Pith Number

pith:Y4YKF6HT

pith:2026:Y4YKF6HTMFCPQGRAIPP2OLNORV

not attested not anchored not stored refs pending

Murmurations of quadratic Hecke $L$-functions of the Gaussian field

Liangyi Zhao, Peng Gao

arxiv:2607.20853 v1 · 2026-07-23 · 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{Y4YKF6HTMFCPQGRAIPP2OLNORV}

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	2026-07-24T00:23:38.221088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c730a2f8f36144f81a2043dfa72dae8d5d2ed22a786864099230dd24a36ecba2

Aliases

arxiv: 2607.20853 · arxiv_version: 2607.20853v1 · doi: 10.48550/arxiv.2607.20853 · pith_short_12: Y4YKF6HTMFCP · pith_short_16: Y4YKF6HTMFCPQGRA · pith_short_8: Y4YKF6HT

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/Y4YKF6HTMFCPQGRAIPP2OLNORV \
  | 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: c730a2f8f36144f81a2043dfa72dae8d5d2ed22a786864099230dd24a36ecba2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f72ef855ca0689ee8046d1b6d3ce3549b79d7c692bdbdc8de9e2cced03ab1805",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-23T02:23:53Z",
    "title_canon_sha256": "f920f3c0a0cfa14e7c323095ad728aeded1dc435348361d0e1a031e0610f2350"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20853",
    "kind": "arxiv",
    "version": 1
  }
}