Pith Number

pith:JDLRTLVB

pith:2026:JDLRTLVBR7SLHAJCHEVJMMB3OD

not attested not anchored not stored refs resolved

Optimal Diameters of High Multiplicity g-Golomb Rulers

Aditya Gupta, Kevin O'Bryant

For g at least roughly 1.75 times b to the 3/2 power, the shortest g-Golomb ruler with g plus b marks has diameter exactly g plus 2b minus 2.

arxiv:2605.14229 v1 · 2026-05-14 · math.CO

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\usepackage{pith}
\pithnumber{JDLRTLVBR7SLHAJCHEVJMMB3OD}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

for all b≥1, if g ≥ (7/4)(b^{3/2} - b) +1, then G(g,g+b)=g+2b-2

C2weakest assumption

The arithmetic property of integers not belonging to a g-Golomb ruler is strong enough to force the diameter lower bound via the newly defined LM rulers.

C3one line summary

G(g, g+b) equals g + 2b - 2 when g meets the threshold (7/4)(b^{3/2} - b) + 1, with new bounds sqrt(8/9)(n-1)^{3/2} to (7/4)((n+1)^{3/2} - (n+1)) for the minimal diameter L(n) of n-element LM rulers.

References

8 extracted · 8 resolved · 0 Pith anchors

[1] M. D. Atkinson and A. Hassenklover,Sets of integers with distinct differences, Sch Comput. Sci. (Aug 1984). Rep. SCS-TR-63. 14 1984

[2] M. D. Atkinson, N. Santoro, and J. Urrutia,Integer Sets with Distinct Sums and Differences and Car- rier Frequency Assignments for Nonlinear Repeaters, IEEE Transactions on Communications34(June 1986) 1986

[3] J´ ozsef Balogh, Zolt´ an F¨ uredi, and Souktik Roy,An upper bound on the size of Sidon sets, Amer. Math. Monthly130(2023), no. 5, 437–445, DOI 10.1080/00029890.2023.2176667.MR 4580380 2023 · doi:10.1080/00029890.2023.2176667.mr

[4] Martos, and Carlos A 2015 · doi:10.18273/revint.v33n2-2015006

[5] D. Carter, Z. Hunter, and K. O’Bryant,On the diameter of finite Sidon sets, Acta Math. Hungar.175 (2025), no. 1, 108–126, DOI 10.1007/s10474-024-01499-8.MR 4880650 2025 · doi:10.1007/s10474-024-01499-8.mr

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:10.751873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48d719aea18fe4b38122392a96303b70ece6ef53ee8c478d83233ec66c8cfaad

Aliases

arxiv: 2605.14229 · arxiv_version: 2605.14229v1 · doi: 10.48550/arxiv.2605.14229 · pith_short_12: JDLRTLVBR7SL · pith_short_16: JDLRTLVBR7SLHAJC · pith_short_8: JDLRTLVB

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JDLRTLVBR7SLHAJCHEVJMMB3OD \
  | 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: 48d719aea18fe4b38122392a96303b70ece6ef53ee8c478d83233ec66c8cfaad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b093b283b622f632f26d67fd84263b15f81d089324ae56f6829260a15bfc5a78",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T00:47:08Z",
    "title_canon_sha256": "2689b1dee4d64e1887b510125b0d3da6f0a696f29b5f7efef0953a6322d80f73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14229",
    "kind": "arxiv",
    "version": 1
  }
}