Pith Number

pith:7TZHKKXU

pith:2025:7TZHKKXUUKIWDCMTQ64N62RB5S

not attested not anchored not stored refs pending

First Moment of Quadratic Hecke $L$-Functions with Lower Order Term

Liangyi Zhao, Peng Gao

arxiv:2512.22509 v2 · 2025-12-27 · 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{7TZHKKXUUKIWDCMTQ64N62RB5S}

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	2026-06-23T01:11:59.762633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcf2752af4a29161899387b8df6a21ec9cfe4874bdc4081186ddf9dd573ac47d

Aliases

arxiv: 2512.22509 · arxiv_version: 2512.22509v2 · doi: 10.48550/arxiv.2512.22509 · pith_short_12: 7TZHKKXUUKIW · pith_short_16: 7TZHKKXUUKIWDCMT · pith_short_8: 7TZHKKXU

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/7TZHKKXUUKIWDCMTQ64N62RB5S \
  | 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: fcf2752af4a29161899387b8df6a21ec9cfe4874bdc4081186ddf9dd573ac47d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43d21c64833e9bdbf398d11ea29e0f50a483634972154b09d766a06afa79fabe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-12-27T07:52:18Z",
    "title_canon_sha256": "5e27e7165871ebddd3c010f5e8b9ed55c74724ea16d97c3b86c44f36e729cf0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.22509",
    "kind": "arxiv",
    "version": 2
  }
}