Pith Number

pith:ZZNZCJWI

pith:2018:ZZNZCJWIZLA35Q2M2BSHLQBGN4

not attested not anchored not stored refs pending

Lech's inequality, the St\"{u}ckrad--Vogel conjecture, and uniform behavior of Koszul homology

Ilya Smirnov, Linquan Ma, Patricia Klein, Pham Hung Quy, Yongwei Yao

arxiv:1808.01051 v2 · 2018-08-03 · 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{ZZNZCJWIZLA35Q2M2BSHLQBGN4}

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	2026-05-17T23:52:58.985187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce5b9126c8cac1bec34cd06475c0266f257d9f57ac4b9ff9c072fb66678ab4a6

Aliases

arxiv: 1808.01051 · arxiv_version: 1808.01051v2 · doi: 10.48550/arxiv.1808.01051 · pith_short_12: ZZNZCJWIZLA3 · pith_short_16: ZZNZCJWIZLA35Q2M · pith_short_8: ZZNZCJWI

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/ZZNZCJWIZLA35Q2M2BSHLQBGN4 \
  | 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: ce5b9126c8cac1bec34cd06475c0266f257d9f57ac4b9ff9c072fb66678ab4a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acbf5ade3d18ef1824de46345df7578d155e0cd27adcf6c2d0eadd6d5cef435b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2018-08-03T00:09:58Z",
    "title_canon_sha256": "2394e310488108857eb333e29f266c2b39d828b2cf9bf41fcbc58fb598ee9f6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.01051",
    "kind": "arxiv",
    "version": 2
  }
}