Pith Number

pith:2QJYGLWI

pith:2015:2QJYGLWIICAAOLRO7GBORKQGW6

not attested not anchored not stored refs pending

A gradient estimate for positive functions on graphs

Shuang Liu, Yong Lin, Yunyan Yang

arxiv:1509.07981 v1 · 2015-09-26 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2QJYGLWIICAAOLRO7GBORKQGW6}

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	2026-05-18T01:31:54.993151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d413832ec84080072e2ef982e8aa06b7bdc44b793de96501317a0d183a4a3cbe

Aliases

arxiv: 1509.07981 · arxiv_version: 1509.07981v1 · doi: 10.48550/arxiv.1509.07981 · pith_short_12: 2QJYGLWIICAA · pith_short_16: 2QJYGLWIICAAOLRO · pith_short_8: 2QJYGLWI

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/2QJYGLWIICAAOLRO7GBORKQGW6 \
  | 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: d413832ec84080072e2ef982e8aa06b7bdc44b793de96501317a0d183a4a3cbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "458bc6e3f3ea5222b8275dba540b081041f980381181978a6af9b07b483cb06e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-09-26T14:05:24Z",
    "title_canon_sha256": "c6de6d8e51b4a8ee8ed7e918d01840fa4d215237fe90ac3e6bc210000081efd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07981",
    "kind": "arxiv",
    "version": 1
  }
}