Pith Number

pith:FS2NF5WM

pith:2020:FS2NF5WMVDSYD4EDRA3KGHP2XP

not attested not anchored not stored refs pending

Infinite sums of Brooks quasimorphisms and cup products in bounded cohomology

Francesco Fournier-Facio

arxiv:2002.10323 v1 · 2020-02-24 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FS2NF5WMVDSYD4EDRA3KGHP2XP}

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 of groups acting on trees with almost prescribed local actions

Receipt and verification

First computed	2026-07-05T02:52:12.207388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cb4d2f6cca8e581f0838836a31dfabbc6a55b2bf0c0d29b7b0a878078fc5931

Aliases

arxiv: 2002.10323 · arxiv_version: 2002.10323v1 · doi: 10.48550/arxiv.2002.10323 · pith_short_12: FS2NF5WMVDSY · pith_short_16: FS2NF5WMVDSYD4ED · pith_short_8: FS2NF5WM

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/FS2NF5WMVDSYD4EDRA3KGHP2XP \
  | 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: 2cb4d2f6cca8e581f0838836a31dfabbc6a55b2bf0c0d29b7b0a878078fc5931

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e78f1dd3a8c102778c0cb0e0d97d57fa735ff88e80f3afc37115d6e190fecaf1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2020-02-24T15:50:06Z",
    "title_canon_sha256": "ce4c96bc6bb2687c8ac9d0fed1726e4778d8c2d7716e6254a229e56d888316cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.10323",
    "kind": "arxiv",
    "version": 1
  }
}