Pith Number

pith:W6Q7355O

pith:2011:W6Q7355ODPNI3ZCAMEBPSRSYP2

not attested not anchored not stored refs pending

A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases

Alexander Fribergh, Gerard Ben Arous, Vladas Sidoravicius

arxiv:1111.5865 v1 · 2011-11-24 · 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{W6Q7355ODPNI3ZCAMEBPSRSYP2}

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	2026-05-18T04:07:42.102662Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7a1fdf7ae1bda8de4406102f946587e8fd7305fa727a3343048717918de66ac

Aliases

arxiv: 1111.5865 · arxiv_version: 1111.5865v1 · doi: 10.48550/arxiv.1111.5865 · pith_short_12: W6Q7355ODPNI · pith_short_16: W6Q7355ODPNI3ZCA · pith_short_8: W6Q7355O

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/W6Q7355ODPNI3ZCAMEBPSRSYP2 \
  | 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: b7a1fdf7ae1bda8de4406102f946587e8fd7305fa727a3343048717918de66ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "411c9215d304db5204c0aef76bccd17f762496305c5b80b11c00768ae9c1e6ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-24T22:33:35Z",
    "title_canon_sha256": "a234b2c0dc3350eee1a368ceffb473297fc50b98d0044bdcbaf029141f7b9e8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5865",
    "kind": "arxiv",
    "version": 1
  }
}