Pith Number

pith:TRJF63FM

pith:2016:TRJF63FMJSXDLFBZMQGTVMNDSU

not attested not anchored not stored refs pending

Optimal quantizers for some absolutely continuous probability measures

Mrinal Kanti Roychowdhury

arxiv:1608.03815 v5 · 2016-08-12 · 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{TRJF63FMJSXDLFBZMQGTVMNDSU}

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	2026-05-18T00:40:46.684759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c525f6cac4cae359439640d3ab1a395246ce51ab0c350514436e8befdc9c7b0

Aliases

arxiv: 1608.03815 · arxiv_version: 1608.03815v5 · doi: 10.48550/arxiv.1608.03815 · pith_short_12: TRJF63FMJSXD · pith_short_16: TRJF63FMJSXDLFBZ · pith_short_8: TRJF63FM

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/TRJF63FMJSXDLFBZMQGTVMNDSU \
  | 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: 9c525f6cac4cae359439640d3ab1a395246ce51ab0c350514436e8befdc9c7b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "191de0cc6ad8df514d638f8e17421def5350a739ae6ab0000e935236127a96d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-08-12T14:57:14Z",
    "title_canon_sha256": "8405ecf36db7ecf5462db740afce28b0d70a0f4cdb632356d326e7ad0c81ade8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.03815",
    "kind": "arxiv",
    "version": 5
  }
}