Pith Number

pith:VURCTGI6

pith:2011:VURCTGI6Y3YS5XI6AZMUVI2QLI

not attested not anchored not stored refs pending

Cubic Harmonics and Bernoulli Numbers

Katsunori Iwasaki

arxiv:1110.5540 v1 · 2011-10-25 · 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{VURCTGI6Y3YS5XI6AZMUVI2QLI}

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	2026-05-18T04:10:22.676920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad2229991ec6f12edd1e06594aa3505a3347baa7d61585eca8abfc2b1d33cd63

Aliases

arxiv: 1110.5540 · arxiv_version: 1110.5540v1 · doi: 10.48550/arxiv.1110.5540 · pith_short_12: VURCTGI6Y3YS · pith_short_16: VURCTGI6Y3YS5XI6 · pith_short_8: VURCTGI6

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/VURCTGI6Y3YS5XI6AZMUVI2QLI \
  | 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: ad2229991ec6f12edd1e06594aa3505a3347baa7d61585eca8abfc2b1d33cd63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75317b87cde409a840f1f08edcd4bb62b5f5da3a10440863427a5b7b5708fe01",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-25T15:40:37Z",
    "title_canon_sha256": "2c94f88b9cdcd004b1f277f61755d804a2969e7e45e633a89f4711e5508eaf2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5540",
    "kind": "arxiv",
    "version": 1
  }
}