Pith Number

pith:TZM56WIT

pith:2026:TZM56WITTNORPEKCAIN3BUGKZ3

not attested not anchored not stored refs pending

Geometric approximation for the number of returns of a transient Markov chain to its origin

Fraser Daly, Seva Shneer

arxiv:2606.05039 v1 · 2026-06-03 · 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{TZM56WITTNORPEKCAIN3BUGKZ3}

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	2026-06-04T01:10:03.535064Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e59df59139b5d179142021bb0d0caced4cecd286d4855f9a52f101c449ee1c0

Aliases

arxiv: 2606.05039 · arxiv_version: 2606.05039v1 · doi: 10.48550/arxiv.2606.05039 · pith_short_12: TZM56WITTNOR · pith_short_16: TZM56WITTNORPEKC · pith_short_8: TZM56WIT

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/TZM56WITTNORPEKCAIN3BUGKZ3 \
  | 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: 9e59df59139b5d179142021bb0d0caced4cecd286d4855f9a52f101c449ee1c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88595c96e9923ff463799baa16bbe6a716d88040dd2cff6124fe9126c4d58bd8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-03T16:03:10Z",
    "title_canon_sha256": "5ce50fe630b34c314575c5b386a382b80c7760ab101adeee704a1ec60d68d5d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05039",
    "kind": "arxiv",
    "version": 1
  }
}