Pith Number

pith:ERPBYY6V

pith:2018:ERPBYY6VEA6I5CJ6RRILKQTIQI

not attested not anchored not stored refs pending

Poincar\'e type and spectral gap inequalities with fractional Laplacians on Hamming cube

Alexander Volberg, Dong Li

arxiv:1802.04411 v1 · 2018-02-13 · math.AP · math.CA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ERPBYY6VEA6I5CJ6RRILKQTIQI}

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	2026-05-18T00:23:44.273266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

245e1c63d5203c8e893e8c50b542688211358f5ce2b74bff025c264154c2e06c

Aliases

arxiv: 1802.04411 · arxiv_version: 1802.04411v1 · doi: 10.48550/arxiv.1802.04411 · pith_short_12: ERPBYY6VEA6I · pith_short_16: ERPBYY6VEA6I5CJ6 · pith_short_8: ERPBYY6V

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/ERPBYY6VEA6I5CJ6RRILKQTIQI \
  | 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: 245e1c63d5203c8e893e8c50b542688211358f5ce2b74bff025c264154c2e06c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03b5c5a507b1f035b5736386e4cc83a8462b7bb02e9ac3b28e297b14cf05e93c",
    "cross_cats_sorted": [
      "math.CA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-02-13T00:46:21Z",
    "title_canon_sha256": "09efce7cebf461c632c4065c2de2e9ef31fbceae609e2794fd33b21a33c60e5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.04411",
    "kind": "arxiv",
    "version": 1
  }
}