Pith Number

pith:MTK3NB5N

pith:2024:MTK3NB5NFYNKGB6RJL4H5432ZF

not attested not anchored not stored refs pending

A Short Proof of Knuth's Old Sum

Kunle Adegoke

arxiv:2412.00040 v2 · 2024-11-22 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MTK3NB5NFYNKGB6RJL4H5432ZF}

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	2026-07-05T11:17:38.414302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64d5b687ad2e1aa307d14af87ef37ac9446c38aa12755458a32ebb57f5e1ed8c

Aliases

arxiv: 2412.00040 · arxiv_version: 2412.00040v2 · doi: 10.48550/arxiv.2412.00040 · pith_short_12: MTK3NB5NFYNK · pith_short_16: MTK3NB5NFYNKGB6R · pith_short_8: MTK3NB5N

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/MTK3NB5NFYNKGB6RJL4H5432ZF \
  | 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: 64d5b687ad2e1aa307d14af87ef37ac9446c38aa12755458a32ebb57f5e1ed8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f09daf2178012c536c7fe45b32fe0ead474e3074bd95b621a332975bc7a88edd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2024-11-22T11:44:02Z",
    "title_canon_sha256": "d94c98e2e95c0df5fa036adfba85b80f888aa4b9683730098c08f9e8997e8cff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.00040",
    "kind": "arxiv",
    "version": 2
  }
}