Pith Number

pith:YP4DAW2R

pith:2016:YP4DAW2RZLJQKD4SUN3QFLXXCU

not attested not anchored not stored refs pending

Liouville first passage percolation: geodesic length exponent is strictly larger than 1 at high temperatures

Fuxi Zhang, Jian Ding

arxiv:1610.02766 v2 · 2016-10-10 · 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{YP4DAW2RZLJQKD4SUN3QFLXXCU}

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	2026-05-17T23:51:09.917735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3f8305b51cad3050f92a37702aef715032bf1761ae03ce6a206bc2f39266c38

Aliases

arxiv: 1610.02766 · arxiv_version: 1610.02766v2 · doi: 10.48550/arxiv.1610.02766 · pith_short_12: YP4DAW2RZLJQ · pith_short_16: YP4DAW2RZLJQKD4S · pith_short_8: YP4DAW2R

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/YP4DAW2RZLJQKD4SUN3QFLXXCU \
  | 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: c3f8305b51cad3050f92a37702aef715032bf1761ae03ce6a206bc2f39266c38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "908886533b4c89a666993407461e6026cffe4ed265429a6e3785d29d1a732c2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-10T03:42:54Z",
    "title_canon_sha256": "40ef616ec7debd0764d1bcd05e4f24c31a8ac9fc9122465b2fa529928db6fa2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.02766",
    "kind": "arxiv",
    "version": 2
  }
}