Pith Number

pith:P766EQME

pith:2015:P766EQMEQ7BR7BFWQJZ72LQKZO

not attested not anchored not stored refs pending

On the inequalities of S\'andor mean

Barkat Ali Bhayo

arxiv:1509.01977 v3 · 2015-09-07 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P766EQMEQ7BR7BFWQJZ72LQKZO}

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	2026-05-18T01:33:23.725796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ffde2418487c31f84b68273fd2e0acb9b2d31378ad6b6d79f947eecebe28350

Aliases

arxiv: 1509.01977 · arxiv_version: 1509.01977v3 · doi: 10.48550/arxiv.1509.01977 · pith_short_12: P766EQMEQ7BR · pith_short_16: P766EQMEQ7BR7BFW · pith_short_8: P766EQME

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/P766EQMEQ7BR7BFWQJZ72LQKZO \
  | 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: 7ffde2418487c31f84b68273fd2e0acb9b2d31378ad6b6d79f947eecebe28350

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b47494f83ee043e26ba358cc5e9260fe95e3b6f37b13709dfa0473bdb7442293",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-07T10:31:31Z",
    "title_canon_sha256": "4d3ac10efe16aa653efff94e8d5c194b1ee3cbcd1f03e3ab3b334da721fe4e9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01977",
    "kind": "arxiv",
    "version": 3
  }
}