Pith Number

pith:7CDKFBOL

pith:2014:7CDKFBOLV7CY4XZUFOSTCEDUZO

not attested not anchored not stored refs pending

Quotients of $\mathbb{N}^*$, $\omega$-limit sets, and chain transitivity

William R. Brian

arxiv:1501.00157 v2 · 2014-12-31 · math.DS · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7CDKFBOLV7CY4XZUFOSTCEDUZO}

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	2026-05-17T23:48:07.131159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f886a285cbafc58e5f342ba5311074cb8ef816172807058cf91a5ee94bde2afa

Aliases

arxiv: 1501.00157 · arxiv_version: 1501.00157v2 · doi: 10.48550/arxiv.1501.00157 · pith_short_12: 7CDKFBOLV7CY · pith_short_16: 7CDKFBOLV7CY4XZU · pith_short_8: 7CDKFBOL

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/7CDKFBOLV7CY4XZUFOSTCEDUZO \
  | 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: f886a285cbafc58e5f342ba5311074cb8ef816172807058cf91a5ee94bde2afa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee4ee0764c25d385d48f5a8806dc163fb11c30ce43db6b2f77ba9f6b29a21c8b",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-12-31T15:52:03Z",
    "title_canon_sha256": "dcef7683bdccfe262288724e025cb0b360d3145a4f61dd86f683aea13c23c936"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.00157",
    "kind": "arxiv",
    "version": 2
  }
}