Pith Number

pith:XCH7QNEU

pith:2011:XCH7QNEUVGSHT4MTPWRCANU4JV

not attested not anchored not stored refs pending

Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories

Andrew J. Blumberg, Michael A. Mandell

arxiv:1111.4003 v3 · 2011-11-17 · math.KT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XCH7QNEUVGSHT4MTPWRCANU4JV}

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	2026-05-18T02:56:11.865486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b88ff83494a9a479f1937da220369c4d7779bd48f996534edaa7339f38127947

Aliases

arxiv: 1111.4003 · arxiv_version: 1111.4003v3 · doi: 10.48550/arxiv.1111.4003 · pith_short_12: XCH7QNEUVGSH · pith_short_16: XCH7QNEUVGSHT4MT · pith_short_8: XCH7QNEU

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/XCH7QNEUVGSHT4MTPWRCANU4JV \
  | 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: b88ff83494a9a479f1937da220369c4d7779bd48f996534edaa7339f38127947

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32dd6d5e89396328bb4cda0cef32cba4d349e449b987a773181823fd0d474aea",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2011-11-17T01:39:35Z",
    "title_canon_sha256": "3273d2ef02f200980ba16cb60cbc6c92af4ea952df2173a737535119f4e28bee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4003",
    "kind": "arxiv",
    "version": 3
  }
}