Pith Number

pith:56YJYI5G

pith:2026:56YJYI5GBTUCIVCWP34WC6ZICF

not attested not anchored not stored refs pending

Fine-scale statistics for $\mathbb{Q}^n$

Anish Ghosh, Gaurav Aggarwal, Jens Marklof

arxiv:2606.09591 v1 · 2026-06-08 · math.NT · math.DS · 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{56YJYI5GBTUCIVCWP34WC6ZICF}

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	2026-06-09T02:08:57.780732Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efb09c23a60ce82454567ef9617b281160bd321d4c2909dd3d8603d02422c9f0

Aliases

arxiv: 2606.09591 · arxiv_version: 2606.09591v1 · doi: 10.48550/arxiv.2606.09591 · pith_short_12: 56YJYI5GBTUC · pith_short_16: 56YJYI5GBTUCIVCW · pith_short_8: 56YJYI5G

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/56YJYI5GBTUCIVCWP34WC6ZICF \
  | 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: efb09c23a60ce82454567ef9617b281160bd321d4c2909dd3d8603d02422c9f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d372a0b07a9b3f3af463ac01c13ec7102c5419dbdcffcf31aed86c7a8b5b2cbf",
    "cross_cats_sorted": [
      "math.DS",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-08T15:02:20Z",
    "title_canon_sha256": "5a0f889a98151a92d2be347c7d4aa1f119f3de1d3d92c1c4f10a5044b018e88e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09591",
    "kind": "arxiv",
    "version": 1
  }
}