Pith Number

pith:ZHJ4DBNP

pith:2016:ZHJ4DBNPRYWVYCNYLVO6FRYP5X

not attested not anchored not stored refs pending

The Hoffmann-Jorgensen inequality in metric semigroups

Apoorva Khare, Bala Rajaratnam

arxiv:1610.02324 v3 · 2016-10-07 · 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{ZHJ4DBNPRYWVYCNYLVO6FRYP5X}

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	2026-05-18T00:29:31.320537Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9d3c185af8e2d5c09b85d5de2c70fedfb6bb5b60a90cf3bb28922def4db1d23

Aliases

arxiv: 1610.02324 · arxiv_version: 1610.02324v3 · doi: 10.48550/arxiv.1610.02324 · pith_short_12: ZHJ4DBNPRYWV · pith_short_16: ZHJ4DBNPRYWVYCNY · pith_short_8: ZHJ4DBNP

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/ZHJ4DBNPRYWVYCNYLVO6FRYP5X \
  | 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: c9d3c185af8e2d5c09b85d5de2c70fedfb6bb5b60a90cf3bb28922def4db1d23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcbc3481773f56632b3e0fe7f8576690e4138d1d193ae5c472e7bbbd9ac07b31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-07T15:31:10Z",
    "title_canon_sha256": "bf6c26923da207cca14d505dfe456ea7ee991cd5370f7ea0b3fd9899efbdaf55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.02324",
    "kind": "arxiv",
    "version": 3
  }
}