Pith Number

pith:QJEJTOJM

pith:2026:QJEJTOJMPW36LQEYMIJ3IBDIOE

not attested not anchored not stored refs pending

Determination of the long-time dynamics for the 2D Keller-Segel equation at critical mass

Charles Collot, Federico Buseghin

arxiv:2606.20866 v1 · 2026-06-18 · 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{QJEJTOJMPW36LQEYMIJ3IBDIOE}

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	2026-06-23T00:12:01.201825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

824899b92c7db7e5c0986213b40468711b23c67c25733c8a4987db153cca8ca3

Aliases

arxiv: 2606.20866 · arxiv_version: 2606.20866v1 · doi: 10.48550/arxiv.2606.20866 · pith_short_12: QJEJTOJMPW36 · pith_short_16: QJEJTOJMPW36LQEY · pith_short_8: QJEJTOJM

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/QJEJTOJMPW36LQEYMIJ3IBDIOE \
  | 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: 824899b92c7db7e5c0986213b40468711b23c67c25733c8a4987db153cca8ca3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09f8e6374ce9ecff5d52cbf6c392df4e267ce31581225a9e1cf75062dc0d5bb7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-18T18:53:54Z",
    "title_canon_sha256": "a7174f6c30bda86e64536921628419d9a6d8dff71004e52cc70e2ca59db4b61a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20866",
    "kind": "arxiv",
    "version": 1
  }
}