Pith Number

pith:QRJGTYBS

pith:2024:QRJGTYBSW2DUMY7JBI6FOUY56X

not attested not anchored not stored refs pending

Discrete subgroups of normed spaces are free

Tomasz Kania, Ziemowit Kostana

arxiv:2408.03226 v1 · 2024-08-06 · math.FA · math.GR · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QRJGTYBSW2DUMY7JBI6FOUY56X}

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	2026-07-05T08:52:47.638628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

845269e032b6874663e90a3c57531df5dc1c6bd22802ed1b55626c9573fa5227

Aliases

arxiv: 2408.03226 · arxiv_version: 2408.03226v1 · doi: 10.48550/arxiv.2408.03226 · pith_short_12: QRJGTYBSW2DU · pith_short_16: QRJGTYBSW2DUMY7J · pith_short_8: QRJGTYBS

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/QRJGTYBSW2DUMY7JBI6FOUY56X \
  | 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: 845269e032b6874663e90a3c57531df5dc1c6bd22802ed1b55626c9573fa5227

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75e7520f6f98c21af4b0d1707ee0ac69a915df912f2100c917b37843fd94c852",
    "cross_cats_sorted": [
      "math.GR",
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2024-08-06T14:37:15Z",
    "title_canon_sha256": "c887a65e00d64e37e5e40db4861893aa204f5a2da7021fc5ba43830c3f190a64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.03226",
    "kind": "arxiv",
    "version": 1
  }
}