Pith Number

pith:ZFUMY4LT

pith:2013:ZFUMY4LTNJZOBLYWMBNHFQ5AOL

not attested not anchored not stored refs pending

Normal Numbers and the Borel Hierarchy

Pablo Ariel Heiber, Theodore A. Slaman, Ver\'onica Becher

arxiv:1311.0335 v1 · 2013-11-02 · cs.LO · 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{ZFUMY4LTNJZOBLYWMBNHFQ5AOL}

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	2026-05-18T03:08:06.284801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c968cc71736a72e0af16605a72c3a072c5e94a2484b214a8be69d313ad70862d

Aliases

arxiv: 1311.0335 · arxiv_version: 1311.0335v1 · doi: 10.48550/arxiv.1311.0335 · pith_short_12: ZFUMY4LTNJZO · pith_short_16: ZFUMY4LTNJZOBLYW · pith_short_8: ZFUMY4LT

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/ZFUMY4LTNJZOBLYWMBNHFQ5AOL \
  | 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: c968cc71736a72e0af16605a72c3a072c5e94a2484b214a8be69d313ad70862d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e663b7742c75003b091ed0a0761a2c8df94832fb95efb7f913a1ff387eeef9d",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2013-11-02T03:32:56Z",
    "title_canon_sha256": "cbec0179aeb53348a4ce2b66502f0d832ed7971b33519652442f64923c91635d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0335",
    "kind": "arxiv",
    "version": 1
  }
}