Pith Number

pith:GDQC4QQ3

pith:2011:GDQC4QQ3PFP56AZ6P3QC6GDNOQ

not attested not anchored not stored refs pending

Asymptotic Behavior for Critical Patlak-Keller-Segel model and an Repulsive-Attractive Aggregation Equation

Yao Yao

arxiv:1112.4617 v1 · 2011-12-20 · 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{GDQC4QQ3PFP56AZ6P3QC6GDNOQ}

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	2026-05-18T04:05:58.392163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30e02e421b795fdf033e7ee02f186d74081cf1fc41137bceab1c312925684cc9

Aliases

arxiv: 1112.4617 · arxiv_version: 1112.4617v1 · doi: 10.48550/arxiv.1112.4617 · pith_short_12: GDQC4QQ3PFP5 · pith_short_16: GDQC4QQ3PFP56AZ6 · pith_short_8: GDQC4QQ3

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/GDQC4QQ3PFP56AZ6P3QC6GDNOQ \
  | 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: 30e02e421b795fdf033e7ee02f186d74081cf1fc41137bceab1c312925684cc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5140a9db74b8896c62c8390b4162789a38a55a07f910a9c916ada62003cec8fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-20T09:30:52Z",
    "title_canon_sha256": "904bec2019a7a3584aa1842eeb2613316f5bdd1d09679d9ec6ebc58e8409470a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4617",
    "kind": "arxiv",
    "version": 1
  }
}