Pith Number

pith:VBPIOXUS

pith:2013:VBPIOXUSI6R3QWUPYWBAOFJWG7

not attested not anchored not stored refs pending

The Algebra of a q-Analogue of Multiple Harmonic Series

Yoshihiro Takeyama

arxiv:1306.6164 v2 · 2013-06-26 · math.NT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VBPIOXUSI6R3QWUPYWBAOFJWG7}

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	2026-05-18T03:09:33.396796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a85e875e9247a3b85a8fc58207153637eaa1cf3cf70884b38f8b61f33a6c81b5

Aliases

arxiv: 1306.6164 · arxiv_version: 1306.6164v2 · doi: 10.48550/arxiv.1306.6164 · pith_short_12: VBPIOXUSI6R3 · pith_short_16: VBPIOXUSI6R3QWUP · pith_short_8: VBPIOXUS

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/VBPIOXUSI6R3QWUPYWBAOFJWG7 \
  | 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: a85e875e9247a3b85a8fc58207153637eaa1cf3cf70884b38f8b61f33a6c81b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fda3aceeeff1fdca65425cea68cf991fc0477842f8fd18a59e04640da0fad9b",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-06-26T08:43:02Z",
    "title_canon_sha256": "68fd1252d97cc92bfd22c67e1330d14322a93f4d9f5b230529d6b3a46751fa2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.6164",
    "kind": "arxiv",
    "version": 2
  }
}