Pith Number

pith:TWI3XNDX

pith:2021:TWI3XNDXG7GOSZF4X3QHXA2VXW

not attested not anchored not stored refs pending

Sharpness of phase transition for Voronoi percolation in hyperbolic space

Xinyi Li, Yu Liu

arxiv:2111.07276 v1 · 2021-11-14 · 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{TWI3XNDXG7GOSZF4X3QHXA2VXW}

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	2026-07-05T03:31:38.392109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d91bbb47737cce964bcbee07b8355bd88fc70576bb41ce564f11a73f9a7b28b

Aliases

arxiv: 2111.07276 · arxiv_version: 2111.07276v1 · doi: 10.48550/arxiv.2111.07276 · pith_short_12: TWI3XNDXG7GO · pith_short_16: TWI3XNDXG7GOSZF4 · pith_short_8: TWI3XNDX

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/TWI3XNDXG7GOSZF4X3QHXA2VXW \
  | 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: 9d91bbb47737cce964bcbee07b8355bd88fc70576bb41ce564f11a73f9a7b28b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5b52e612766379a317b3a6d371ee2dde4d3bcd39012ff7e78409b912dd23b2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-11-14T08:20:29Z",
    "title_canon_sha256": "68154565cc44b64140cdcde5023b5fea0da99422711b9f341fc9d95f0eea8d3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.07276",
    "kind": "arxiv",
    "version": 1
  }
}