Pith Number

pith:JCJ5COPF

pith:2026:JCJ5COPFT7RIWZABH7BQHT5LS3

not attested not anchored not stored refs pending

Entropic analogues of Gr\"unbaum's inequality

Lampros Gavalakis, Martin Rapaport, Matthieu Fradelizi

arxiv:2607.23269 v1 · 2026-07-25 · math.PR · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JCJ5COPFT7RIWZABH7BQHT5LS3}

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	2026-07-28T01:22:45.084978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4893d139e59fe28b64013fc303cfab96fe97ec663bd4ca8cbe21d185a9f14df3

Aliases

arxiv: 2607.23269 · arxiv_version: 2607.23269v1 · doi: 10.48550/arxiv.2607.23269 · pith_short_12: JCJ5COPFT7RI · pith_short_16: JCJ5COPFT7RIWZAB · pith_short_8: JCJ5COPF

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/JCJ5COPFT7RIWZABH7BQHT5LS3 \
  | 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: 4893d139e59fe28b64013fc303cfab96fe97ec663bd4ca8cbe21d185a9f14df3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afd343174a4381836dfba9e0c2758a65b9e0c9e1d1044942d27851614daf0048",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-25T16:11:15Z",
    "title_canon_sha256": "2e526a3b5884fa6c53d717cbdeda00be56bd8574cda5fbac8866e0a0d5b3a092"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23269",
    "kind": "arxiv",
    "version": 1
  }
}