Pith Number

pith:I52CH7YK

pith:2017:I52CH7YKND6F4ZNUGFVNUC2URL

not attested not anchored not stored refs pending

Harmonic pre-Schwarzian and its applications

Gang Liu, Saminathan Ponnusamy

arxiv:1707.01572 v1 · 2017-07-05 · 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{I52CH7YKND6F4ZNUGFVNUC2URL}

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	2026-05-18T00:40:48.140022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

477423ff0a68fc5e65b4316ada0b548af6bc4b14c1d6b5afc2fb8e746cbe9b43

Aliases

arxiv: 1707.01572 · arxiv_version: 1707.01572v1 · doi: 10.48550/arxiv.1707.01572 · pith_short_12: I52CH7YKND6F · pith_short_16: I52CH7YKND6F4ZNU · pith_short_8: I52CH7YK

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/I52CH7YKND6F4ZNUGFVNUC2URL \
  | 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: 477423ff0a68fc5e65b4316ada0b548af6bc4b14c1d6b5afc2fb8e746cbe9b43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e728d9f548ac781b27570f604d8ab45c65ed92cb610e082d999f56b115bd846",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2017-07-05T20:35:16Z",
    "title_canon_sha256": "052d2ff459d59bb66a02b57d8e4a6a82e7eec05432e0abd5eeb0c1868c04af3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.01572",
    "kind": "arxiv",
    "version": 1
  }
}