Pith Number

pith:2ZJVHMKJ

pith:2007:2ZJVHMKJGII3X5THIG4VFSG5MA

not attested not anchored not stored refs pending

Product Systems; a Survey with Commutants in View

Michael Skeide

arxiv:0709.0915 v1 · 2007-09-06 · 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{2ZJVHMKJGII3X5THIG4VFSG5MA}

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	2026-05-18T00:37:06.397392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d65353b1493211bbf66741b952c8dd601307774bc48cb93849158c62c03284ad

Aliases

arxiv: 0709.0915 · arxiv_version: 0709.0915v1 · doi: 10.48550/arxiv.0709.0915 · pith_short_12: 2ZJVHMKJGII3 · pith_short_16: 2ZJVHMKJGII3X5TH · pith_short_8: 2ZJVHMKJ

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/2ZJVHMKJGII3X5THIG4VFSG5MA \
  | 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: d65353b1493211bbf66741b952c8dd601307774bc48cb93849158c62c03284ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cdb370a50cb76aac3eb3bac2af1d53a11795d8ec23ac53896285ecb948e646c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2007-09-06T16:39:52Z",
    "title_canon_sha256": "e26983b88b3a2d408e6f21f0b398444cc4b411ac6383e58670d610aec3431920"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.0915",
    "kind": "arxiv",
    "version": 1
  }
}