Pith Number

pith:N7S5GCNA

pith:2012:N7S5GCNAQP3YCGUFBCDBIR2IOY

not attested not anchored not stored refs pending

Stable classification of 4-manifolds obtained by the surgery on loops

Wojciech Politarczyk

arxiv:1209.0644 v3 · 2012-09-04 · 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{N7S5GCNAQP3YCGUFBCDBIR2IOY}

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	2026-05-18T03:27:13.842638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fe5d309a083f7811a8508861447487605dda59cb48b92ebf2faffa1c8f8189b

Aliases

arxiv: 1209.0644 · arxiv_version: 1209.0644v3 · doi: 10.48550/arxiv.1209.0644 · pith_short_12: N7S5GCNAQP3Y · pith_short_16: N7S5GCNAQP3YCGUF · pith_short_8: N7S5GCNA

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/N7S5GCNAQP3YCGUFBCDBIR2IOY \
  | 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: 6fe5d309a083f7811a8508861447487605dda59cb48b92ebf2faffa1c8f8189b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07bdf11e1ebbde9b7bae36f28845b55e5fbdd84639f5e49da7fca8629a9dd3c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-04T13:53:13Z",
    "title_canon_sha256": "de970fd1aa5eb6f6bb6c6298f4ac88c43abd8ed8b401b4427af12b5727c7cd83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0644",
    "kind": "arxiv",
    "version": 3
  }
}