Pith Number

pith:2Y25TXL7

pith:2012:2Y25TXL76BDMHJ4D5MVF377VS3

not attested not anchored not stored refs pending

On Commuting and Semi-commuting Positive Operators

Niushan Gao

arxiv:1208.3495 v1 · 2012-08-16 · 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{2Y25TXL76BDMHJ4D5MVF377VS3}

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	2026-05-18T03:48:35.079584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d635d9dd7ff046c3a783eb2a5dfff596f691ef2744b5baae7d50a4e71a9383f4

Aliases

arxiv: 1208.3495 · arxiv_version: 1208.3495v1 · doi: 10.48550/arxiv.1208.3495 · pith_short_12: 2Y25TXL76BDM · pith_short_16: 2Y25TXL76BDMHJ4D · pith_short_8: 2Y25TXL7

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/2Y25TXL76BDMHJ4D5MVF377VS3 \
  | 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: d635d9dd7ff046c3a783eb2a5dfff596f691ef2744b5baae7d50a4e71a9383f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43c221721275864620f5c6b0d01b8a2ae03fda5aece69f3920ade057113d8265",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-08-16T21:26:40Z",
    "title_canon_sha256": "1b3316a9cdf490e27becb44caf707f8b56a37ee49ac28ae92aa826208d71335c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3495",
    "kind": "arxiv",
    "version": 1
  }
}