Pith Number

pith:PDBLLQBH

pith:2022:PDBLLQBH77ITOSWTRH6MG75AOU

not attested not anchored not stored refs pending

3-Spheres in the 4-Sphere and Pseudo-Isotopies of $S^1\times S^3$

David Gabai

arxiv:2212.02004 v2 · 2022-12-05 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PDBLLQBH77ITOSWTRH6MG75AOU}

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.

Cited by

1 paper in Pith

Smoothing topological pseudo-isotopies of 4-manifolds

Receipt and verification

First computed	2026-07-05T08:24:35.524863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78c2b5c027ffd1374ad389fcc37fa075302fc1c4f5e20e56405390e97e126e24

Aliases

arxiv: 2212.02004 · arxiv_version: 2212.02004v2 · doi: 10.48550/arxiv.2212.02004 · pith_short_12: PDBLLQBH77IT · pith_short_16: PDBLLQBH77ITOSWT · pith_short_8: PDBLLQBH

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/PDBLLQBH77ITOSWTRH6MG75AOU \
  | 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: 78c2b5c027ffd1374ad389fcc37fa075302fc1c4f5e20e56405390e97e126e24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d26ffdaee4450a6bbded81ac097658b00ad8ee546452c8d9b8f72f2d0cacc4b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2022-12-05T03:28:10Z",
    "title_canon_sha256": "677ce299dbcf6d031cae2ff9fd077f10a5d8af1faff14d7dd9bf21eaf7db6034"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.02004",
    "kind": "arxiv",
    "version": 2
  }
}