Pith Number

pith:23ZURQF5

pith:2008:23ZURQF5HJBZBGPZ7P3H3ZYB6W

not attested not anchored not stored refs pending

Poisson Geometry of Directed Networks in an Annulus

Alek Vainshtein, Michael Gekhtman, Michael Shapiro

arxiv:0901.0020 v3 · 2008-12-31 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{23ZURQF5HJBZBGPZ7P3H3ZYB6W}

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	2026-05-18T01:14:36.549746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6f348c0bd3a439099f9fbf67de701f5b6e4a8b7393714a9ef45c95a90b79b5a

Aliases

arxiv: 0901.0020 · arxiv_version: 0901.0020v3 · doi: 10.48550/arxiv.0901.0020 · pith_short_12: 23ZURQF5HJBZ · pith_short_16: 23ZURQF5HJBZBGPZ · pith_short_8: 23ZURQF5

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/23ZURQF5HJBZBGPZ7P3H3ZYB6W \
  | 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: d6f348c0bd3a439099f9fbf67de701f5b6e4a8b7393714a9ef45c95a90b79b5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe51bce1910ae8096ec09a4c153d7abb90f0242298d66e241160805c6942348f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2008-12-31T00:08:51Z",
    "title_canon_sha256": "2e13d631ecb82febfc08c11aad145d5e0264117ba02bc81d4005dd52f4fa0c4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.0020",
    "kind": "arxiv",
    "version": 3
  }
}