Pith Number

pith:MRMFSLL5

pith:2026:MRMFSLL56RKYUENSH74XILNMQO

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Non-Redundancy of Low-Arity Symmetric Boolean CSPs

Amatya Sharma, Santhoshini Velusamy

Symmetric Boolean CSPs of arity at most 5 have their non-redundancy growth rates classified as O(n), O(n^2), or O(n^3), with all arity-4 cases and most arity-5 cases resolved.

arxiv:2605.14007 v1 · 2026-05-13 · cs.DS · cs.CC

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Claims

C1strongest claim

Our main result is a near-complete classification of the asymptotic growth of NRD_n(R) for symmetric Boolean predicates of arity at most 5. We resolve every predicate of arity at most 4 and all but two predicates of arity 5.

C2weakest assumption

The computational experiments are assumed to have exhaustively enumerated and correctly classified all symmetric Boolean relations of arity at most 4 and all but two of arity 5; the algebraic criteria for t-balancedness are assumed to be tight for the unresolved cases.

C3one line summary

Symmetric Boolean CSP predicates of arity at most 5 have their non-redundancy NRD_n(R) classified as O(n^t) for small t, with all arity-4 cases and all but two arity-5 cases resolved via t-balancedness and OR-reductions.

References

16 extracted · 16 resolved · 3 Pith anchors

[1] Half-Approximating Maximum Dicut in the Streaming Setting 2012

[2] Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT 2019 · doi:10.1109/focs.2019.00021.url:https://doi.org/10.1109/focs.2019.00021

[3] Schloss Dagstuhl — Leibniz- Zentrum f ¨ur Informatik, July 2022, 38:1–38:23.DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022 2022 · doi:10.4230/lipics.approx/random.2022

[4] by Stefano Leonardi and Anupam Gupta 2005 · doi:10.1145/3519935.3519983

[5] Near-Optimal Space Lower Bounds for Streaming CSPs 1998 · arXiv:2604.01400

Cited by

1 paper in Pith

Super-linear Lower Bounds for CSP Non-Redundancy via Shrinking Instances

Receipt and verification

First computed	2026-05-17T23:39:13.098198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6458592d7df4558a11b23ff9742dac83a56fdac4e052b07fef2615a8ba4b3fe4

Aliases

arxiv: 2605.14007 · arxiv_version: 2605.14007v1 · doi: 10.48550/arxiv.2605.14007 · pith_short_12: MRMFSLL56RKY · pith_short_16: MRMFSLL56RKYUENS · pith_short_8: MRMFSLL5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MRMFSLL56RKYUENSH74XILNMQO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 6458592d7df4558a11b23ff9742dac83a56fdac4e052b07fef2615a8ba4b3fe4

Canonical record JSON

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    "abstract_canon_sha256": "3b60a5212f51cf2ed406f3196d1e773646e47697c5440c1bc94e659ce467dfa6",
    "cross_cats_sorted": [
      "cs.CC"
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-13T18:12:58Z",
    "title_canon_sha256": "f430cdd24c4dce717a3c54c7d259b3ce2dd0ed2d56c0a48902eecb2f47e42826"
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