Pith Number

pith:BNQ4DB7J

pith:2020:BNQ4DB7J6D3VC3YA3UP2PFGS5C

not attested not anchored not stored refs pending

Foundations of geometric approximate group theory

Matthew Cordes, Tobias Hartnick, Vera Toni\'c

arxiv:2012.15303 v3 · 2020-12-30 · 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{BNQ4DB7J6D3VC3YA3UP2PFGS5C}

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

Quasimorphisms and Poincar\'e duality in dimension 3

Receipt and verification

First computed	2026-07-05T08:02:40.101734Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b61c187e9f0f7516f00dd1fa794d2e88430fa4f8137f2b62f5211d8ea80407b

Aliases

arxiv: 2012.15303 · arxiv_version: 2012.15303v3 · doi: 10.48550/arxiv.2012.15303 · pith_short_12: BNQ4DB7J6D3V · pith_short_16: BNQ4DB7J6D3VC3YA · pith_short_8: BNQ4DB7J

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/BNQ4DB7J6D3VC3YA3UP2PFGS5C \
  | 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: 0b61c187e9f0f7516f00dd1fa794d2e88430fa4f8137f2b62f5211d8ea80407b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fadc94dbb4c0f629c92b20a5e25d864003474067882cfa8106286b9cc5b502c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2020-12-30T19:48:06Z",
    "title_canon_sha256": "38f3345ee3a904413dbc183de500d1a1e27527e0056c5c86d14bbe410f5e5c2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.15303",
    "kind": "arxiv",
    "version": 3
  }
}