Pith Number

pith:LLZGB6PA

pith:2015:LLZGB6PA5QVLZPS4IJV5PPI6SW

not attested not anchored not stored refs pending

Recognizable sets and Woodin cardinals: Computation beyond the constructible universe

Merlin Carl, Philipp Schlicht, Philip Welch

arxiv:1512.06101 v1 · 2015-12-18 · 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{LLZGB6PA5QVLZPS4IJV5PPI6SW}

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	2026-05-18T01:24:05.321716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5af260f9e0ec2abcbe5c426bd7bd1e959b99ec4bfb27b850cbcc4d9a179b41d2

Aliases

arxiv: 1512.06101 · arxiv_version: 1512.06101v1 · doi: 10.48550/arxiv.1512.06101 · pith_short_12: LLZGB6PA5QVL · pith_short_16: LLZGB6PA5QVLZPS4 · pith_short_8: LLZGB6PA

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/LLZGB6PA5QVLZPS4IJV5PPI6SW \
  | 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: 5af260f9e0ec2abcbe5c426bd7bd1e959b99ec4bfb27b850cbcc4d9a179b41d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3d7c551ea0a2507f363e06fc614586f46a28ee064c332ef8d09b772d02843b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2015-12-18T20:27:42Z",
    "title_canon_sha256": "a8f138ae37154dff6a1b385135cbb356babc0adff9c490a70855fb75d1f79cbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06101",
    "kind": "arxiv",
    "version": 1
  }
}