Pith Number

pith:AJQ5HIUX

pith:2011:AJQ5HIUXYAHLXKFX644WCPH2RK

not attested not anchored not stored refs pending

Sum formulas for double polylogarithms with a shifting parameter and their derivatives

Hirofumi Tsumura, Kohji Matsumoto

arxiv:1110.3493 v1 · 2011-10-16 · 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{AJQ5HIUXYAHLXKFX644WCPH2RK}

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	2026-05-18T02:43:59.491625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0261d3a297c00ebba8b7f739613cfa8aaa0e12136c6bc2a2ab2a4e55d8586559

Aliases

arxiv: 1110.3493 · arxiv_version: 1110.3493v1 · doi: 10.48550/arxiv.1110.3493 · pith_short_12: AJQ5HIUXYAHL · pith_short_16: AJQ5HIUXYAHLXKFX · pith_short_8: AJQ5HIUX

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/AJQ5HIUXYAHLXKFX644WCPH2RK \
  | 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: 0261d3a297c00ebba8b7f739613cfa8aaa0e12136c6bc2a2ab2a4e55d8586559

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "760bb4564a327e0ec6ad61407566eff179082b7d8a2289ad26126078648075a0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-10-16T15:30:52Z",
    "title_canon_sha256": "5dc902b261510e850465b4e7e308bd55cdb4b09f9af9c5dfff83e2a02fee1322"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3493",
    "kind": "arxiv",
    "version": 1
  }
}