Pith Number

pith:F62NY5XC

pith:2014:F62NY5XCX4Z7AKTKV4Q4XLA6R6

not attested not anchored not stored refs pending

A homological upper bound on critical probabilities for hyperbolic percolation

Gilles Z\'emor, Nicolas Delfosse

arxiv:1408.4031 v2 · 2014-08-18 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F62NY5XCX4Z7AKTKV4Q4XLA6R6}

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	2026-05-18T00:56:36.303391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fb4dc76e2bf33f02a6aaf21cbac1e8fb2e1dbc381adcd6770cb35b2c59212f2

Aliases

arxiv: 1408.4031 · arxiv_version: 1408.4031v2 · doi: 10.48550/arxiv.1408.4031 · pith_short_12: F62NY5XCX4Z7 · pith_short_16: F62NY5XCX4Z7AKTK · pith_short_8: F62NY5XC

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/F62NY5XCX4Z7AKTKV4Q4XLA6R6 \
  | 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: 2fb4dc76e2bf33f02a6aaf21cbac1e8fb2e1dbc381adcd6770cb35b2c59212f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bc1d14ed54678f406236fd5bbc7c7d80acd73d34d106e47c44f607143d1e4b6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-08-18T15:03:39Z",
    "title_canon_sha256": "d20306161f925430857353213805ef649c4229f2c5e2170b993eea4a912ed8a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.4031",
    "kind": "arxiv",
    "version": 2
  }
}