Bell Compatibility and Terminal Record Neutrality within the Selective Transient Field Framework
Z. Paz
Version 1.4 — 22 August 2026
High-redshift Cosmic Bell experiments severely restrict local-realist accounts in which measurement settings and hidden variables are coordinated by a common cause in their accessible past. They do not test every time-symmetric or all-at-once formulation, and they neither verify nor falsify the Selective Transient Field (STF) framework. Their relevance to STF is architectural: any extension of the framework to quantum measurement must reproduce Bell nonfactorizability while preserving operational no-signaling and measurement independence.
The Clock-Separation Theorem establishes that the oscillating STF amplitude cannot also generate a continuous universal time direction through its normalized gradient. The present framework therefore assigns distinct roles to the scalar’s cyclic Compton phase, the record clocks of local systems, and the universal ordering selected by global closure geometry. Following The Universal Clock Carrier, the preferred carrier of that ordering is not a new propagating khronon but a boundary-selected constant-mean-curvature (CMC) normal
\[ N^\mu_{\rm CMC} =N^\mu_{\rm CMC} [g;\Sigma_{\rm closure},\Sigma_{\rm terminal},V_4]. \]
Within this architecture we construct a time-symmetric transaction functional. Conditional on an anti-linear outcome-fiber adjoint, a positive matter-state inner product, normalized amplitudes, and ordinary record decoherence, the functional is Hermitian and positive semidefinite and reproduces Born-diagonal weights. Supplying the standard \(SU(2)\) singlet state and local quantum instruments then reproduces the Bell joint distribution, no-signaling marginals, and the Tsirelson bound. This is a faithful STF embedding of quantum probability, not yet an STF derivation of it: the topology fixes the \(4\pi^2\) normalization of closure but does not by itself determine the amplitudes, their adjoint, or their probabilistic interpretation.
The construction also distinguishes ontic record, perspectival access, and public objectivity. Every internal clock accesses only the records contained in its local filtration; observation is therefore necessarily perspective-indexed without being mentally created or dependent on consciousness. Public objectivity arises when causally reunited observers map their local records through shared units, calibrations, synchronization rules, languages, and protocols into a common record algebra. Conventions make records comparable; they do not create the invariant relations on which agreement is based. Spatial distance behaves the same way: every element of a Bell experiment is registered locally and compared at a common future event, cosmic distance enters the causal-admissibility analysis rather than the correlation law, and the causal structure itself is not conventional. The universal CMC background orders the arena but does not presently select which quantum alternative becomes the unique actual record.
A future heat-death macrocondition can preserve ordinary statistics if it is effectively neutral on finite local record algebras. We state the precise conditional neutrality lemma and its superselection and quantum-field-theory qualifications. The more speculative identification of holographic state capacity with an STF transaction budget, and of failed closure with a gravitating residue, is developed separately in Holographic Closure Capacity and Transactional Exhaust so that it does not alter the proof status of the quantum embedding established here.
Bell-inequality violations exclude the conjunction of assumptions used to derive Bell factorization. Cosmic Bell experiments strengthened the freedom-of-choice test by using photons emitted by distant astronomical sources to determine the detector settings. In the quasar experiment, the relevant setting-generating emissions occurred billions of years in the past, forcing any local common-past coordination mechanism into a correspondingly remote region of the experiments’ joint past.
The directional qualification is essential. These experiments strongly constrain a local-realist mechanism of the form
\[ \rho(\lambda\mid a,b)\ne\rho(\lambda) \]
when the dependence is attributed to a common cause propagating forward from the accessible past. They do not directly test an all-at-once boundary-value description, nor do they establish such a description. They therefore leave STF with an obligation rather than a confirmation: the framework must reproduce the observed Bell probabilities without introducing controllable backward signaling or a hidden common-past conspiracy.
The quantum embedding developed below adopts the cleaner of two logically distinct routes. It introduces no Bell hidden variable \(\lambda\), retains measurement independence, and places the failure of Bell factorization in the nonseparable global quantum state. The STF retarded/advanced geometry supplies a possible home for the doubled probability structure; it is not used as a setting-dependent signal sent into the past.
Status. The Cosmic Bell experiments constrain common-past local-realist coordination. They do not confirm STF. The construction below must stand on its own mathematical consistency.
Let a scalar \(q\) with timelike gradient define
\[ n_q^\mu=-\frac{\nabla^\mu q} {\sqrt{-\nabla q\cdot\nabla q}}. \]
Along an integral curve of \(n_q^\mu\),
\[ n_q^\mu\nabla_\mu q =\sqrt{-\nabla q\cdot\nabla q}>0, \]
up to the overall orientation convention. The generating scalar is therefore strictly monotonic wherever its normalized gradient exists.
The STF amplitude instead oscillates,
\[ \phi\simeq A\cos\Theta_I, \qquad \Theta_I\simeq m_sT_U+\delta\pmod{2\pi}. \]
At each turning point \(d\phi/dT_U=0\), the normalized amplitude gradient is undefined and changes chart orientation. The amplitude cannot be the global clock carrier. This is the proved content of clock separation.
The theorem does not uniquely require a second propagating scalar. It requires the carrier of universal ordering to be mathematically distinct from the oscillating amplitude. The current STF carrier program favors a geometric, boundary-selected construction:
\[ N^\mu=N^\mu_{\rm CMC} [g;\Sigma_{\rm closure},\Sigma_{\rm terminal},V_4]. \]
The CMC lapse is fixed elliptically by the geometry and boundary data. It introduces no independently specifiable local clock wave. Accumulated four-volume orders its leaves, but the numerical leaf label is not itself an observable clock rate.
The phrase “internal clock” has been used for two distinct local structures. They must be notationally separated:
These are three roles at two descriptive levels: one global ordering and a family of local cyclic or record clocks. The Clock-Separation Theorem proves that \(\phi\) cannot collapse all three roles into one amplitude. The CMC construction is the present candidate for the global role; its global existence, uniqueness, and full causal completion remain open.
For a closed loop \(\gamma\) in the sphere of null directions, let \(T^2_\gamma\) be its Hopf preimage. The retarded Hopf and advanced anti-Hopf sectors carry primitive one-forms \(\omega_R\) and \(\omega_A\) satisfying
\[ \int_{T^2_\gamma}\omega_R\wedge\omega_A=4\pi^2. \]
This fixes the normalization of a completed topological transaction. It does not determine a matter amplitude or a probability measure.
For a possible outcome \(k\), retain the matter-and-apparatus coefficient \(\mathcal A_k\):
\[ \Psi^R_k=\mathcal A_k\omega_R. \]
The required quantum embedding assumes an anti-linear outcome-fiber map
\[ J(\mathcal A_k\omega_R) =\overline{\mathcal A_k}\omega_A. \]
Anti-linearity is physically motivated by the retarded/advanced adjoint relation, but it is not yet derived from the topology of the complexified null cone. This is the open Outcome-Fiber Adjoint problem.
Conditional on \(J\), define
\[ D_U(k,\ell) =\frac{1}{4\pi^2} \int_{T^2_\gamma} (\mathcal A_k\omega_R)\wedge (\overline{\mathcal A_\ell}\omega_A) =\mathcal A_k\overline{\mathcal A_\ell}. \]
The \(4\pi^2\) factor cancels. Its job is to normalize the closure integral; the complex conjugation producing the quadratic diagonal entered through \(J\).
Attach record vectors \(|R_k(\tau_R)\rangle\) to the alternatives:
\[ D_{\rm STF}(k,\ell) =\mathcal A_k\overline{\mathcal A_\ell} \langle R_\ell(\tau_R)|R_k(\tau_R)\rangle. \]
The record-overlap matrix is a Gram matrix and is positive semidefinite. The full kernel is its Schur (entrywise) product with the rank-one positive semidefinite matrix \(\mathcal A_k\overline{\mathcal A_\ell}\), and is therefore positive semidefinite by the Schur product theorem, under the stated Hilbert-space assumptions. Before stable recording, off-diagonal overlaps permit interference. After environmental decoherence,
\[ \langle R_\ell|R_k\rangle\simeq\delta_{k\ell}, \]
and the diagonal becomes
\[ D_{\rm STF}(k,k)=|\mathcal A_k|^2. \]
For normalized exhaustive alternatives, the imported quantum probability rule then gives
\[ p_k=\frac{D_{\rm STF}(k,k)}{\sum_jD_{\rm STF}(j,j)} =|\mathcal A_k|^2. \]
This is a natural and internally consistent embedding of Born weights. It is not yet a derivation of the Born rule. Such a derivation would additionally have to establish from STF geometry:
Status. Hermiticity and positivity are conditional algebraic results. Born compatibility is established. Born derivation remains open.
For two spin-\(1/2\) systems, rotational invariance selects the antisymmetric singlet tensor \(\epsilon_{\alpha\beta}\). Supplying the normalized singlet state and the usual local projective instruments yields
\[ P(A,B\mid\mathbf a,\mathbf b) =\frac14\left(1-AB\,\mathbf a\cdot\mathbf b\right), \qquad A,B\in\{-1,+1\}. \]
Consequently,
\[ E(\mathbf a,\mathbf b)=-\mathbf a\cdot\mathbf b. \]
For linear photon-polarization analyzers with physical angles \(a\) and \(b\), the Bloch-sphere angle is doubled and the corresponding expression is
\[ E(a,b)=-\cos 2(a-b). \]
The singlet and detector operators are matter-sector quantum data. They are not generated by the \(4\pi^2\) closure integral.
Before Alice receives any record from Bob, her internal record algebra traces over Bob’s alternatives. Completeness of Bob’s local instrument gives
\[ \sum_B\Pi^b_B=I_B, \]
and therefore
\[ P(A\mid\mathbf a,\mathbf b) =\sum_BP(A,B\mid\mathbf a,\mathbf b) =\frac12. \]
The remote setting disappears from the local marginal. This establishes no-signaling within the embedded quantum construction. It is inherited from the nonseparable state together with complete, trace-preserving local instruments; the one-bit topological lemma alone would not suffice, because one controllable bit is still a signal.
For local dichotomic quantum observables, the usual CHSH operator obeys
\[ \|\mathcal B_{\rm CHSH}\|\le2\sqrt2. \]
With the singlet and optimal analyzer settings, the embedded functional reaches that value. STF therefore reproduces the Tsirelson bound once the standard quantum operator algebra is supplied. It does not presently derive the bound from topological closure alone.
The two-clock architecture nevertheless contributes a useful interpretive separation:
This is a reconciliation of local records with global correlations. It is not an independent dynamical selection rule for which outcome occurs.
Status. Bell and Tsirelson compatibility are established conditionally on standard quantum matter and instrument structure. No-signaling is preserved. Outcome actualization remains a separate ontological question.
The measured/observed distinction implies that an observation is always made from within a bounded record process. That perspectival restriction must not be confused with the claim that consciousness creates the event or that physical facts are merely subjective.
Three layers must be separated:
Let observer or detector \(i\) possess a record filtration
\[ \mathcal F_i(\tau_i), \]
and let its accessible record at internal time \(\tau_i\) be
\[ R_i(\tau_i)\in\mathcal A_i(\tau_i), \qquad \mathcal A_i(\tau_i)\subseteq\mathcal F_i(\tau_i). \]
No local observer reads the complete universal history directly. It reads a bounded algebra selected by its causal past, apparatus, resolution, memory, and internal clock. Observation is therefore necessarily perspective-indexed.
Suppose observers \(A\) and \(B\) later enter a common causal future. Let
\[ \Gamma_A:\mathcal A_A\longrightarrow\mathcal A_{\rm shared}, \qquad \Gamma_B:\mathcal A_B\longrightarrow\mathcal A_{\rm shared} \]
be their calibration and translation maps. These maps encode conventions such as
Operational objectivity is obtained when the translated records agree on the relevant invariant content,
\[ \Gamma_A(R_A) \simeq \Gamma_B(R_B), \]
within their declared uncertainty and resolution.
The equivalence is convention-mediated but not convention-created. Changing meters to feet, coordinates, database formats, or synchronization labels changes the representation. It does not change a causal coincidence, dimensionless correlation, detector count, or properly transformed physical interval. If a common invertible recoding \(f\) is applied,
\[ \Gamma_i\longrightarrow f\circ\Gamma_i, \]
the invariant agreement must survive. This covariance under admissible re-description separates public objectivity from mere social consensus.
In a Bell experiment, Alice’s outcome is an objective local record in \(\mathcal F_A\), and Bob’s is an objective local record in \(\mathcal F_B\). Neither wing locally observes the joint correlation. The correlation becomes operationally accessible only after trial labels, settings, outcomes, timing, and sampling rules are translated into a shared record algebra in their common causal future.
The conventions identify which records are to be compared and how. They do not create the nonfactorizable correlation. With valid calibration changes, the dimensionless Bell statistic is invariant.
The universal background must not be assigned a result not yet derived. The boundary-selected CMC carrier supplies global ordering. The universal closure functional constrains or weights admissible completed histories. Local interaction and decoherence establish stable record alternatives. None of these steps presently proves why one alternative rather than another is the unique actual record.
Accordingly, “the universal background materializes uncertainty into our internal clock” can be used only as a conditional interpretation:
\[ \text{universal admissibility} \longrightarrow \text{local stable record} \longrightarrow \text{convention-mediated public objectivity}. \]
The first arrow still requires the universal-to-local gluing and outcome-fiber adjoint structure; selection of one actual history remains the Single-Transaction Ontology commitment. The universal carrier does not function as a dynamical collapse field.
Convention-Mediated Objectivity Proposition — conditional. If stable local records belong to one globally consistent history, then observation is necessarily indexed to the internal filtration in which a record is available. Public objectivity is obtained when causally connected observers translate their records into a shared algebra and recover invariant agreement under admissible changes of convention.
Status. Filtration-relative access is entailed by the two-clock record architecture. The translation criterion is an operational construction. It does not prove actualization, make consciousness necessary for records, or reduce physical invariants to convention.
Section 1 fixed what the Cosmic Bell experiments constrain and what they do not. This section fixes the complementary operational point: where Bell correlations are registered, and what role cosmic distance plays in each part of the analysis. It is a clarification drawn from the record architecture of §§4.4–4.5, not a new theorem, and it adds no premise to the embedding.
Every physically registered quantity is registered at an event. A photodetection at wing \(A\) is a record in \(\mathcal F_A\), localized at its detection event; an astronomical setting photon is registered where it is absorbed, not where it was emitted. The emission event \(E\) enters the analysis only through its causal relation to the registration event \(O\),
\[ E\in\partial J^-(O), \]
as a constraint on admissible influences — never as a remote fact read at a distance. This relation is invariant under every admissible change of coordinates, units, or synchronization convention. [standard]
No apparatus measures \(E(\mathbf a,\mathbf b)\) across the spatial interval. As §4.5 records, each wing’s outcome is an objective local record in its own filtration; the joint correlation becomes operationally accessible only after both data streams are carried into a common causal future and translated into a shared record algebra at a comparison event \(C\):
\[ C_{AB} =F\!\left(R_A,\,R_B,\,a,\,b\right)\big|_{C}, \]
where \(F\) is the declared estimation protocol applied to the translated records. \(C\) is precisely where the translation maps \(\Gamma_A,\Gamma_B\) of §4.5 converge. The correlation is a property of the pair of records as compared at \(C\); nothing is read “across” the interval. [The operational fact is standard; its \(\mathcal F/\Gamma\) formulation is this work.]
The ideal singlet correlation law of §4.1, \(E(\mathbf a,\mathbf b)=-\mathbf a\cdot\mathbf b\), contains no dependence on the spatial separation of the wings: the same law governs a tabletop pair and a cosmological baseline. It does not follow that distance is irrelevant. Distance is the resource the Cosmic Bell experiments spend. In the quasar experiment [3], the pair-1 setting photons left their sources at lookback times of 7.78 and 12.21 Gyr; since the bound is set by the more recent emission, any local-realist common-cause mechanism is constrained to have acted no more recently than 7.78 Gyr ago, excluding such mechanisms from 96.0% of the space-time volume of the experiment’s past light cone (pair 2: 3.22 Gyr, 63.5%). Cosmic distance is absent from the correlation law and central to the causal-exclusion budget. The two statements are compatible because they answer different questions. [Numerical values from Rauch et al. [3]; the division of labor is standard.]
Within the two-clock architecture, the spatial distance between registration events has the same status §4.5 assigns to every compared quantity: it is computed at \(C\) from translated records — timing records, a synchronization convention, a metric model — and its numerical representation is covariant under admissible recoding. What is not conventional is the causal character of the separation: timelike, null, or spacelike relations, and memberships such as \(E\in\partial J^-(O)\), survive every admissible change of convention. Changing units or synchronization changes the representation of an interval; it never changes the sign of its causal character. Where this reading touches the transaction functional it inherits §4’s conditionality on the outcome-fiber adjoint; the operational content above does not depend on it. [Mapping onto the record architecture: this work.]
Local-Registration/Relational-Distance Proposition — clarification. Every element of a Bell experiment’s data is registered locally. The correlation exists operationally only at a common comparison event, where translated records meet. The ideal correlation law contains no distance; distance enters through causal admissibility, where it does exclusion work. The record is local; the relation is global; distance is the translated representation of that relation.
Status. Operational restatement of standard relativity together with the §4.5 record architecture; nothing here adds a premise, a parameter, or a falsifier. Its purpose is to block two symmetric misreadings now recorded in the ledger: that Bell correlations are directly observed across the spatial interval, and that causal separation is merely a convention.
For class operators \(C_\alpha\), initial state \(\rho_i\), and terminal effect \(E_f\), a time-neutral decoherence functional takes the form
\[ D_f(\alpha,\beta) =\frac{\operatorname{Tr} \!\left(E_fC_\alpha\rho_iC_\beta^\dagger\right)} {\operatorname{Tr}(E_f\rho_i)}. \]
Three terminal choices must be distinguished:
The future boundary must therefore be a macrocondition rather than an outcome-specific pure microstate if ordinary Born statistics are to survive.
Let the regulated Hilbert space factor locally as
\[ \mathcal H=\mathcal H_{\rm cosmic}\otimes\mathcal H_R. \]
If
\[ [E_f,I\otimes U_R]=0 \]
for every unitary \(U_R\) generating the full irreducible record algebra \(\mathcal B(\mathcal H_R)\), then the commutant theorem implies
\[ E_f=E_{\rm cosmic}\otimes I_R. \]
This is a correct conditional lemma. Heat death does not by itself prove its hypothesis.
If only charge-preserving transformations are permitted, the record representation generally decomposes into superselection sectors and the conclusion weakens to
\[ E_f=\bigoplus_q E_q\otimes I_q. \]
Different sectors may carry different terminal weights. Even the factorized form is not sufficient if the rest-sector effect becomes branch-dependent through intervening dynamics. Born recovery therefore requires effective branch neutrality, not merely a formal tensor factorization.
In an infinite-dimensional quantum field theory, \(I_R\) is not a trace-class density operator. A heat-death boundary must instead be represented through a regulated macro-subspace,
\[ E_f\propto P_{\rm HD}, \]
or through an appropriate algebraic or KMS-type macrostate.
Terminal neutrality allows a future macroboundary to anchor the global boundary-value description without micromanaging laboratory records. It does not select one record. The statement that one closed history is actual is the Single-Transaction Ontology: a framework commitment, not a consequence of the \(4\pi^2\) winding number.
The “garbage collection” language may be retained as a metaphor: heat death destroys the practical accessibility of microscopic record pointers through thermalization and scrambling. It has not been shown that a literal memory register is erased, that entropy capacity is thereby recovered, or that only a topological checksum remains as a physical degree of freedom.
Status. Record neutrality is a sufficient conditional structure, motivated but not derived by heat death. Actualization and repeated-trial typicality remain open.
| Statement | Status |
|---|---|
| An oscillating amplitude cannot be a global normalized-gradient clock | proved |
| STF therefore needs a universal carrier distinct from \(\phi\) | conditional entailment within STF |
| The carrier must be a propagating khronon | false; not required |
| Boundary-selected CMC ordering is the preferred carrier candidate | derived candidate; global completion open |
| The Hopf/anti-Hopf pairing has normalization \(4\pi^2\) | established within the STF topological construction |
| The conditional transaction kernel is Hermitian and positive semidefinite | algebraic lemma |
| \(4\pi^2\) alone derives the Born rule | false |
| STF embeds Born weights after an anti-linear adjoint and quantum record structure are supplied | established conditionally |
| The singlet insertion reproduces Bell probabilities and no-signaling | established conditionally |
| STF topology independently derives the Tsirelson bound | not established |
| Observation is indexed to an internal record filtration | entailment of the record architecture |
| A stable detector record is merely subjective or consciousness-created | false |
| Shared conventions make local records operationally comparable | constructed criterion |
| Conventions create the invariant physical relation | false |
| The universal CMC carrier selects the unique quantum outcome | false on the present formalism |
| Public objectivity is invariant agreement after translation into a shared record algebra | conditional operational proposition |
| Bell correlations are directly observed across the spatial interval | false |
| The Bell correlation is computed at a common comparison event from translated local records | standard operational fact; \(\mathcal F/\Gamma\) formulation this work |
| Cosmic distance is irrelevant to the freedom-of-choice bound | false; it sets the causal-exclusion budget |
| Causal separation is merely conventional | false |
| Distance between registration events is a convention-mediated representation with invariant causal content | clarification within the record architecture |
| A record-neutral terminal effect preserves ordinary statistics | conditional lemma |
| Heat death proves exact record neutrality | not established |
| Topological closure selects one actual outcome | false on the present formalism |
The paper reduces the remaining work to identifiable problems.
The closure-coding and dark-exhaust programs are downstream conjectures treated in the separate companion paper. They cannot repair a missing upstream gluing or carrier theorem.
An exact embedding of the known quantum probability structure is not independently falsifiable by quantum experiment: wherever quantum mechanics is confirmed, the embedding is confirmed with it. That is a property of the claim, not a weakness, and the honest falsification statement has three parts.
Inherited falsifiers. This paper rests on the same physics as The Universal Embedding Principle, and inherits that paper’s §9 falsifiers rather than adding new ones: (i) curvature- or scalar-background-dependent Bell correlations — in particular, a CHSH deficit tracking the 3.32-year internal phase would kill the common-mode result on which the embedding relies; and (ii) Bell violations modulated by local \(\chi_{\rm local}\) activation. Either observation would falsify the underlying STF quantum sector, and this construction with it.
A mathematical falsifier. The entire construction is conditional on the anti-linear outcome-fiber adjoint \(J\) (§3.1). If the Outcome-Fiber Adjoint problem returns a no-go — a proof that no such \(J\) exists on the complexified null cone — the embedding fails by theorem rather than by experiment. Few physical proposals carry that exposure; it is a point in this one’s favour.
A neutrality signature. The Terminal Record-Neutrality Lemma (§5.2) has an observational shadow the conditional statement does not by itself supply: if the terminal macrocondition is not record-neutral, Born weights would be distorted in a way plausibly dependent on cosmic epoch, and high-redshift quantum measurements — Cosmic Bell tests among them — are where such a distortion would show. Observed Born statistics at high redshift are therefore consistent with, though they do not prove, effective terminal neutrality.
The two-clock STF architecture provides a coherent geometric setting in which local records and global Bell correlations can coexist without a physical superluminal collapse signal. Clock separation prevents the oscillating STF amplitude from being misused as the universal clock, while boundary-selected CMC geometry supplies the present nonpropagating candidate for universal ordering. The Hopf/anti-Hopf pairing then gives a natural normalized arena for a retarded/advanced transaction functional.
What has been achieved is an embedding with sharp mathematical content. Given an anti-linear outcome-fiber adjoint and standard quantum matter and record structure, the functional is Hermitian, positive, interference-preserving before recording, Born-diagonal after decoherence, Bell-compatible, and no-signaling. The \(4\pi^2\) topology normalizes closure; it does not yet choose the quantum adjoint, determine amplitude ratios, or select one actual outcome.
The terminal heat-death boundary can be made compatible with ordinary statistics if it is a record-neutral macrocondition, but neutrality is a condition to derive rather than a fact supplied by the name “heat death.”
The framework also gives observation a precise perspectival status. A local clock never reads the universal history without mediation; it accesses a finite record filtration. That does not make the record mental or arbitrary. When separate records enter a common causal future, shared conventions translate them into a common algebra, while invariant relations supply the criterion of objectivity. Conventions construct comparability, not physical truth. The CMC background orders this process but does not select the unique outcome whose record is compared.
In metaphorical terms, STF may ultimately describe part of the operating architecture of spacetime. In present mathematical terms, its strongest result is more precise: the two-clock closure geometry can host the known quantum probability structure without contradiction, while exposing exactly which gluing, carrier, and boundary theorems remain to be proved.
The superdeterminism and measurement-independence questions raised by the Bell discussion above are treated in full in Bell Autonomy and Superdeterminism in the Two-Clock STF Framework (V2.0), the canonical synthesis of the thirteen-paper Bell-autonomy sequence.