Pith Number

pith:2BUTUOE3

pith:2012:2BUTUOE3IM7AWGZQ3EZGMBKCV7

not attested not anchored not stored refs pending

A Taylor-like Expansion of a Commutator with a Function of Self-Adjoint, Pairwise Commuting Operators

Morten Grud Rasmussen

arxiv:1205.2008 v1 · 2012-01-16 · 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{2BUTUOE3IM7AWGZQ3EZGMBKCV7}

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	2026-05-18T03:39:05.120890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0693a389b433e0b1b30d932660542afd1ad7a2a2556b672b0ec1c151ffecb1e

Aliases

arxiv: 1205.2008 · arxiv_version: 1205.2008v1 · doi: 10.48550/arxiv.1205.2008 · pith_short_12: 2BUTUOE3IM7A · pith_short_16: 2BUTUOE3IM7AWGZQ · pith_short_8: 2BUTUOE3

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/2BUTUOE3IM7AWGZQ3EZGMBKCV7 \
  | 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: d0693a389b433e0b1b30d932660542afd1ad7a2a2556b672b0ec1c151ffecb1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "343368008a90cdaa079a112f37e268023a7f1bab576d70c54ac1ef9e8a77efe7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-01-16T10:34:58Z",
    "title_canon_sha256": "70a6f33ecb5a7789a657926abbca6337a74111de7229c7e80b3f89c4f1752063"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2008",
    "kind": "arxiv",
    "version": 1
  }
}