Pith Number

pith:XGG3EEJR

pith:2012:XGG3EEJRT4I23TWQ4UABXBJWSM

not attested not anchored not stored refs pending

Some sharp Hodge Laplacian and Steklov eigenvalue estimates for differential forms

Kwok-Kun Kwong

arxiv:1207.3999 v2 · 2012-07-17 · 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{XGG3EEJRT4I23TWQ4UABXBJWSM}

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	2026-05-18T01:17:01.523967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b98db211319f11adced0e5001b8536931d041bb7d568b3c99910a5f7efbc1d2f

Aliases

arxiv: 1207.3999 · arxiv_version: 1207.3999v2 · doi: 10.48550/arxiv.1207.3999 · pith_short_12: XGG3EEJRT4I2 · pith_short_16: XGG3EEJRT4I23TWQ · pith_short_8: XGG3EEJR

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/XGG3EEJRT4I23TWQ4UABXBJWSM \
  | 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: b98db211319f11adced0e5001b8536931d041bb7d568b3c99910a5f7efbc1d2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2bd7c403810f9b5b3853eede7408ddbf43f0c990850161c24664989483f0da37",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-07-17T14:08:54Z",
    "title_canon_sha256": "eba8de1a5ced853484701e42e19556ff46116ee45f49f7c8619f55419a422509"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3999",
    "kind": "arxiv",
    "version": 2
  }
}