Pith Number

pith:B2ZTMYQE

pith:2005:B2ZTMYQEWSOULSASN2CTUIVGOI

not attested not anchored not stored refs pending

Multiplicity of critical points of master functions and Schubert calculus

Alexander Varchenko, Evgeny Mukhin, Prakash Belkale

arxiv:math/0503132 v3 · 2005-03-07 · math.QA · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B2ZTMYQEWSOULSASN2CTUIVGOI}

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	2026-05-18T01:05:23.677221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0eb3366204b49d45c8126e853a22a67208de65aa3903067253185d882a5f7049

Aliases

arxiv: math/0503132 · arxiv_version: math/0503132v3 · doi: 10.48550/arxiv.math/0503132 · pith_short_12: B2ZTMYQEWSOU · pith_short_16: B2ZTMYQEWSOULSAS · pith_short_8: B2ZTMYQE

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/B2ZTMYQEWSOULSASN2CTUIVGOI \
  | 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: 0eb3366204b49d45c8126e853a22a67208de65aa3903067253185d882a5f7049

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a44f5060b70e6ad00d13e393b5683f730e19e33e20ba9b8e4fc5e66dbb2a94a",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2005-03-07T21:45:02Z",
    "title_canon_sha256": "2408372ba2d1f13a3d8179a7c4d0fd91890b6055bc64f20b50044cf49657cb6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0503132",
    "kind": "arxiv",
    "version": 3
  }
}