Pith Number

pith:HERHNKMN

pith:2015:HERHNKMN7X5P4VEPZLVHKLXYCH

not attested not anchored not stored refs pending

Matrix Poincar\'e, \Phi-Sobolev inequalities, and quantum ensembles

Hao-Chung Cheng, Min-Hsiu Hsieh

arxiv:1506.06801 v2 · 2015-06-22 · quant-ph · cs.IT · math-ph · math.IT · math.MP · 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{HERHNKMN7X5P4VEPZLVHKLXYCH}

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	2026-05-17T23:47:08.894453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

392276a98dfdfafe548fcaea752ef811ffdd0ea6ab7c2f9f0a1c30680191f601

Aliases

arxiv: 1506.06801 · arxiv_version: 1506.06801v2 · doi: 10.48550/arxiv.1506.06801 · pith_short_12: HERHNKMN7X5P · pith_short_16: HERHNKMN7X5P4VEP · pith_short_8: HERHNKMN

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/HERHNKMN7X5P4VEPZLVHKLXYCH \
  | 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: 392276a98dfdfafe548fcaea752ef811ffdd0ea6ab7c2f9f0a1c30680191f601

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "784f1a626c3e1047bd7c0735faef86461420193a011dbaed1a5e5d461fadf938",
    "cross_cats_sorted": [
      "cs.IT",
      "math-ph",
      "math.IT",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-06-22T21:56:02Z",
    "title_canon_sha256": "a2e08f46888f4838cd234d48804e9cf7868e339e953223f661fa44d6aa544841"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.06801",
    "kind": "arxiv",
    "version": 2
  }
}