Pith Number

pith:I3LSEP7J

pith:2013:I3LSEP7JIB7DZ3CRXA5TMIKPKU

not attested not anchored not stored refs pending

Subgroups of direct products closely approximated by direct sums

Dmitri Shakhmatov, Maria V. Ferrer, Salvador Hernandez

arxiv:1306.3954 v1 · 2013-06-17 · math.GN · cs.IT · math.GR · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I3LSEP7JIB7DZ3CRXA5TMIKPKU}

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	2026-05-18T00:32:32.835714Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46d7223fe9407e3cec51b83b36214f55265deb4dfba92306cfc5dc41814f9445

Aliases

arxiv: 1306.3954 · arxiv_version: 1306.3954v1 · doi: 10.48550/arxiv.1306.3954 · pith_short_12: I3LSEP7JIB7D · pith_short_16: I3LSEP7JIB7DZ3CR · pith_short_8: I3LSEP7J

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/I3LSEP7JIB7DZ3CRXA5TMIKPKU \
  | 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: 46d7223fe9407e3cec51b83b36214f55265deb4dfba92306cfc5dc41814f9445

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acf030eefeba89a87f2bad19a4c7a68c5da8f36fb90c58d14bdae4afeca303c7",
    "cross_cats_sorted": [
      "cs.IT",
      "math.GR",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2013-06-17T19:10:43Z",
    "title_canon_sha256": "d58f5a584ffc21c251caae39ac0239690b8dc79afb243e5b402d98ffe1d89d52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3954",
    "kind": "arxiv",
    "version": 1
  }
}