Pith Number

pith:XHD2H2AP

pith:2021:XHD2H2APVH4BU7ASOB6MEXXPVN

not attested not anchored not stored refs pending

The space of non-extendable quasimorphisms

Masato Mimura, Mitsuaki Kimura, Morimichi Kawasaki, Shuhei Maruyama, Takahiro Matsushita

arxiv:2107.08571 v5 · 2021-07-19 · math.GR · math.FA · math.GT · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XHD2H2APVH4BU7ASOB6MEXXPVN}

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.

Cited by

1 paper in Pith

Bounded cohomology, quotient extensions, and hierarchical hyperbolicity

Receipt and verification

First computed	2026-07-05T11:06:06.224909Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9c7a3e80fa9f81a7c12707cc25eefab70b513ef43a10063200ad0e27b644025

Aliases

arxiv: 2107.08571 · arxiv_version: 2107.08571v5 · doi: 10.48550/arxiv.2107.08571 · pith_short_12: XHD2H2APVH4B · pith_short_16: XHD2H2APVH4BU7AS · pith_short_8: XHD2H2AP

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/XHD2H2APVH4BU7ASOB6MEXXPVN \
  | 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: b9c7a3e80fa9f81a7c12707cc25eefab70b513ef43a10063200ad0e27b644025

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52c36894c944eecf497ebb86f0a14e462dac0e1da298d511970d4fc06752fc18",
    "cross_cats_sorted": [
      "math.FA",
      "math.GT",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-07-19T01:17:34Z",
    "title_canon_sha256": "777ec27f8fb2fce5b85d39f20ee163629792cf7685410440a887f4cd2fc84cd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.08571",
    "kind": "arxiv",
    "version": 5
  }
}