Pith Number

pith:4GZCOSZY

pith:2026:4GZCOSZYDCOR6JL24N3QMFQPHY

not attested not anchored not stored refs pending

A Hexagonal Counterexample to Log-Convexity of Fisher Information Along the Heat Flow

Jia Wang, Jiayang Gao, Jiayang Zou, Luyao Fan

arxiv:2605.18081 v1 · 2026-05-18 · 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{4GZCOSZYDCOR6JL24N3QMFQPHY}

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	2026-05-20T00:05:15.045402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1b2274b38189d1f257ae37706160f3e0e99253d5c5c495c01ab613701e1b393

Aliases

arxiv: 2605.18081 · arxiv_version: 2605.18081v1 · doi: 10.48550/arxiv.2605.18081 · pith_short_12: 4GZCOSZYDCOR · pith_short_16: 4GZCOSZYDCOR6JL2 · pith_short_8: 4GZCOSZY

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/4GZCOSZYDCOR6JL24N3QMFQPHY \
  | 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: e1b2274b38189d1f257ae37706160f3e0e99253d5c5c495c01ab613701e1b393

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4aa8bf321065ea4a8d6138cd3e6fa51c76656925c1c5c658de97e91d325bf44f",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-18T08:58:32Z",
    "title_canon_sha256": "3e0bcd29b098dd86082e2e9473926c6c5a14440f6a1b746a08cbc8f76724de78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18081",
    "kind": "arxiv",
    "version": 1
  }
}