Pith Number

pith:HJER44UU

pith:2013:HJER44UUFELQJNF4KSMYZRRX5W

not attested not anchored not stored refs pending

The Quantum Variance of the Modular Surface

Appendix by Michael Woodbury, Peng Zhao, Peter Sarnak

arxiv:1303.6972 v3 · 2013-03-27 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HJER44UUFELQJNF4KSMYZRRX5W}

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	2026-05-18T00:23:46.365427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a491e7294291704b4bc54998cc637edb35f1d4fd5964d4c42fe93cbcedadbc1

Aliases

arxiv: 1303.6972 · arxiv_version: 1303.6972v3 · doi: 10.48550/arxiv.1303.6972 · pith_short_12: HJER44UUFELQ · pith_short_16: HJER44UUFELQJNF4 · pith_short_8: HJER44UU

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/HJER44UUFELQJNF4KSMYZRRX5W \
  | 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: 3a491e7294291704b4bc54998cc637edb35f1d4fd5964d4c42fe93cbcedadbc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25b8f2b8ed81d8f4eed4950e759247042eaa387c6bf5082020085e45763f4da3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-03-27T20:10:32Z",
    "title_canon_sha256": "0ddf53f80ce5348be072d8a07c51fdf6a9bd0279825399761ea609a91d1e0558"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.6972",
    "kind": "arxiv",
    "version": 3
  }
}