Pith Number

pith:7QJVVWUL

pith:2007:7QJVVWUL5WMITS4OUNEEJKTLT4

not attested not anchored not stored refs pending

Some Problems in Number Theory I: The Circle Problem

Julius L. Shaneson, Sylvain E. Cappell

arxiv:math/0702613 v4 · 2007-02-21 · 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{7QJVVWUL5WMITS4OUNEEJKTLT4}

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	2026-05-18T02:42:37.745765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc135ada8bed9889cb8ea34844aa6b9f1e8e83ec9f5256f4a8895fd9c6053114

Aliases

arxiv: math/0702613 · arxiv_version: math/0702613v4 · doi: 10.48550/arxiv.math/0702613 · pith_short_12: 7QJVVWUL5WMI · pith_short_16: 7QJVVWUL5WMITS4O · pith_short_8: 7QJVVWUL

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/7QJVVWUL5WMITS4OUNEEJKTLT4 \
  | 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: fc135ada8bed9889cb8ea34844aa6b9f1e8e83ec9f5256f4a8895fd9c6053114

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce51e40338e75867a06cdfa2214130c74b8553797a154354d74b3354d0ffa75c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-02-21T16:09:05Z",
    "title_canon_sha256": "21b356982614a16193f6a2e35d8ab82325017b7432692fb911c1d8b85cb7c951"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0702613",
    "kind": "arxiv",
    "version": 4
  }
}