Pith Number

pith:TKXE7ORJ

pith:2015:TKXE7ORJ6L6CNHAHWXZLDRRGQU

not attested not anchored not stored refs pending

Bivariant $K$-theory with $R/Z$-coefficients and rho classes of unitary representations

Georges Skandalis, Paolo Antonini, Sara Azzali

arxiv:1504.04495 v1 · 2015-04-17 · math.OA · math.KT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TKXE7ORJ6L6CNHAHWXZLDRRGQU}

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	2026-05-18T02:18:32.244609Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9aae4fba29f2fc269c07b5f2b1c6268504712c56a2ab1ec8e7b82694db1be02d

Aliases

arxiv: 1504.04495 · arxiv_version: 1504.04495v1 · doi: 10.48550/arxiv.1504.04495 · pith_short_12: TKXE7ORJ6L6C · pith_short_16: TKXE7ORJ6L6CNHAH · pith_short_8: TKXE7ORJ

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/TKXE7ORJ6L6CNHAHWXZLDRRGQU \
  | 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: 9aae4fba29f2fc269c07b5f2b1c6268504712c56a2ab1ec8e7b82694db1be02d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f52ee54a2192f2ccf5aa277ca28f55b8d7677fa8991e3f48c965ee3c09b4c638",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-04-17T12:51:33Z",
    "title_canon_sha256": "9e67866ce73cd6158cf3875b58814993e718eb83bd9261b034e83306c032750a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04495",
    "kind": "arxiv",
    "version": 1
  }
}