Pith Number

pith:LLFBM7U3

pith:2015:LLFBM7U3R2EZ6TP7QDUVC3RPWZ

not attested not anchored not stored refs pending

Curvature and transport inequalities for Markov chains in discrete spaces

Max Fathi, Yan Shu

arxiv:1509.07160 v1 · 2015-09-23 · math.PR · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LLFBM7U3R2EZ6TP7QDUVC3RPWZ}

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	2026-05-18T01:32:11.219791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5aca167e9b8e899f4dff80e9516e2fb67137d277bf8c5a2539e039de347523fd

Aliases

arxiv: 1509.07160 · arxiv_version: 1509.07160v1 · doi: 10.48550/arxiv.1509.07160 · pith_short_12: LLFBM7U3R2EZ · pith_short_16: LLFBM7U3R2EZ6TP7 · pith_short_8: LLFBM7U3

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/LLFBM7U3R2EZ6TP7QDUVC3RPWZ \
  | 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: 5aca167e9b8e899f4dff80e9516e2fb67137d277bf8c5a2539e039de347523fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb9b681ea907fdc4f5cbe52088dd46c2707c03ddffd9eec6c545aeafc34aa4d0",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-23T21:11:10Z",
    "title_canon_sha256": "79e30cc0f9114895a9ac7868e974199d5ddac01be303a3f01b783663b48c9990"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07160",
    "kind": "arxiv",
    "version": 1
  }
}