Pith Number

pith:P3PCEFPL

pith:2009:P3PCEFPLSJB5ASFESLDOUMUNH7

not attested not anchored not stored refs pending

Homotopical stable ranks for Banach algebras

Bogdan Nica

arxiv:0911.2945 v2 · 2009-11-16 · 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{P3PCEFPLSJB5ASFESLDOUMUNH7}

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	2026-05-18T04:14:55.236387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ede2215eb9243d048a492c6ea328d3ff704a7d8277655cd87a9b8a1cde79bea

Aliases

arxiv: 0911.2945 · arxiv_version: 0911.2945v2 · doi: 10.48550/arxiv.0911.2945 · pith_short_12: P3PCEFPLSJB5 · pith_short_16: P3PCEFPLSJB5ASFE · pith_short_8: P3PCEFPL

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/P3PCEFPLSJB5ASFESLDOUMUNH7 \
  | 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: 7ede2215eb9243d048a492c6ea328d3ff704a7d8277655cd87a9b8a1cde79bea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f62c774b081f3889b0adff8231aeab3b5f9badefe90acd3766babbde74ddf19f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-11-16T03:49:42Z",
    "title_canon_sha256": "cde4410e81597cec0302eb9c029a3aea9492af136f29ff28df6f86425597f1a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2945",
    "kind": "arxiv",
    "version": 2
  }
}