Pith Number

pith:VPKAESQ4

pith:2022:VPKAESQ4ZOD5LXHGGALGXSB54M

not attested not anchored not stored refs pending

Global-in-time Boundedness of solution for Cauchy problem to the Parabolic-Parabolic Keller-Segel system with logistic growth

Xiaoxin Zheng, Yao Nie

arxiv:2201.01477 v1 · 2022-01-05 · 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{VPKAESQ4ZOD5LXHGGALGXSB54M}

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	2026-07-05T03:46:06.035654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd4024a1ccb87d5dce630166bc83de30ba696333c49d2cc3cde73b81eba1625

Aliases

arxiv: 2201.01477 · arxiv_version: 2201.01477v1 · doi: 10.48550/arxiv.2201.01477 · pith_short_12: VPKAESQ4ZOD5 · pith_short_16: VPKAESQ4ZOD5LXHG · pith_short_8: VPKAESQ4

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/VPKAESQ4ZOD5LXHGGALGXSB54M \
  | 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: abd4024a1ccb87d5dce630166bc83de30ba696333c49d2cc3cde73b81eba1625

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae0b061e8c052cc86473157af6ba5d2f95c5ee3683c0d1e940683c39741e596c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-01-05T06:44:24Z",
    "title_canon_sha256": "3ff7db58d9290eddb596571460b3ad7c7c95fc3233e0d723a2c88fe7e81aa23f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.01477",
    "kind": "arxiv",
    "version": 1
  }
}