Pith Number

pith:K2HHRN6M

pith:2012:K2HHRN6MXFGGHX2K5KHWEM73SW

not attested not anchored not stored refs pending

Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound

Aaron Naber, Daniele Valtorta

arxiv:1208.3507 v4 · 2012-08-16 · math.DG · 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{K2HHRN6MXFGGHX2K5KHWEM73SW}

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	2026-05-18T03:00:26.936597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

568e78b7ccb94c63df4aea8f6233fb95a588418edbc631786fbabc9fe0ca47cd

Aliases

arxiv: 1208.3507 · arxiv_version: 1208.3507v4 · doi: 10.48550/arxiv.1208.3507 · pith_short_12: K2HHRN6MXFGG · pith_short_16: K2HHRN6MXFGGHX2K · pith_short_8: K2HHRN6M

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/K2HHRN6MXFGGHX2K5KHWEM73SW \
  | 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: 568e78b7ccb94c63df4aea8f6233fb95a588418edbc631786fbabc9fe0ca47cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4917926487ad7594a5a87af7e55f8985ef276ebc7f0ce1f9f98ee49104d2767",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-08-16T22:43:52Z",
    "title_canon_sha256": "b42e09c65504ab4877d4fc34f2ec110d843d5143630d8a9d49f0eb422fa01c3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3507",
    "kind": "arxiv",
    "version": 4
  }
}