Pith Number

pith:5ZW2CE3B

pith:2015:5ZW2CE3BIF2NOJ74KLYRRUJ5K6

not attested not anchored not stored refs pending

Zero-sum Subsequences of Length kq over Finite Abelian p-Groups

Xiaoyu He

arxiv:1503.06905 v1 · 2015-03-24 · math.CO · 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{5ZW2CE3BIF2NOJ74KLYRRUJ5K6}

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	2026-05-18T00:40:08.615985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee6da113614174d727fc52f118d13d57936331ee73950d26f2b49a009550064c

Aliases

arxiv: 1503.06905 · arxiv_version: 1503.06905v1 · doi: 10.48550/arxiv.1503.06905 · pith_short_12: 5ZW2CE3BIF2N · pith_short_16: 5ZW2CE3BIF2NOJ74 · pith_short_8: 5ZW2CE3B

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/5ZW2CE3BIF2NOJ74KLYRRUJ5K6 \
  | 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: ee6da113614174d727fc52f118d13d57936331ee73950d26f2b49a009550064c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e68167d4e49a454f01295c271cff8944b2bf47fb9b5511e3460ef66c02e05ca1",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-03-24T03:54:18Z",
    "title_canon_sha256": "dd5becbefb1f4e05509fbd638e1280e2bb912d94bccafad138ed6985be9b45d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06905",
    "kind": "arxiv",
    "version": 1
  }
}