Pith Number

pith:U675WFUW

pith:2012:U675WFUW74VE23MAZOPZ2M73WW

not attested not anchored not stored refs pending

Chebyshev polynomials, Zolotarev polynomials and plane trees

Yury Kochetkov

arxiv:1212.6317 v1 · 2012-12-27 · math.CO · 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{U675WFUW74VE23MAZOPZ2M73WW}

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	2026-05-18T03:37:40.170559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7bfdb1696ff2a4d6d80cb9f9d33fbb5ae0e8094a4044263c970047cdfa8af86

Aliases

arxiv: 1212.6317 · arxiv_version: 1212.6317v1 · doi: 10.48550/arxiv.1212.6317 · pith_short_12: U675WFUW74VE · pith_short_16: U675WFUW74VE23MA · pith_short_8: U675WFUW

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/U675WFUW74VE23MAZOPZ2M73WW \
  | 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: a7bfdb1696ff2a4d6d80cb9f9d33fbb5ae0e8094a4044263c970047cdfa8af86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e68aa1cc560c21adcff6e6be8c0e2833af7823acb6fa76b71f2223a24bb872b",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-27T07:10:13Z",
    "title_canon_sha256": "22219958d5c4845be92007ea2b7f2c7a6e3a70cd3dbddff43ea36289cd219ac8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6317",
    "kind": "arxiv",
    "version": 1
  }
}