Pith Number

pith:FNVF4YR2

pith:2012:FNVF4YR23IG4KQAVLZ7HRXTP6Z

not attested not anchored not stored refs pending

Critical Points and Gr\"obner Bases: the Unmixed Case

Jean-Charles Faug\`ere, Mohab Safey El Din, Pierre-Jean Spaenlehauer

arxiv:1202.0179 v1 · 2012-02-01 · cs.SC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FNVF4YR23IG4KQAVLZ7HRXTP6Z}

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	2026-05-18T04:03:19.943913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b6a5e623ada0dc540155e7e78de6ff65f684ceff8fd97df3b1de998dd615bb1

Aliases

arxiv: 1202.0179 · arxiv_version: 1202.0179v1 · doi: 10.48550/arxiv.1202.0179 · pith_short_12: FNVF4YR23IG4 · pith_short_16: FNVF4YR23IG4KQAV · pith_short_8: FNVF4YR2

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/FNVF4YR23IG4KQAVLZ7HRXTP6Z \
  | 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: 2b6a5e623ada0dc540155e7e78de6ff65f684ceff8fd97df3b1de998dd615bb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "517c908740e97f03cbb81520b52c937912a769b8b4fd8284a944878c2c1bc5d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SC",
    "submitted_at": "2012-02-01T14:42:59Z",
    "title_canon_sha256": "2272a82b2747660e1ad0550391d826aa3729ba21035580adadb88235dfe1e69f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.0179",
    "kind": "arxiv",
    "version": 1
  }
}