Pith Number

pith:NYAL66QM

pith:2025:NYAL66QM3KGHWBKYDWWZXMRXLK

not attested not anchored not stored refs pending

One-level density of zeros of $\Gamma_1(q)$ $L$-functions

Arijit Paul

arxiv:2512.20066 v2 · 2025-12-23 · 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{NYAL66QM3KGHWBKYDWWZXMRXLK}

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	2026-05-21T01:05:13.988851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e00bf7a0cda8c7b05581dad9bb2375a95f0e5db153d7475266db47ad731e5db

Aliases

arxiv: 2512.20066 · arxiv_version: 2512.20066v2 · doi: 10.48550/arxiv.2512.20066 · pith_short_12: NYAL66QM3KGH · pith_short_16: NYAL66QM3KGHWBKY · pith_short_8: NYAL66QM

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/NYAL66QM3KGHWBKYDWWZXMRXLK \
  | 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: 6e00bf7a0cda8c7b05581dad9bb2375a95f0e5db153d7475266db47ad731e5db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb2105567446a9b631fcbe8c45355c65f2608c2946ff04aa1de70bfa4eebac24",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-12-23T05:35:39Z",
    "title_canon_sha256": "545547041fdb5486c988bdaf28d9d4b657c17bddd5e8eb8d22d4134b2056b222"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.20066",
    "kind": "arxiv",
    "version": 2
  }
}