Pith Number

pith:7WHXXSJV

pith:2015:7WHXXSJVR65XCI4TJT6HHVNLGD

not attested not anchored not stored refs pending

Harnack inequalities and Gaussian estimates for random walks on metric measure spaces

Laurent Saloff-Coste, Mathav Murugan

arxiv:1506.07539 v1 · 2015-06-24 · math.PR · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7WHXXSJVR65XCI4TJT6HHVNLGD}

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	2026-05-18T01:38:51.564382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd8f7bc9358fbb7123934cfc73d5ab30e36ad4464cde447952faed2fb81df28b

Aliases

arxiv: 1506.07539 · arxiv_version: 1506.07539v1 · doi: 10.48550/arxiv.1506.07539 · pith_short_12: 7WHXXSJVR65X · pith_short_16: 7WHXXSJVR65XCI4T · pith_short_8: 7WHXXSJV

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/7WHXXSJVR65XCI4TJT6HHVNLGD \
  | 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: fd8f7bc9358fbb7123934cfc73d5ab30e36ad4464cde447952faed2fb81df28b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1958c847a57910b5d7d356409260d9f88feb7763b4fb8037985f04d8003d04fa",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-24T20:04:24Z",
    "title_canon_sha256": "fdd98fdf9872df4d586dfa7fd30f19c1c4809508b9c3329707975a78416096b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.07539",
    "kind": "arxiv",
    "version": 1
  }
}