Pith Number

pith:6VX5OSWS

pith:2016:6VX5OSWSPJGXE5KFHOHZX774QW

not attested not anchored not stored refs pending

On groups, slow heat kernel decay yields Liouville property and sharp entropy bounds

Tianyi Zheng, Yuval Peres

arxiv:1609.05174 v2 · 2016-09-16 · math.PR · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6VX5OSWSPJGXE5KFHOHZX774QW}

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	2026-05-18T00:42:39.376975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f56fd74ad27a4d7275453b8f9bfffc859750d037bbdad3aefbb3d2ae4186803c

Aliases

arxiv: 1609.05174 · arxiv_version: 1609.05174v2 · doi: 10.48550/arxiv.1609.05174 · pith_short_12: 6VX5OSWSPJGX · pith_short_16: 6VX5OSWSPJGXE5KF · pith_short_8: 6VX5OSWS

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/6VX5OSWSPJGXE5KFHOHZX774QW \
  | 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: f56fd74ad27a4d7275453b8f9bfffc859750d037bbdad3aefbb3d2ae4186803c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73fdddc3e1536d02d100aeca4fd1cb229862775846e64ca38d0170de17d4b1d8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-16T18:57:53Z",
    "title_canon_sha256": "4df39c1df5213a9cede1b81d72befee37823ddf6c95df8f37afb2221040ee2dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05174",
    "kind": "arxiv",
    "version": 2
  }
}