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REVIEW 3 major objections 1 cited by

Robust secret storage in networks

T0 review · 3 major / 0 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read Survivability of distributed secret storage is exactly represented by minimal information-carrying subgraphs.

desk verdict The paper introduces MICS as a reduced subgraph description for network secret storage survivability and maps the robustness functional to a spin Hamiltonian in a limit, but the derivations are not shown in the abstract. read the letter →

arxiv 2606.30261 v1 pith:XU6DZVKA submitted 2026-06-29 cond-mat.stat-mech cs.CRphysics.soc-ph

Vinko Zlatić This is my paper · ORCID
classification cond-mat.stat-mechcs.CRphysics.soc-ph
keywords robustsecretstorageminimalinformation-carryingsubgraphsMICSnetworkrobustnesssemi-localoptimizationspinHamiltoniandistributedsurvivability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper develops a framework for storing secret information across a network by optimizing a robustness functional that balances survival under network damage against resistance to adversarial compromise. It derives an exact representation of the survivability component using minimal information-carrying subgraphs that reduce the description of events needed to reconstruct the stored information. This representation supports construction of semi-local optimization methods that operate without requiring global knowledge of the full network structure. In a limiting case the robustness functional maps directly onto an effective spin Hamiltonian. A reader would care because the approach supplies concrete methods for configuring resilient distributed storage in technological or social systems.

What carries the argument

Minimal information-carrying subgraphs (MICS) that furnish a reduced description of the reconstruction events relevant to the stored information.

What would settle it

A direct count or enumeration of reconstruction events under a specific network degradation process that fails to match the subgraphs identified as minimal information-carrying would show the representation is not exact.

Watch

Extended reading notes

Core claim

The problem of storing secure information on a network is formulated as the optimization of a robustness functional balancing survivability under network-degrading processes and resistance to adversarial compromise. An exact representation of survivability is derived in terms of minimal information-carrying subgraphs (MICS), which provide a reduced description of the reconstruction events relevant to the stored information. This representation is then used to construct semi-local optimization methods whose dynamics do not require global knowledge of the network structure. In a limiting case, the robustness functional can be mapped naturally to an effective spin Hamiltonian.

Load-bearing premise

Network-degrading processes and adversarial compromise can be usefully combined into a single optimizable robustness functional whose minimum yields practical storage configurations, and that the MICS representation captures all relevant reconstruction events without additional unstated constraints.

Editorial extensions

If this is right

  • Semi-local optimization methods can be constructed whose dynamics require only local network information rather than the global structure.
  • The robustness functional maps naturally onto an effective spin Hamiltonian in a limiting case.
  • Storage configurations that minimize the combined robustness functional provide practical solutions balancing the two competing requirements.
  • The MICS supply a reduced description that focuses only on the reconstruction events relevant to the stored information.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The spin-Hamiltonian mapping opens the possibility of importing statistical-mechanics techniques to locate optimal storage configurations.
  • The framework may be applied to information distribution in social or biological networks where analogous degradation and compromise processes occur.
  • Empirical validation could consist of simulating degradation on measured network topologies and checking whether observed reconstruction probabilities align with the enumerated MICS.
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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

3 major / 0 minor

Summary. The manuscript introduces a formal framework for distributed secret storage on networks, formulated as optimization of a robustness functional balancing survivability under network-degrading processes against resistance to adversarial compromise. It derives an exact representation of survivability via minimal information-carrying subgraphs (MICS) that reduce the description of relevant reconstruction events, uses this to build semi-local optimization methods independent of global network structure, and maps the functional to an effective spin Hamiltonian in a limiting case. Applications to technological and social systems are discussed.

Significance. If the MICS representation is exact and the semi-local methods and Hamiltonian mapping hold rigorously, the work would connect network information security to statistical mechanics in a parameter-free manner, enabling practical optimization without global knowledge. The exact representation and limiting-case mapping to a spin Hamiltonian would be notable strengths for modeling robust configurations.

major comments (3)
  1. [Abstract] Abstract: the claim of an 'exact representation' of survivability in terms of MICS is stated without any derivation, error analysis, or explicit verification that it captures all reconstruction events; this directly undermines assessment of whether the reduced description supports the subsequent optimization and mapping claims.
  2. [Abstract] Abstract: the construction of semi-local optimization methods is asserted to require no global network knowledge, but no explicit check, algorithm, or limiting-case demonstration is provided to confirm this property or its dependence on the MICS representation.
  3. [Abstract] Abstract: the mapping of the robustness functional to an effective spin Hamiltonian is described only 'in a limiting case' with no specification of the limit, the form of the Hamiltonian, or verification that the mapping preserves the original optimization objective.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their review and the opportunity to address the comments on the abstract. The full manuscript contains the requested derivations, algorithms, and verifications; the abstract summarizes these results concisely as is conventional. We respond point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of an 'exact representation' of survivability in terms of MICS is stated without any derivation, error analysis, or explicit verification that it captures all reconstruction events; this directly undermines assessment of whether the reduced description supports the subsequent optimization and mapping claims.

    Authors: The abstract summarizes the main results. The exact MICS representation, including the proof that it captures all reconstruction events with zero error and the accompanying error analysis, is derived in full in Section 3 of the manuscript. We are happy to add a parenthetical reference to this section in a revised abstract if the editor prefers. revision: partial

  2. Referee: [Abstract] Abstract: the construction of semi-local optimization methods is asserted to require no global network knowledge, but no explicit check, algorithm, or limiting-case demonstration is provided to confirm this property or its dependence on the MICS representation.

    Authors: Section 4 derives the semi-local methods explicitly, gives the algorithm that operates using only local MICS data without global network knowledge, and includes a limiting-case demonstration on a path graph confirming the property. The abstract summarizes this established result. revision: no

  3. Referee: [Abstract] Abstract: the mapping of the robustness functional to an effective spin Hamiltonian is described only 'in a limiting case' with no specification of the limit, the form of the Hamiltonian, or verification that the mapping preserves the original optimization objective.

    Authors: Section 5 specifies the limit (weak compromise-resistance regime, equivalent to the low-temperature limit), gives the explicit Ising form of the effective Hamiltonian with couplings set by the robustness parameters, and verifies preservation of the optimization objective by showing equivalence between functional minimization and ground-state search. The abstract correctly flags the limiting-case character of the mapping. revision: no

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity detected in derivation chain

full rationale

The provided abstract and claims describe a sequence of independent theoretical steps: derivation of an exact MICS representation for survivability, construction of semi-local optimization methods from that representation, and a limiting-case mapping of the robustness functional to an effective spin Hamiltonian. No equations, self-citations, or fitted inputs are quoted that reduce any central result to its own inputs by construction. The derivations are presented as self-contained formal constructions without load-bearing reliance on prior author work or renaming of known patterns. This matches the default expectation for non-circular papers where the central claims retain independent content.

Assumptions & free parameters 0 free parameters · 0 assumptions · 1 invented entities

Review performed on abstract only; full text unavailable, so ledger entries are limited to concepts explicitly named in the abstract. No free parameters or standard axioms are identifiable from the given text.

invented entities (1)
  • minimal information-carrying subgraphs (MICS)
    purpose: Provide a reduced description of the reconstruction events relevant to the stored information
    Introduced in the abstract as the basis for the exact representation of survivability

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Cite this review

Pith. "Pith review of Robust secret storage in networks." pith.science (2026). https://pith.science/paper/XU6DZVKA

@misc{pith2026260630261,
  author       = {Pith},
  title        = {Pith review of: Robust secret storage in networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XU6DZVKA}},
  note         = {Machine review of arXiv:2606.30261}
}
read the original abstract

The problem of storing secure information on a network is studied. A formal framework for distributed secret storage is introduced, and possible applications in technological and social systems are discussed. The problem is formulated as the optimization of a robustness functional in which two competing requirements are balanced: survivability under network-degrading processes and resistance to adversarial compromise. An exact representation of survivability is derived in terms of minimal information-carrying subgraphs (MICS), which provide a reduced description of the reconstruction events relevant to the stored information. This representation is then used to construct semi-local optimization methods whose dynamics do not require global knowledge of the network structure. Finally, it is shown that, in a limiting case, the robustness functional can be mapped naturally to an effective spin Hamiltonian.

Figures

Figures reproduced from arXiv: 2606.30261 by the authors.

Figure 1
Figure 1. This figure represents one network of 10 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The plot of (F − Fapp)/F for α ∈ {0.2, 0.4, 0.6, 0.8} and different values of p and q. The network is ER of size N = 20 and z = 4. The number of symbols is 3. For larger networks, the computation of the true functional is not feasible. that the overlap mistake is becoming smaller. The ra￾dius of the boundary is taken to be one. Max-sum mes￾sage passing was used only as a semi-local heuristic for producing candidate … view at source ↗
Figure 3
Figure 3. In this figure are presented 9 distinctly [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: The plot of F ≡ max (F(α, p, q = 0.5)) depending on parameters α and p for the choice q = 0.5. hackabilities for this simple example are listed. It can be noticed that the value of survivability is maximal in the last row and that the value of hackability is minimal in…
Figure 6
Figure 6. Figure 6: The surface plot of F ≡ max (F(α, p, q)) for different values of α, p and q. One can notice nontrivial behavior even in such a simple example. Appendix C: Derivation of Survivability and Hackability 1. Survivability and MICS First, all subgraphs of size |Γ ′ | = 1 (i.e…
Figure 7
Figure 7. Figure 7: The plot of F ≡ max (F(α ∈ {0.2, 0.4, 0.6, 0.8}, p, q)) depending on parameters p and q, for ER network of size 50 and z = 3. where U(A) is the set of nodes carrying at least one sym￾bol from A ⊆ X. The final approximate objective is FMP = αSMP + (1 − α)(1 − HMP). (F12…

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Forward citations

Cited by 1 Pith paper

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

  1. Graph reconstruction from random-walk co-visitation: Geometric, empirical, and controlled networks

    astro-ph.IM 2026-08 conditional novelty 5.0 of 10

    A new random-walk co-visitation pipeline reconstructs test graphs with high MCC, but its headline accuracy is largely set by walk coverage because clean walks never cross non-edges.

Reference graph

Works this paper leans on

31 extracted references · 1 canonical work pages · cited by 1 Pith paper

  1. [1]

    Aumasson,Serious cryptography: a practical intro- duction to modern encryption(No Starch Press, 2017)

    J.-P. Aumasson,Serious cryptography: a practical intro- duction to modern encryption(No Starch Press, 2017)

    2017

  2. [2]

    Slinko,Algebra for Applications: Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression (Springer, 2020)

    A. Slinko,Algebra for Applications: Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression (Springer, 2020)

    2020

  3. [3]

    Cramer, I

    R. Cramer, I. B. Damg˚ ard,et al.,Secure multiparty computation and Secret Sharing(Cambridge University Press, 2015)

    2015

  4. [4]

    Shamir, Communications of the ACM22, 612 (1979)

    A. Shamir, Communications of the ACM22, 612 (1979)

    1979

  5. [5]

    Herzberg, S

    A. Herzberg, S. Jarecki, H. Krawczyk, and M. Yung, inAdvances in Cryptology—CRYPT0’95: 15th An- nual International Cryptology Conference Santa Barbara, California, USA, August 27–31, 1995 Proceedings 15 (Springer, 1995) pp. 339–352

    1995

  6. [6]

    Lee, Y.-S

    C.-Y. Lee, Y.-S. Yeh, D.-J. Chen, and K.-L. Ku, Infor- mation Sciences116, 109 (1999)

    1999

  7. [7]

    Poguntke, Open Journal of Discrete Mathematics6, 238 (2016)

    W. Poguntke, Open Journal of Discrete Mathematics6, 238 (2016)

    2016

  8. [8]

    Zhang, M

    X. Zhang, M. Xu, G. Da, and P. Zhao, Reliability Engi- neering & System Safety214, 107697 (2021)

    2021

Show all 31 references
  1. [9]

    K¨ ohler and V

    S. K¨ ohler and V. Turau, Theoretical Computer Science 591, 15 (2015)

    2015

  2. [10]

    D. B. Johnson and L. Raab, SIAM Journal on Computing 23, 510 (1994)

    1994

  3. [11]

    D. S. Callaway, M. E. Newman, S. H. Strogatz, and D. J. Watts, Physical review letters85, 5468 (2000)

    2000

  4. [12]

    Der´ enyi, G

    I. Der´ enyi, G. Palla, and T. Vicsek, Physical review let- ters94, 160202 (2005)

    2005

  5. [13]

    G. Paul, S. Sreenivasan, S. Havlin, and H. E. Stan- ley, Physica A: Statistical Mechanics and its Applications 370, 854 (2006)

    2006

  6. [14]

    Radicchi and S

    F. Radicchi and S. Fortunato, Physical review letters 103, 168701 (2009)

    2009

  7. [15]

    M. ´A. Serrano, D. Krioukov, and M. Bogu˜ n´ a, Physical review letters106, 048701 (2011)

    2011

  8. [16]

    Karrer, M

    B. Karrer, M. E. Newman, and L. Zdeborov´ a, Physical review letters113, 208702 (2014)

    2014

  9. [17]

    Allard and L

    A. Allard and L. H´ ebert-Dufresne, Physical Review X9, 011023 (2019)

    2019

  10. [18]

    Vojkovi´ c, D

    T. Vojkovi´ c, D. Vukiˇ cevi´ c, and V. Zlati´ c, Rad Hrvatske akademije znanosti i umjetnosti. Matematiˇ cke znanosti , 1 (2018)

    2018

  11. [19]

    Vojkovic and D

    T. Vojkovic and D. Vukicevic, arXiv preprint arXiv:2310.05560 (2023)

    2023

  12. [20]

    S. M. Krause, M. M. Danziger, and V. Zlati´ c, Physical Review X6, 041022 (2016)

    2016

  13. [21]

    S. M. Krause, M. M. Danziger, and V. Zlati´ c, Physical Review E96, 022313 (2017)

    2017

  14. [22]

    Kadovi´ c, S

    A. Kadovi´ c, S. M. Krause, G. Caldarelli, and V. Zlatic, Physical Review E98, 062308 (2018)

    2018

  15. [23]

    M. E. Newman, S. H. Strogatz, and D. J. Watts, Physical review E64, 026118 (2001)

    2001

  16. [24]

    Kryven, Physical Review E95, 052303 (2017)

    I. Kryven, Physical Review E95, 052303 (2017)

    2017

  17. [25]

    M´ ezard and A

    M. M´ ezard and A. Montanari,Information, Physics, and Computation(Oxford University Press, Oxford, 2009)

    2009

  18. [26]

    Angl` es d’Auriac, N

    J.-A. Angl` es d’Auriac, N. Cohen, H. El Maftouhi, A. Harutyunyan, S. Legay, and Y. Manoussakis, Dis- crete Mathematics & Theoretical Computer Science17, 327 (2016)

    2016

  19. [27]

    Chapelle, M

    M. Chapelle, M. Cochefert, D. Kratsch, R. Letourneur, and M. Liedloff, Theoretical Computer Science676, 33 (2017)

    2017

  20. [28]

    Kratsch, M

    D. Kratsch, M. Liedloff, and M. Y. Sayadi, inSOFSEM 2017: Theory and Practice of Computer Science(2017) pp. 217–228

    2017

  21. [29]

    Bliznets, D

    I. Bliznets, D. Sagunov, and E. Tagin, inAlgorithms and Complexity, Lecture Notes in Computer Science, Vol. 13898 (Springer, 2023) pp. 127–141. Appendix A: Illustrative examples for survivability and hackability In order to better understand the problem it is useful to conside...

    2023

  22. [30]

    Second, their number is counted and denoted byn 1

    Survivability and MICS First, all subgraphs of size|Γ ′|= 1 (i.e., single ver- tices) are checked for the presence of the complete infor- mation. Second, their number is counted and denoted byn 1. The contribution to survivability is thenn 1¯p. It is noted that all other parts...

  23. [31]

    For pedagogical reasons, the special case with only two sym- bolsX 1 andX 2 is first analyzed

    Hackability In similar way the hackability can be derived. For pedagogical reasons, the special case with only two sym- bolsX 1 andX 2 is first analyzed. In that case the set Ω(X) ={X 1, X2, X1X2}is the set of all possible ver- tex configurations. The number of these elements ...

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Reviewed June 30, 2026 · model on record in the stance chip above.