Pith Number

pith:QBZ27SQM

pith:2019:QBZ27SQMXLA7V7CMSLT2PHK33Z

not attested not anchored not stored refs pending

Phase transitions and bump solutions of the Keller-Segel model with volume exclusion

Jose A. Carrillo, Lu Zhang, Qi Wang, Xinfu Chen, Zhian Wang

arxiv:1904.11937 v1 · 2019-04-26 · 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{QBZ27SQMXLA7V7CMSLT2PHK33Z}

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	2026-05-17T23:47:40.576164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8073afca0cbac1fafc4c92e7a79d5bde5a46dbd4fbb88fbea096b01b74ff931b

Aliases

arxiv: 1904.11937 · arxiv_version: 1904.11937v1 · doi: 10.48550/arxiv.1904.11937 · pith_short_12: QBZ27SQMXLA7 · pith_short_16: QBZ27SQMXLA7V7CM · pith_short_8: QBZ27SQM

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/QBZ27SQMXLA7V7CMSLT2PHK33Z \
  | 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: 8073afca0cbac1fafc4c92e7a79d5bde5a46dbd4fbb88fbea096b01b74ff931b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33a40b3a3537a5a51e39b0b1dca37a248cf21671d2ea86f4f14f798bbe441652",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-04-26T17:17:16Z",
    "title_canon_sha256": "02b8f87fded5a433237fce830c79ac95e4363fef0897f682d082aa59205a11d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.11937",
    "kind": "arxiv",
    "version": 1
  }
}