Pith Number

pith:JSACKNPF

pith:2013:JSACKNPFWNPJUHZFNIRL6UDSZ3

not attested not anchored not stored refs pending

Cross commutators of Rudin's submodules

Arup Chattopadhyay, B. Krishna Das, Jaydeb Sarkar

arxiv:1312.0070 v2 · 2013-11-30 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JSACKNPFWNPJUHZFNIRL6UDSZ3}

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	2026-05-18T03:02:20.162231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c802535e5b35e9a1f256a22bf5072cee2b37473aa36f0022b17f7838d9fcfa0

Aliases

arxiv: 1312.0070 · arxiv_version: 1312.0070v2 · doi: 10.48550/arxiv.1312.0070 · pith_short_12: JSACKNPFWNPJ · pith_short_16: JSACKNPFWNPJUHZF · pith_short_8: JSACKNPF

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/JSACKNPFWNPJUHZFNIRL6UDSZ3 \
  | 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: 4c802535e5b35e9a1f256a22bf5072cee2b37473aa36f0022b17f7838d9fcfa0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9e4276fff5be260fe785c4e00a5c3a3ab593dcce0662c1738299b14772ef370",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-11-30T06:46:09Z",
    "title_canon_sha256": "3f788e9735af30309cfcf4b158cc75f4204e03450905da82fee9f08882406a17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0070",
    "kind": "arxiv",
    "version": 2
  }
}