Pith Number

pith:6PSJBELQ

pith:2016:6PSJBELQY2T73UDHHYO77KOJRT

not attested not anchored not stored refs pending

Poincar\'e, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature

Matthias Erbar, Max Fathi

arxiv:1612.00514 v1 · 2016-12-01 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6PSJBELQY2T73UDHHYO77KOJRT}

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	2026-05-18T00:55:59.812695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3e4909170c6a7fdd0673e1dffa9c98ce5d9fce440bf5562baf2658bede0c36e

Aliases

arxiv: 1612.00514 · arxiv_version: 1612.00514v1 · doi: 10.48550/arxiv.1612.00514 · pith_short_12: 6PSJBELQY2T7 · pith_short_16: 6PSJBELQY2T73UDH · pith_short_8: 6PSJBELQ

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/6PSJBELQY2T73UDHHYO77KOJRT \
  | 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: f3e4909170c6a7fdd0673e1dffa9c98ce5d9fce440bf5562baf2658bede0c36e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bbec950b60980b53f2c63bf5dae2f87d190415dac07817bf6814c66db574e29",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-01T23:20:06Z",
    "title_canon_sha256": "a0aac6f721876efe2d23567fbfa1eed7e159f54c3c2f0fda601583f7afc66fa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00514",
    "kind": "arxiv",
    "version": 1
  }
}