Pith Number

pith:7XXI3ZS2

pith:2015:7XXI3ZS2KFVYLL3VPOTOVUUUY6

not attested not anchored not stored refs pending

Visible lattice points in random walks

Javier Cilleruelo, Jos\'e L. Fern\'andez, Pablo Fern\'andez

arxiv:1512.04722 v1 · 2015-12-15 · math.NT · 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{7XXI3ZS2KFVYLL3VPOTOVUUUY6}

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	2026-05-18T01:24:15.753663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdee8de65a516b85af757ba6ead294c792c91462b5c7c13db2d1ba610bfef17b

Aliases

arxiv: 1512.04722 · arxiv_version: 1512.04722v1 · doi: 10.48550/arxiv.1512.04722 · pith_short_12: 7XXI3ZS2KFVY · pith_short_16: 7XXI3ZS2KFVYLL3V · pith_short_8: 7XXI3ZS2

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/7XXI3ZS2KFVYLL3VPOTOVUUUY6 \
  | 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: fdee8de65a516b85af757ba6ead294c792c91462b5c7c13db2d1ba610bfef17b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c2eed8d2eb3284033c24f104b9522b5759af3a41382d13aea605d197a885fad",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-15T11:02:27Z",
    "title_canon_sha256": "865a62a4b32a2834b2d02022c54ec48394097f534a733d73faf81a1ace5c114d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04722",
    "kind": "arxiv",
    "version": 1
  }
}