Pith Number

pith:3SVYPV2T

pith:2015:3SVYPV2TWBZ4LG3AXBECLH43O2

not attested not anchored not stored refs pending

A congruence involving alternating harmonic sums modulo $p^{\alpha}q^{\beta}$

Tianxin Cai, Zhongyan Shen

arxiv:1503.03154 v1 · 2015-03-11 · 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{3SVYPV2TWBZ4LG3AXBECLH43O2}

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	2026-05-18T02:25:04.208206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcab87d753b073c59b60b848259f9b76a268faec076f2177baa30bd00abf7930

Aliases

arxiv: 1503.03154 · arxiv_version: 1503.03154v1 · doi: 10.48550/arxiv.1503.03154 · pith_short_12: 3SVYPV2TWBZ4 · pith_short_16: 3SVYPV2TWBZ4LG3A · pith_short_8: 3SVYPV2T

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/3SVYPV2TWBZ4LG3AXBECLH43O2 \
  | 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: dcab87d753b073c59b60b848259f9b76a268faec076f2177baa30bd00abf7930

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c80b6c71ed14c3ad357e820d77a21332780558eab81c6c5c7292ab6616fb0f19",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-03-11T02:43:32Z",
    "title_canon_sha256": "d3e2c2cb542e0b189924baf7541842c1cdd9b2d537bd3d23ad0370abbd25b733"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.03154",
    "kind": "arxiv",
    "version": 1
  }
}