Pith Number

pith:MANHG57P

pith:2018:MANHG57P33KYEHLJMTLNIDC2QC

not attested not anchored not stored refs pending

Weighted sum formula for multiple harmonic sums modulo primes

Hideki Murahara, Minoru Hirose, Shingo Saito

arxiv:1808.00844 v1 · 2018-08-02 · 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{MANHG57P33KYEHLJMTLNIDC2QC}

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	2026-05-18T00:09:01.229096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

601a7377efded5821d6964d6d40c5a80a815313b9c00a1360fa5e07c01e1dc6d

Aliases

arxiv: 1808.00844 · arxiv_version: 1808.00844v1 · doi: 10.48550/arxiv.1808.00844 · pith_short_12: MANHG57P33KY · pith_short_16: MANHG57P33KYEHLJ · pith_short_8: MANHG57P

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/MANHG57P33KYEHLJMTLNIDC2QC \
  | 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: 601a7377efded5821d6964d6d40c5a80a815313b9c00a1360fa5e07c01e1dc6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a5c79890f175ffb18e3e9c42689828a1f0abab3eb72bcd102916e81813ac15b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-08-02T14:58:05Z",
    "title_canon_sha256": "be8a0d0f1f7cbd0b1ab335c0eef63db7f867b993b41c4b6ae703fc8391a918ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.00844",
    "kind": "arxiv",
    "version": 1
  }
}