Pith Number

pith:XJKW56FN

pith:2018:XJKW56FNWGUECXNOGPUB2LXA6P

not attested not anchored not stored refs pending

The relevance of Freiman's theorem for combinatorial commutative algebra

Guangjun Zhu, J\"urgen Herzog, Takayuki Hibi

arxiv:1801.05129 v1 · 2018-01-16 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XJKW56FNWGUECXNOGPUB2LXA6P}

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	2026-05-18T00:25:47.843582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba556ef8adb1a8415dae33e81d2ee0f3e9c3514a872f3670941c55f1fd23f639

Aliases

arxiv: 1801.05129 · arxiv_version: 1801.05129v1 · doi: 10.48550/arxiv.1801.05129 · pith_short_12: XJKW56FNWGUE · pith_short_16: XJKW56FNWGUECXNO · pith_short_8: XJKW56FN

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/XJKW56FNWGUECXNOGPUB2LXA6P \
  | 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: ba556ef8adb1a8415dae33e81d2ee0f3e9c3514a872f3670941c55f1fd23f639

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "025edd89ed0ea4a7d79e9ad56184dec06e307d253988ce5e4c5454c4a78dad9f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2018-01-16T06:26:32Z",
    "title_canon_sha256": "ed6ca6aeac6ca0cbdcd6bef4302146e32cf020d765aec747b740686ce35a6e1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.05129",
    "kind": "arxiv",
    "version": 1
  }
}