Pith Number

pith:ZRCSZJM2

pith:2024:ZRCSZJM2XRYSDSQAHKFYQ3OQRB

not attested not anchored not stored refs pending

The Keller-Segel model with mass critical exponent

Shen Bian, Yichen Zou

arxiv:2412.12586 v1 · 2024-12-17 · 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{ZRCSZJM2XRYSDSQAHKFYQ3OQRB}

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	2026-07-05T09:50:17.494068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc452ca59abc7121ca003a8b886dd0885729809ca3df862184b31bba36a9f367

Aliases

arxiv: 2412.12586 · arxiv_version: 2412.12586v1 · doi: 10.48550/arxiv.2412.12586 · pith_short_12: ZRCSZJM2XRYS · pith_short_16: ZRCSZJM2XRYSDSQA · pith_short_8: ZRCSZJM2

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/ZRCSZJM2XRYSDSQAHKFYQ3OQRB \
  | 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: cc452ca59abc7121ca003a8b886dd0885729809ca3df862184b31bba36a9f367

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efc265a0ab463396a54062f6329fc9b1d68a7bf49aa16913f635c826125a07bf",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-17T06:41:40Z",
    "title_canon_sha256": "0e30df7e4f9b72a51e11483e46050f20d13170131656a144149befafb5a03075"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.12586",
    "kind": "arxiv",
    "version": 1
  }
}