Pith Number

pith:I7B2IB7R

pith:2021:I7B2IB7RYGKY6IEOKC5JCXETDD

not attested not anchored not stored refs pending

The average number of integral points on the congruent number curves

Stephanie Chan

arxiv:2112.01615 v2 · 2021-12-02 · 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{I7B2IB7RYGKY6IEOKC5JCXETDD}

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	2026-07-05T09:06:51.624265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47c3a407f1c1958f208e50ba915c9318e9dea8e60443804e33578ed81a195a75

Aliases

arxiv: 2112.01615 · arxiv_version: 2112.01615v2 · doi: 10.48550/arxiv.2112.01615 · pith_short_12: I7B2IB7RYGKY · pith_short_16: I7B2IB7RYGKY6IEO · pith_short_8: I7B2IB7R

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/I7B2IB7RYGKY6IEOKC5JCXETDD \
  | 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: 47c3a407f1c1958f208e50ba915c9318e9dea8e60443804e33578ed81a195a75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66799340ede50658d3193c877a3f1960513dfc2e83ab272025c372bf1d8b9c35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-12-02T21:46:34Z",
    "title_canon_sha256": "49dcd90daac92bfe9a3db4f30c241ac1859c624266ddb02047af05be9ca94025"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.01615",
    "kind": "arxiv",
    "version": 2
  }
}