Pith Number

pith:OSNWJREJ

pith:2018:OSNWJREJBMB7EWXDSOANXWLIY4

not attested not anchored not stored refs pending

Eisenstein series of weight one, $q$-averages of the $0$-logarithm and periods of elliptic curves

Daniel R. Grayson, Dinakar Ramakrishnan

arxiv:1806.04925 v2 · 2018-06-13 · 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{OSNWJREJBMB7EWXDSOANXWLIY4}

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	2026-05-18T00:13:16.911195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

749b64c4890b03f25ae39380dbd968c70060b67634724416ad55aec12e31dfb8

Aliases

arxiv: 1806.04925 · arxiv_version: 1806.04925v2 · doi: 10.48550/arxiv.1806.04925 · pith_short_12: OSNWJREJBMB7 · pith_short_16: OSNWJREJBMB7EWXD · pith_short_8: OSNWJREJ

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/OSNWJREJBMB7EWXDSOANXWLIY4 \
  | 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: 749b64c4890b03f25ae39380dbd968c70060b67634724416ad55aec12e31dfb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4031924848d4c3d1cd3da1b3fd60a76d3b4454d8f0a0f5e26d88662050df6980",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-06-13T10:12:18Z",
    "title_canon_sha256": "80df1b20622b8d1313e0b92790c67c96cd1995a892038a9221ef53469bd2b691"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.04925",
    "kind": "arxiv",
    "version": 2
  }
}