Pith Number

pith:HWP7NK33

pith:2016:HWP7NK33C6XLRO6RV54A6A4PPM

not attested not anchored not stored refs pending

The degree of commutativity and lamplighter groups

Charles Garnet Cox

arxiv:1605.04829 v2 · 2016-05-16 · 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{HWP7NK33C6XLRO6RV54A6A4PPM}

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	2026-05-18T00:07:19.030273Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d9ff6ab7b17aeb8bbd1af780f038f7b3b932fe3084e2651d20dd63e33f71473

Aliases

arxiv: 1605.04829 · arxiv_version: 1605.04829v2 · doi: 10.48550/arxiv.1605.04829 · pith_short_12: HWP7NK33C6XL · pith_short_16: HWP7NK33C6XLRO6R · pith_short_8: HWP7NK33

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/HWP7NK33C6XLRO6RV54A6A4PPM \
  | 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: 3d9ff6ab7b17aeb8bbd1af780f038f7b3b932fe3084e2651d20dd63e33f71473

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6067e991cf6a5e0758dd1f6ade40b81ea62badf90e8c903adaacdb441cd59ff9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-05-16T16:34:59Z",
    "title_canon_sha256": "3159409cc293584913dd6b0047ab523d2a8edd4b4b100d554bbb125e64c9b7a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.04829",
    "kind": "arxiv",
    "version": 2
  }
}