Pith Number

pith:2GT5FOD7

pith:2010:2GT5FOD7FKCNQB2LCBSVUFDVQQ

not attested not anchored not stored refs pending

Embedding topological semigroups into the hyperspaces over topological groups

Olena Hryniv, Taras Banakh

arxiv:1012.2550 v1 · 2010-12-12 · 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{2GT5FOD7FKCNQB2LCBSVUFDVQQ}

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	2026-05-18T04:15:04.162681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1a7d2b87f2a84d8074b10655a14758410a7b6da3e8418223358c1bb47ba6e7f

Aliases

arxiv: 1012.2550 · arxiv_version: 1012.2550v1 · doi: 10.48550/arxiv.1012.2550 · pith_short_12: 2GT5FOD7FKCN · pith_short_16: 2GT5FOD7FKCNQB2L · pith_short_8: 2GT5FOD7

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/2GT5FOD7FKCNQB2LCBSVUFDVQQ \
  | 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: d1a7d2b87f2a84d8074b10655a14758410a7b6da3e8418223358c1bb47ba6e7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2df85357435c95d723575285dbeef0a3ba7714cc2a76f33e1d12bb80338bca9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-12T15:32:15Z",
    "title_canon_sha256": "2f9f124364828e119bfbbf33b85e7955a2b06be1e1cb2b1a218a5a272ac98c11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2550",
    "kind": "arxiv",
    "version": 1
  }
}