Pith Number

pith:VYUUIYYD

pith:2025:VYUUIYYDMAJSBZCKRZPLIVKF5D

not attested not anchored not stored refs pending

Mean squares of quadratic twists of the Fourier coefficients of modular forms

Peng Gao, Yuetong Zhao

arxiv:2506.22256 v1 · 2025-06-27 · 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{VYUUIYYDMAJSBZCKRZPLIVKF5D}

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	2026-07-05T11:28:24.333677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae29446303601320e44a8e5eb45545e8c140c0bcaaca520f4e9d7a9b99fdc9cd

Aliases

arxiv: 2506.22256 · arxiv_version: 2506.22256v1 · doi: 10.48550/arxiv.2506.22256 · pith_short_12: VYUUIYYDMAJS · pith_short_16: VYUUIYYDMAJSBZCK · pith_short_8: VYUUIYYD

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/VYUUIYYDMAJSBZCKRZPLIVKF5D \
  | 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: ae29446303601320e44a8e5eb45545e8c140c0bcaaca520f4e9d7a9b99fdc9cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff7f552c0a6c29e51a17783eb06f805885c945d0cf1113e751eeafa08b1553f7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-06-27T14:25:14Z",
    "title_canon_sha256": "f073aeb7f425bd5b4f8b783467eb62bedc07f42615c63c369b0080af960202da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.22256",
    "kind": "arxiv",
    "version": 1
  }
}