Pith Number

pith:MRIWB7AR

pith:2026:MRIWB7ARTMDJWMJUQQ2YBF5VFS

not attested not anchored not stored refs pending

Forcing $\mathbf{\Sigma}^1_1$-Separation on $\omega_1^{\omega_1}$

Stefan Hoffelner

arxiv:2605.21175 v1 · 2026-05-20 · 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{MRIWB7ARTMDJWMJUQQ2YBF5VFS}

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	2026-05-21T01:05:41.165940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

645160fc119b069b313484358097b52cb09478e126455c5b1eb3d440adf35dc1

Aliases

arxiv: 2605.21175 · arxiv_version: 2605.21175v1 · doi: 10.48550/arxiv.2605.21175 · pith_short_12: MRIWB7ARTMDJ · pith_short_16: MRIWB7ARTMDJWMJU · pith_short_8: MRIWB7AR

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/MRIWB7ARTMDJWMJUQQ2YBF5VFS \
  | 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: 645160fc119b069b313484358097b52cb09478e126455c5b1eb3d440adf35dc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a87d34fbd91a84bcd4bf98d3b9d1ff2379ee750797537293e97df0a897ab1a7e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-20T13:43:33Z",
    "title_canon_sha256": "8fdbced413dc8c7785df81910f2003775c4ae48e788f8d196282a63d38fa20b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21175",
    "kind": "arxiv",
    "version": 1
  }
}