Pith Number

pith:NM5M4F7O

pith:2024:NM5M4F7OXPUEIV4647WUAH24DT

not attested not anchored not stored refs pending

On the Within-perfect Numbers

Chung-Hang Kwan, Steven J. Miller

arxiv:2406.06892 v2 · 2024-06-11 · 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{NM5M4F7OXPUEIV4647WUAH24DT}

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	2026-07-05T09:04:57.732901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b3ace17eebbe844579ee7ed401f5c1cf3cf4bdc9de06c4f488ec19daa622664

Aliases

arxiv: 2406.06892 · arxiv_version: 2406.06892v2 · doi: 10.48550/arxiv.2406.06892 · pith_short_12: NM5M4F7OXPUE · pith_short_16: NM5M4F7OXPUEIV46 · pith_short_8: NM5M4F7O

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/NM5M4F7OXPUEIV4647WUAH24DT \
  | 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: 6b3ace17eebbe844579ee7ed401f5c1cf3cf4bdc9de06c4f488ec19daa622664

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88aa08e6f2dc6655d43938644f7292ec6d337988aa4b0e2a5be63e12d37e3f7d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-06-11T02:13:48Z",
    "title_canon_sha256": "e554e0b67c795ddbaf80500041f2e659a3ed192a5ef9e5974fff3de17561ea36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2406.06892",
    "kind": "arxiv",
    "version": 2
  }
}