Pith Number

pith:ZYVYQQMI

pith:2015:ZYVYQQMIL7TGNV3XFW3SR6ILDY

not attested not anchored not stored refs pending

When all closed subsets are recurrent?

Jie Li, Piotr Oprocha, Ruifeng Zhang, Xiangdong Ye

arxiv:1504.08191 v1 · 2015-04-30 · 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{ZYVYQQMIL7TGNV3XFW3SR6ILDY}

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	2026-05-18T02:17:23.071819Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce2b8841885fe666d7772db728f90b1e142e50eba3da91961c97462662b0adc2

Aliases

arxiv: 1504.08191 · arxiv_version: 1504.08191v1 · doi: 10.48550/arxiv.1504.08191 · pith_short_12: ZYVYQQMIL7TG · pith_short_16: ZYVYQQMIL7TGNV3X · pith_short_8: ZYVYQQMI

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/ZYVYQQMIL7TGNV3XFW3SR6ILDY \
  | 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: ce2b8841885fe666d7772db728f90b1e142e50eba3da91961c97462662b0adc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dc36f61856ce78733fe45fb16d3330c42839cbeabcd449c7a45be8bcdcd7a35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-04-30T12:27:23Z",
    "title_canon_sha256": "76fbf01b5d5a367a1580d649124377a2efba34facd4ffa5617f53fea9388ee5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.08191",
    "kind": "arxiv",
    "version": 1
  }
}