Pith Number

pith:JMDZIJB6

pith:2011:JMDZIJB6IVDPXPWLXLKJW7HNPW

not attested not anchored not stored refs pending

Exponential sums with coefficients of certain Dirichlet series

Stephan Baier

arxiv:1108.2715 v2 · 2011-08-12 · 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{JMDZIJB6IVDPXPWLXLKJW7HNPW}

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	2026-05-18T04:13:38.753792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b0794243e4546fbbecbbad49b7ced7d90a6b4ff3cbcbb7a6136d0e1c4b2c23c

Aliases

arxiv: 1108.2715 · arxiv_version: 1108.2715v2 · doi: 10.48550/arxiv.1108.2715 · pith_short_12: JMDZIJB6IVDP · pith_short_16: JMDZIJB6IVDPXPWL · pith_short_8: JMDZIJB6

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/JMDZIJB6IVDPXPWLXLKJW7HNPW \
  | 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: 4b0794243e4546fbbecbbad49b7ced7d90a6b4ff3cbcbb7a6136d0e1c4b2c23c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90c200d5d2a3ac4401dd2bb5917c876dd57d54f9eaf813c3f7fd875bb3e38a55",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-12T20:52:25Z",
    "title_canon_sha256": "8209682baa96a4640f87935ebcbe5e815da04a059729cf295f0126281a704140"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.2715",
    "kind": "arxiv",
    "version": 2
  }
}