Pith Number

pith:ABIEQNCC

pith:2012:ABIEQNCCQD2MDJ7B5KQRT4GPDN

not attested not anchored not stored refs pending

On the distance between perfect numbers

Philippe Ellia

arxiv:1210.0450 v1 · 2012-10-01 · 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{ABIEQNCCQD2MDJ7B5KQRT4GPDN}

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	2026-05-18T03:44:22.443295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

005048344280f4c1a7e1eaa119f0cf1b5743195a2991cb92ea9f82f2df79f7a6

Aliases

arxiv: 1210.0450 · arxiv_version: 1210.0450v1 · doi: 10.48550/arxiv.1210.0450 · pith_short_12: ABIEQNCCQD2M · pith_short_16: ABIEQNCCQD2MDJ7B · pith_short_8: ABIEQNCC

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/ABIEQNCCQD2MDJ7B5KQRT4GPDN \
  | 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: 005048344280f4c1a7e1eaa119f0cf1b5743195a2991cb92ea9f82f2df79f7a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0870d241fd890ea5686e16d3aa7c6a0b909f13e5bde043a84f29eac62cee5958",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-01T15:55:34Z",
    "title_canon_sha256": "beacb48665cf4646647f03231973208ed1660e3d18ac3e5d95bee481edf189f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0450",
    "kind": "arxiv",
    "version": 1
  }
}