Pith Number

pith:MD7NTBD3

pith:2009:MD7NTBD3HJ7KP3Q436ZT2JPO6J

not attested not anchored not stored refs pending

The second moment of quadratic twists of modular $L$-functions

K. Soundararajan, Matthew P. Young

arxiv:0907.4747 v1 · 2009-07-27 · 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{MD7NTBD3HJ7KP3Q436ZT2JPO6J}

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	2026-05-18T03:29:51.419211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60fed9847b3a7ea7ee1cdfb33d25eef25e73e585758b353cb5e664d5e17d24f7

Aliases

arxiv: 0907.4747 · arxiv_version: 0907.4747v1 · doi: 10.48550/arxiv.0907.4747 · pith_short_12: MD7NTBD3HJ7K · pith_short_16: MD7NTBD3HJ7KP3Q4 · pith_short_8: MD7NTBD3

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/MD7NTBD3HJ7KP3Q436ZT2JPO6J \
  | 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: 60fed9847b3a7ea7ee1cdfb33d25eef25e73e585758b353cb5e664d5e17d24f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be4b4f1c34da0517e10d9ef5a555856f1de2b6031ea5fcb302ad3093ea21b5c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-07-27T19:53:30Z",
    "title_canon_sha256": "149aa7789179e812746baa0c2296265e8bb5bf6686abb2e0ca73b387d49d552b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.4747",
    "kind": "arxiv",
    "version": 1
  }
}