Pith Number

pith:PIVIRA5G

pith:2015:PIVIRA5GRUVRR5XBS3AWSAKHKT

not attested not anchored not stored refs pending

New Congruences on Multiple Harmonic Sums and Bernoulli Numbers

Liuquan Wang

arxiv:1504.03227 v4 · 2015-04-13 · 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{PIVIRA5GRUVRR5XBS3AWSAKHKT}

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	2026-05-18T01:21:47.462695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a2a8883a68d2b18f6e196c169014754ec23147981ea9e93305664d22a008b39

Aliases

arxiv: 1504.03227 · arxiv_version: 1504.03227v4 · doi: 10.48550/arxiv.1504.03227 · pith_short_12: PIVIRA5GRUVR · pith_short_16: PIVIRA5GRUVRR5XB · pith_short_8: PIVIRA5G

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/PIVIRA5GRUVRR5XBS3AWSAKHKT \
  | 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: 7a2a8883a68d2b18f6e196c169014754ec23147981ea9e93305664d22a008b39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ece822046272d4361697851a1e3d5987d68c4703e8617d3090b2077a3c257240",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-04-13T15:49:16Z",
    "title_canon_sha256": "39f868b7ba09bcca9e13b2bcac762c7cd8d6afa878f35630918c466c3eb8355d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03227",
    "kind": "arxiv",
    "version": 4
  }
}