Pith Number

pith:45H52BCR

pith:2016:45H52BCRLEICKIJQLLG3S4TUWB

not attested not anchored not stored refs pending

A combinatorial refinement of the Kronecker-Hurwitz class number relation

Alexandru A. Popa, Don Zagier

arxiv:1604.02822 v1 · 2016-04-11 · 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{45H52BCRLEICKIJQLLG3S4TUWB}

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	2026-05-18T01:17:22.080503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e74fdd045159102521305acdb97274b06e89251354617c9eee3d3fe67c81bbbe

Aliases

arxiv: 1604.02822 · arxiv_version: 1604.02822v1 · doi: 10.48550/arxiv.1604.02822 · pith_short_12: 45H52BCRLEIC · pith_short_16: 45H52BCRLEICKIJQ · pith_short_8: 45H52BCR

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/45H52BCRLEICKIJQLLG3S4TUWB \
  | 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: e74fdd045159102521305acdb97274b06e89251354617c9eee3d3fe67c81bbbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed62af62f31cd1878ebd167996c021c1c591178893d13a90b16400c272f1b7a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-04-11T08:00:40Z",
    "title_canon_sha256": "4fe07a6458ce48393f9ed32b7764aed619621af95a218d9f8caf7da37a5a100e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.02822",
    "kind": "arxiv",
    "version": 1
  }
}