Pith Number

pith:K27GULUI

pith:2015:K27GULUIHMBWWYS6BKOQ6MFE5C

not attested not anchored not stored refs pending

Generic properties of subgroups of free groups and finite presentations

Cyril Nicaud (LIGM), Fr\'ed\'erique Bassino (LIPN), Pascal Weil (LaBRI)

arxiv:1507.01088 v2 · 2015-07-04 · math.GR · cs.DM · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K27GULUIHMBWWYS6BKOQ6MFE5C}

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	2026-05-18T00:17:46.613624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56be6a2e883b036b625e0a9d0f30a4e8bcb0165b8b4e580c445eeb0fd850fb98

Aliases

arxiv: 1507.01088 · arxiv_version: 1507.01088v2 · doi: 10.48550/arxiv.1507.01088 · pith_short_12: K27GULUIHMBW · pith_short_16: K27GULUIHMBWWYS6 · pith_short_8: K27GULUI

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/K27GULUIHMBWWYS6BKOQ6MFE5C \
  | 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: 56be6a2e883b036b625e0a9d0f30a4e8bcb0165b8b4e580c445eeb0fd850fb98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2432294ae98d22ea7b6329acf999d986c135170ae5a7be7c3ede8d2b898a66be",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-07-04T09:24:22Z",
    "title_canon_sha256": "90da1bdbddf7fb33f9c5c3cd0b3b3ac0bad397da47e9c0cbf1527fba1c5defb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.01088",
    "kind": "arxiv",
    "version": 2
  }
}