Pith Number

pith:45CV4YWX

pith:2016:45CV4YWXLN3TWG4FBUZ5QWKEM5

not attested not anchored not stored refs pending

Inequalities of Levin-Ste\v{c}kin, Clausing and Chebyshev revisited

Alfred Witkowski

arxiv:1612.05373 v1 · 2016-12-16 · 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{45CV4YWXLN3TWG4FBUZ5QWKEM5}

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	2026-05-18T00:54:51.941310Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7455e62d75b773b1b850d33d8594467502b0f4afe257e0d075a8befc6c453d2

Aliases

arxiv: 1612.05373 · arxiv_version: 1612.05373v1 · doi: 10.48550/arxiv.1612.05373 · pith_short_12: 45CV4YWXLN3T · pith_short_16: 45CV4YWXLN3TWG4F · pith_short_8: 45CV4YWX

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/45CV4YWXLN3TWG4FBUZ5QWKEM5 \
  | 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: e7455e62d75b773b1b850d33d8594467502b0f4afe257e0d075a8befc6c453d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd832c1c13feaa6c8b63be6d3daf35220b9a7be1542b228e8766644686e85a1e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-12-16T05:34:37Z",
    "title_canon_sha256": "75846ce89a7c858added5329cd4663b091aade4e9f19216a0d37ca3db88b12a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05373",
    "kind": "arxiv",
    "version": 1
  }
}