Pith Number

pith:2XRHMJDH

pith:2018:2XRHMJDHQFYRAGSKAEMVOL2MVS

not attested not anchored not stored refs pending

Cutoff at the entropic time for random walks on covered expander graphs

Charles Bordenave, Hubert Lacoin

arxiv:1812.06769 v3 · 2018-12-17 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2XRHMJDHQFYRAGSKAEMVOL2MVS}

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

Cutoff for random lifts of weighted graphs

Receipt and verification

First computed	2026-07-05T02:15:20.631306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5e27624678171101a4a0119572f4caca0a5d00552df71d537a62b0cf3088e1e

Aliases

arxiv: 1812.06769 · arxiv_version: 1812.06769v3 · doi: 10.48550/arxiv.1812.06769 · pith_short_12: 2XRHMJDHQFYR · pith_short_16: 2XRHMJDHQFYRAGSK · pith_short_8: 2XRHMJDH

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/2XRHMJDHQFYRAGSKAEMVOL2MVS \
  | 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: d5e27624678171101a4a0119572f4caca0a5d00552df71d537a62b0cf3088e1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0510fe114b1926a9e21a3d28f444582d359f86b65d70d1630f5cfcc76efb8a2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-12-17T13:56:08Z",
    "title_canon_sha256": "42f800ac32c75f5570d569a9f959c7dd01c79402d26eb30c523741b83a09186c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.06769",
    "kind": "arxiv",
    "version": 3
  }
}