Pith Number

pith:U2W7FE3Y

pith:2016:U2W7FE3YRYMQWX5EH4BBDYJ6VM

not attested not anchored not stored refs pending

Sharpness of the phase transition for continuum percolation in R^2

Augusto Teixeira, Daniel Ahlberg, Vincent Tassion

arxiv:1605.05926 v1 · 2016-05-19 · 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{U2W7FE3YRYMQWX5EH4BBDYJ6VM}

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	2026-05-18T01:14:27.979298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6adf293788e190b5fa43f0211e13eab330dd9052f5e679f03b900a68c6acc4e

Aliases

arxiv: 1605.05926 · arxiv_version: 1605.05926v1 · doi: 10.48550/arxiv.1605.05926 · pith_short_12: U2W7FE3YRYMQ · pith_short_16: U2W7FE3YRYMQWX5E · pith_short_8: U2W7FE3Y

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/U2W7FE3YRYMQWX5EH4BBDYJ6VM \
  | 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: a6adf293788e190b5fa43f0211e13eab330dd9052f5e679f03b900a68c6acc4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06548a101e76304b1a22805beec6b30f2ecdbc964194378e703880fa4b4bbf63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-05-19T12:53:48Z",
    "title_canon_sha256": "1d12258c8636a3783e12d521a63d591017a8b225468902452043e9f9d4083bd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.05926",
    "kind": "arxiv",
    "version": 1
  }
}