Pith Number

pith:FVRFBWD3

pith:2021:FVRFBWD3FWQJ3BXIDRRHF5DJQI

not attested not anchored not stored refs pending

Integral representations for local dilogarithm and trilogarithm functions

Masato Kobayashi

arxiv:2108.12543 v2 · 2021-08-28 · 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{FVRFBWD3FWQJ3BXIDRRHF5DJQI}

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	2026-07-05T03:17:33.447750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d6250d87b2da09d86e81c6272f4698211ee34a01051ac65f068be757bc98f66

Aliases

arxiv: 2108.12543 · arxiv_version: 2108.12543v2 · doi: 10.48550/arxiv.2108.12543 · pith_short_12: FVRFBWD3FWQJ · pith_short_16: FVRFBWD3FWQJ3BXI · pith_short_8: FVRFBWD3

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/FVRFBWD3FWQJ3BXIDRRHF5DJQI \
  | 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: 2d6250d87b2da09d86e81c6272f4698211ee34a01051ac65f068be757bc98f66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66012fb281959665c1dae530c4569e211b93beda57d0a3e36ea5f278ec06a439",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-08-28T01:22:41Z",
    "title_canon_sha256": "9da0ff9f4dde4d97579c6b321d24b9393a261a52c8b28e29e5c0f2cb01992dd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.12543",
    "kind": "arxiv",
    "version": 2
  }
}