Pith Number

pith:5GPILIZC

pith:2017:5GPILIZCB4553L26A2YL7MTYFC

not attested not anchored not stored refs pending

A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass

Gabriella Zecca, Nikos I. Kavallaris, Tonia Ricciardi

arxiv:1703.01636 v1 · 2017-03-05 · 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{5GPILIZCB4553L26A2YL7MTYFC}

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	2026-05-18T00:49:30.062858Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e99e85a3220f3bddaf5e06b0bfb278288f0c69fb46ca75e7a80af045db3220dc

Aliases

arxiv: 1703.01636 · arxiv_version: 1703.01636v1 · doi: 10.48550/arxiv.1703.01636 · pith_short_12: 5GPILIZCB455 · pith_short_16: 5GPILIZCB4553L26 · pith_short_8: 5GPILIZC

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/5GPILIZCB4553L26A2YL7MTYFC \
  | 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: e99e85a3220f3bddaf5e06b0bfb278288f0c69fb46ca75e7a80af045db3220dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4de1e462683185b67c7956888f344739e58b5e35c0d14bbbf0342e094afe2243",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-03-05T17:54:21Z",
    "title_canon_sha256": "bea175c41a336a06677ec061af55af431b28a4c4d4f5d4a4e73cfe2dc6158b08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.01636",
    "kind": "arxiv",
    "version": 1
  }
}