Pith Number

pith:NTU7KBGI

pith:2009:NTU7KBGI5GCQAVGD247ABZEPHA

not attested not anchored not stored refs pending

Prime chains and Pratt trees

Florian Luca, Kevin Ford, Sergei V. Konyagin

arxiv:0904.0473 v4 · 2009-04-02 · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NTU7KBGI5GCQAVGD247ABZEPHA}

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.

Cited by

1 paper in Pith

Bounded-box reductions in the Subbarao-Warren problem for unitary perfect numbers

Receipt and verification

First computed	2026-05-18T04:34:37.369147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ce9f504c8e9850054c3d73e00e48f383adf967a24b30b98088ccdeee0ad5225

Aliases

arxiv: 0904.0473 · arxiv_version: 0904.0473v4 · doi: 10.48550/arxiv.0904.0473 · pith_short_12: NTU7KBGI5GCQ · pith_short_16: NTU7KBGI5GCQAVGD · pith_short_8: NTU7KBGI

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/NTU7KBGI5GCQAVGD247ABZEPHA \
  | 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: 6ce9f504c8e9850054c3d73e00e48f383adf967a24b30b98088ccdeee0ad5225

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13e512503900397c303fb369c4709587577cf35add7b3cae8b87ecb9809cba0b",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-04-02T21:46:53Z",
    "title_canon_sha256": "4e19c563f49c95b1bfd5f88963e8d924d2e2638c183259aa4e0e5e8f532a680f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.0473",
    "kind": "arxiv",
    "version": 4
  }
}