Pith Number

pith:MSLGJZFQ

pith:2020:MSLGJZFQNAEUJSZTJT2PFPMGOJ

not attested not anchored not stored refs pending

Lower bounds for moments of zeta and $L$-functions revisited

K. Soundararajan, Winston Heap

arxiv:2007.13154 v1 · 2020-07-26 · 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{MSLGJZFQNAEUJSZTJT2PFPMGOJ}

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	2026-07-05T01:22:07.193977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

649664e4b0680944cb334cf4f2bd86726201bfce10f446711d689f5462a6d9a1

Aliases

arxiv: 2007.13154 · arxiv_version: 2007.13154v1 · doi: 10.48550/arxiv.2007.13154 · pith_short_12: MSLGJZFQNAEU · pith_short_16: MSLGJZFQNAEUJSZT · pith_short_8: MSLGJZFQ

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/MSLGJZFQNAEUJSZTJT2PFPMGOJ \
  | 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: 649664e4b0680944cb334cf4f2bd86726201bfce10f446711d689f5462a6d9a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d22a0fd423b305e6febf2596e30e459c8b09e777db1340cf789644775bf2d62",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-07-26T15:47:30Z",
    "title_canon_sha256": "cc70938b9d3d5b2e9996c5679110679c81ba3aee44028f400d0dd3b619666be7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.13154",
    "kind": "arxiv",
    "version": 1
  }
}