Pith Number

pith:BGCCXEZY

pith:2012:BGCCXEZYYVYLO2D6NPAUJTLPNA

not attested not anchored not stored refs pending

Approximate Double Commutants and Distance Formulas

Don Hadwin, Junhao Shen

arxiv:1210.5285 v1 · 2012-10-18 · math.OA · 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{BGCCXEZYYVYLO2D6NPAUJTLPNA}

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	2026-05-18T03:42:45.615556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09842b9338c570b7687e6bc144cd6f6829802c77985aaa67d3a234881501a263

Aliases

arxiv: 1210.5285 · arxiv_version: 1210.5285v1 · doi: 10.48550/arxiv.1210.5285 · pith_short_12: BGCCXEZYYVYL · pith_short_16: BGCCXEZYYVYLO2D6 · pith_short_8: BGCCXEZY

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/BGCCXEZYYVYLO2D6NPAUJTLPNA \
  | 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: 09842b9338c570b7687e6bc144cd6f6829802c77985aaa67d3a234881501a263

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8c9e393435c697aaac4848cebc26c32a8690ae5ed8421af6b8d82ef96b79145",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-10-18T23:57:53Z",
    "title_canon_sha256": "9cc5a0b11e1032099b41dc74d3a04e645ab377492ea96816802024b957937016"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5285",
    "kind": "arxiv",
    "version": 1
  }
}