Pith Number

pith:L2LT6DR2

pith:2023:L2LT6DR2U6IAUM7RNOMWHTYXLO

not attested not anchored not stored refs pending

Bakry-\'Emery calculus for entropic curvature, new diameter estimates, and spectral gaps

Florentin M\"unch, Norbert Peyerimhoff, Shiping Liu, Supanat Kamtue

arxiv:2312.09686 v1 · 2023-12-15 · math.DG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L2LT6DR2U6IAUM7RNOMWHTYXLO}

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.

Cited by

1 paper in Pith

Retention Profiles and KL Contraction Bounds in Finite Markov Chains

Receipt and verification

First computed	2026-07-05T07:24:29.260820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e973f0e3aa7900a33f16b9963cf175b8f39947b09b8c36a9f0fc720bfa19de3

Aliases

arxiv: 2312.09686 · arxiv_version: 2312.09686v1 · doi: 10.48550/arxiv.2312.09686 · pith_short_12: L2LT6DR2U6IA · pith_short_16: L2LT6DR2U6IAUM7R · pith_short_8: L2LT6DR2

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/L2LT6DR2U6IAUM7RNOMWHTYXLO \
  | 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: 5e973f0e3aa7900a33f16b9963cf175b8f39947b09b8c36a9f0fc720bfa19de3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ed42e10d1c562d5e602756d0accd2c10af1f27743e53cbc30a1947e7d6b1d8b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2023-12-15T11:00:05Z",
    "title_canon_sha256": "4f56f44c88b85b5ff7a053e012a439176a021a64139c28c011d7476114c36e68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.09686",
    "kind": "arxiv",
    "version": 1
  }
}