Pith Number

pith:KHLV3W6S

pith:2016:KHLV3W6SDMCSYMNM3DC3SKPDL4

not attested not anchored not stored refs pending

Li-Yau inequality on virtually Abelian groups

Gabor Lippner, Shuang Liu

arxiv:1610.05227 v1 · 2016-10-17 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KHLV3W6SDMCSYMNM3DC3SKPDL4}

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	2026-05-18T01:02:05.802308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51d75ddbd21b052c31acd8c5b929e35f1e8b9db65de4dca7792246e41d026cdd

Aliases

arxiv: 1610.05227 · arxiv_version: 1610.05227v1 · doi: 10.48550/arxiv.1610.05227 · pith_short_12: KHLV3W6SDMCS · pith_short_16: KHLV3W6SDMCSYMNM · pith_short_8: KHLV3W6S

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/KHLV3W6SDMCSYMNM3DC3SKPDL4 \
  | 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: 51d75ddbd21b052c31acd8c5b929e35f1e8b9db65de4dca7792246e41d026cdd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebd48cfbcc5c7727a70b45224cf50ce9f56b15d2fe3e78c843acace048032a17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-10-17T17:47:27Z",
    "title_canon_sha256": "342234796820521770916255b72f94a82d7df33c84f37daebce8b5b928722d3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05227",
    "kind": "arxiv",
    "version": 1
  }
}