Pith Number

pith:56TNFAZO

pith:2018:56TNFAZOC3OQ7IXFILO2LRCMEC

not attested not anchored not stored refs pending

On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami

Vassily Lyubetsky, Vladimir Kanovei

arxiv:1810.12542 v2 · 2018-10-30 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{56TNFAZOC3OQ7IXFILO2LRCMEC}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:01:06.585255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efa6d2832e16dd0fa2e542dda5c44c20a3f9702c7a2931fad89286f928b38afe

Aliases

arxiv: 1810.12542 · arxiv_version: 1810.12542v2 · doi: 10.48550/arxiv.1810.12542 · pith_short_12: 56TNFAZOC3OQ · pith_short_16: 56TNFAZOC3OQ7IXF · pith_short_8: 56TNFAZO

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/56TNFAZOC3OQ7IXFILO2LRCMEC \
  | 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: efa6d2832e16dd0fa2e542dda5c44c20a3f9702c7a2931fad89286f928b38afe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6d9a2e7bae546409a2851a80f65bf7a89282fdd8b219c2e8c01d091acc3ed80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2018-10-30T06:25:41Z",
    "title_canon_sha256": "3a62457e7bc960c9e6fac43cd3b728176ff1e91e77d1785907f626d2637b355f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.12542",
    "kind": "arxiv",
    "version": 2
  }
}