Pith Number

pith:TYM7NQCA

pith:2015:TYM7NQCAYASDC3FBWRTY3X5XCY

not attested not anchored not stored refs pending

Cocompact amenable closed subgroups: weakly inequivalent representations in the left-regular representation

Sven Raum

arxiv:1510.06215 v3 · 2015-10-21 · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TYM7NQCAYASDC3FBWRTY3X5XCY}

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	2026-05-18T01:22:11.188657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e19f6c040c024316ca1b4678ddfb7162607b8cc4c2617893f142bdd8eb019ab

Aliases

arxiv: 1510.06215 · arxiv_version: 1510.06215v3 · doi: 10.48550/arxiv.1510.06215 · pith_short_12: TYM7NQCAYASD · pith_short_16: TYM7NQCAYASDC3FB · pith_short_8: TYM7NQCA

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/TYM7NQCAYASDC3FBWRTY3X5XCY \
  | 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: 9e19f6c040c024316ca1b4678ddfb7162607b8cc4c2617893f142bdd8eb019ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f82d322f5ebeda9135d27ac3786074892cf61d94e5d97263f773657b6274bd0",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-10-21T11:32:49Z",
    "title_canon_sha256": "ee571cc5736ec058e7e1a4fa594e9348803d2fa877a088bc8e131277cd2b0a60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06215",
    "kind": "arxiv",
    "version": 3
  }
}