Pith Number

pith:6XKPSG3E

pith:2011:6XKPSG3EACEIUX7LKCVLQON4OC

not attested not anchored not stored refs pending

Gradient estimate for eigenforms of Hodge Laplacian

Jiaping Wang, Linfeng Zhou

arxiv:1109.4968 v3 · 2011-09-22 · 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{6XKPSG3EACEIUX7LKCVLQON4OC}

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	2026-05-18T04:08:34.484798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5d4f91b6400888a5feb50aab839bc708f642f9a1804c678e981db7f19dfd095

Aliases

arxiv: 1109.4968 · arxiv_version: 1109.4968v3 · doi: 10.48550/arxiv.1109.4968 · pith_short_12: 6XKPSG3EACEI · pith_short_16: 6XKPSG3EACEIUX7L · pith_short_8: 6XKPSG3E

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/6XKPSG3EACEIUX7LKCVLQON4OC \
  | 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: f5d4f91b6400888a5feb50aab839bc708f642f9a1804c678e981db7f19dfd095

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cfa59e3b50851844c81475112b7e35fb16e6f0bfb671b544934bd8e0215c769",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-09-22T23:10:30Z",
    "title_canon_sha256": "9808ec5d45c82138e8e3cf6ce15ec6f90f6ed3b9d14045efb1eb266d7b741593"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4968",
    "kind": "arxiv",
    "version": 3
  }
}