Pith Number

pith:ECXRASRF

pith:2013:ECXRASRFEEPIF2SRGBLU65GJFJ

not attested not anchored not stored refs pending

Isocapacity Estimates for Hessian Operators

Jie Xiao, Ning Zhang

arxiv:1305.0721 v2 · 2013-05-03 · math.FA · math.AP · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ECXRASRFEEPIF2SRGBLU65GJFJ}

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	2026-05-18T02:54:21.497977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20af104a25211e82ea5130574f74c92a5cae7d10e40e00a4482f1092efc09b79

Aliases

arxiv: 1305.0721 · arxiv_version: 1305.0721v2 · doi: 10.48550/arxiv.1305.0721 · pith_short_12: ECXRASRFEEPI · pith_short_16: ECXRASRFEEPIF2SR · pith_short_8: ECXRASRF

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/ECXRASRFEEPIF2SRGBLU65GJFJ \
  | 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: 20af104a25211e82ea5130574f74c92a5cae7d10e40e00a4482f1092efc09b79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fee239a345917b96c4895906aa33f86ca126d7cc54894c832197731883550f9",
    "cross_cats_sorted": [
      "math.AP",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-05-03T14:25:29Z",
    "title_canon_sha256": "a8ebc1aab2edc78b2eb7b9034532b58d0f6e2da087dfa70a33398767b28d8ff9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.0721",
    "kind": "arxiv",
    "version": 2
  }
}