Pith Number

pith:PRQJ5Z7H

pith:2015:PRQJ5Z7HIT2TK3C64RQKDZUMOQ

not attested not anchored not stored refs pending

The multiplication groups of 2-dimensional topological loops

\'Agota Figula

arxiv:1507.00148 v1 · 2015-07-01 · 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{PRQJ5Z7HIT2TK3C64RQKDZUMOQ}

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	2026-05-18T01:37:30.401329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c609ee7e744f5356c5ee460a1e68c743115c2a6c4ecedf0cffd2dfb4cd2f6ab

Aliases

arxiv: 1507.00148 · arxiv_version: 1507.00148v1 · doi: 10.48550/arxiv.1507.00148 · pith_short_12: PRQJ5Z7HIT2T · pith_short_16: PRQJ5Z7HIT2TK3C6 · pith_short_8: PRQJ5Z7H

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/PRQJ5Z7HIT2TK3C64RQKDZUMOQ \
  | 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: 7c609ee7e744f5356c5ee460a1e68c743115c2a6c4ecedf0cffd2dfb4cd2f6ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84d61a43355c5fe78453883f209a6703334a331567a6304af752417a386dddc3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-07-01T08:39:40Z",
    "title_canon_sha256": "4def53a0f67aaca42da4276790374dff38ab5c1a32603fae86d6e7c975f81775"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.00148",
    "kind": "arxiv",
    "version": 1
  }
}