Pith Number

pith:KPCQYDUR

pith:2019:KPCQYDURMFY7OSWEDEWLQDUCCT

not attested not anchored not stored refs pending

On Patlak-Keller-Segel system for several populations: a gradient flow approach

Debabrata Karmakar, Gershon Wolansky

arxiv:1902.10736 v1 · 2019-02-27 · 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{KPCQYDURMFY7OSWEDEWLQDUCCT}

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	2026-05-17T23:52:29.860209Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53c50c0e916171f74ac4192cb80e8214e9a2431065906ac30340ee36a3b36f45

Aliases

arxiv: 1902.10736 · arxiv_version: 1902.10736v1 · doi: 10.48550/arxiv.1902.10736 · pith_short_12: KPCQYDURMFY7 · pith_short_16: KPCQYDURMFY7OSWE · pith_short_8: KPCQYDUR

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/KPCQYDURMFY7OSWEDEWLQDUCCT \
  | 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: 53c50c0e916171f74ac4192cb80e8214e9a2431065906ac30340ee36a3b36f45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7b35bb7b0b23d7f811e039aa1bc7cb664db12bc36625daf62313a3e24ae63ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-02-27T19:10:16Z",
    "title_canon_sha256": "1ed22298ea840061ce63b2b2588f7c4507d0e421e720939be234978a7880d169"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.10736",
    "kind": "arxiv",
    "version": 1
  }
}