Pith Number

pith:J3ZMV6FH

pith:2011:J3ZMV6FHR7I6MRSTUBTB2H6FKX

not attested not anchored not stored refs pending

Multiple Commutator Formulas

R. Hazrat, Z. Zhang

arxiv:1107.3056 v1 · 2011-07-15 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J3ZMV6FHR7I6MRSTUBTB2H6FKX}

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	2026-05-18T04:18:14.837676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ef2caf8a78fd1e64653a0661d1fc555c53d794b6293cab1dc7bcc704358c322

Aliases

arxiv: 1107.3056 · arxiv_version: 1107.3056v1 · doi: 10.48550/arxiv.1107.3056 · pith_short_12: J3ZMV6FHR7I6 · pith_short_16: J3ZMV6FHR7I6MRST · pith_short_8: J3ZMV6FH

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/J3ZMV6FHR7I6MRSTUBTB2H6FKX \
  | 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: 4ef2caf8a78fd1e64653a0661d1fc555c53d794b6293cab1dc7bcc704358c322

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ed2f0436a362db71cb58310db1b50ff69367cc441ce7d00c01ed2b444449f88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-07-15T12:29:25Z",
    "title_canon_sha256": "1125a325a8c18ee3f5a31c91e7965e65f2f3815ee128e012f6585998446bf75a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3056",
    "kind": "arxiv",
    "version": 1
  }
}