Pith Number

pith:QAU7VI4X

pith:2025:QAU7VI4XVTJGVF2YOMGQJKRSYR

not attested not anchored not stored refs pending

P\'olya's conjecture up to $\epsilon$-loss and quantitative estimates for the remainder of Weyl's law

Fanghua Lin, Renjin Jiang

arxiv:2507.04307 v4 · 2025-07-06 · math.SP · math-ph · math.AP · math.CA · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QAU7VI4XVTJGVF2YOMGQJKRSYR}

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	2026-05-28T02:04:41.705758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8029faa397acd26a9758730d04aa32c471b90769e77d41a188c31d9483b42b37

Aliases

arxiv: 2507.04307 · arxiv_version: 2507.04307v4 · doi: 10.48550/arxiv.2507.04307 · pith_short_12: QAU7VI4XVTJG · pith_short_16: QAU7VI4XVTJGVF2Y · pith_short_8: QAU7VI4X

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/QAU7VI4XVTJGVF2YOMGQJKRSYR \
  | 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: 8029faa397acd26a9758730d04aa32c471b90769e77d41a188c31d9483b42b37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c73194b789350fd323092a701bccc4ee0f16ae562245ae1d3d56498cf05a093",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.CA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2025-07-06T09:18:20Z",
    "title_canon_sha256": "ebbea08794cf4a939d2e563cefa5badfa05e6ebd200aefd4dd540a3aba9da2f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.04307",
    "kind": "arxiv",
    "version": 4
  }
}