Pith Number

pith:GJ6X76L4

pith:2025:GJ6X76L4HAYOK63JS3CSSITIU6

not attested not anchored not stored refs pending

The Eighth Power Moments of $\Delta(x)$

Junhao Liao, Junjie Liao

arxiv:2507.19528 v1 · 2025-07-21 · 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{GJ6X76L4HAYOK63JS3CSSITIU6}

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	2026-07-05T11:43:35.900113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

327d7ff97c3830e57b6996c5292268a797ff185497a2953a9baa81648d1e9935

Aliases

arxiv: 2507.19528 · arxiv_version: 2507.19528v1 · doi: 10.48550/arxiv.2507.19528 · pith_short_12: GJ6X76L4HAYO · pith_short_16: GJ6X76L4HAYOK63J · pith_short_8: GJ6X76L4

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/GJ6X76L4HAYOK63JS3CSSITIU6 \
  | 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: 327d7ff97c3830e57b6996c5292268a797ff185497a2953a9baa81648d1e9935

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a5880424d0537bceb0f8c81104775a57f5cb802acc3350deeed28f821982ade",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-07-21T04:02:24Z",
    "title_canon_sha256": "16c4dd714f9607d7764c965edcdf87b830768be3b2235035ad88538e165f231a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.19528",
    "kind": "arxiv",
    "version": 1
  }
}