Pith Number

pith:Q3KLZWLA

pith:2015:Q3KLZWLARX6ZPCC7L7MZGLPA2I

not attested not anchored not stored refs pending

A countable free closed non-reflexive subgroup of Z^c

Dmitri Shakhmatov, Maria Vincenta Ferrer, Salvador Hern\'andez

arxiv:1512.09007 v1 · 2015-12-30 · math.GN · math.FA · 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{Q3KLZWLARX6ZPCC7L7MZGLPA2I}

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	2026-05-18T00:44:19.896330Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86d4bcd9608dfd97885f5fd9932de0d20be615a23f4ef023a444605c0e6669ae

Aliases

arxiv: 1512.09007 · arxiv_version: 1512.09007v1 · doi: 10.48550/arxiv.1512.09007 · pith_short_12: Q3KLZWLARX6Z · pith_short_16: Q3KLZWLARX6ZPCC7 · pith_short_8: Q3KLZWLA

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/Q3KLZWLARX6ZPCC7L7MZGLPA2I \
  | 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: 86d4bcd9608dfd97885f5fd9932de0d20be615a23f4ef023a444605c0e6669ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b9c27cf0123d7f53d8963e4cdde209f5f56929a2c5afa883c727ce552bd59c5",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2015-12-30T16:45:35Z",
    "title_canon_sha256": "8b826c73eda7b8b8056854a834772f80671210889db2fd323f19cc53baa3b713"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.09007",
    "kind": "arxiv",
    "version": 1
  }
}