Pith Number

pith:4SKNVK5I

pith:2024:4SKNVK5IICOWNNVEJEVDAKD3C5

not attested not anchored not stored refs pending

Higher Kazhdan projections and delocalised $\ell^ 2$-Betti numbers

Hang Wang, Sanaz Pooya

arxiv:2405.03837 v1 · 2024-05-06 · math.OA · math.GR · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4SKNVK5IICOWNNVEJEVDAKD3C5}

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	2026-05-20T14:03:17.536890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e494daaba8409d66b6a4492a30287b176c6e68bec2aec36e86e037e1058a5f9d

Aliases

arxiv: 2405.03837 · arxiv_version: 2405.03837v1 · doi: 10.48550/arxiv.2405.03837 · pith_short_12: 4SKNVK5IICOW · pith_short_16: 4SKNVK5IICOWNNVE · pith_short_8: 4SKNVK5I

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/4SKNVK5IICOWNNVEJEVDAKD3C5 \
  | 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: e494daaba8409d66b6a4492a30287b176c6e68bec2aec36e86e037e1058a5f9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "021c27f6f516ecd6e85f96c483ac44a6ebd9f192bc8ee2fc0f3089cc7b0e2b01",
    "cross_cats_sorted": [
      "math.GR",
      "math.KT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2024-05-06T20:40:24Z",
    "title_canon_sha256": "bf808ec8b19f1fd537e5b081416503bb46e4e535b153011dcab9df7ec1c391e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.03837",
    "kind": "arxiv",
    "version": 1
  }
}