Pith Number

pith:CRYC4TGK

pith:2018:CRYC4TGKPRXQH5HK7DV6CXSX5B

not attested not anchored not stored refs pending

Approximate functional equation and upper bounds for the Barnes double zeta-function

Takashi Miyagawa

arxiv:1810.08295 v2 · 2018-10-18 · 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{CRYC4TGKPRXQH5HK7DV6CXSX5B}

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	2026-05-17T23:50:33.681632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14702e4cca7c6f03f4eaf8ebe15e57e849a55af056d219caa531daba5055a8f4

Aliases

arxiv: 1810.08295 · arxiv_version: 1810.08295v2 · doi: 10.48550/arxiv.1810.08295 · pith_short_12: CRYC4TGKPRXQ · pith_short_16: CRYC4TGKPRXQH5HK · pith_short_8: CRYC4TGK

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/CRYC4TGKPRXQH5HK7DV6CXSX5B \
  | 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: 14702e4cca7c6f03f4eaf8ebe15e57e849a55af056d219caa531daba5055a8f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87923506d47fa6ace57387c919229021f54974d1cebd585928ca66a25eeaf951",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-18T22:48:37Z",
    "title_canon_sha256": "02fe48deea4041dca76bfda30c2e8e911f7de13ee1cc3cda148cecb5e90610f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.08295",
    "kind": "arxiv",
    "version": 2
  }
}