Pith Number

pith:CBYV7FKJ

pith:2019:CBYV7FKJSBC23X3HQ4WFJNBJGO

not attested not anchored not stored refs pending

Extensions of Schreiber's theorem on discrete approximate subgroups in $\mathbb{R}^d$

Alexander Fish

arxiv:1901.08055 v1 · 2019-01-23 · math.DS · math.CO · 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{CBYV7FKJSBC23X3HQ4WFJNBJGO}

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	2026-05-17T23:55:37.965759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10715f95499045addf67872c54b42933a0961e7778d49b877a7af01a3883f1a1

Aliases

arxiv: 1901.08055 · arxiv_version: 1901.08055v1 · doi: 10.48550/arxiv.1901.08055 · pith_short_12: CBYV7FKJSBC2 · pith_short_16: CBYV7FKJSBC23X3H · pith_short_8: CBYV7FKJ

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/CBYV7FKJSBC23X3HQ4WFJNBJGO \
  | 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: 10715f95499045addf67872c54b42933a0961e7778d49b877a7af01a3883f1a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29ef2dd4dc4ad9b2ee583a4535b39aef05a91dfb07d114770639072756709e0f",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-01-23T06:53:15Z",
    "title_canon_sha256": "0f2a17d7c803b9955775625eac00256279c755c32ff230ef7f8f8bacf9b22091"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.08055",
    "kind": "arxiv",
    "version": 1
  }
}