Pith Number

pith:7WQ3CYYU

pith:2015:7WQ3CYYUNHHPODQOTSPYFQAGP3

not attested not anchored not stored refs pending

Ultracontractivity and functional inequalities on infinite graphs

Hongye Song, Shuang Liu, Yong Lin

arxiv:1502.01958 v1 · 2015-02-06 · math.DG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7WQ3CYYUNHHPODQOTSPYFQAGP3}

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	2026-05-18T02:27:50.376791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fda1b1631469cef70e0e9c9f82c0067ef687fee2d207f1644f3951d3e74b2ef9

Aliases

arxiv: 1502.01958 · arxiv_version: 1502.01958v1 · doi: 10.48550/arxiv.1502.01958 · pith_short_12: 7WQ3CYYUNHHP · pith_short_16: 7WQ3CYYUNHHPODQO · pith_short_8: 7WQ3CYYU

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/7WQ3CYYUNHHPODQOTSPYFQAGP3 \
  | 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: fda1b1631469cef70e0e9c9f82c0067ef687fee2d207f1644f3951d3e74b2ef9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92a65a5411e4e40538ade77884500adbbadd48034fe007e9eb92219a94a6c472",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-02-06T17:03:19Z",
    "title_canon_sha256": "7c44ac9d22ebe0c170d23254a5426453ba8316cbfdd63c33ccdf489a4494de7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01958",
    "kind": "arxiv",
    "version": 1
  }
}