Pith. sign in

REVIEW 5 minor 4 cited by

Holographic multi-entropy vectors form a rational polyhedral cone whose complete n=3,4 facets refine the usual entropy cone.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-15 10:46 UTC pith:HDI5IK5A

load-bearing objection Clean, rigorous extension of the HEC program: polyhedrality + multicontraction certificates + complete n=3,4 facets (seven orbits, five new) with explicit graph rays; two well-marked conjectures.

arxiv 2606.15173 v2 pith:HDI5IK5A submitted 2026-06-13 hep-th

The Holographic Multi-Entropy Cone

Xin-Xiang Ju , Yang Zhao This is my paper
classification hep-th
keywords holographic multi-entropy conemulti-entropyholographic entropy conemulticontraction mapsmultipartite entanglementAdS/CFTgraph models
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper enlarges the holographic entropy cone by adjoining multi-entropy coordinates—multipartite analogues of entanglement entropy dual to minimal multiway soap-films—to the usual bipartition entropy vector. The resulting multi-entropy vectors of holographic states form a rational polyhedral cone, so only finitely many linear inequalities can be tight. Multicontraction maps on label-string spaces give exact certificates for those inequalities, generalizing the familiar contraction-map proofs. The authors compute the complete cones for three and four labels (including the purifier): two fundamental inequality orbits for n=3 and five new ones for n=4, each certified by multicontraction maps and realized by explicit weighted graphs for every extremal ray. Familiar constraints such as subadditivity and monogamy of mutual information appear as convex combinations of these finer multi-entropy facets. Two structural conjectures are proposed: every holographic entropy-cone facet is such a combination, and genuine multi-entropy facets live only in intermediate balance sectors rather than arbitrarily high-party-balanced spaces.

Core claim

Holographic multi-entropy vectors form a rational polyhedral cone C_HMEC_n in multi-entropy space. Multicontraction maps certify all holographic multi-entropy inequalities, and the complete facet lists for n=3 (two orbits) and n=4 (seven orbits, five of them new) are obtained by those certificates together with graph realizations of every extremal ray. Standard holographic entropy inequalities such as subadditivity and monogamy of mutual information arise as positive combinations of these multi-entropy facets.

What carries the argument

The multicontraction map: a function from left-hand-side multiway label-strings to right-hand-side label-strings that preserves boundary occurrence vectors and does not increase the weighted Hamming distance. Its existence proves that a proposed multi-entropy inequality holds for every graph model and therefore for every holographic state.

Load-bearing premise

The continuum multi-entropy of a holographic state is dual to the area of a minimal multiway soap-film that can be faithfully discretized by multiway cuts on a weighted graph whose chambers obey bottleneck and high-cost conditions.

What would settle it

Find a continuum holographic geometry whose multi-entropy vector lies outside the polyhedral cone generated by the n=3 or n=4 facet inequalities, or construct a multi-entropy inequality that holds for all graph models yet admits no multicontraction map.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 5 minor

Summary. The paper generalizes the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining partition-labeled multi-entropy coordinates S^{(|π|)}(π) to the bipartition entropy vector. Using a total-label convention that includes the purifier, it shows that holographic multi-entropy vectors form a rational polyhedral cone C_HMEC_n. The argument proceeds via a geometry–graph dictionary (minimal multiway soap-films ↔ multiway cuts with bottleneck necks and high-cost chambers), a universal complete graph with label-string vertices (Lemma 2.1), and a finite partition of the weight orthant by multiway-cut cost hyperplanes. Multicontraction maps on label-string spaces are defined and proved to certify holographic multi-entropy inequalities (Theorem 2.3). Complete facet lists are obtained for n=3 (two orbits: P_A and K_ABC) and n=4 (seven orbits, five new, including F4.1–F4.5), with multicontraction certificates and explicit graph realizations of all extremal rays (4 rays for n=3; 49 rays in 9 orbits for n=4). Two structural conjectures are proposed: HEC facets arise as convex combinations of HMEC facets, and HMEC facets obey a balanced-but-not-too-balanced principle, supported by a projected-simplex obstruction in the 11-dimensional 4-party-balanced sector of M_5.

Significance. If the continuum multi-entropy dual and the graph dictionary hold, the work supplies a systematic multipartite refinement of the HEC program. The complete n=3,4 facet enumerations, multicontraction certificates, and graph-realized extremal rays constitute concrete, checkable data that refine subadditivity and MMI into multi-entropy inequalities and organize multipartite holographic signals. The multicontraction method and the two conjectures give a clear route for higher-n work and for relating multipartite signals to classical bulk geometry. Strengths include explicit multicontraction tables (e.g., Tables 1–2), full ray realizations (Table 4, Fig. 2), and a finite projected-simplex certificate for the n=5 high-balance obstruction (Table 6, Fig. 5). These are standard, reproducible tools of the HEC literature extended to multiway cuts.

minor comments (5)
  1. In Sec. 2.1 the multi-entropy vector length is written |Π*([n])|=B_n−1; a short parenthetical that the trivial one-block partition is excluded would remove any ambiguity for readers less familiar with Bell numbers.
  2. Tables 1 and 2 use block labels as elements of Λ_π; a one-sentence reminder that this is only a convenient identification (not a change of the abstract label-string definition) would help when the same tables are reused for higher-n inequalities.
  3. Fig. 2 and Fig. 5 are dense; increasing edge-weight font size or adding a brief caption note that isolated terminals are intentional would improve readability without changing content.
  4. The phrase “balanced-but-not-too-balanced” is vivid but informal for a conjecture title; a more technical name (e.g., “intermediate-party balance conjecture”) in the abstract and Sec. 4.2 would match the tone of the rest of the paper.
  5. A few typos appear (e.g., “vestor” in the Table 4 caption; occasional missing spaces around math). A light copy-edit pass would clean them.

Circularity Check

1 steps flagged

No significant circularity: polyhedrality, multicontraction certificates, and n=3,4 facet lists are self-contained from the graph-model axioms; self-citations supply only motivation and balance definitions for conjectures.

specific steps
  1. self citation load bearing [Sec. 4.2, Table 5 and surrounding text on k-party balance]
    "In [27], a framework was developed to derive all k-party-balanced multi-entropy combinations, with genuine multi-entropy signals [39, 43] as special cases. The result shows that the k-party balanced signals form a subspace in the multi-entropy space."

    The definition of the 4-party-balanced subspace V_4-bal used for the n=5 obstruction certificate (and for the balanced-but-not-too-balanced conjecture) is imported from the authors’ own concurrent preprint [27]. This is a minor self-citation that supplies the coordinate basis for a secondary conjecture, not a load-bearing lemma for the polyhedrality proof or the n=3,4 facet lists; the obstruction itself is independently verified by explicit multiway-cut projections of 12 graphs.

full rationale

The derivation chain begins from the multi-entropy vector definition (adjoining partition-labeled multi-entropies to bipartition entropies), proceeds via the geometry-to-graph and graph-to-geometry dictionary (bottleneck necks + high-cost chambers, Sec. 2.2–2.3), establishes rational polyhedrality by the universal complete graph and finite multiway-cut chambers (Lemma 2.1 + Sec. 2.4), and certifies inequalities by the multicontraction-map definition and Theorem 2.3 (which recombines left-hand multiway cuts into feasible right-hand cuts under the weighted Hamming contraction condition). Completeness for C_HMEC_3 and C_HMEC_4 rests on explicit multicontraction tables (e.g., Tables 1–2) plus concrete graph realizations of every extremal ray (4 rays for n=3; 49 rays in 9 orbits for n=4, Fig. 2 and Table 4). These steps do not reduce by construction to fitted parameters, self-defined targets, or unproved external lemmas. Self-citations ([27] for k-party balance definitions used in the conjectures of Sec. 4, and [51,52] for planned follow-ups) appear only as motivation or for the non-central conjectures; the facet enumerations and polyhedrality proofs stand independently once the graph model is granted. The continuum dual (minimal multiway soap-film) is an assumption shared with the HEC literature, not a circular reduction inside the paper. Hence the strongest claims are not circular.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 2 invented entities

The central claims rest on the standard holographic dictionary for multi-entropy, the graph-model equivalence, and ordinary convex-geometry facts. No free parameters are fitted; the invented technical objects (multicontraction maps, universal label-string graphs) are defined and used constructively rather than postulated as new physical entities.

axioms (4)
  • domain assumption Multi-entropy S^(q) of a boundary partition is dual to the area of a minimal multiway soap-film (brane web) homologous to that partition.
    Invoked throughout Sec. 2.1–2.3 as the continuum starting point; taken from the cited multi-entropy literature [24–26].
  • domain assumption Any bulk geometry admits a weighted graph model whose multiway-cut values reproduce all multi-entropies, and conversely any finite weighted graph can be realized by a multi-mouth wormhole with bottleneck and high-cost chambers.
    Sec. 2.2–2.3; the discrete–continuum dictionary that reduces polyhedrality and inequality proofs to graph combinatorics.
  • standard math The set of multi-entropy vectors is closed under positive scaling and addition (disjoint union of geometries).
    Used in Sec. 2.1 to establish the cone property, identical to the HEC argument.
  • standard math Minimum multiway-cut costs on a finite weighted graph are piecewise-linear functions of the edge weights, with finitely many linear pieces.
    Sec. 2.4; guarantees that the image of the weight orthant is a finite union of rational polyhedral cones.
invented entities (2)
  • Multicontraction map independent evidence
    purpose: Certificate that a linear multi-entropy inequality holds for every graph model (and hence every holographic state).
    Defined in Def. 2.2 as a map between left- and right-hand label-string spaces that preserves boundary occurrence vectors and does not increase weighted Hamming distance; proved sufficient in Thm 2.3.
  • Universal complete graph with label-string vertices independent evidence
    purpose: Show that every multi-entropy vector arises from a single fixed graph topology with variable non-negative edge weights, implying rational polyhedrality.
    Constructed in Lemma 2.1 by generalizing the bit-string vertices of the ordinary HEC to multi-block label strings.

pith-pipeline@v1.1.0-grok45 · 25789 in / 2755 out tokens · 24752 ms · 2026-07-15T10:46:16.063110+00:00 · methodology

0 comments
read the original abstract

We generalize the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the $n=3,4$ HMECs, where $n$ includes the purifier, and obtain seven fundamental HMEI orbits: two for $n=3$ and five for $n=4$. We further propose two structural conjectures: HEC facet inequalities are convex combinations of HMEC facet inequalities, and HMEC facets obey a balanced-but-not-too-balanced principle.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Complexity Inequalities for Quantum Subsystems

    hep-th 2026-06 unverdicted novelty 7.0

    Introduces tripartite complexity and complexity gap for three-region subsystems and reports that the gap has a definite sign in holographic volume complexity, Fisher-Rao Gaussian complexity, and Krylov-space approaches.

  2. Complexity Inequalities for Quantum Subsystems

    hep-th 2026-06 unverdicted novelty 7.0

    Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for comp...

  3. Constraints on four-party entanglement in holography

    hep-th 2026-05 unverdicted novelty 6.0

    In time-reflection-symmetric holographic states, I3 is necessary for non-vanishing four-party entanglement signals, bounds multi-entropy measures, and implies vanishing of Q4.

  4. Constraints on four-party entanglement in holography

    hep-th 2026-05 unverdicted novelty 5.0

    In time-reflection-symmetric holographic states, I3 implies vanishing of multiple four-party entanglement measures and bounds those from multi-entropy, though Q4 is not quantitatively bounded by I3.

Reference graph

Works this paper leans on

52 extracted references · 38 linked inside Pith · cited by 2 Pith papers

  1. [1]

    Ryu and T

    S. Ryu and T. Takayanagi,Holographic derivation of entanglement entropy from ads/cft, Phys. Rev. Lett.96(2006) 181602, [hep-th/0603001]

    Pith/arXiv arXiv 2006

  2. [2]

    Ryu and T

    S. Ryu and T. Takayanagi,Aspects of holographic entanglement entropy,JHEP08(2006) 045, [hep-th/0605073]

    Pith/arXiv arXiv 2006

  3. [3]

    V. E. Hubeny, M. Rangamani and T. Takayanagi,A covariant holographic entanglement entropy proposal,JHEP07(2007) 062, [0705.0016]

    Pith/arXiv arXiv 2007

  4. [4]

    Rangamani and T

    M. Rangamani and T. Takayanagi,Holographic Entanglement Entropy, vol. 931 ofLecture Notes in Physics. Springer, 2017, 10.1007/978-3-319-52573-0

    doi:10.1007/978-3-319-52573-0 2017

  5. [5]

    Van Raamsdonk,Building up spacetime with quantum entanglement,Gen

    M. Van Raamsdonk,Building up spacetime with quantum entanglement,Gen. Rel. Grav.42 (2010) 2323–2329, [1005.3035]

    Pith/arXiv arXiv 2010

  6. [6]

    N. Bao, S. Nezami, H. Ooguri, B. Stoica, J. Sully and M. Walter,The holographic entropy cone,JHEP09(2015) 130, [1505.07839]

    Pith/arXiv arXiv 2015

  7. [7]

    Hayden, M

    P. Hayden, M. Headrick and A. Maloney,Holographic mutual information is monogamous, Phys. Rev. D87(2013) 046003, [1107.2940]. – 24 –

    Pith/arXiv arXiv 2013

  8. [8]

    Hern´ andez-Cuenca,The holographic entropy cone for five regions,arXiv preprint(2019) , [1903.09148]

    S. Hern´ andez-Cuenca,The holographic entropy cone for five regions,arXiv preprint(2019) , [1903.09148]

    Pith/arXiv arXiv 2019

  9. [9]

    Avis and S

    D. Avis and S. Hern´ andez-Cuenca,On the foundations and extremal structure of the holographic entropy cone,Discrete Appl. Math.328(2023) 16–39, [2102.07535]

    Pith/arXiv arXiv 2023

  10. [10]

    V. E. Hubeny, M. Rangamani and M. Rota,Holographic entropy relations,Fortsch. Phys.66 (2018) 1800067, [1808.07871]

    Pith/arXiv arXiv 2018

  11. [11]

    V. E. Hubeny, M. Rangamani and M. Rota,The holographic entropy arrangement,Fortsch. Phys.67(2019) 1900011, [1812.08133]

    Pith/arXiv arXiv 2019

  12. [12]

    T. He, M. Headrick and V. E. Hubeny,Holographic Entropy Relations Repackaged,JHEP10 (2019) 118, [1905.06985]

    Pith/arXiv arXiv 2019

  13. [13]

    T. He, V. E. Hubeny and M. Rangamani,Superbalance of Holographic Entropy Inequalities, JHEP07(2020) 245, [2002.04558]

    Pith/arXiv arXiv 2020

  14. [14]

    Czech and X

    B. Czech and X. Dong,Holographic Entropy Cone with Time Dependence in Two Dimensions,JHEP10(2019) 177, [1905.03787]

    Pith/arXiv arXiv 2019

  15. [15]

    Grado-White, G

    B. Grado-White, G. Grimaldi, M. Headrick and V. E. Hubeny,Testing holographic entropy inequalities in 2 + 1 dimensions,JHEP01(2025) 065, [2407.07165]

    Pith/arXiv arXiv 2025

  16. [16]

    Grado-White, G

    B. Grado-White, G. Grimaldi, M. Headrick and V. E. Hubeny,Minimax surfaces and the holographic entropy cone,JHEP05(2025) 104, [2502.09894]

    Pith/arXiv arXiv 2025

  17. [17]

    Czech, S

    B. Czech, S. Shuai, Y. Wang and D. Zhang,Holographic Entropy Inequalities and the Topology of Entanglement Wedge Nesting,Phys. Rev. D109(2024) L101903, [2309.15145]

    Pith/arXiv arXiv 2024

  18. [18]

    Czech, Y

    B. Czech, Y. Liu and B. Yu,Two infinite families of facets of the holographic entropy cone, SciPost Phys.17(2024) 084, [2401.13029]

    Pith/arXiv arXiv 2024

  19. [19]

    Bao and J

    N. Bao and J. Naskar,Properties of the contraction map for holographic entanglement entropy inequalities,JHEP06(2024) 039, [2403.13283]

    Pith/arXiv arXiv 2024

  20. [20]

    N. Bao, K. Furuya and J. Naskar,Towards a complete classification of holographic entropy inequalities,JHEP03(2025) 117, [2409.17317]

    Pith/arXiv arXiv 2025

  21. [21]

    Czech and Y

    B. Czech and Y. Wang,A holographic inequality forN= 7regions,JHEP01(2023) 101, [2209.10547]

    Pith/arXiv arXiv 2023

  22. [22]

    Hern´ andez-Cuenca, V

    S. Hern´ andez-Cuenca, V. E. Hubeny and H. F. Jia,Holographic entropy inequalities and multipartite entanglement,JHEP08(2024) 238, [2309.06296]

    Pith/arXiv arXiv 2024

  23. [23]

    T. He, V. E. Hubeny and M. Rota,Algorithmic construction of ssa-compatible extreme rays of the subadditivity cone and then= 6solution,JHEP06(2025) 055, [2412.15364]

    Pith/arXiv arXiv 2025

  24. [24]

    Gadde, V

    A. Gadde, V. Krishna and T. Sharma,A new multi-partite entanglement measure and its holographic dual,Phys. Rev. D106(2022) 126001, [2206.09723]

    Pith/arXiv arXiv 2022

  25. [25]

    Gadde, V

    A. Gadde, V. Krishna and T. Sharma,Towards a classification of holographic multi-partite entanglement measures,JHEP08(2023) 202, [2304.06082]

    Pith/arXiv arXiv 2023

  26. [26]

    Penington, M

    G. Penington, M. Walter and F. Witteveen,Fun with replicas: tripartitions in tensor networks and gravity,JHEP05(2023) 008, [2211.16045]

    Pith/arXiv arXiv 2023

  27. [27]

    Ju, Y.-W

    X.-X. Ju, Y.-W. Sun and Y. Zhao,Sperner state and multipartite entanglement signals, 2602.12664

    arXiv

  28. [28]

    Iizuka and A

    N. Iizuka and A. Miyata,Where multipartite entanglement localizes: The junction law for – 25 – genuine multi-entropy,2602.16331

    arXiv

  29. [29]

    Iizuka and A

    N. Iizuka and A. Miyata,The Junction Law for Multipartite Entanglement in Confining Holographic Backgrounds,2604.10583

    Pith/arXiv arXiv

  30. [30]

    Balasubramanian, M

    V. Balasubramanian, M. J. Kang, C. Murdia and S. F. Ross,Signals of multiparty entanglement and holography,JHEP06(2025) 068, [2411.03422]

    Pith/arXiv arXiv 2025

  31. [31]

    Akella, A

    S. Akella, A. Gadde and J. Pandey,Multi-invariants in stabilizer states,2601.16258

    arXiv

  32. [32]

    Czech, Y

    B. Czech, Y. Feng, X. Wu and M. Xie,Fun with graph states: Nonlocal bell pairs and the arf invariant,2606.06582

    Pith/arXiv arXiv

  33. [33]

    Ju, W.-B

    X.-X. Ju, W.-B. Pan, Y.-W. Sun and Y. Zhao,Entanglement wedge cross section triangle information and holographic entanglement of assistance,2512.21679

    arXiv

  34. [34]

    N. Bao, K. Furuya and J. Naskar,Tripartite correlation signal from multipartite entanglement of purification,JHEP05(2026) 236, [2509.08209]

    Pith/arXiv arXiv 2026

  35. [35]

    Ju, W.-B

    X.-X. Ju, W.-B. Pan, Y.-W. Sun and Y. Zhao,Holographic multipartite entanglement from the upper bound ofn-partite information,2411.07790

    Pith/arXiv arXiv

  36. [36]

    Ju, W.-B

    X.-X. Ju, W.-B. Pan, Y.-W. Sun, Y.-T. Wang and Y. Zhao,More on the upper bound of holographicn-partite information,JHEP03(2025) 184, [2411.19207]

    Pith/arXiv arXiv 2025

  37. [37]

    Ju, Y.-W

    X.-X. Ju, Y.-W. Sun and Y. Zhao,Upper bound of holographic entanglement entropy combinations,JHEP09(2025) 085, [2505.11059]

    Pith/arXiv arXiv 2025

  38. [38]

    Ju, B.-H

    X.-X. Ju, B.-H. Liu, Y.-W. Sun, B.-Y. Xu and Y. Zhao,Holographic multipartite entanglement structures in IR modified geometries,JHEP03(2026) 095, [2512.20397]

    arXiv 2026

  39. [39]

    Gadde,On genuine multipartite entanglement signals,2603.07680

    A. Gadde,On genuine multipartite entanglement signals,2603.07680

    arXiv

  40. [40]

    Balasubramanian, M

    V. Balasubramanian, M. J. Kang, C. Cummings, C. Murdia and S. F. Ross,Purely Greenberger-Horne-Zeilinger-like entanglement is forbidden in holography,Phys. Rev. Lett. 136(2026) 031602, [2509.03621]

    arXiv 2026

  41. [41]

    Balasubramanian, H

    V. Balasubramanian, H. Jiang and S. F. Ross,Time Evolution of Multi-Party Entanglement Signals,2511.16729

    arXiv

  42. [42]

    Naskar,On a mixed-state extension of the holographic signal inequality,2605.26617

    J. Naskar,On a mixed-state extension of the holographic signal inequality,2605.26617

    Pith/arXiv arXiv

  43. [43]

    Iizuka and M

    N. Iizuka and M. Nishida,Genuine multi-entropy and holography,Phys. Rev. D112(2025) 026011, [2502.07995]

    Pith/arXiv arXiv 2025

  44. [44]

    Balasubramanian, W

    V. Balasubramanian, W. K. L. Chan, M. J. Kang, C. Murdia and S. F. Ross,Constraints on four-party entanglement in holography,arXiv preprint(2026) , [2606.00210]

    Pith/arXiv arXiv 2026

  45. [45]

    X. Chen, X. Ji, W.-P. Li and Y.-W. Sun,Detecting Topological Transitions and Anisotropy through Multipartite Entanglement in Holographic Weyl Semimetals,2606.05757

    Pith/arXiv arXiv

  46. [46]

    X. Chen, X. Ji and Y.-W. Sun,Multipartite entanglement characterizing topological phase transitions in holographic nodal line semimetals,2602.01545

    Pith/arXiv arXiv

  47. [47]

    L. R. Ford and D. R. Fulkerson,Flows in Networks. Princeton University Press, 1962

    1962

  48. [48]

    Dahlhaus, D

    E. Dahlhaus, D. S. Johnson, C. H. Papadimitriou, P. D. Seymour and M. Yannakakis,The complexity of multiterminal cuts,SIAM Journal on Computing23(1994) 864–894

    1994

  49. [49]

    Czech, S

    B. Czech, S. Shuai and Y. Wang,Entropy inequalities constrain holographic erasure correction,Phys. Rev. Lett.135(2025) 141603, [2502.12246]. – 26 –

    Pith/arXiv arXiv 2025

  50. [50]

    Czech and S

    B. Czech and S. Shuai,Renormalization group is the principle behind the holographic entropy cone,2601.02472

    arXiv

  51. [51]

    Czech, Y

    B. Czech, Y. Feng, X.-X. Ju and Y. Zhao. In preparation

  52. [52]

    Resolution signal of multipartite entanglement

    X.-X. Ju, Y.-W. Sun and Y. Zhao, “Resolution signal of multipartite entanglement.” 2026. – 27 –

    2026