Pith Number

pith:EGAQVTC6

pith:2016:EGAQVTC6XRIB3IN5LP573QI3UI

not attested not anchored not stored refs pending

The Liouville function in short intervals [after Matomaki and Radziwill]

Kannan Soundararajan

arxiv:1606.08021 v1 · 2016-06-26 · 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{EGAQVTC6XRIB3IN5LP573QI3UI}

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	2026-05-18T01:11:53.970996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21810acc5ebc501da1bd5bfbfdc11ba232272b17e92ef7f0d908bcbc2a326562

Aliases

arxiv: 1606.08021 · arxiv_version: 1606.08021v1 · doi: 10.48550/arxiv.1606.08021 · pith_short_12: EGAQVTC6XRIB · pith_short_16: EGAQVTC6XRIB3IN5 · pith_short_8: EGAQVTC6

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/EGAQVTC6XRIB3IN5LP573QI3UI \
  | 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: 21810acc5ebc501da1bd5bfbfdc11ba232272b17e92ef7f0d908bcbc2a326562

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc2be28f42369f3a6bd2d3fa6e0b497553f841c87b2be172c549a49863d67de5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-26T10:57:19Z",
    "title_canon_sha256": "55c2e4f7460f17b0ac4a5c8f03df3b9d0a1665b2bdea0abc7ef45a0e53c5a2e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08021",
    "kind": "arxiv",
    "version": 1
  }
}