Pith Number

pith:UNDUISBL

pith:2013:UNDUISBL66WADFVYH5IQIUBHOY

not attested not anchored not stored refs pending

On the number of populations of critical points of master functions

Alexander Varchenko, Evgeny Mukhin

arxiv:1306.4429 v3 · 2013-06-19 · math.AG · 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{UNDUISBL66WADFVYH5IQIUBHOY}

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	2026-05-18T03:18:42.056995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a34744482bf7ac0196b83f510450277606de84e564cb50d0f16843c8cb4d5b2a

Aliases

arxiv: 1306.4429 · arxiv_version: 1306.4429v3 · doi: 10.48550/arxiv.1306.4429 · pith_short_12: UNDUISBL66WA · pith_short_16: UNDUISBL66WADFVY · pith_short_8: UNDUISBL

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/UNDUISBL66WADFVYH5IQIUBHOY \
  | 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: a34744482bf7ac0196b83f510450277606de84e564cb50d0f16843c8cb4d5b2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e24d23bfc9a4741e4549443b46e5f43789606cfe84ee591164529e6262566cd6",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-06-19T05:33:51Z",
    "title_canon_sha256": "6ecbf7321d9f08c6c16e29bd311e4652182e01c259b3dc16a936149aa042ff21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.4429",
    "kind": "arxiv",
    "version": 3
  }
}