Pith Number

pith:VBZAHVTH

pith:2005:VBZAHVTHAPJCINMKQR2EOCJ3SO

not attested not anchored not stored refs pending

Average values of modular L-series via the relative trace formula

Dinakar Ramakrishnan, Jonathan Rogawski

arxiv:math/0510113 v2 · 2005-10-06 · 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{VBZAHVTHAPJCINMKQR2EOCJ3SO}

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	2026-07-04T14:51:10.869722Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a87203d66703d224358a847447093b938f1904edffb639aa9403150b943edec0

Aliases

arxiv: math/0510113 · arxiv_version: math/0510113v2 · doi: 10.48550/arxiv.math/0510113 · pith_short_12: VBZAHVTHAPJC · pith_short_16: VBZAHVTHAPJCINMK · pith_short_8: VBZAHVTH

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/VBZAHVTHAPJCINMKQR2EOCJ3SO \
  | 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: a87203d66703d224358a847447093b938f1904edffb639aa9403150b943edec0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e99e82e8ac1c2f7c50c6dd1513475c078b4b77610e21543f3bebc63b92191ed4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-10-06T07:02:17Z",
    "title_canon_sha256": "523b279dfe6171ae0db0d3f7b6b40edabbc8d4d39e00acbfc0a54ba40c809c7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0510113",
    "kind": "arxiv",
    "version": 2
  }
}