Pith Number

pith:YTSX24MI

pith:2018:YTSX24MIHZGGRUT2OX27DBGWOR

not attested not anchored not stored refs pending

Lower central subgroups of a free group and its subgroup

Minkyoung Song

arxiv:1807.04002 v1 · 2018-07-11 · math.GT · 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{YTSX24MIHZGGRUT2OX27DBGWOR}

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	2026-05-18T00:10:58.345106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4e57d71883e4c68d27a75f5f184d6746674ae9c36dc1dbdfb362a2ff848f6d0

Aliases

arxiv: 1807.04002 · arxiv_version: 1807.04002v1 · doi: 10.48550/arxiv.1807.04002 · pith_short_12: YTSX24MIHZGG · pith_short_16: YTSX24MIHZGGRUT2 · pith_short_8: YTSX24MI

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/YTSX24MIHZGGRUT2OX27DBGWOR \
  | 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: c4e57d71883e4c68d27a75f5f184d6746674ae9c36dc1dbdfb362a2ff848f6d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0d79a1d3901b558fbf37eedb3429611df117e3c74b973058a116b24f6dcc9d4",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-07-11T08:47:06Z",
    "title_canon_sha256": "7084add27782ecf02bef51f28c5b017ed636a61fc8e6ddd503e850e397399b3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.04002",
    "kind": "arxiv",
    "version": 1
  }
}