Pith Number

pith:WFRL7IBS

pith:2011:WFRL7IBSQD4EYYMTT44IYTAFXV

not attested not anchored not stored refs pending

Spectral flow and the unbounded Kasparov product

Jens Kaad, Matthias Lesch

arxiv:1110.1472 v1 · 2011-10-07 · math.OA · math.DG · 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{WFRL7IBSQD4EYYMTT44IYTAFXV}

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	2026-05-18T03:13:43.750510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b162bfa03280f84c61939f388c4c05bd498cb677d852149877eaecaf167104cf

Aliases

arxiv: 1110.1472 · arxiv_version: 1110.1472v1 · doi: 10.48550/arxiv.1110.1472 · pith_short_12: WFRL7IBSQD4E · pith_short_16: WFRL7IBSQD4EYYMT · pith_short_8: WFRL7IBS

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/WFRL7IBSQD4EYYMTT44IYTAFXV \
  | 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: b162bfa03280f84c61939f388c4c05bd498cb677d852149877eaecaf167104cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26fae012a1942352ace03fdc2c37f90ce7e37dc712a1192f8f8e02cdd944b1f6",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-10-07T10:00:43Z",
    "title_canon_sha256": "e39c1280e3aea1714a37c636163cdcc295b210e45ea969691efd2e9514bcac58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1472",
    "kind": "arxiv",
    "version": 1
  }
}