Pith Number

pith:M2A3WD4K

pith:2019:M2A3WD4K5XUOTBO6EHCQWUU5DQ

not attested not anchored not stored refs pending

Vanishing cross-diffusion limit in a Keller-Segel system with additional cross-diffusion

Ansgar J\"ungel, Oliver Leingang, Shu Wang

arxiv:1907.11387 v1 · 2019-07-26 · 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{M2A3WD4K5XUOTBO6EHCQWUU5DQ}

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	2026-05-17T23:39:29.263089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6681bb0f8aede8e985de21c50b529d1c2e86d9a74d9dc0b1d3de6cd733e85f49

Aliases

arxiv: 1907.11387 · arxiv_version: 1907.11387v1 · doi: 10.48550/arxiv.1907.11387 · pith_short_12: M2A3WD4K5XUO · pith_short_16: M2A3WD4K5XUOTBO6 · pith_short_8: M2A3WD4K

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/M2A3WD4K5XUOTBO6EHCQWUU5DQ \
  | 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: 6681bb0f8aede8e985de21c50b529d1c2e86d9a74d9dc0b1d3de6cd733e85f49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0920fbff08885704b60188cfc054aadf4f4584870f3bc2d6cc488f4c9cd5474",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-07-26T06:06:39Z",
    "title_canon_sha256": "918c141c6bae51b6479cea665336b0e602ab0a7fb6ac25f9afbbd92717c14565"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.11387",
    "kind": "arxiv",
    "version": 1
  }
}