Pith Number

pith:CPEX4JNA

pith:2022:CPEX4JNA7TYLUX3FMCDYQ77A2X

not attested not anchored not stored refs pending

Oriented Random Walk on the Heisenberg Group and Percolation

Itai Benjamini, Oded Schramm

arxiv:2202.01519 v1 · 2022-02-03 · 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{CPEX4JNA7TYLUX3FMCDYQ77A2X}

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	2026-07-05T03:53:55.212563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13c97e25a0fcf0ba5f656087887fe0d5ccfad648f9f5607ec6f184ea0ee40e3c

Aliases

arxiv: 2202.01519 · arxiv_version: 2202.01519v1 · doi: 10.48550/arxiv.2202.01519 · pith_short_12: CPEX4JNA7TYL · pith_short_16: CPEX4JNA7TYLUX3F · pith_short_8: CPEX4JNA

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/CPEX4JNA7TYLUX3FMCDYQ77A2X \
  | 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: 13c97e25a0fcf0ba5f656087887fe0d5ccfad648f9f5607ec6f184ea0ee40e3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aaab8e43c4a0eea67618016126aefc4e880cbc74caaa0a5aff18c2945e14b7b9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-02-03T11:00:33Z",
    "title_canon_sha256": "0b59fe902715328a88a94e60a6fbfade202cdf0200feec99ec1ab770ea7cbf8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2202.01519",
    "kind": "arxiv",
    "version": 1
  }
}