Pith Number

pith:Q7EHKP4Q

pith:2012:Q7EHKP4QWCX6QRPHHNFBDZZDII

not attested not anchored not stored refs pending

Non-splittability of the rational homology cobordism group of 3-manifolds

Charles Livingston, Se-Goo Kim

arxiv:1211.3712 v1 · 2012-11-15 · 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{Q7EHKP4QWCX6QRPHHNFBDZZDII}

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	2026-05-18T01:22:25.972493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87c8753f90b0afe845e73b4a11e72342347281a5d0313f7ba026d92bc5baf6d9

Aliases

arxiv: 1211.3712 · arxiv_version: 1211.3712v1 · doi: 10.48550/arxiv.1211.3712 · pith_short_12: Q7EHKP4QWCX6 · pith_short_16: Q7EHKP4QWCX6QRPH · pith_short_8: Q7EHKP4Q

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/Q7EHKP4QWCX6QRPHHNFBDZZDII \
  | 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: 87c8753f90b0afe845e73b4a11e72342347281a5d0313f7ba026d92bc5baf6d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dac282b5e9ab0c8dd640fa618611d7ecf5152225939749e2bdc235bd1caeecb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-11-15T20:03:19Z",
    "title_canon_sha256": "435c98b976a399284c7695f3d1a2c8ae5ec55d248c18c429e2a3edbd02fdee24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3712",
    "kind": "arxiv",
    "version": 1
  }
}