Pith Number

pith:5R6P3UQN

pith:2024:5R6P3UQN7BKX76QGVCVN6QBCT7

not attested not anchored not stored refs pending

Inverse problems for sumset sizes of finite sets of integers

Melvyn B. Nathanson

arxiv:2412.16154 v3 · 2024-12-20 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5R6P3UQN7BKX76QGVCVN6QBCT7}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

1 paper in Pith

On Nathanson's Triangular Number Phenomenon

Receipt and verification

First computed	2026-07-05T10:23:27.740832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec7cfdd20df8557ffa06a8aadf40229fed1fa9752166ab0ea29eadce6924943c

Aliases

arxiv: 2412.16154 · arxiv_version: 2412.16154v3 · doi: 10.48550/arxiv.2412.16154 · pith_short_12: 5R6P3UQN7BKX · pith_short_16: 5R6P3UQN7BKX76QG · pith_short_8: 5R6P3UQN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5R6P3UQN7BKX76QGVCVN6QBCT7 \
  | 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: ec7cfdd20df8557ffa06a8aadf40229fed1fa9752166ab0ea29eadce6924943c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab353f4effb7220d7dabcd7b821a18b06883c24b6dfd42beee9beb2604dd9510",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-12-20T18:58:21Z",
    "title_canon_sha256": "60c392d79e69caf06ab94922cf46db792960b30f3063b8db67e43234a0ec1930"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.16154",
    "kind": "arxiv",
    "version": 3
  }
}