Pith Number

pith:BQSWWT3R

pith:2019:BQSWWT3RU723U244IOU7EQJSRM

not attested not anchored not stored refs pending

Averages and the $\ell^{q,1}$-cohomology of Heisenberg groups

Francesca Tripaldi, Pierre Pansu

arxiv:1904.06669 v1 · 2019-04-14 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BQSWWT3RU723U244IOU7EQJSRM}

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	2026-05-17T23:48:36.571959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c256b4f71a7f5ba6b9c43a9f241328b0f3c57d606c30a5c893cc20dcb5a85ee

Aliases

arxiv: 1904.06669 · arxiv_version: 1904.06669v1 · doi: 10.48550/arxiv.1904.06669 · pith_short_12: BQSWWT3RU723 · pith_short_16: BQSWWT3RU723U244 · pith_short_8: BQSWWT3R

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/BQSWWT3RU723U244IOU7EQJSRM \
  | 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: 0c256b4f71a7f5ba6b9c43a9f241328b0f3c57d606c30a5c893cc20dcb5a85ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5a2164be8040f31ec41dc885af0fb113160a5fcd4d821650ff20976b05d4abf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-04-14T10:06:55Z",
    "title_canon_sha256": "686a820cc764150d71506deff3a4d5f0a30e1dd869f4d44d0b12aac3a9960bea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.06669",
    "kind": "arxiv",
    "version": 1
  }
}