Pith Number

pith:7YYNROFD

pith:2013:7YYNROFDAHDERWISLPG3ZHL74G

not attested not anchored not stored refs pending

Doubly commuting submodules of the Hardy module over polydiscs

Amol Sasane, Brett D. Wick, Jaydeb Sarkar

arxiv:1302.5312 v3 · 2013-02-21 · math.FA · math.CV · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7YYNROFDAHDERWISLPG3ZHL74G}

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	2026-05-18T03:12:34.964663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe30d8b8a301c648d9125bcdbc9d7fe1a2addb898d599ed5792eb042852429ca

Aliases

arxiv: 1302.5312 · arxiv_version: 1302.5312v3 · doi: 10.48550/arxiv.1302.5312 · pith_short_12: 7YYNROFDAHDE · pith_short_16: 7YYNROFDAHDERWIS · pith_short_8: 7YYNROFD

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/7YYNROFDAHDERWISLPG3ZHL74G \
  | 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: fe30d8b8a301c648d9125bcdbc9d7fe1a2addb898d599ed5792eb042852429ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ff480f851daa767cd0029b4371f5e5d4b87b3bfbaa8c0f9a7a81aa0fe53c0fc",
    "cross_cats_sorted": [
      "math.CV",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-02-21T15:43:57Z",
    "title_canon_sha256": "752d495d21faf64b27a0f9ef0800ec4027240767409e2f1d2b9c114addcbd2fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5312",
    "kind": "arxiv",
    "version": 3
  }
}