Pith Number

pith:FQPANQOY

pith:2015:FQPANQOYIUAYBHCYUZC7X5O6L4

not attested not anchored not stored refs pending

Matrix inequalities for the difference between arithmetic mean and harmonic mean

Junliang Wu, Wenshi Liao

arxiv:1501.04823 v1 · 2015-01-20 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FQPANQOYIUAYBHCYUZC7X5O6L4}

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	2026-05-18T02:29:02.202875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c1e06c1d84501809c58a645fbf5de5f050fc071d5f52e62a2d70f83f6b05683

Aliases

arxiv: 1501.04823 · arxiv_version: 1501.04823v1 · doi: 10.48550/arxiv.1501.04823 · pith_short_12: FQPANQOYIUAY · pith_short_16: FQPANQOYIUAYBHCY · pith_short_8: FQPANQOY

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/FQPANQOYIUAYBHCYUZC7X5O6L4 \
  | 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: 2c1e06c1d84501809c58a645fbf5de5f050fc071d5f52e62a2d70f83f6b05683

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c1b1d63b2257467627b0d7e428fea8b294454205d76b05cc55cad4fa4a3503d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-01-20T14:37:59Z",
    "title_canon_sha256": "532befb98cc774b71d4eb6cd4a9ada9f2546bf7bce01e894e7f9d81b517cdbe3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.04823",
    "kind": "arxiv",
    "version": 1
  }
}