Pith Number

pith:GHQHZENB

pith:2011:GHQHZENBR2FPQWFIUSCFKIN6PA

not attested not anchored not stored refs pending

The group law on the tropical Hesse pencil

Atsushi Nobe

arxiv:1111.0131 v1 · 2011-11-01 · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GHQHZENBR2FPQWFIUSCFKIN6PA}

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	2026-05-18T00:24:32.306586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31e07c91a18e8af858a8a4845521be782edc00118ac6d3051e5167c3c657b51b

Aliases

arxiv: 1111.0131 · arxiv_version: 1111.0131v1 · doi: 10.48550/arxiv.1111.0131 · pith_short_12: GHQHZENBR2FP · pith_short_16: GHQHZENBR2FPQWFI · pith_short_8: GHQHZENB

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/GHQHZENBR2FPQWFIUSCFKIN6PA \
  | 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: 31e07c91a18e8af858a8a4845521be782edc00118ac6d3051e5167c3c657b51b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7c1c2302a8b625d7caf7231a30588da14902c6b912e110fd049001b0925c10d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.SI",
    "submitted_at": "2011-11-01T07:36:39Z",
    "title_canon_sha256": "560f34917aa373f03913a5c68c95d3d194f5675084e9767fa9d8c02b65342213"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0131",
    "kind": "arxiv",
    "version": 1
  }
}