Pith Number

pith:7UHIX5YS

pith:2016:7UHIX5YS56UPJNTN5UDKN2GD5Z

not attested not anchored not stored refs pending

Morita invariance of unbounded bivariant K-theory

Jens Kaad

arxiv:1612.08405 v1 · 2016-12-26 · math.KT · 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{7UHIX5YS56UPJNTN5UDKN2GD5Z}

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	2026-05-18T00:53:53.135366Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd0e8bf712efa8f4b66ded06a6e8c3ee728101be3d2cccd5b863f7f5ac26b8f0

Aliases

arxiv: 1612.08405 · arxiv_version: 1612.08405v1 · doi: 10.48550/arxiv.1612.08405 · pith_short_12: 7UHIX5YS56UP · pith_short_16: 7UHIX5YS56UPJNTN · pith_short_8: 7UHIX5YS

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/7UHIX5YS56UPJNTN5UDKN2GD5Z \
  | 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: fd0e8bf712efa8f4b66ded06a6e8c3ee728101be3d2cccd5b863f7f5ac26b8f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12a3f1d6fbb592108ae9392ed5f18541b1f7ca9a49fad6e4b0c3120ac0b14947",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2016-12-26T15:40:40Z",
    "title_canon_sha256": "dc43b0639d9895f092c030a5ce7e7bca9bb2610dddbbd6c1d689237afd38f8dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08405",
    "kind": "arxiv",
    "version": 1
  }
}