Pith Number

pith:D27JV4HX

pith:2015:D27JV4HXHJVYFZJBUA5DKDBVTE

not attested not anchored not stored refs pending

Etale groupoids arising from products of shifts of finite type

Hiroki Matui

arxiv:1512.01724 v1 · 2015-12-06 · math.OA · math.DS · 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{D27JV4HXHJVYFZJBUA5DKDBVTE}

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	2026-05-18T01:25:10.527270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ebe9af0f73a6b82e521a03a350c3599175d37a3b9ac144f9244132940a9a757

Aliases

arxiv: 1512.01724 · arxiv_version: 1512.01724v1 · doi: 10.48550/arxiv.1512.01724 · pith_short_12: D27JV4HXHJVY · pith_short_16: D27JV4HXHJVYFZJB · pith_short_8: D27JV4HX

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/D27JV4HXHJVYFZJBUA5DKDBVTE \
  | 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: 1ebe9af0f73a6b82e521a03a350c3599175d37a3b9ac144f9244132940a9a757

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2aeac3ebe5dba9b2bcb54e896f2264b83c1f0b25bb2920930cedeea63b100d97",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-12-06T02:00:56Z",
    "title_canon_sha256": "67ce6206881e4d5483d7a6862d11dae72aacbc7cd08e5b1fe963e6e07e797509"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01724",
    "kind": "arxiv",
    "version": 1
  }
}