Pith Number

pith:RRF6MJA6

pith:2015:RRF6MJA6L6MIO5ERL6R45RXKVF

not attested not anchored not stored refs pending

A Mathematical Theory for Clustering in Metric Spaces

Cheng-Shang Chang, Li-Heng Liou, Wanjiun Liao, Yu-Sheng Chen

arxiv:1509.07755 v1 · 2015-09-25 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RRF6MJA6L6MIO5ERL6R45RXKVF}

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	2026-05-18T01:20:22.137283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c4be6241e5f988774915fa3cec6eaa979289d427509e8626d4b2e418fbc94a0

Aliases

arxiv: 1509.07755 · arxiv_version: 1509.07755v1 · doi: 10.48550/arxiv.1509.07755 · pith_short_12: RRF6MJA6L6MI · pith_short_16: RRF6MJA6L6MIO5ER · pith_short_8: RRF6MJA6

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/RRF6MJA6L6MIO5ERL6R45RXKVF \
  | 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: 8c4be6241e5f988774915fa3cec6eaa979289d427509e8626d4b2e418fbc94a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c2e10ebcc04743ffb9faf3eac4942a0a2cd5c033bb40f7353156efeaea4e9d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2015-09-25T15:30:18Z",
    "title_canon_sha256": "5786e5762ace97a242f01cfbfbe64303139b7a2ad50e311d9e88b1a29b2ff338"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07755",
    "kind": "arxiv",
    "version": 1
  }
}