Pith Number

pith:52FIHRPN

pith:2011:52FIHRPNXS2U7WIUD2WWHMDIYY

not attested not anchored not stored refs pending

Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system

Michael Winkler

arxiv:1112.4156 v1 · 2011-12-18 · 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{52FIHRPNXS2U7WIUD2WWHMDIYY}

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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.

Cited by

1 paper in Pith

Refined temporal asymptotics near blow-up points in the planar Keller-Segel system

Receipt and verification

First computed	2026-05-18T04:06:06.929593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee8a83c5edbcb54fd9141ead63b068c62a4877c234f3151a4d5440dcf06bde7c

Aliases

arxiv: 1112.4156 · arxiv_version: 1112.4156v1 · doi: 10.48550/arxiv.1112.4156 · pith_short_12: 52FIHRPNXS2U · pith_short_16: 52FIHRPNXS2U7WIU · pith_short_8: 52FIHRPN

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/52FIHRPNXS2U7WIUD2WWHMDIYY \
  | 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: ee8a83c5edbcb54fd9141ead63b068c62a4877c234f3151a4d5440dcf06bde7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d18584faf9c63a32c31a871ea0e50dd6ae255558d25a9042dce024da09b3e26d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-18T13:42:57Z",
    "title_canon_sha256": "5bd3b9db1399869715fd7954d77c2dfd25ea4c5abca49e27d6d2d66c91cbf477"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4156",
    "kind": "arxiv",
    "version": 1
  }
}