Pith Number

pith:TMBHIZYA

pith:2026:TMBHIZYAS6ZWFQEUVGLWIXWF67

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Integer points in a simplex and related Diophantine problems: Hardy--Littlewood asymptotics in higher dimensions

M.M.Skriganov

Hardy-Littlewood asymptotic counts of integer points inside triangles extend to simplices in any dimension under the same irrationality conditions on the boundaries.

arxiv:2605.14446 v1 · 2026-05-14 · math.CO

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\pithnumber{TMBHIZYAS6ZWFQEUVGLWIXWF67}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations 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

We extend their results to higher dimensions.

C2weakest assumption

The irrationality conditions on the boundaries that worked in two dimensions continue to suffice for controlling the error terms in higher dimensions without new obstructions arising from the geometry of simplices.

C3one line summary

Extends Hardy-Littlewood asymptotics on lattice points in irrational triangles to higher-dimensional simplices.

References

32 extracted · 32 resolved · 1 Pith anchors

[1] in Math., Springer, Tokyo, 2014 2014

[2] Number Theor.10(5), (2000), 1321–1335 2000

[3] J.Beck,Probabilistic Diophantine approximation. I. Kronecker sequences., Ann. Math., 140(2), (1994), 449–502 1994

[4] Integer-point enumeration in poly- hedra, Undergrad 2015

[5] B.Borda,Lattice points in algebraic cross–polytopes and simplices, Discr. Comput. Geom., 60(1), (2018), 145–169 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:06.954866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b0274670097b362c094a997645ec5f7c7676acc91971ef416f6e12928766105

Aliases

arxiv: 2605.14446 · arxiv_version: 2605.14446v1 · doi: 10.48550/arxiv.2605.14446 · pith_short_12: TMBHIZYAS6ZW · pith_short_16: TMBHIZYAS6ZWFQEU · pith_short_8: TMBHIZYA

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TMBHIZYAS6ZWFQEUVGLWIXWF67 \
  | 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: 9b0274670097b362c094a997645ec5f7c7676acc91971ef416f6e12928766105

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d8d0cde7dde2276d7f1022aa6b02b5ae8f5e04afde1c8ad6f2cb8203dffb6d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T06:39:47Z",
    "title_canon_sha256": "758eabbb11d0869eaa54e071d596d4b6207e70dfb7b44af4fceee0151ac7550e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14446",
    "kind": "arxiv",
    "version": 1
  }
}