Pith Number

pith:BPISCBNM

pith:2012:BPISCBNMXOKXGF4DCLIC32MQ3T

not attested not anchored not stored refs pending

Tropical matrix groups

Marianne Johnson, Mark Kambites, Zur Izhakian

arxiv:1203.2449 v1 · 2012-03-12 · math.GR · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BPISCBNMXOKXGF4DCLIC32MQ3T}

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	2026-05-18T04:00:25.417543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bd12105acbb9573178312d02de990dcdaae37539df8fd22acd092b16ad211a2

Aliases

arxiv: 1203.2449 · arxiv_version: 1203.2449v1 · doi: 10.48550/arxiv.1203.2449 · pith_short_12: BPISCBNMXOKX · pith_short_16: BPISCBNMXOKXGF4D · pith_short_8: BPISCBNM

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/BPISCBNMXOKXGF4DCLIC32MQ3T \
  | 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: 0bd12105acbb9573178312d02de990dcdaae37539df8fd22acd092b16ad211a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3e671a6b3dc846b050dda754053da03503613860775ee358e6703d2bbf71fa7",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-03-12T10:28:07Z",
    "title_canon_sha256": "94f03c78a0aa31ba92578fd7ff37f8456bfd69419391c8910d3cae2c11df5069"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2449",
    "kind": "arxiv",
    "version": 1
  }
}