Pith Number

pith:T7AA5KSR

pith:2023:T7AA5KSR7YN3QFNDCHKL27CVGV

not attested not anchored not stored refs pending

Exponential decay of the volume for Bernoulli percolation: a proof via stochastic comparison

Hugo Vanneuville

arxiv:2304.12110 v3 · 2023-04-24 · 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{T7AA5KSR7YN3QFNDCHKL27CVGV}

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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

Exponential decay for the random connection model using asymptotic transitivity

Receipt and verification

First computed	2026-07-05T09:16:43.955119Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fc00eaa51fe1bb815a311d4bd7c55357b17ca313a23abd38f0c90af313c0e74

Aliases

arxiv: 2304.12110 · arxiv_version: 2304.12110v3 · doi: 10.48550/arxiv.2304.12110 · pith_short_12: T7AA5KSR7YN3 · pith_short_16: T7AA5KSR7YN3QFND · pith_short_8: T7AA5KSR

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/T7AA5KSR7YN3QFNDCHKL27CVGV \
  | 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: 9fc00eaa51fe1bb815a311d4bd7c55357b17ca313a23abd38f0c90af313c0e74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "195a9b27f9a3b73cec2e616a1c129482137dd3a7b637eb542829ecb89300459a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-04-24T14:13:09Z",
    "title_canon_sha256": "6c2e01d3d6d26e56b286c6a1b3a428ef5390a79dbd4192103f5399f49527d31e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.12110",
    "kind": "arxiv",
    "version": 3
  }
}