Pith Number

pith:VVMCXYCO

pith:2009:VVMCXYCOHDOZXZ3ATAPUSDDZEN

not attested not anchored not stored refs pending

Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities

Khristo N. Boyadzhiev

arxiv:0912.5376 v1 · 2009-12-29 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VVMCXYCOHDOZXZ3ATAPUSDDZEN}

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	2026-05-18T01:02:59.696498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad582be04e38dd9be760981f490c79236f56ef01c674d9a222ebb717cc4fe223

Aliases

arxiv: 0912.5376 · arxiv_version: 0912.5376v1 · doi: 10.48550/arxiv.0912.5376 · pith_short_12: VVMCXYCOHDOZ · pith_short_16: VVMCXYCOHDOZXZ3A · pith_short_8: VVMCXYCO

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/VVMCXYCOHDOZXZ3ATAPUSDDZEN \
  | 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: ad582be04e38dd9be760981f490c79236f56ef01c674d9a222ebb717cc4fe223

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e464fadf57feb5b78ec4b876ff08ef03c7200d394325e871084784da8ae71a07",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-12-29T21:45:32Z",
    "title_canon_sha256": "2c9ce80f709f9ff1ecca3bb7ad96563be2be27cf875dd3996345659f30927252"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.5376",
    "kind": "arxiv",
    "version": 1
  }
}