Pith Number

pith:CKCOSDT3

pith:2016:CKCOSDT3IBHSBGF2HO6F3O5M5X

not attested not anchored not stored refs pending

Brascamp-Lieb Inequality and Its Reverse: An Information Theoretic View

Jingbo Liu, Paul Cuff, Sergio Verdu, Thomas A. Courtade

arxiv:1605.02818 v1 · 2016-05-10 · 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{CKCOSDT3IBHSBGF2HO6F3O5M5X}

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	2026-05-18T01:15:13.065990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1284e90e7b404f2098ba3bbc5dbbacede69f2d935ca22b1cd20f2127899ef55b

Aliases

arxiv: 1605.02818 · arxiv_version: 1605.02818v1 · doi: 10.48550/arxiv.1605.02818 · pith_short_12: CKCOSDT3IBHS · pith_short_16: CKCOSDT3IBHSBGF2 · pith_short_8: CKCOSDT3

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/CKCOSDT3IBHSBGF2HO6F3O5M5X \
  | 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: 1284e90e7b404f2098ba3bbc5dbbacede69f2d935ca22b1cd20f2127899ef55b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f51ee7a48741421e27fcccff24e411ac901e57f1af21a6129decff0b7226912",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2016-05-10T01:48:17Z",
    "title_canon_sha256": "56919c99d1a2875c618d9abc135ffe712986105eb35594a136dbe03021f024ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.02818",
    "kind": "arxiv",
    "version": 1
  }
}