| < |Ω|, a label function L : Ω → Λ necessarily merges distinct provenance records and therefore cannot uniquely reconstruct schema-complete provenance.
- Exclusive AI provenance requires AI provenance for every provenance-relevant materially creative unit in the chosen schema. A non-AI materially creative unit falsifies exclusive AI provenance but does not establish exclusive human provenance.
- Provenance of the underlying musical work and provenance of the sound recording are distinct domains; neither determines the other without an additional constraint on the admissible provenance space.
- Prompt count, interaction count, or the mere use of a generative system does not determine schema-complete creative provenance. What matters under the model is the provenance of the materially creative decision units actually instantiated during the process.
- A summary label is sufficient for a downstream rule E if and only if E is constant on every fiber of the label function, equivalently if and only if E factors through the label as
E = g ∘ L.
Accordingly,
Summary Label ≠ Schema-Complete Creative Provenance
A summary label may be useful, transparent, and operationally appropriate; it is nevertheless a compression of the provenance record defined by the model. Its use as the sole input to a downstream decision is mathematically warranted only when the information discarded by that compression cannot change the decision.