Pith Number

pith:O64CWC5G

pith:2021:O64CWC5GZP6LFDP5JWWLEKBA7Q

not attested not anchored not stored refs pending

Gaps in N-expansions

C. Kraaikamp, H. Nakada, J. de Jonge

arxiv:2107.06722 v1 · 2021-07-14 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O64CWC5GZP6LFDP5JWWLEKBA7Q}

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	2026-07-05T02:58:00.839217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77b82b0ba6cbfcb28dfd4dacb22820fc169f25b65dedf67707cc41096cd505ee

Aliases

arxiv: 2107.06722 · arxiv_version: 2107.06722v1 · doi: 10.48550/arxiv.2107.06722 · pith_short_12: O64CWC5GZP6L · pith_short_16: O64CWC5GZP6LFDP5 · pith_short_8: O64CWC5G

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/O64CWC5GZP6LFDP5JWWLEKBA7Q \
  | 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: 77b82b0ba6cbfcb28dfd4dacb22820fc169f25b65dedf67707cc41096cd505ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5793175a3c7b773809c9547e6c42ca8ba538d13c25947649a46182fcb43fb4c",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-07-14T14:13:12Z",
    "title_canon_sha256": "441104d982afa082d07cceefdce2024a3cb16547df1faa64b1e5f6278c5a321a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.06722",
    "kind": "arxiv",
    "version": 1
  }
}