Pith Number

pith:M2U5U4UY

pith:2019:M2U5U4UY4JQYA2MDD3WIIIZHRV

not attested not anchored not stored refs pending

Non-separating immersions of spheres and Bing houses

Michael Freedman, T. Tam Nguyen Phan

arxiv:1911.08858 v2 · 2019-11-20 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M2U5U4UY4JQYA2MDD3WIIIZHRV}

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	2026-07-05T00:34:19.555952Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66a9da7298e2618069831eec8423278d43ac882f8cc84232fbd3743fbbb83cca

Aliases

arxiv: 1911.08858 · arxiv_version: 1911.08858v2 · doi: 10.48550/arxiv.1911.08858 · pith_short_12: M2U5U4UY4JQY · pith_short_16: M2U5U4UY4JQYA2MD · pith_short_8: M2U5U4UY

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/M2U5U4UY4JQYA2MDD3WIIIZHRV \
  | 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: 66a9da7298e2618069831eec8423278d43ac882f8cc84232fbd3743fbbb83cca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b894adfb3c0bbcc58f02e6c5ca461d8c51c7894ae9ed85a6c0094ac788db602",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-11-20T12:32:17Z",
    "title_canon_sha256": "31a1e020cff5ed9d341c2eeb42971a96c023ed937fdd18dd58823f772aab6497"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.08858",
    "kind": "arxiv",
    "version": 2
  }
}