Pith Number

pith:3GFNYEOD

pith:2012:3GFNYEODOJNO52Q2HFMZXV4LJE

not attested not anchored not stored refs pending

A functional framework for the Keller-Segel system: logarithmic Hardy-Littlewood-Sobolev and related spectral gap inequalities

DIM), Jean Dolbeault (CEREMADE), Juan Campos Serrano (CEREMADE

arxiv:1206.2000 v1 · 2012-06-10 · 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{3GFNYEODOJNO52Q2HFMZXV4LJE}

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	2026-05-18T03:39:06.271927Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d98adc11c3725aeeea1a39599bd78b492deff84dfd56da4939d0a2650f7d5fe6

Aliases

arxiv: 1206.2000 · arxiv_version: 1206.2000v1 · doi: 10.48550/arxiv.1206.2000 · pith_short_12: 3GFNYEODOJNO · pith_short_16: 3GFNYEODOJNO52Q2 · pith_short_8: 3GFNYEOD

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/3GFNYEODOJNO52Q2HFMZXV4LJE \
  | 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: d98adc11c3725aeeea1a39599bd78b492deff84dfd56da4939d0a2650f7d5fe6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "903559dbc0dc02914d7d2f120fe47390fce557cf5f6e3b64f833c5cd3efb50b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-10T07:10:55Z",
    "title_canon_sha256": "f4ad107af168ce6782bf30592f3c2d245fbe505e9c87ffd200ebf8a7edf33328"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2000",
    "kind": "arxiv",
    "version": 1
  }
}