Pith Number

pith:VWX4HYPD

pith:2011:VWX4HYPDY7GUKTIWQ4P4P6TWZP

not attested not anchored not stored refs pending

Morita base change in Hopf-cyclic (co)homology

Laiachi El Kaoutit, Niels Kowalzig

arxiv:1111.3890 v2 · 2011-11-16 · math.QA · 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{VWX4HYPDY7GUKTIWQ4P4P6TWZP}

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	2026-05-18T01:59:32.210895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adafc3e1e3c7cd454d16871fc7fa76cbe597c2525c30aad0c9341ebcf4f17a7a

Aliases

arxiv: 1111.3890 · arxiv_version: 1111.3890v2 · doi: 10.48550/arxiv.1111.3890 · pith_short_12: VWX4HYPDY7GU · pith_short_16: VWX4HYPDY7GUKTIW · pith_short_8: VWX4HYPD

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/VWX4HYPDY7GUKTIWQ4P4P6TWZP \
  | 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: adafc3e1e3c7cd454d16871fc7fa76cbe597c2525c30aad0c9341ebcf4f17a7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f9381b82c488d62ca3bd791cb96d698b126a3d301b508d817231a38e3ac10ca",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2011-11-16T17:57:04Z",
    "title_canon_sha256": "19ff5a96d1d770db0f452d9bc20d401867c9a2e2fbe000b47367bd7e35be2648"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3890",
    "kind": "arxiv",
    "version": 2
  }
}