Pith Number

pith:FEXKN7W3

pith:2013:FEXKN7W3CIJRYWMYIWSGZ3C6VM

not attested not anchored not stored refs pending

Stationary solutions of Keller-Segel type crowd motion and herding models: multiplicity and dynamical stability

Gaspard Jankowiak (CEREMADE), Jean Dolbeault (CEREMADE), Peter Markowich (DAMTP)

arxiv:1305.1715 v2 · 2013-05-08 · 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{FEXKN7W3CIJRYWMYIWSGZ3C6VM}

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	2026-05-18T01:22:25.409145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

292ea6fedb12131c599845a46cec5eab2307c2a6d4bec540269a432532319b7c

Aliases

arxiv: 1305.1715 · arxiv_version: 1305.1715v2 · doi: 10.48550/arxiv.1305.1715 · pith_short_12: FEXKN7W3CIJR · pith_short_16: FEXKN7W3CIJRYWMY · pith_short_8: FEXKN7W3

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/FEXKN7W3CIJRYWMYIWSGZ3C6VM \
  | 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: 292ea6fedb12131c599845a46cec5eab2307c2a6d4bec540269a432532319b7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46cccf834a64faf3401944cbb6078ae698eab2993339b9f646ed441d605c8955",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-05-08T04:33:29Z",
    "title_canon_sha256": "835bb8d60bf54f60b292087d57d5a0a324acc7abc860d9441d68513e92eb9df7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.1715",
    "kind": "arxiv",
    "version": 2
  }
}