Pith Number

pith:UU4YPNU7

pith:2012:UU4YPNU7GJ6DVBKCD5KF7M35XA

not attested not anchored not stored refs pending

Singular cardinals and strong extenders

Arthur W. Apter, James Cummings, Joel David Hamkins

arxiv:1206.3703 v1 · 2012-06-16 · 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{UU4YPNU7GJ6DVBKCD5KF7M35XA}

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	2026-05-18T03:53:19.025861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a53987b69f327c3a85421f545fb37db80f0a64a132a39a745585e0300f4eda9e

Aliases

arxiv: 1206.3703 · arxiv_version: 1206.3703v1 · doi: 10.48550/arxiv.1206.3703 · pith_short_12: UU4YPNU7GJ6D · pith_short_16: UU4YPNU7GJ6DVBKC · pith_short_8: UU4YPNU7

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/UU4YPNU7GJ6DVBKCD5KF7M35XA \
  | 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: a53987b69f327c3a85421f545fb37db80f0a64a132a39a745585e0300f4eda9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "428c1db58383e241fd2329d221b070092463da4012ca567abc71e49f5ce3badf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2012-06-16T20:37:14Z",
    "title_canon_sha256": "847fc3c45697d1833fc8a37d6dd08cd0692de4719298eb7147a6ffdc680151bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3703",
    "kind": "arxiv",
    "version": 1
  }
}