Pith Number

pith:2YJ74HFV

pith:2012:2YJ74HFVPL4QKD3XPCZRGKHCXI

not attested not anchored not stored refs pending

Sharp bounds for the first eigenvalue and the torsional rigidity related to some anisotropic operators

Francesco Della Pietra, Nunzia Gavitone

arxiv:1210.5848 v1 · 2012-10-22 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2YJ74HFVPL4QKD3XPCZRGKHCXI}

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	2026-05-18T03:01:11.042781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d613fe1cb57af9050f7778b31328e2ba3f697e04420eb8eef81387dd8160588e

Aliases

arxiv: 1210.5848 · arxiv_version: 1210.5848v1 · doi: 10.48550/arxiv.1210.5848 · pith_short_12: 2YJ74HFVPL4Q · pith_short_16: 2YJ74HFVPL4QKD3X · pith_short_8: 2YJ74HFV

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/2YJ74HFVPL4QKD3XPCZRGKHCXI \
  | 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: d613fe1cb57af9050f7778b31328e2ba3f697e04420eb8eef81387dd8160588e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77e3d2061b7b372662272ceea8434a32d1356619b97e4b50c85e0b984238de30",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-22T09:47:01Z",
    "title_canon_sha256": "f461360ba6d70543439a860f1357f92f50b59ac9038ac33840d2733a8ca141e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5848",
    "kind": "arxiv",
    "version": 1
  }
}