Pith Number

pith:4OA4DBH5

pith:2017:4OA4DBH53PCBVY5ATXHZ2U5UO5

not attested not anchored not stored refs pending

Explicit $\ell^1$-efficient cycles and amenable normal subgroups

Clara Loeh

arxiv:1704.05345 v2 · 2017-04-18 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4OA4DBH53PCBVY5ATXHZ2U5UO5}

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	2026-05-18T00:45:25.536409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e381c184fddbc41ae3a09dcf9d53b4774a9104f0452deffdc4955db5c08c9490

Aliases

arxiv: 1704.05345 · arxiv_version: 1704.05345v2 · doi: 10.48550/arxiv.1704.05345 · pith_short_12: 4OA4DBH53PCB · pith_short_16: 4OA4DBH53PCBVY5A · pith_short_8: 4OA4DBH5

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/4OA4DBH53PCBVY5ATXHZ2U5UO5 \
  | 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: e381c184fddbc41ae3a09dcf9d53b4774a9104f0452deffdc4955db5c08c9490

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca7e157b40043475af5006fcacb4c52e1c57f7b7054f34065948abb2254aa2bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2017-04-18T14:03:33Z",
    "title_canon_sha256": "c06868e52392abf330fb4c5d3d4f2ee77cbfd992120f0bda88663f7809c601ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.05345",
    "kind": "arxiv",
    "version": 2
  }
}