Pith Number

pith:TK7K4YJP

pith:2015:TK7K4YJP27LYV3CNTFMQF4FPN4

not attested not anchored not stored refs pending

Notes on twisted equivariant $\mathrm{K}$-theory for $\mathrm{C}^*$-algebras

Yosuke Kubota

arxiv:1511.05312 v3 · 2015-11-17 · math.KT · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TK7K4YJP27LYV3CNTFMQF4FPN4}

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	2026-05-18T01:21:04.144186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9abeae612fd7d78aec4d995902f0af6f2150597296ddc199798c4b06fe2ea00f

Aliases

arxiv: 1511.05312 · arxiv_version: 1511.05312v3 · doi: 10.48550/arxiv.1511.05312 · pith_short_12: TK7K4YJP27LY · pith_short_16: TK7K4YJP27LYV3CN · pith_short_8: TK7K4YJP

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/TK7K4YJP27LYV3CNTFMQF4FPN4 \
  | 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: 9abeae612fd7d78aec4d995902f0af6f2150597296ddc199798c4b06fe2ea00f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "832c485c217270d7dea27dd21ab6d50c8c7b94d40ebf04becacd54daf3ae2fc1",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2015-11-17T08:55:37Z",
    "title_canon_sha256": "a968b0ef6791b1d56176aa0e0babab49d8abfa0040f189fdd9761d77cbd3857a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.05312",
    "kind": "arxiv",
    "version": 3
  }
}