Pith Number

pith:WI4PZG6U

pith:2018:WI4PZG6UNDYX5S4X5MMYDEEUPM

not attested not anchored not stored refs pending

Second-Order Converses via Reverse Hypercontractivity

Jingbo Liu, Ramon van Handel, Sergio Verd\'u

arxiv:1812.10129 v2 · 2018-12-25 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WI4PZG6UNDYX5S4X5MMYDEEUPM}

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	2026-07-05T00:19:19.123907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b238fc9bd468f17ecb97eb198190947b09d525595f0c7ea67309f69cd503b0e9

Aliases

arxiv: 1812.10129 · arxiv_version: 1812.10129v2 · doi: 10.48550/arxiv.1812.10129 · pith_short_12: WI4PZG6UNDYX · pith_short_16: WI4PZG6UNDYX5S4X · pith_short_8: WI4PZG6U

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/WI4PZG6UNDYX5S4X5MMYDEEUPM \
  | 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: b238fc9bd468f17ecb97eb198190947b09d525595f0c7ea67309f69cd503b0e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d276ee259d24efbf405566982d65fe5035c48650a722b3eca8eed9f79aa7f341",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2018-12-25T16:21:36Z",
    "title_canon_sha256": "8074d952734560b98ff44a68cb7c6fee34f23fb1c4a4e3815c8e7bbe037eb5b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.10129",
    "kind": "arxiv",
    "version": 2
  }
}