Pith Number

pith:P7YPUSC3

pith:2026:P7YPUSC3ZYZ222CNJXBZBTX6AI

not attested not anchored not stored refs pending

Borel graphs generated by finitely many bounded-to-1 commuting Borel functions and hyperfinite equivalence relations

Ruijun Wang

arxiv:2608.01231 v1 · 2026-08-02 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P7YPUSC3ZYZ222CNJXBZBTX6AI}

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	2026-08-04T02:02:14.324497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ff0fa485bce33ad684d4dc390cefe023b98e443ffe64120239f190e41be5800

Aliases

arxiv: 2608.01231 · arxiv_version: 2608.01231v1 · doi: 10.48550/arxiv.2608.01231 · pith_short_12: P7YPUSC3ZYZ2 · pith_short_16: P7YPUSC3ZYZ222CN · pith_short_8: P7YPUSC3

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/P7YPUSC3ZYZ222CNJXBZBTX6AI \
  | 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: 7ff0fa485bce33ad684d4dc390cefe023b98e443ffe64120239f190e41be5800

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c25e351b76a573a3449a657871d4591dd38e120602e9a5b8dbae582ee812271c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-08-02T13:28:32Z",
    "title_canon_sha256": "e61c5bcc9510d2781c2b0dc53a83d84bf127110a81cfab234e8776767d6bb89c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.01231",
    "kind": "arxiv",
    "version": 1
  }
}