Pith Number

pith:4HIZ3CIR

pith:2015:4HIZ3CIRRJ2HTOIQ7XOVEOX6WZ

not attested not anchored not stored refs pending

Relations between counting functions on free groups and free monoids

Alexey Talambutsa, Tobias Hartnick

arxiv:1508.03166 v1 · 2015-08-13 · math.GR · 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{4HIZ3CIRRJ2HTOIQ7XOVEOX6WZ}

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	2026-05-18T01:35:21.558343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1d19d89118a7479b910fddd523afeb67a9a33ea9c89aef96d250f51ced478ec

Aliases

arxiv: 1508.03166 · arxiv_version: 1508.03166v1 · doi: 10.48550/arxiv.1508.03166 · pith_short_12: 4HIZ3CIRRJ2H · pith_short_16: 4HIZ3CIRRJ2HTOIQ · pith_short_8: 4HIZ3CIR

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/4HIZ3CIRRJ2HTOIQ7XOVEOX6WZ \
  | 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: e1d19d89118a7479b910fddd523afeb67a9a33ea9c89aef96d250f51ced478ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a24e444e152ce9300b2ed9b9a97fd6a8d267297186db4940e679f06203936131",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-08-13T10:29:13Z",
    "title_canon_sha256": "ce4faa1a8a458bf427e205a9c8e9e1d11f520151fb43f7e8f22527b12870b151"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03166",
    "kind": "arxiv",
    "version": 1
  }
}