Pith Number

pith:WLLZ6W2P

pith:2014:WLLZ6W2PJLJGIXW5LKMIDUOUUM

not attested not anchored not stored refs pending

The Cross Number of Minimal Zero-sum Sequences in Finite Abelian Groups

Bumsoo Kim

arxiv:1410.6867 v3 · 2014-10-25 · 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{WLLZ6W2PJLJGIXW5LKMIDUOUUM}

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	2026-05-18T02:00:02.503445Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2d79f5b4f4ad2645edd5a9881d1d4a324bd322d5a870ecc86d37e7ee5608fbb

Aliases

arxiv: 1410.6867 · arxiv_version: 1410.6867v3 · doi: 10.48550/arxiv.1410.6867 · pith_short_12: WLLZ6W2PJLJG · pith_short_16: WLLZ6W2PJLJGIXW5 · pith_short_8: WLLZ6W2P

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/WLLZ6W2PJLJGIXW5LKMIDUOUUM \
  | 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: b2d79f5b4f4ad2645edd5a9881d1d4a324bd322d5a870ecc86d37e7ee5608fbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0b737ff8bc00c4fa7079806056650419aa542efc2f7f15f0e81208d45eb7106",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-10-25T01:53:53Z",
    "title_canon_sha256": "9beb1f1cc8e7b8f2ebbea92725dcb4e75d11f929897414b6ed4329c51b190140"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.6867",
    "kind": "arxiv",
    "version": 3
  }
}