Pith Number

pith:QWPZDGH5

pith:2018:QWPZDGH5QMVFMI7H5K4ZN4EQMM

not attested not anchored not stored refs pending

Ergodicity of the number of infinite geodesics originating from zero

Shuta Nakajima

arxiv:1807.05900 v1 · 2018-07-16 · 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{QWPZDGH5QMVFMI7H5K4ZN4EQMM}

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	2026-05-18T00:10:42.265040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

859f9198fd832a5623e7eab996f0906325d27b31903c89582b60dbf2273c2101

Aliases

arxiv: 1807.05900 · arxiv_version: 1807.05900v1 · doi: 10.48550/arxiv.1807.05900 · pith_short_12: QWPZDGH5QMVF · pith_short_16: QWPZDGH5QMVFMI7H · pith_short_8: QWPZDGH5

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/QWPZDGH5QMVFMI7H5K4ZN4EQMM \
  | 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: 859f9198fd832a5623e7eab996f0906325d27b31903c89582b60dbf2273c2101

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "386e003831a17ca2bb6d0c470c7723833c092b4cbaa5e2a18198f7e3ca92db1a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-07-16T14:54:39Z",
    "title_canon_sha256": "a0b2ced5890fdc422da2c439779d3397fc19c90615aa2ede6f16c6d07dab6d1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.05900",
    "kind": "arxiv",
    "version": 1
  }
}