Pith Number

pith:ELEFTF7T

pith:2019:ELEFTF7TY6UMQPZ5HS4QNK664K

not attested not anchored not stored refs pending

When do cross-diffusion systems have an entropy structure?

Ansgar J\"ungel, Xiuqing Chen

arxiv:1908.06873 v1 · 2019-08-19 · 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{ELEFTF7TY6UMQPZ5HS4QNK664K}

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	2026-07-04T23:58:20.568472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22c85997f3c7a8c83f3d3cb906abdee2a97821938c3d769390cdb2400cc201bf

Aliases

arxiv: 1908.06873 · arxiv_version: 1908.06873v1 · doi: 10.48550/arxiv.1908.06873 · pith_short_12: ELEFTF7TY6UM · pith_short_16: ELEFTF7TY6UMQPZ5 · pith_short_8: ELEFTF7T

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/ELEFTF7TY6UMQPZ5HS4QNK664K \
  | 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: 22c85997f3c7a8c83f3d3cb906abdee2a97821938c3d769390cdb2400cc201bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16e02dacf07e1e8cb46b6e8f5124116c72c6a929f9c9363037d3bacee74956bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-19T15:14:03Z",
    "title_canon_sha256": "8e2a45ba6a9d4c6805c9c886b6593064bd0026e05a4b6fd82079493f8e89056c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06873",
    "kind": "arxiv",
    "version": 1
  }
}