Pith Number

pith:GZ4FH4RN

pith:2013:GZ4FH4RNCKK3L7RQIGREXRQ2XE

not attested not anchored not stored refs pending

A classification of disjoint unions of two or three copies of the free monogenic semigroup

J. D. Mitchell, N. Abu-Ghazalh, N. Ru\v{s}kuc, Y. P\'eresse

arxiv:1312.5518 v2 · 2013-12-19 · math.RA · 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{GZ4FH4RNCKK3L7RQIGREXRQ2XE}

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	2026-05-18T02:50:33.891688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

367853f22d1295b5fe3041a24bc61ab91ccac714f462e9d08dd9ab65dc296960

Aliases

arxiv: 1312.5518 · arxiv_version: 1312.5518v2 · doi: 10.48550/arxiv.1312.5518 · pith_short_12: GZ4FH4RNCKK3 · pith_short_16: GZ4FH4RNCKK3L7RQ · pith_short_8: GZ4FH4RN

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/GZ4FH4RNCKK3L7RQIGREXRQ2XE \
  | 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: 367853f22d1295b5fe3041a24bc61ab91ccac714f462e9d08dd9ab65dc296960

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd116ba6a7a55a7f952300e97020955e0d0952954139ce6507ee1d1eeb8b3e21",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-12-19T12:43:46Z",
    "title_canon_sha256": "2958d168fea0b3da7c035be3d8a669dfc51ea6b9a025cd65d13becb40ad2bcf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5518",
    "kind": "arxiv",
    "version": 2
  }
}