Pith Number

pith:VGKSFRMY

pith:2016:VGKSFRMYO4RFP3Y76DDBFRLOBD

not attested not anchored not stored refs pending

A compact minimal space $Y$ such that its square $Y\times Y$ is not minimal

Alex Clark, J. P. Boronski, P. Oprocha

arxiv:1612.09179 v3 · 2016-12-29 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VGKSFRMYO4RFP3Y76DDBFRLOBD}

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	2026-05-18T00:27:57.520405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a99522c598772257ef1ff0c612c56e08e2fd0bdb24ad0d8a4b7e9e805972cf24

Aliases

arxiv: 1612.09179 · arxiv_version: 1612.09179v3 · doi: 10.48550/arxiv.1612.09179 · pith_short_12: VGKSFRMYO4RF · pith_short_16: VGKSFRMYO4RFP3Y7 · pith_short_8: VGKSFRMY

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/VGKSFRMYO4RFP3Y76DDBFRLOBD \
  | 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: a99522c598772257ef1ff0c612c56e08e2fd0bdb24ad0d8a4b7e9e805972cf24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ff2746795863690a160f57c36c626ecb4d2901800cf3b4a0818b15a9617049a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-12-29T15:56:31Z",
    "title_canon_sha256": "5c2e77f70aa90195dbd786e39b25c82c97822b978e3925b3afbaefd5a8b93123"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09179",
    "kind": "arxiv",
    "version": 3
  }
}