Pith Number

pith:Z4U7VQTR

pith:2017:Z4U7VQTR4MSWEZDGWICZOBEI25

not attested not anchored not stored refs pending

The cup product of Brooks quasimorphisms

Michelle Bucher, Nicolas Monod

arxiv:1710.02392 v2 · 2017-10-06 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z4U7VQTR4MSWEZDGWICZOBEI25}

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	2026-05-18T00:31:23.517486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf29fac271e325626466b205970488d7437894dc943d53f9087a605646ca5b60

Aliases

arxiv: 1710.02392 · arxiv_version: 1710.02392v2 · doi: 10.48550/arxiv.1710.02392 · pith_short_12: Z4U7VQTR4MSW · pith_short_16: Z4U7VQTR4MSWEZDG · pith_short_8: Z4U7VQTR

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/Z4U7VQTR4MSWEZDGWICZOBEI25 \
  | 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: cf29fac271e325626466b205970488d7437894dc943d53f9087a605646ca5b60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eef39a9ab1e51c1f9252089c726b513123bafc58b6c1c45a65124291fab745a1",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-10-06T13:19:46Z",
    "title_canon_sha256": "b8165eb72812369d447c8f1c130fbbe597ca924044b5b2e7473af41ef6a677f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.02392",
    "kind": "arxiv",
    "version": 2
  }
}