Pith Number

pith:ARFJCXBT

pith:2013:ARFJCXBTO6DH3OAIWUALXO3LLK

not attested not anchored not stored refs pending

A converse of the Gauss--Lucas theorem

Blagovest Sendov, Nikolai Nikolov

arxiv:1307.8236 v1 · 2013-07-31 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ARFJCXBTO6DH3OAIWUALXO3LLK}

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	2026-05-18T02:38:37.436342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

044a915c3377867db808b500bbbb6b5aa20e0f0ce74028db83761a8ec1ed6e9a

Aliases

arxiv: 1307.8236 · arxiv_version: 1307.8236v1 · doi: 10.48550/arxiv.1307.8236 · pith_short_12: ARFJCXBTO6DH · pith_short_16: ARFJCXBTO6DH3OAI · pith_short_8: ARFJCXBT

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/ARFJCXBTO6DH3OAIWUALXO3LLK \
  | 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: 044a915c3377867db808b500bbbb6b5aa20e0f0ce74028db83761a8ec1ed6e9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29f434d33d1888da19b96f0f387ab2acdf2860b5f18f932003775ae2b051f951",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2013-07-31T06:52:24Z",
    "title_canon_sha256": "59b5c372f78ee63b3eb765d44ac91c8c248fd8f6bed01f67c32ae17fa1df340b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.8236",
    "kind": "arxiv",
    "version": 1
  }
}