Pith Number

pith:X52SQKO5

pith:2018:X52SQKO5DXPWOHSHSFLERI4EKD

not attested not anchored not stored refs pending

Relatively irreducible free subroups in Out($\mathbb{F}$)

Pritam Ghosh

arxiv:1802.05705 v3 · 2018-02-15 · 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{X52SQKO5DXPWOHSHSFLERI4EKD}

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	2026-05-18T00:16:07.857981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf752829dd1ddf671e47915648a38450ec42f89e0884d9b9a821b46808778f3d

Aliases

arxiv: 1802.05705 · arxiv_version: 1802.05705v3 · doi: 10.48550/arxiv.1802.05705 · pith_short_12: X52SQKO5DXPW · pith_short_16: X52SQKO5DXPWOHSH · pith_short_8: X52SQKO5

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/X52SQKO5DXPWOHSHSFLERI4EKD \
  | 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: bf752829dd1ddf671e47915648a38450ec42f89e0884d9b9a821b46808778f3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "817cf3a4e6e7b36906dd276c23e97175709f088371ba249e8ab68bfbc087d883",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-02-15T18:58:12Z",
    "title_canon_sha256": "b15c682471a91f00199db14eac9812bb33631584e169a763d65654ebd4ec64c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.05705",
    "kind": "arxiv",
    "version": 3
  }
}