Pith Number

pith:K3QM33MK

pith:2008:K3QM33MKJPQ7LYF57SWR3FKWPS

not attested not anchored not stored refs pending

Crossed interval groups and operations on the Hochschild cohomology

Martin Markl, Michael Batanin

arxiv:0803.2249 v4 · 2008-03-14 · math.AT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K3QM33MKJPQ7LYF57SWR3FKWPS}

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	2026-05-18T03:48:59.469594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56e0cded8a4be1f5e0bdfcad1d95567cbfa06daaf7f8d5047bf3e404c4bdeb01

Aliases

arxiv: 0803.2249 · arxiv_version: 0803.2249v4 · doi: 10.48550/arxiv.0803.2249 · pith_short_12: K3QM33MKJPQ7 · pith_short_16: K3QM33MKJPQ7LYF5 · pith_short_8: K3QM33MK

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/K3QM33MKJPQ7LYF57SWR3FKWPS \
  | 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: 56e0cded8a4be1f5e0bdfcad1d95567cbfa06daaf7f8d5047bf3e404c4bdeb01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e53b1cac6b801f09ad31bfd67731f19087032f681c018f9bb88a4cf2cdad8d2",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-03-14T21:16:50Z",
    "title_canon_sha256": "ccd8804b42da9b0b82a1e237034707abed512ebd9c35f606ec3c4e6ca4c6fa5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0803.2249",
    "kind": "arxiv",
    "version": 4
  }
}