Pith Number

pith:2PATK5S5

pith:2014:2PATK5S5ZXSN73MDTBRM2WLDQZ

not attested not anchored not stored refs pending

On the Minimum Size of Signed Sumsets in Elementary Abelian Groups

Bela Bajnok, Ryan Matzke

arxiv:1412.1609 v1 · 2014-12-04 · 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{2PATK5S5ZXSN73MDTBRM2WLDQZ}

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.

Receipt and verification

First computed	2026-05-18T02:32:06.864894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3c135765dcde4dfed839862cd596386502a4ac26109e836621ca6c6b648e62d

Aliases

arxiv: 1412.1609 · arxiv_version: 1412.1609v1 · doi: 10.48550/arxiv.1412.1609 · pith_short_12: 2PATK5S5ZXSN · pith_short_16: 2PATK5S5ZXSN73MD · pith_short_8: 2PATK5S5

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/2PATK5S5ZXSN73MDTBRM2WLDQZ \
  | 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: d3c135765dcde4dfed839862cd596386502a4ac26109e836621ca6c6b648e62d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a41945fc2d4366704396931c9f218ec26a0a0c94229ab67b6ba93e2cd0627ea3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-12-04T10:24:20Z",
    "title_canon_sha256": "6070598b1381033a50e02229cde98041703932dec1d3efeab77ec2868fea8b84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.1609",
    "kind": "arxiv",
    "version": 1
  }
}